Memory-based and disk-based algorithms for very high degree permutation groups
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The flexibility to solve today’s tough problems...and get ready for tomorrowAgilentESA-E SeriesSpectrum AnalyzersThe Agilent ESA-E seriesFull measurement accuracy after just a five minute warm-up.Built-in tracking generator provides an RF source for scalar network analysis (optional).External mixing extends frequency range to 325 GHz. (optional)Weather resistant front panel allows operation in rain and high humidity.Built-in help function eliminates the need to carry manuals into the field.Zoom windows provides split screen display with both wide and narrow spans.Large high-resolution,high-contrast color display makes viewing multiple traces easy.Rugged case with rubber encased front and rear frames resists transportation stresses.Flexible hardware/software environment allows focused applications like GSM and cdmaOne.Built-in floppy disk drive provides PC compatibility and data archiving.Speed, accuracy, and dynamic range ...with a flexible platform for the future!2Built-in counter precisely identifies signals using the 1 Hz marker-basedcounter.A platformbuilt for speedAgilent uses the latest digital, RF and microwave designs to deliver the performance typically found in more expensive spectrum analyzers. The ESA-E series portable spectrum analyzers have a remarkableone-millisecond RF sweep timeand virtual real-time measurement updates to the display or through GPIB. Along with narrow digital resolution bandwidth filters (10 Hz to 300 Hz), and fast, time-domain sweeps you’ll spend less time testing and have your product to market faster.Specification summary*Designed for performance measurements and...• Fast test times• Superior resolution• Wide dynamic range• Measurement confidence*Includes optional performance, see ESA-E series technical specifications for complete details, literature number 5968-3386E.3 Frequency range summary*Choose the performance you need, when you need itThe Agilent ESA-E’s flexible platform means you can get exactly what you need today while still protecting your investment into the future. The six-slot option card cage lets you choose only the performance you need now (without paying for unneeded capability) and upgrade in the future.This scalable performance in com-bination with Agilent measurement personalities, downloaded into the internal memory, transform the ESA-E analyzer into an application-focused solution built around your unique needs.Built-in card cageprovides the flexibility to add application-specific performance....the flexibility to tailor that performance to your needs...Designed for upgradeabilityAfter the purchase of your analyzer,most optional performance can be installed and calibrated at an Agilent Service Center or in many cases, installed in your facility.Firmware upgrades, including many performance enhancements, are available free by download from the Agilent Web site.Over 35 options tochoose from...and more in the futureIncluding:•Digital resolution bandwidth filters of 10, 30, 100, 200 EMI, and 300 Hz •Time-gated spectrum analysis •FM demodulation/deviationmeasurements plus tune and listen •TV trigger with color picture on screen•1.5/3.0 GHz built-in tracking generator•30 Hz low frequency extension •Fast time-domain sweeps to 25 ns •Additional user memory to 10 MB •External mixing capability to 325 GHz•RF and digital demodulation/communication hardware •75 Ωinput•Snap on battery pack or 12 Vdc operation•Decreased phase noise at wide offsets for greater ACPR dynamic range•Software to perform remote spectrum analyzer control over the internetFor a complete list of options and accessories with ordering andcompatibility information please see the Agilent ESA/EMC Spectrum Analyzer Configuration Guide (literature #5968-3412E).4We’ll build one just for you.5...then add measurement personalities to create application focused solutions.Combine the ESA-E seriesoptional hardware configurations with downloadable measurement personalities to create application specific solutions.Measurement personalitiesFor a growing number of applications Agilent offers unique softwareprograms (provided on 3.5-in. disks)designed specifically for the ESA-E series. Downloaded into analyzer memory, each measurement person-ality provides measurement setups,routines,and results specific to your application, including a user interface with related terminology.Cable fault locationOptions 225 (measurement personali-ty), 1DN (tracking generator)and B7K (measurement kit) combine to identify distance to cable discontinuities for fault location and troubleshooting ofcable installation and maintenance.•Easy to use one-button measurements•Complex algorithms executed with a button press•Improved accuracy and repeatability•Operator independent results •Decreased training time •Improved productivityPhase noiseOption 226 (measurement personality)provides a log plot of phase noise in dBc/Hz versus offset frequency.Cable TV service and installationOption 227 (measurement personality)provides Cable TV operators fast,accurate and rugged spectrumanalysis for field installation, ingress evaluation and troubleshooting.General purpose measurement personalities6cdmaOneOptions BAC (measurement personality) and B74 (RF and digital demodulation hardware) combine to make the cdmaOne standard tests such as ACPR that are required to verify the perform-ance of cdmaOne transmitters.GSM/GPRSOptions BAH (measurement person-ality) and B74 (digital demodulation hardware) combine to provide all the GSM 450/900, DCS1800, PCS1900 tests required to verify the performance of GSM/GPRS mobile and BTS transmitters.Bluetooth ™Option 304 (measurement personality and digital demodulation hardware)provides one-button standard compliant Bluetooth transmitter measurements.Communication focused measurement personalities7Modulation analysisOption 229 (measurement person-ality) and B74 (RF and digitaldemodulation hardware) combine to allow measurements of EVM and related metrics for all major 2G/3G formats. Constellation and eye diagrams are provided to helpverify modulation quality.PerformancePortability8Ease-of-use9Productivity with speed,accuracy and dynamic rangeUp to 220 times faster than analogNow you don’t have to buy a high-priced spectrum analyzer to get advanced technology. The ESA-E series with its optional digital 10 Hz resolution bandwidth gives you sweep times up to 220 times faster than analog!Optional digital narrow resolution bandwidth filters (10 Hz, 30 Hz, 100 Hz,200 Hz and 300 Hz) provide the resolving power to measure closely spaced signals, plus give a narrow shape factor (≤5:1) for superior resolution. The filters deliver a lower noise floor and increased measurement sensitivity for a larger measurement range.Verify your designs with confidenceReduce project time with spectrum-analysis capabilities that optimize your designs. The ESA-E seriesoffers ±1 dB amplitude accuracy, 0.5%span accuracy,±101 Hz frequency accuracy,and a continuously phase-locked synthesizer for stability and repeatability. Calibrate out the frequency-related amplitude effects with built-in amplitude correction.The automatic background alignment offers continuous calibration toassure measurement confidence.Fewer measurement constraintsWhen a passband contains two or more signals such as CDMA or TDMA modulation, you don’t want dynamic range to limit your measurements.The ESA-E series has sensitivity down to –153 dBm, plus a third-order intercept point of +12.5 dBm (typically +16 dBm) and a second harmonic intercept point of+45 dBm to give you wide distortion free measurement range.Research and development10MeasureOne-button results with measurement personalitiesMeasure your designs easier with Agilent modulation analysis,Bluetooth ™, GSM/GPRS, cdmaOne,and phase noise measurement personalities. Execute complex algorithms with the press of a button by utilizing downloaded measurement personalities incombination with optional hardware.Expert yet easy EMI measurementsThe Agilent E7400A series of EMC analyzers takes advantage of the ESA-E series platform to provide precompliance measurements fordesign analysis.For more information see the Agilent EMC Analyzers and EMI Software brochure , literature number 5968-2516.View only the signals ofinterest with segmented sweep - paste together up to 32 discontinuous spans in to one sweep.CaptureCapture measurement results easily and quickly with IntuiLinkIntuiLink PC software provides easy transfer of ESA measurement trace data and images directly into MS Excel and Word documents for analysis, archiving, presentations, or printing. Transfer data and images over GPIB, RS232, or LAN.Save and restore analyzer states.Utilize automatic measurementtransfers by date and time. IntuiLink is included standard with GPIB and RS232 options.AnalyzeAnalyze measurement resultsAnalyze breadboard results easier with ESA instrument links supported by the Agilent EEsof Advanced Design System.Research and development11Characterize power statistics of nextgeneration digitally-modulated signals with leading test methods. Power Complementary Cumulative Distribution Function (CCDF)curves provide the peak to average data needed by 3G component designers.Six-offsets in ACPR allow convenient measurements on components subject to multi-carrier signals, (e.g. MCPAs).Every millisecond countsReal-time responseWhether you are tuning oscillators manually or performing high-volume, automatic tests on wireless products, the ESA-E series of spectrum analyzers gives a real-time response with up to 45 measurements per second. Eliminate your measurement-speed bottlenecks to help meet your production goals.This family of spectrum analyzers offers improved productivity, witha one-millisecond sweep time andas low as 25 ns in zero span.Use variable sweep points to optimize speed versus frequency resolution. Maximize speed by measuring only the frequencies of interest with segmented sweep.Unparalleled speed for manual or remote operationThe ESA-E series spectrum analyzers offer the following features to help you quickly build and test your products:•One-millisecond RF sweep time •25 ns zero span sweep time (optional)•Up to 45 measurements per second update to the display•Large 13.8-cm color VGA TFT active matrix display with wide viewing angle•Color VGA display output connector•Enhanced circuit tuning with continuous peak search•Instant printing (PCL5 printers)•Limit lines with large, colorfulpass/fail messagesMeasurements per secondESA-E series45 updates/sec. display45 updates/sec. GPIB8566B Turbo24 updates/sec. display 15 updates/sec. GPIB Swept-tuned spectrum analysis speedSetting a new standard for speed!Surpassing the GPIB speed record The ESA-E series surpasses the speed of the record-holding Agilent 8566B high-performance spectrum analyzer for moving data from the analyzerto a computer. Vastly improved sweep time and measurement update rate eliminate the GPIB data-rate bottleneck to help you more easily meet your productivity goals.• 45 measurements per second transferred to a computer•75 ms RF center frequencytuning time• Standard Commands for Programmable Instruments (SCPI) compliant• The Agilent 8590-series/ESA programming conversion guide • VXI plug&play drivers for ease of program development12Reduce test marginsThe excellent measurement accuracy reduces measurement uncertainty to allow for narrower test margins and improved yields. With an overall amplitude accuracy of ±1 dB,and a frequency accuracy of ±101 Hz plus the continuously phase-locked synthesizer, you get the performance you need to have confidence in your tests.Individual calibration certificate included standard with every analyzer.Built-in preamplifier maximizes sensitivityWhen your application calls for measurements of very low-level signals, the optional built-in preamplifier (to 3 GHz)in theESA-E series increases sensitivity.This high-gain, low-noise preamplifier lets you use wider bandwidths for even faster sweep times when searching for low-level signals.For circuit adjustments withreal-time results, the ESA-E series spectrum analyzers offers a one-millisecond sweep time and up to 45 measurement updates per second.13The ESA-E series hasdigital narrow resolution bandwidth filters and internal preamplifiers so you can identify low-level spurs.Leverage your software investmentIn the past decade, many manufactur-ers have installed Agilent 8590-series spectrum analyzers in automated production lines. If you are considering upgrading your automated stations to take advantage of the ESA-E series capabilities, Agilent can help preserve your software investment and minimize your change-over costs. An optional 8590-series programming code compatibility mode is available,which enables ESA-E series analyzers to work with more than 120 commonly used 8590-series programming commands.Calibrated field measurements in just FIVE minutes!The ESA-E series takes only 5 minutes to warm-up so technicians spend little time waiting for instrument stabilization. The automatic, internal background alignment feature gives consistently accurate results over varying temperatures. Measurement results are easily saved, printed or integrated into external tools for analysis and documentation using the standard 3.5 in floppy disk drive. The easy-to-use file manager with a time and date stamp helps to organize storage of measurement data. And, the optional rechargeable battery provides up to 1.9 hours of cordless operation.The tough ESA-E is field-rugged, yet offers uncompromising performance Snap-on battery provides freedomfrom AC power mains 14Easy,worry-free measurementsThe ESA-E series offers outstanding lab-grade performance, and protec-tion from the elements along with convenience and ease-of-use features tailored to field service.•Rubber-encased frames and the lack of vibration-prone internal adjustments improve reliability during transportation.•Snap-on rechargeable battery provides up to 1.9 hours of cordless operation (optional).•12 Vdc operation from automotive electrical systems•Rain-resistant front panel, shielded vents, and side-mounted fanprotect the instrument in adverse environments.•Vibration and shock resistance with solid state internal memory.Get accurate measurementsin every kind of field condition• Continuous automatic background alignment provides accuracy over varying temperature conditions.• Hard transit case, soft operating/carrying case or backpack provides choice of convenient transportation aids.•Flexible tilt handle optimizes line of sight whether the analyzer is viewed from the bench or ground.•Color display provides optimum readability regardless of lighting and viewing angle.•Find cable problems with the fault location measurement personality.•Troubleshoot cellular base stations with GSM and cdmaOne measurement personalities.•Make one-button RF power measurements for all the major2G/3G formats.Backpack with ESA to remote locations15Agilent ESA-E series – a whole product solution The performance of the ESA-E series spectrum analyzer isonly a small part of what you get from Agilent Technologies.Agilent strives to provide complete solutions that gobeyond our customers’ expectations. Only Agilent offersthe depth and breadth of enhancements, software,services, connectivity,accessibility and support to helpour customers reach their measurements objectives.Please contact Agilent for more information.Post-sales support• Standard three-year globalwarranty• Worldwide call center and calibrationservice center support network• One-year calibration intervals• FREE Firmware upgrades and servicenotes available from Agilent’s Web site• PC-based calibration software•Computer-based service training onCD-ROM•Flexible support options to meetyour needsThe Agilent ESA-E series ismanufactured in an ISO 9001registered facility to Agilent’sexacting standards.Training and access toinformation• Printer support matrix onAgilent’s Web site• Factory service training• Web-based support of frequentlyasked questions• Operation , programming andcalibration manuals on CD-ROM andon Agilent’s Web site• User and applications training•T echnical seminars•Cellular/PCS base stationtroubleshooting course•Calibration certificate standard•Localized operation manualsPC connectivity & software• Floppy disk drive• GPIB or RS232 interfaces• VXI plug&play drivers• IntuiLink spectrum analyzer software• EEsof Advanced Design Systemdriver (instrument link)•Programming examples on CD-ROM• SCPI (Standard Commands forProgrammable Instruments)• Custom software service• BenchLink web remote control software• 8590-series programming codecompatibility• 8590-series/ESA programmingconversion guideProduct peripherals andaccessories• Battery packs and 12 Vdc cables•Rack mounts•Operating/carrying, backpack andtransit cases•External mixers to 110 GHz•Preamplifiers to 26.5 GHz•High-impedance active probes•RF/MW limiters, adapters & cablesPre-sales services•Rentals, leasing, and financing• Application engineering andconsulting services• Application notes• Custom product modifications• Custom downloadable programs• Product literature available fromAgilent’s Web site• Demonstration units availablefor evaluation• Trade-up programs• Support at least 5 years beyondproduction life of product16Add an external VGA color monitor.12 Vdc operation from automotive batteries.Parallel port supports most HP printers (optional).Supports Agilent preselected external mixers (optional).Digital demodulation hardware for current and future communications systems (optional).Snap-on battery pack for portability (optional).Use an external frequency reference for even more accuracy.Input signal down converted to 21.4 MHz (optional).High speed GPIB interface(optional).17Ordering information ESA-E seriesAgilent E4401B Spectrum Analyzer 9 kHz to 1.5 GHz Agilent E4402B Spectrum Analyzer 9 kHz to 3.0 GHz Agilent E4404B Spectrum Analyzer 9 kHz to 6.7 GHz Agilent E4405B Spectrum Analyzer 9 kHz to 13.2 GHz Agilent E4407B Spectrum Analyzer 9 kHz to 26.5 GHzAdditional informationAgilent literatureNumber ESA-E Series Technical Specifications 5968-3386E ESA-E Series Configuration Guide 5968-3412E Spectrum Analyzer Selection Guide 5968-3413E ESA-E Series Self-Guided Demo 5968-3658E ESA Battery Pack Product Overview 5966-1851E EMI Pre-compliance Brochure5968-2516E N2717A Calibration Software Product Overview 5968-5478E GSM/GPRS Measurements Product Overview 5968-6871E cdmaOne Measurements Product Overview 5968-6869E TV Transmission Quality Measurements Flyer 5968-6874E Measuring Signals Above 26.5 GHz Flyer 5968-6873E Cable Fault Location Product Overview 5980-1915E Phase Noise Product Overview 5980-1191E Cable TV Product Overview5980-2297E Bluetooth™ Measurement Solutions Product Overview5980-2786EN Modulation Analysis Measurements Product Overview5988-2116EN IntuiLink Software Data Sheet 15980-3115EN BenchLink Web Remote Control Software Product Overview5988-2610ENFor the latest information on the Agilent ESA-E series see our Web page at: 1. For more information about IntuiLink software visit our Web site at: /find/IntuiLink1819Agilent Technologies’ Test and Measurement Support, Services, and AssistanceAgilent Technologies aims to maximize the value you receive, while minimizing your risk and problems. We strive to ensure that you get the test and measurement capabilities you paid for and obtain the support you need. Our extensive support resources and services can help you choose the right Agilent products for your applications and apply them successfully. Every instrument and system we sell has a global warranty. Support is available for at least five years beyond the production life of the product. Two concepts underlie Agilent’s overall support policy: “Our Promise” and “Your Advantage.”Our PromiseOur Promise means your Agilent test and measurement equipment will meet its advertised performance and functionality. When you are choosing new equipment, wewill help you with product information, including realistic performance specifications and practical recommendations from experienced test engineers. When you use Agilent equipment, we can verify that it works properly, help with product operation, and provide basic measurement assistance for the use of specified capabilities, at no extra cost upon request. Many self-help tools are available. Your AdvantageYour Advantage means that Agilent offersa wide range of additional expert test and measurement services, which you can purchase according to your unique technical and business needs. Solve problems efficiently and gain a competitive edge by contracting with us for calibration, extra-cost upgrades, out-of-warranty repairs, and on-site education and training,as well as design, system integration, project management, and other professional engineering services. Experienced Agilent engineers and technicians worldwide canhelp you maximize your productivity, optimize the return on investment of your Agilent instruments and systems, and obtain dependable measurement accuracy for thelife of those products.By internet, phone, or fax, get assistance with all your test and measurement needs.Online assistance:/find/assist Phone or Fax:United States:(tel)180****4844Canada:(tel)187****4414(fax) (905) 282-6495Europe:(tel) (31 20) 547 2323(fax) (31 20) 547 2390Japan:(tel) (81) 426 56 7832(fax) (81) 426 56 7840Latin America:(tel) (305) 269 7500(fax) (305) 269 7599Australia:(tel) 1 800 629 485(fax) (61 3) 9210 5947New Zealand:(tel) 0 800 738 378(fax) 64 4 495 8950Asia Pacific:(tel) (852) 3197 7777(fax) (852) 2506 9284Product specifications and descriptions in this document subject to change without notice. Copyright © 2000, 2001 Agilent Technologies Printed in USA, March 27, 20015968-3278EMicrosoft Excel® and Microsoft Word® are U.S. registered trademarks of Microsoft Corp. Bluetooth™ is a trademark owned by Telefonaktiebolaget LM Ericsson, Sweden and licensed to Agilent Technologies.。
State-of-the-art Performance and Data ProtectionReadyNAS 3312 and 4312X are best-in-class high performance network attached storage systems. The RR4312X has two built-in 10 Gigabit Ethernet interfacesto further meet the storage demandsof next generation business networks. Featuring an architecture powered by blazing fast quad-core 5th generation Intel Xeon processors along with DDR4 ECC memory that is expandable up to 64GB, the RR3312 and RR4312 are the no compromise, high performing data storage systems of choice for businesses that need the very best in capacity, performance and security.ReadyNAS brings state-of-the-art datastorage and protection technologies inan affordable and easy-to-use system tothe SMB. All ReadyNAS are built on therevolutionary ReadyNAS OS 6 operatingsystem and next-gen BTRFS file system.A best-in-class 5 levels of data protection- X-RAID, Unlimited Snapshots, Bit rotprotection, real-time anti-virus and easyoffsite replication work in concert to securelyprotect your data from common risks.All ReadyNAS systems utilize proprietaryReadyCLOUD technology. WithReadyCLOUD, remotely accessing andsharing files in your own secure privatecloud has never been easier. No VPNsetup, no port forwarding, no dynamicDNS required. Designed specificallyfor the unique needs of business users,RR3312 and RR4312X are virtualization-ready with iSCSI support, thin provisioningcapability and VMware certified.To maximize storage capacity, an SASexpansion card (RRSASEXP-10000S) canbe purchased separately for expansionsupport. Expansion chassis fromNETGEAR, EDA2000 and EDA4000, offer12 and 24 bay expansion, respectively.Key Business Features and Solutions• Automatic Backup & Sync: Using the ReadyCLOUD app for PC, scheduled protection is easier than ever before• Bit Rot Protection: A proprietary technology protecting your files from unplanned degradation• Unlimited Snapshots: Unlimited data snapshot capability for on-box protection and flexible data recovery • X-RAID & Instant Provisioning: Easily expand capacity and feel confident knowing that data is always protected • Cloud-managed Replication: Maintaindata sets in multiple locations or ensureprotection of data from remoteor branch office locations• iSCSI and Thin Provisioning: Powerfultools for a businesses taking advantageof virtual infrastructures• Anti-virus & Encryption: Keep dataprotected from outside threats and safefrom prying eyes• Modern GUI and ReadyCLOUDManagement: Sleek, modern interfacethat puts the tools you need, where andwhen you need them• File Server: Unified storage platform forsharing files between Windows, Macand Linux-based computers• Backup: RAID redundancy withautomatic expansion and unlimited datasnapshots for point-in-time restore• Disaster Recovery: Cloud-managedreplication for maintaining multiple setsof data and performing easy restores incase of disaster• Virtualization: Thin provisioning, iSCSIsupport and certified with VMwareHardware ReadyNAS 3312ReadyNAS 4312S ReadyNAS 4312XCPU-10000S Intel Xeon E3-1225v63.3GHzQuad Core Processor,Max Turbo Speed3.7GHzIntel® Xeon E3-1245v6 3.5GHzQuad Core, HyperThreaded Processor,Max Turbo Speed3.9GHzIntel® Xeon E3-1245v6 3.5GHzQuad Core, HyperThreaded Processor,Max Turbo Speed3.9GHzCPU-20000S Intel Xeon E3-1225v63.3GHz, Max TurboSpeed 3.7GHzIntel Xeon E3-1245v63.5GHz, Max TurboSpeed 3.9GHzIntel Xeon E3-1245v63.5GHz, Max TurboSpeed 3.9GHzMemory8GB DDR4 ECC16GB DDR4 ECC16GB DDR4 ECC Memory Expansion64GB DDR464GB DDR464GB DDR4 Drive Bays121212Drive T ypes Supported SATA/SSD 2.5” or 3.5”SATA/SSD 2.5” or 3.5”SATA/SSD 2.5” or 3.5”Hot Swappable Drives Yes Yes Yes eSATA Ports222SAS Ports for Expansion Chassis (sold separately)222 Gigabit LAN Ports44410Gbps LAN Optical SFP+02010Gbps LAN Copper 10GBase-T002USB Ports2x USB3.02x USB3.02x USB3.0Power SupplyDual RedundantInternal 550 W; input100-240V AC,50-60HzDual RedundantInternal 550 W; input100-240V AC,50-60HzDual RedundantInternal 550 W; input100-240V AC,50-60HzChassis Warranty5 years including5 years NextBusiness Day hard-ware replacement5 years including5 years NextBusiness Day hard-ware replacement5 years including5 years NextBusiness Day hard-ware replacementFan (mm) 3 x 80 3 x 80 3 x 80 Dimensions DxWxH (mm)707 x 445 x 88 707 x 445 x 88 707 x 445 x 88 Weight (diskless) (kg)11.96 11.96 11.96 Software and Functionality ReadyNAS 3312ReadyNAS 4312S ReadyNAS 4312XCertification and Compatibility VMware vSphereESXi 6.0 VMware vSphereESXi 6.0VMware vSphereESXi 6.0Cloud-discovery, Setup and Management Yes Yes Yes Data Protection with Unlimited Snapshots Yes Yes Yes Web-managed Replication for Disaster Recovery Yes Yes Yes Real-time Antivirus Yes Yes Yes iSCSI and Thin Provisioning Yes Yes Yes ReadyNAS Rackmount ComparisonTechnical SpecificationsData Protection (Backup & Replication)• Unlimited block-based snapshots for continuous data protection• Restore Snapshots to any point in time• Restore Snapshot data from local admin GUI, ReadyCLOUD, or native Windows File Explorer• Scheduled and manual snapshots• File Synchronization (rsync)• Encrypted Remote Replication• Data compression• Cloud managed Remote Replication (ReadyNAS to ReadyNAS). No licenses required for ReadyNAS OS 6 devices.• AES 256-bit volume based encryption• X-RAID (automatic single volume online expansion)• Single Disk, JBOD• RAID Levels: 0, 1, 5, 6, 10, 50, 60• RAID Global Hot Spare• Backup to external storage (USB/eSATA)• Apple Time Machine support• Amazon Cloud Drive synchronization (requires Amazon account)• ReadyNAS Vault™ Cloud backup (optional service)• Dropbox™ file synchronization (requires Dropbox account)• Real-time Anti-Virus scanning using signature and heuristic algorithms. (No end-user licenses required)Protection for viruses, malware, worms, and Trojans.• Bitrot automatic detection & correction for degraded mediaStorage Area Networks (SAN), Virtualization• Unlimited iSCSI LUN Snapshot• Thin or thick provision LUNs• Multi-LUN per target• LUN mapping and masking• SPC-3 Persistent Reservation (iSCSI)• MPIO and MC/S (iSCSI)• Max # iSCSI Target: 256• Max # iSCSI LUN: 256• VMware vSphere 6• Citrix XenServer 6• Windows Server 2008 Hyper-V• Windows Server 2008 Failover Clustering• Windows Server 2012 R2ReadyCLOUD (cloud access to ReadyNAS• ReadyCLOUD portal based data access and management• Upgrade firmware remotely• VPN quality remote data transfer and management• Share data with friends & co-workers directly from portal• Share file via email linkReadyCLOUD Client Applications• ReadyCLOUD client applications for Apple OS X, Microsoft Windows, Android, and Apple iOS• VPN quality remote data transfer and management• Simple remote access through ReadyCLOUD client (no firewall or router configuration needed)• Sync files/folders between PC (Mac/Windows) & ReadyNAS• Sync files/folders between multiple PCs and ReadyNAS• Sync files/folders between multiple users and ReadyNAS• Backup files/folders from PC to ReadyNASFile System & Transfer Protocols• ReadyNAS OS 6.5 or later• Linux 4.x• Internal File System: BTRFS• External File System: EXT3, EXT4, NTFS, FAT32, HFS+• Copy-on-write file system• Microsoft Network (CIFS/SMB 3)• Apple OS X (AFP 3.3)• Linux/Unix (NFS v4)• Internet (HTTP)• Secure Internet (HTTPS)• File Transfer Protocol (FTP)• FTP over SSL / TLS (explicit)• FTP Passive mode with port range setup• FTP Bandwidth control• FTP Anonymous• FTP Transfer Log• Secure Shell (SSH)• Web Authoring (WebDAV)• Storage Array Network (iSCSI)• File Synchronization (rsync)• Local web file managerUsers/Groups• Max # Users: 8192• Max # User Groups: 8192• Max # Share Folder: 1024• Max # Concurrent Connections: 1024• Share Folder Level ACL Support• Advanced Folder Permissions with Subfolder ACL support for CIFS/SMB, AFP, FTP• Microsoft Active Directory (AD) Domain Controller Authentication• Local access list• ReadyCLOUD based ACL• Domain user login via CIFS/SMB, AFP, FTPManagement• ReadyCLOUD cloud based discovery and management• RAIDar local discovery agent (Windows/Mac)• Save and restore system configuration (clone devices)• Local event log• Local Graphical User Interface (GUI) Languages: English, German, French, Japanese, Chinese (Traditional &Simplified), Russian, Swedish, Portuguese, Italian, Spanish, Polish, Czech, Dutch, Korean• Unicode support• Volume Management• Thin provision Shares and LUNs• Instant Provisioning/Expansion with data protection• Restore to factory default• Operating Systems supported: Microsoft Windows 7, 8/8.1, 10, Microsoft Windows Server 2008 R2/2012, AppleOS X, Linux/Unix, Solaris, Apple iOS, Google Android• Supported Web Browsers (Microsoft Internet Explorer 9+, Microsoft Edge, Mozilla Firefox 14+, Google Chrome50+, Apple Safari 5+)System Monitoring• Device capacity, performance, resource and health monitoring• Bad block scan• Hard Drive S.M.A.R.T.• File System Check• Disk Scrubbing• Disk Defragment• Volume balance• Alerts (SMTP email, SNMP, local log)• Auto-shutdown (hard drive, fan, UPS)• Auto-restart on power recoveryNetworking Protocols• TCP/IP• IPv4• IPv6• Static IP Address• Dynamic IP Address• Multiple IP Settings• DHCP Client• UPnP Discovery• Bonjour Discovery• Link Aggregation IEEE 802.3ad• Port Trunking (balanced round robin, active backup, balance xor, broadcast, 802.3ad link aggregation LACP,transmit load balancing, adaptive load balancing)• Hash Types IEEE 802.3ad LACP or XOR (Layer 2, Layer3, Layer 4)• Jumbo Frames• Static routes• Secure Shell (SSH)• Simple Network Management Protocol v2, v3• Network Time Protocol (NTPMedia• ReadyDLNA (UPnP DLNA Media Server)• ReadyDLNA streams to any compliant device including Playstation and Xbox• ReadyDLNA mobile clients for remote media streaming (iOS, Android)• ReadyDLNA supported music formats (wav, wma, pcm, ogg, mp3, m4a, flac, aac)• ReadyDLNA supported photo formats (jpg, jpeg)• ReadyDLNA supported video formats (3gp, mp4, wmv, xvid, vob, ts, tivo, mts, mpeg, mpg, mp4, mov, mkv, m4v,m4p, m2t, m2ts, flv, flc, fla, divx, avi, asf)• ReadyDLNA supported playlist formats (pls, m3u)• ReadyNAS Surveillance (free trial, license required) supports over 70 brands and 1600 models of IP cameras• iTunes Server• iTunes supported audio formats (mp3, m4a, m4p, wav, aif)• iTunes supported video formats (m4v, mov, mp4)• iTunes supported playlist formats (m3u, wpl)• TiVo Archiving• Plex Media Server streams to DLNA and Plex clients (mobile, desktop, Android TV, Roku, Samsung & LG TVs)HardwareCPU• ReadyNAS 3312: Intel® Xeon E3-1225v5 3.3GHz Quad Core Processor, Max Turbo Speed 3.7GHz• ReadyNAS 4312S: Intel® Xeon E3-1245v5 3.5GHz Quad Core, Hyper Threaded Processor, Max Turbo Speed 3.9GHz• ReadyNAS 4312X: Intel® Xeon E3-1245v5 3.5GHz Quad Core, Hyper Threaded Processor, Max Turbo Speed 3.9GHzMemory• ReadyNAS 3312: 8GB DDR4 ECC• ReadyNAS 4312S:16GB DDR4 ECC• ReadyNAS 4312X:16GB DDR4 ECC• Memory Expansion: 64GB DDR4• Flash: 256MB for OS• 12 Hot Swappable Drive Bays• Drive Types Supported: SATA/SSD 2.5” or 3.5”• Two eSATA ports• Two USB3.0 ports• Total solution capacity: 120TB w/o expansion 600TB w/ 2 x EDA4000• RR4312X: dual 10GbE copper ports• RR4312S: dual 10GbE SFP+ ports• Quad Gigabit Ethernet ports with link aggregation and failover• LEDs: Power, System, 4 x LAN• Three 80mm fans• Dimensions (DxWxH):707mm x 445mm x 88mm• Weight (diskless): 11.96 kg• Dual 550 watt redundant power supplies• Power cord localized to country of sale• Rackmount sliding rail includedCompliance• ENGR 10049 EST Environmental Stress Test Guideline• ENGR 10045 EVT Engineering Validation Test Guideline• ENGR 10048 CVT Compliance Validation Test Guideline• ENGR 10046 System Validation Test Guideline• ENGR 10023 HALT Accelerated Life Test 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Disulfide by Design Version 1.20© Wayne State University 2003, All Rights Reserved09/16/03Users’ GuideAlan A. Dombkowski, Ph.D., Institute of Environmental Health Sciences,Wayne State University, Detroit, MI domski@Contents1 Description (2)Requirements (2)2 System3 Installation (2)4 Running Disulfide by Design (2)4.1 Loading a PDB file (3)4.2 Run (4)4.3 Output (4)4.4 SavingResults (4)4.5 Creating a mutant PDB file (5)5 Options (5)Intra-chain (5)and5.1 InterCβ for glycines (5)5.2 Building5.3 Chi3 torsion angle tolerance (5)5.4 Ca-Cb-S angle tolerance (6)Details (6)6 TechnicalNotes (7)7 Release8 References (7)1 DescriptionDisulfide by Design is an application for the rational design of disulfide bonds in proteins. For a given protein structural model, all residue pairs are rapidly assessed for proximity and geometry consistent with disulfide formation, assuming the residues were mutated to cysteines. The output displays residue pairs meeting the appropriate criteria. The input model will typically be a Protein Data Bank (PDB) structure for the protein of interest; however, structures developed through homology modeling may also be used. Engineered disulfides have proven useful for increasing the stability of proteins and to assist the investigation of protein dynamics and interactions. This software was written by Dr. Alan Dombkowski and based on algorithms created for disulfide identification in protein fold recognition methods (Dombkowski & Crippen, 2000). The Disulfide by Design algorithm has been successfully used for disulfide engineering (Anthony et al., 2002; Anthony & Burgess, 2002).2 System RequirementsDisulfide by Design is currently available for the Windows operating system. It has been tested with Windows 98, NT, 2000 and XP. The application uses about five megabytes of memory and less than one megabyte of disk space. Monitor resolution should be a minimum of 1024 x 768 with 16 or 32 bit color.3 InstallationSimply double click on “Disulfide by Design Install.exe” and the installer will step you through the installation process. A license agreement will be displayed during the installation process. Proceeding with installation requires agreement with the software license. Upon installation, an icon will be installed under the “Programs” tab of the “Start” menu. To run the program simply double-click the icon. The software can be uninstalled using the Add/Remove Programs tab of the control panel.4 Running Disulfide by DesignRunning Disulfide by Design is as simple as loading a PDB file then pressing “Run.” The default option settings are recommended for general use. However, it may be desirable to change option settings, such as to increase assessment criteria stringency. The options are discussed in greater detail below.4.1 Loading a PDB fileThe input file must be in PDB format with atomic coordinates. File selection isperformed with the “Load Structure” button. All residues with a complete main chainbackbone and a Cβ atom are used in the analysis. In the case of glycine, a Cβ will becreated if the “Build Cb for Gly” check box is selected. After the structure file has beenread a message is displayed showing the number of residues having a complete backbone and Cβ. For NMR structures with multiple models only the first model will be used.124.2 RunAfter successful loading of a PDB file, simply press “Run” to start the analysis. Each possible pair of residues will be assessed for potential disulfide formation, assuming the residues were mutated to cysteines. With the default setting, both inter and intra-chain disulfides are analyzed. Deselect the appropriate check box to change the intra/inter-chain setting.4.3 OutputThe output text box displays one line per potential disulfide. Each line shows a pair of residues that have the appropriate geometry to form a disulfide bond if the residues were mutated to cysteines. The analysis is based on the assumption that the mutations would not significantly perturb the protein backbone conformation. Each displayed disulfide meets the minimum geometric criteria, including user-selected parameters. The chain id, residue number, and original amino acid type are shown for each residue in the pair. Chain id and residue number are consistent with the input PDB designations. Also shown are the estimated χ3 torsion angle and an energy value in kcal/mol. χ3 angles of known disulfides have a bimodal distribution with peaks observed at +100 and -80 (Petersen et al., 1999), see figure in technical details. These values provide useful selection criteria for disulfide design. The estimated chirality and torsion angle are based on the best possible orientation of putative mutant cysteine Sγ atoms, as determined by an energy minimization performed within Disulfide by Design (see technical details below). The energy value is useful for comparison of potential disulfides to select the best possible candidates. Disulfides with a lower energy value are preferential to those with a higher score. The calculated energy is not intended as a comprehensive assessment of conformational energy, but it is provided to allow comparisons of prospective disulfide bonds. Figure 3 is a histogram of energy values calculated for 706 known disulfides using the Disulfide by Design algorithm. This data reveals the distribution of energy values for naturally occurring disulfides and may be helpful when selecting putative bonds for disulfide engineering. The mean energy value is 1.07 kcal/mol and the maximum observed value is 7.91 kcal/mol.4.4 Saving ResultsResults displayed in the output text box can be saved to a user-specified file using the “Save Results” button. Text is saved in tab-delimited format, so the data can easily be imported into Excel or other spreadsheet software.4.5 Creating a mutant PDB fileA modified form of the original input PDB file can be created by selecting one or more of the potential disulfides then pressing “Create PDB File.” Disulfides are selected by simply pointing the mouse at the desired line then left-clicking. Disulfides may be deselected by clicking a second time. For each disulfide selected, the original amino acids are replaced in the PDB file with cysteines. The respective SSBOND records are inserted near the beginning of the mutant PDB file. The mutant PDB file can be subsequently imported into molecular modeling software such as Rasmol for visualization of the designed disulfides.5 Options5.1 Inter and Intra-chainBy default, Disulfide by Design checks all potential inter and intra-chain disulfides. However, it may be desirable to restrict analysis to either inter or intra-chain. This is accomplished by simply deselecting the appropriate check box.5.2 Building Cβ for glycinesThe disulfide design algorithm requires coordinates for Cβ atoms to determine the potential for disulfide formation. Since glycine residues do not include a Cβ atom they cannot be used in the analysis unless a Cβ is created. The “Build Cb for Gly” check box enables the construction of Cβ atoms. The Cβ location is determined by using the coordinates of the residue backbone atoms. The algorithm was tested by building Cβatoms for cysteine residues of proteins with a known structure. The coordinates of the constructed atoms were compared with the actual Cβ locations, and the average distance was only 0.12 Å indicating accurate modeling of the Cβ atoms.5.3 Chi3 torsion angle toleranceThe χ3 torsion angle is formed by the Cβ-Sγ-Sγ-Cβ bonds, with rotation about the Sγ-Sγbond (see Figure 1 below). The distribution of χ3 angles observed in disulfides of known protein structures is bimodal with sharp peaks at +100 and -80 (see Figure 2 below). It may be desirable to restrict candidate disulfides to those having an estimated χ3 value that falls within the region of observed χ3 values. The χ3 angle tolerance can be selected in the options box. The default setting is +100 ± 30º and -80 ± 30º. If numerous putative disulfides are identified using the default setting it may be useful to decrease the tolerance resulting in a shorter list with preferential characteristics.5.4 Ca-Cb-S angle toleranceThe distribution of C α−C β−S γ angles observed in known disulfides has a peak near 115º and covers a range from approximately 105º to 125º (Petersen et al., 1999). The tolerance of this bond angle is selectable, with a default setting of 114.6 ± 10º.6 Technical DetailsFigure (1) represents a cysteine pair coupled by a disulfide bond. The approach uses a disulfide model with fixed C β-S γ and S γ-S γ bond lengths, 1.81 and 2.04 Å respectively, and fixed C β-S γ-S γ bond angles of 104.15º. These bond lengths and angles are consistent with values observed in a survey of protein disulfide bonds (Petersen et al ., 1999). The χ3 torsion angle, formed by rotation of the C β atoms about the S γ-S γ bond, is allowed to vary in the model and can be described as a function of the distance between C β atoms(Dombkowski & Crippen, 2000). To “fit” the disulfide model between a pair of residues, the algorithm simply rotates the χ3 angle to obtain a C β-C β distance that matches the C β-C β distance measured between the residues. Numerous S γ locations are possible, so all possible S γ orientations are examined and the atomic coordinates providing the lowest energy (E ij ) are selected, based on the χ1 and χ3 torsion angles and the two C α-C β-S γ angles. The χ1 torsion angle is defined by the N-C α-C β-S γ atoms . E ij is calculated per equations (1-4), where i and j are residue indices, θ is the C α-C β-S γ angle, and θ0 is set to 114.6º. Energy units are kcal/mol.)()()()()(3,1,1j i j i ij E E E E E E θθχχχ++++=(1)[])3cos(14.1)(11χχ+=E (2)[])1602cos(10.4)(33+−=χχE (3)[]200.55)(θθθ−=E (4)The energy calculation provides minima at χ3 values of +100º and -80º and χ1 values of ±60º and ±180º, consistent with values observed in the latest survey of disulfide bonds (Petersen et al ., 1999). Since the disulfide model uses fixed bond lengths, no term is included for bond stretching. The energy calculation provides a means to compare potential disulfides during disulfide design. The distribution of energy values for 706 known disulfide bonds reveals a mean energy value, calculated per equations (1-4), of 1.07 kcal/mol and a maximum of 7.91 kcal/mol.7 Release NotesChanges in version 1.20 include:•Corrected bug that caused text to go beyond the right-hand border of the dialog box with some terminal settings.Changes in version 1.12 include:•Energy units are now in kcal/mol.•For residues with multiple conformers only the first set of coordinates encountered are used.•For NMR structures with multiple models only the first model found in the PDB file is used.•Fixed bug in torsion angle calculation that caused crashes for a small number of PDB structures.8 ReferencesDombkowski A.A., 2003, Disulfide by Design: A computational method for the rational design of disulfide bonds in proteins, Bioinformatics, vol. 19 no. 14, 22 Sep.2003.Anthony, L.C. and Burgess, R.R., 2002, Conformational Flexibility in sigma 70 Region 2 during Transcription Initiation, J Biol Chem. Nov 29;277(48):46433-46441.Anthony, L.C., Dombkowski, A.A., and Burgess, R.R., 2002, Using disulfide engineering to study conformational changes in the β’260-309 coiled-coil region of E. Coli RNA polymerase during σ70 binding, J Bacteriol. May;184(10):2634-41.Dombkowski A.A.and Crippen G.M., 2000, Disulfide recognition in an optimized threading potential, Protein Engineering, vol. 13 no. 10, 679-689.Petersen, M., Jonson, P.H., and Petersen, S.B., 1999, Amino acid neighbours and detailed conformational analysis of cysteines in proteins, Protein Engineering, vol. 12, no 7, 535-548.-80+100 Figure 2。
Memristor-based Memory:The Sneak Paths Problem and Solutions Mohammed Affan Zidan a,Hossam Aly Hassan Fahmy b,Muhammad Mustafa Hussain a,Khaled Nabil Salama aa Electrical Engineering,King Abdullah University of Science and Technology(KAUST),Thuwal23955-6900,Saudi Arabiab Electronics and Communication Department,Faculty of Engineering,Cairo University,Cairo,EgyptAbstractIn this paper,we investigate the read operation of memristor-based memories.We analyze the sneak paths problem and provide a noise margin metric to compare the various solutions proposed in the literature.We also analyze the power consumption associated with these solutions.Moreover,we study the effect of the aspect ratio of the memory array on the sneak paths.Finally,we introduce a new technique for solving the sneak paths problem by gating the memory cell using a three-terminal memistor device. Keywords:Nanotechnology,Memory,Memory Array,Memristor,Sneak Paths1.IntroductionMemristors(memory resistors)offer a promising alternative to conventional memory devices.According to the Interna-tional Technology Road-map for Semiconductors(ITRS),cur-rent memory technologies(DRAM,SRAM,and NAND Flash) will soon be facing design challenges related to their contin-ued scaling-down[1].Memristors are considered to be a very good candidate for future memory devices when compared to other emerging technologies such as Magnetoresistive RAM (MRAM)and Phase Change RAM(PCM/PCRAM)[2].The main advantage these emerging technologies share is the prop-erty of retaining data after bias removal.Moreover,memristor-based memories have many unique advantages including very high density compared to other memory technologies and hard disk drives.The memristor is a nonlinear resistor which changes its state relative to the net charge(or net electricflux)passing through its two terminals.It saves its state after an electrical bias is removed.The memristor(M),which was described by Chua in1971[3],is generally thought of as the fourth of the two-terminal basic passive elements,alongside the resistor(R),ca-pacitor(C),and inductor(L).Thefirst reported passive imple-mentation of the memristor was the TiO2-based device intro-duced by HP in2008[4].Recently,devices based on different materials have been introduced[5–9].In addition,several mod-els for memristors has been introduced[10–16].Since thefirst reported use of the memristor,it received a significant of at-tention in the research community.In addition to be used as a memory element[2,17–26],the memristor has found many applications in oscillators[27–30],logic and arithmetic cir-cuits[31,32],programmable analog circuits[33,34],and in modeling and emulation of natural phenomena[35,36].Email addresses:mohammed.zidan@.sa(Mohammed Affan Zidan),hfahmy@(Hossam Aly Hassan Fahmy), muhammadmustafa.hussain@.sa(Muhammad Mustafa Hussain),khaled.salama@.sa(Khaled Nabil Salama)One of the main challenges facing the memristor at the circuit and architecture level is the sneak paths problem.In this paper we introduce a new way to analyze the sneak paths using nor-malized noise margins.Our analysis is based on simulations for different memory array sizes,data sets,and architectures using the models presented in[17].Moreover,we study the effect of the aspect ratio of the memory array on the sneak paths.Finally, a new method is introduce for solving the sneak paths based on a new gating technique by using three-terminal memistor device as a gate for the memristor memory cell.The following section discusses the main concept of the memristor-based memory.The Section3describes the sneak paths analysis,and Section4summarized the main solutions for the sneak paths that have been described in the literature. Then,the new proposed solution is given in Section5.2.Memristor-Based MemoryMemristor-based memories are fabricated as a high-density crossbar architecture.Memristor devices are located at each intersection between two bars,as shown in Fig.1.Typical memristor-based memories do not use transistors for cell gat-ing.The advantage of these devices is that they have a retain-able memory and a very high density compared to otherstorage Figure1:A simple memristor-based memory array showing how a memristor device is located at the intersection between two bars of the array.纵横比Table1:Detailed comparison between memristor-based memory,traditional memories,and other emerging memories according to the2011ITRS report[1].The abbreviations used are:T–transistor,C–capacitor,R–resistor,and D–diode.The bold font indicates the best value per row.Traditional Memories Other Emerging Technologies Redox DRAM SRAM NOR Flash NAND Flash FeRAM MRAM PCRAM Including Memristor Cell Element1T1C6T1T1T1T1C1(2)T1R1T(D)1R(1D)(1T)1R Feature Size(nm)36-6545902218065459 Density(Gbit/cm2)0.8-130.4 1.2520.14 1.212154-309 Read Time(ns)2-100.215100453512<50 Write Time(ns)2-100.210710665351000.3 Retention Time4-64ms N/A10years10years10years>10years>10years>10yearssystems.Table1shows a detailed comparison between memristor-based memory,traditional memories,and other emerging mem-ories.The memristor memory is4x as dense as the hard disk drive(HDD)[37],and23x as dense as DRAM.As a result, memristor-based memories are a good candidate for replacing both the permanent and running storages,therefore approaching the ideal model of having oneflat memory instead of memory hierarchy.The current reading and writing speeds are slower than DRAM and SRAM,but are very fast compared toflash memories,as shown in Table1.These numbers show that mem-ristors could easily replaceflash memories,while further speed enhancement is required for replacing CMOS memories.HP Labs are currently reporting a fast switching time of less than 2ns[38].Recently,Elpida Memory Inc.,reported the develop-ment of a high-speed non-volatile resistance memory[39].It is to be noted that any resistor with a hysteresis curve is consid-ered a memristor[40].HP Labs expects to come up with their memristor-based memory chip replacingflash and solid-state drives(SSD)in2013[41].2.1.Writing OperationData are stored in the memristor in the form of its resistance value,where each of the limiting resistances R o f f and R on are assigned to the two Boolean values‘0’and‘1’.R o f f and R on are the maximum and minimum resistances of the device,respec-tively.Writing one of these values is simply done by passing current through the cell of interest until the memristor’s resis-tance saturates.The saturation value(R on or R o f f)depends on the direction of the writing current.Even this simple writing operation could consume considerable of energy,depending on the values of the memristor’s resistances.2.2.Reading OperationWhile writing to the memristor is a straightforward opera-tion,reading is more challenging.In the memristor memory array,we are trying to sense a cell resistance merged in a com-plete resistive structure.This could be compared to the problem offinding a needle in a haystack.Moreover,the reading oper-ation itself could be destructive to the cell data,depending onthe device properties.2.3.Multilevel MemoryMultilevel memory is one promising application for the memristor ing such a technique would enormously increase the density of memristor-based memory,but wouldalso reduce the noise margin significantly.The current pro-posed techniques for building binary memristor-based memorysuffer from many problems that could be fatal for the multi-level memory.Some researchers believe1M is insufficient forbuilding multilevel memory,and that1M1T(one memristor andone transistor)or1M1D(one memristor and one diode)areneeded[42].We believe that addressing the current challengesfacing the binary memristor-based memory will directly solvethe multilevel memory problems.3.Sneak Paths AnalysisSneak paths are undesired paths for current,parallel to the intended path.The source of the sneak paths is the fact thatthe crossbar architecture is based on the memristor as the only memory element,without gating.Fig.2a shows an array witha simple voltage divider and its equivalent circuit.Thefigureshows the ideal case in which the currentflows from the sourceto the ground passing through only the desired cell at the inter-section between the activated column and row.Unfortunatelythis is not the real case as shown in Fig.2b.The currentflowsthrough many sneak paths beside the desired one.These pathsact as an unknown parallel resistance to the desired cell resis-tance as shown in Fig.2b.What makes the sneak paths problemharder to solve is the fact that the paths depend on the contentof the memory.This is due to the fact that the current will sneakwith more intensity through the paths with smaller resistance,which is memory content dependent.The added resistance of the sneak paths significantly narrowsthe noise margin and reduces the maximum possible size of a memristor array.To study the effect of the sneak paths on thenoise margin,we simulate memristor-based memory arrays of漏电流路径更趋向于电阻小的通路,所以漏电流依赖于存储的内容V (a)R M R SP(b)Figure 2:The reading current path through a memristor memory array and the equivalent circuit for (a)the ideal case where the current flows only through the target cell and (b)an example of a real case where current sneaks through di fferent undesired paths.The green lines show the desired path and the red ones show the e ffective sneak paths.di fferent sizes and with di fferent data sets.The sets are selected to reflect both the worst and best cases for the memory content.The worst case for the sneak paths is a memory full of “ones”since the e ffect of the sneak paths becomes more dominant as their resistance decreases.On the other hand the “all zeros”case is the best case condition since all the sneak paths are made of R o f f resistances in series.In addition tothe previouscases,checkered casestypical of real data and interleaved rows (or columns)are also used.These cases are considered as normal test cases since ones and zeros are present in equal numbers and are uniformly distributed.The simulation result is independent of the location of the cell in the array if we neglect the rows’and columns’pad resistances.We can interpret the array as a complete sphere,since connecting the terminals of each row or column will not introduce any change to the equivalent circuit as shown in Fig.3.Hence all the cell locations are equivalent from the sneak paths point of view.All the simulations werewhere a and k x are constants.The reported feasible values in [17]for the constants are a =3−1and k on =10−8A and k o f f =10−11A for the ON and OFF states of the device respec-tively.In conventional CMOS circuits,there are two regions defined for accepted values of ONEs and ZEROs [43],as shown in Fig.4.For typical CMOS circuits,the prefect ONE has the value of V OH =V dd and the perfect ZERO is V OL =GND .However,the circuit can tolerate shift in values of the input of the value detected for ONE or ZERO noise.For a given ence between voltages values representing ONE and ZERO at the target cell is a perfect measure for the sneak-path e ffect.We define a total noise margin as the region between the ON (2)the such V ol cir-and 忆阻器的位置对漏电影响不大To study the effect of the array size on the sneak-paths we de-fined a normalized value,where the∆is compared to its best case,as:∆′=∆Array∆Device(3)where∆Device is the case of one device used(the best case)while ∆Array is for the array case.∆Array is highly dependent on the data stored in the memory as shown later.3.1.Floating ArrayThe basic structure for a memory array is to leave the un-used array terminalsfloating.Simulation results for thefloat-ing memristor array are shown in Fig.5a.Thefigure shows∆′versus the array size for four different data sets.The simula-tions show that the noise margins of both the“all ones”and the “interleaved”cases almost vanish at a very small array size of 4kbit.At the array size of16kbit,∆′reaches a negligible value of0.00145and0.00323for the“all ones”and the“interleaved”cases respectively.This shows how the sneak paths affect the noise margins and consequently limit the maximum capacity of the array.On the other hand,the noise margin for the best case condition is almost unaffected by the array size.The reason for this is that the large R o f f/R on(k o f f/k on)ratio of103makes sneak paths of resistances R o f f in series ineffective.3.2.Grounded ArrayGrounding the unselected rows and columns might be con-sidered as a mean of preventing sneak paths.In[20]the equiv-alent circuits for all the possibilities of grounding thefloating terminals are given.None of the four possibilities of:1)float-ing rows and columns,2)floating rows and grounded columns, 3)grounded rows andfloating columns,and4)grounded rows and columns,could solve the sneak paths problem.The idea behind grounding thefloating terminals is to provide paths for the sneaking current to the ground rather than the sense cir-cuit.However,part of the current will stillfind its path to the ground through the load resistance.Effectively grounding rows or columns or both will move part of the unknown resistance of the sneak paths so that it is parallel to the total resistance of the equivalent circuit instead of R M,which does not solve the problem.While grounding the array’sfloating terminals does not solve the sneak paths problem,it does marginally improve the noise margin.Fig.5b-d shows the simulation results for∆′versus the array size for the grounded terminals cases.For the grounded rows and columns case,the simulations show that the noise margin still vanishes as the array size increases but at a slower rate than in thefloating terminals case.At an array size of 16kbit,∆′reaches a negligible values of0.052and0.096for the “all ones”and the“interleaved”cases respectively,but on the other hand these values are higher than for thefloating terminals case.The two cases of grounding either columns or rows showslightly better results.This is due to fact that grounding both rows and columns at the same time is equivalent to short circuit any element not in the selected row or column.Since each of Figure5:Noise margins(∆′)versus the array size containing four different data sets.Figure 6:Power consumption versus array size plotted logarith-mically for the cases of grounded and floating array terminals.The dotted line shows the ideal case without the sneak paths e ffect.these unselected elements two terminals will be connected to ground.Therefore,the total resistance of the sneak-path will be less than the case of grounding either rows or columns sepa-rately.The main disadvantage of the grounded technique is the huge power consumption for the reading operation compared to the floating terminals case.Fig.6shows a logarithmic plot of the average power consumption for the cases of floating and grounded terminals.The figure shows the enormous increase in power consumption for the grounded terminals case com-pared to the floating terminals case.Fig.7shows that the in-crease in power consumption is much more than the increase in noise margin.At an array size of 16kbit,an averagepower of 12.77µW is consumed in the grounded terminals case,com-pared to 48.88nW in the case of floating terminals,i.e.power grounded terminals solution impractical.Also,at large array sizes,the improvement in the noise margin is impractical since the margin almost vanishes.4.Sneak Paths SolutionsIn this section the main solutions proposed in the literature for the sneak paths are discussed.4.1.Multistage ReadingThis method was introduced in [17]by the HP Labs team.Their technique attempts to overcome the sneak paths problem using a straightforward,but long,algorithm.The reading pro-cedure is given as:1)perform current measurement for the tar-get cell,2)put the target cell in the OFF state,and perform current measurement for the target cell,3)put the target cell in the ON state,and perform current measurement for the target cell,4)compare the measured currents to determine the state of the cell,and 5)return the memory cell to its (assumed)original state.This sensing algorithm requires a large amount of time and also a large sensing circuit (three sample-and-hold circuits,a voltage comparator,voltage divider,and the control circuit).This technique will also be ine fficient for the narrow noise mar-gins at large array sizes,since the e ffect of sneak paths will dominate and the resistance value of the target cell will be neg-ligible.According to the simulations shown in Fig.5a,∆′could be as low as 0.00145for an array size of only 4kbit.4.2.Unfolded ArchitectureThis solution is presented in [20],and is based on having a separate column for each memristor,as shown in Fig.8.While this solution eliminates the sneak paths problem,it enormously reduces the memory density.The decreased density can be de-(4)and will also much less4.3.Diode GatingOne of the proposed solutions for the sneak paths is to add a diode to each memory cell[20],producing a new cell of one diode and one memristor(1D1M),as shown in Fig.9.Such a strategy would eliminate sneak paths.According to[44], adding diodes to the array will increase the delay of the sys-tem by adding capacitive loads and diode threshold voltages will decrease the output swing.However,the major problem facing such a strategy is that it will block the writing process in the native array structure,since writing to a memristor requires two different polarities.In[45]a3D array structure is provided to enable the write operation with a diode present.In this tech-nique,each cell will contain one programming element,two diodes,and four connecting crossbars.While this technique al-lows the write operation,it consumes more area per cell.In addition,the3D alignment for four bars may reduce the array density significantly.Finally,it is not clear that the new struc-ture containing four bars will still eliminate the sneak paths. 4.4.Transistor GatingUsing large transistors for gating the memristor will solve the sneak paths problem.On the other hand this method will ruin the high memristor-memory density,since the gating tran-sistor’s size is much larger than that of the memristor.Although using small devices will reduce the sneak paths it will not elim-inate it.This is due to the fact that the recently introduced small transistors are consider to act as leaky valves.Moreover,these devices with relatively high OFF current will increase the static power component significantly.Finally,it should be mentioned that one of the major issue of using transistor gating is its limi-tation to the3D stacking of memristor arrays.In[46]an array of one transistor and one memristor(1T1M)is reported.They report a gating transistor of10µm channel length and200µm channel width.Moreover,two wires are required for driving each cell;one for the transistor and one for the memristor.plimentary MemristorsIn this technique two complimentary memristors are used a the memory cell,so that their total resistance are always“R on+Figure9:Simple memory array with1D1M used for each mem-ory cell.R o f f”,as introduced in[47].Having always a high resistancecell reduces the sneak-path current significantly.In this methodONE is distinguished from the ZERO by the orientation of thedesired cell,{R on,R o f f}or{R o f f,R on}.Therefore,a complex reading technique is required.Moreover,the system will nottake full advantage of having high R o f f/R on device.ing Memristors NonlinearityThe voltage drop on the desired cell is higher than any of thesneak-path elements,since the shortest sneak-path will containat least three series memristors.In[48],a high nonlinear deviceis reported,such that I(V/2)≈I(V)/100at V≈1V.This veryuseful property will significantly reduce the sneak paths currentrelative to the desired cell current,and will consistently reducethe sneak-path effect by a high factor.This solution also willnot be practical for large memory array.4.7.AC SenseInstead of using regular DC signal an AC signal is used forsensing the data stored in the desired cell,as introduced in[49].This technique uses load capacitance at the input of the senseamplifier to implement a low passfilter,as shown in Fig.10.The response of thefilter is mainly based on the resistive valueof the desired cell.However,this method adds extra complex-ity for the memory system,since AC input and sensing are re-quired.Moreover,this method will not be as effective for largearrays.Figure10:Simple memory array showing the added columncapacitors for the AC sense.5.Array Aspect RatioIn this section we study the effect of the aspect ratio on theperformance of memristor array.Non-unity aspect ratio couldbe thought of as a helping method towards a sneak-paths freememory.The aspect ratio of an array is defined as its numberof columns to the number of rows.Normal square arrays haveaspect ratios of unity.The aspect ratio of the memory array isone of the main parameters which could be used to limit theeffect of the sneak paths.A memory with one row or one col-umn will not suffer from sneak paths at all,since there will beonly one path for the current as shown in Fig.11.As the aspectratio approaches unity,the possibilities for sneak paths increaseand∆′decreases.An unbalanced aspect ratio structure could123123构成低通滤波器be fabricated in a square area by folding the array in a zigzag shape.However,the main cost of using an aspect ratio other than one is the increase in the required area for selection and sensing circuitry.This area could be given as:Sense Circuit Area =√S [θ√A +ρ√A ](5)6.Gating Using Three-Terminal Memistor Device Memristors can be considered better gates compared to tran-sistors or diodes,since they can be characterized by having very high OFF resistance with much smaller area.In [17],memristor devices are reported to have R o f f =1G Ω.Moreover,memris-tors are not intruder species to the memory array,compared to and diodes.However,it is not possible to write on ei-the gate memristor or the data memristor separately,given with high ON /OFF ratios of more than one hundred.trying to introduce extra rows or columns to enable sep-writing will return us to the initial point,where the sneak are dominant.The three-terminal memistor device captures both of the of the memristor and transistor as a gate device.device was introduced prior to the memristor in 1960by [50].The memistor is a three-terminal device whereDesired CellData Device ON Memistor13:Structure of the proposed memristor gated array,an example of selected of selected cell is shown.the resistance between two terminals is controlled using the third one,in the same analogy of transistor but with a mem-ory effect.In other words,the resistance of the device is con-trolled by time integral of the current on the third terminal and not the instantaneous current as the case of transistor,as stated be in[50,51].This means that there is no need to keep an ac-tive bias on the third terminal to keep the device ON(or OFF). The memistor will retain is ON or OFF state after removing the bias from the third terminal.One of the advantages of this bias-less switching is the very low static power consumed.Memis-tors can inherent the high ON/OFF ratio and small footprint of memristors and the high controllability of transistor by having a third terminal.Fig.13shows the structure of the memistor gated array,where each memory cell is gated with a memis-tor device.Extra columns are required for programming the memistor gate.It is a assumed that the memistor has the same ON/OFF values of the data cell.At the desired cell the gate de-vice is turned ON and all the other gates are turned OFF,which is how the desired cell is selected.Therefore,all the sneak paths will contain at least three series high resistances.This will shift the operation of the memory to work equivalently to the best case scenario,where all the sneak paths are made of OFF de-vices.All the unselected cells will have a total resistance higher than R o f f.The resistance of the selected cell,with open gate, will depend mainly on the data device resistance.This resis-tance willbe either2R on or R o f f+R on,with a very high ON/OFF ratio.Our proposed method has a major advantage over the complementary memristors technique that the desired cell has much higher ratio between its ON and OFF states.In comple-mentary structures the total resistance is always(R on+R o f f),in all of the cases.Based on that,our proposed solution has higher average signal to noise ratio.Moreover,the R o f f/R on ratio of the device is directly reflected on desired cell state values. Fig.14show the noise margins for the proposed technique and the normal array withfloating terminals versus the array size for the worst case data set“all ones”.It appears clearly that the memistor gating has a significant impact on the sneak pathsFigure14:Noise margins(∆′)versus the array size for the normal array withfloating terminals and the new introduced memistor gated array for“All Ones”data set.Also the ratio be-tween the two results are shown in green color on the secondary axis.Figure15:Average power consumption versus the array size for the normal array withfloating terminals and the new introduced memistor gated array for“All Ones”data set.effect,where the worst case of the memistor gating is almost as the best case of the normal array withfloating terminals.For 16Kbit array the memristor gating architecture noise margins is 619.5x compared to the normal array withfloating terminals.In the same direction,the worst case power consumption is signif-icantly decreased as shown in Fig.15.For the worst case with the memoryfilled with“all ones”,average power consumption was reduced more thanfive time for an array size of16kbit. This ratio increases as the array size increases.Finally,in worth mentioning that while miniaturizing the three-terminal memis-tor as a single device did not pass the same long path as the two-terminal memristor,we believe that its great advantages as a gating device will motivate the fabrication community for cre-ating better memistor devices.7.ConclusionWe reviewed the main introduced solutions for the memris-tors sneak-paths problem.We proposed a new technique for an-alyzing the sneak paths problem facing memristor-based mem-ory arrays.The new analysis is accompanied by simulations on Cadence Virtuoso6for different memory array sizes,data sets,and architectures.We also studied the memory array as-pect ratio effect on the sneak paths.Finally,we introduced an new solution for the problem based on using the three-terminal memistor device.AcknowledgmentsThe authors would like to thank Dr.Amro Elshurafa for his reviews and valuable suggestions.References[1]International technology roadmap for semiconductors.URL /[2]O.Kavehei,S.Al-Sarawi,K.Cho,K.Eshraghian, D.Abbott,Ananalytical approach for memristive nanoarchitectures,Arxiv preprint arXiv:1106.2927.[3]L.Chua,Memristor-the missing circuit element,IEEE Transactions onCircuit Theory18(5)(1971)507–519.[4] D.B.Strukov,G.S.Snider,D.R.Stewart,R.S.Williams,The missingmemristor found,Nature435(2008)80–83.[5] A.Zakhidov,B.Jung,J.Slinker,H.Abru˜n a,G.Malliaras,A light-emitting memristor,Organic Electronics11(1)(2010)150–153.[6]S.Jo,K.Kim,W.Lu,High-density crossbar arrays based on a si memris-tive system,Nano letters9(2)(2009)870–874.[7]N.Gergel-Hackett, B.Hamadani, B.Dunlap,J.Suehle, C.Richter,C.Hacker,D.Gundlach,Aflexible solution-processed memristor,IEEEElectron Device Letters30(7)(2009)706–708.[8]R.Waser,Resistive non-volatile memory devices,Microelectronic Engi-neering86(7-9)(2009)1925–1928.[9]T.Kim,E.Jang,N.Lee,D.Choi,K.Lee,J.Jang,J.Choi,S.Moon,J.Cheon,Nanoparticle assemblies as memristors,Nano letters9(6) (2009)2229–2233.[10]Z.Biolek,D.Biolek,V.Biolkova,SPICE model of memristor with non-linear dopant drift,Radioengineering18(2)(2009)210–214.[11]J.Valsa,D.Biolek,Z.Biolek,An analogue model of the memristor,Inter-national Journal of Numerical Modelling:Electronic Networks,Devices and Fields24(4)(2011)400–408.[12] A.G.Radwan,M.A.Zidan,K.N.Salama,HP memristor mathematicalmodel for periodic signals and DC,in:IEEE International Midwest Sym-posium on Circuits and Systems(MWSCAS’10),2010,pp.861–864. [13] A.G.Radwan,M.A.Zidan,K.N.Salama,On the mathematical model-ing of memristors,in:IEEE International Conference on Microelectronics (ICM’10),2010,pp.284–287.[14]H.Abdalla,M.Pickett,SPICE modeling of memristors,in:IEEE In-ternational Symposium on Circuits and Systems(ISCAS’11),2011,pp.1832–1835.[15]S.Kvatinsky,E.Friedman,A.Kolodny,U.Weiser,Team:Thresholdadaptive memristor model,Submitted to IEEE Transactions on Circuits and Systems I:Regular Papers,(also CCIT Technical Report#804). [16]T.Prodromakis,B.Peh,C.Papavassiliou,C.Toumazou,A versatile mem-ristor model with nonlinear dopant kinetics,IEEE transactions on electron devices58(9)(2011)3099–3105.[17]P.V ontobel,W.Robinett,P.Kuekes,D.Stewart,J.Straznicky,R.Stan-ley Williams,Writing to and reading from a nano-scale crossbar memory based on memristors,Nanotechnology20(2009)425204.[18]Y.Ho,G.Huang,P.Li,Dynamical properties and design analysis for non-volatile memristor memories,IEEE Transactions on Circuits and Systems I:Regular Papers58(4)(2011)724–736.[19]K.-H.Jo,C.-M.Jung,K.-S.Min,S.-M.Kang,Self-adaptive write circuitfor low-power and variation-tolerant memristors,IEEE Transactions on Nanotechnology9(6)(2010)675–678.[20]H.Manem,G.Rose,X.He,W.Wang,Design considerations for variationtolerant multilevel cmos/nano memristor memory,in:Proceedings of the 20th symposium on Great lakes symposium on VLSI,2010,pp.287–292.[21]Y.Pershin,M.Di Ventra,Experimental demonstration of associativememory with memristive neural networks,Neural Networks23(7)(2010) 881–886.[22]K.Eshraghian,K.Cho,O.Kavehei,S.Kang,D.Abbott,S.Kang,Mem-ristor MOS content addressable memory(MCAM):Hybrid architecture for future high performance search engines,IEEE Transactions on Very Large Scale Integration(VLSI)Systems(99)(2010)1–11.[23] D.Niu,Y.Chen,Y.Xie,Low-power dual-element memristor based mem-ory design,in:The16th ACM/IEEE international symposium on Low power electronics and design,2010,pp.25–30.[24]Y.V.Pershin,M.D.Ventra,Experimental demonstration of associativememory with memristive neural networks,Neural Networks23(7)(2010) 881–886.[25]P.O.V ontobel,W.Robinett,P.J.Kuekes,D.R.Stewart,J.Straznicky,R.S.Williams,Writing to and reading from a nano-scale crossbar mem-ory based on memristors,Nanotechnology20(42)(2009)425204. [26]G.Huang,Y.Ho,P.Li,Memristor system properties and its design ap-plications to circuits such as nonvolatile memristor memories,in:In-ternational Conference on Communications,Circuits and Systems(IC-CCAS’10),2010,pp.805–810.[27] A.Talukdar, A.G.Radwan,K.N.Salama,Generalized model formemristor-based wien family oscillators,Microelectronics Journal42(9) (2011)1032–1038.[28] A.Talukdar,A.G.Radwan,K.N.Salama,Non linear dynamics of mem-ristor based3rd order oscillatory system,Microelectronics Journal43(3) (2012)169–175.[29]M.A.Zidan,H.Omran,A.G.Radwan,K.N.Salama,Memristor-basedreactance-less oscillator,Electronics Letters47(22)(2011)1220–1221.[30]M.Itoh,L.Chua,Memristor oscillators,Int.J.Bifurcation and Chaos18(11)(2008)3183–3206.[31]W.Robinett,M.Pickett,J.Borghetti,Q.Xia,G.Snider,G.Medeiros-Ribeiro,R.Williams,A memristor-based nonvolatile latch circuit,Nan-otechnology21(2010)235203.[32] F.Merrikh-Bayat,S.Shouraki,Memristor-based circuits for performingbasic arithmetic operations,Procedia Computer Science3(2011)128–132.[33]S.Shin,K.Kim,S.-M.Kang,Memristor applications for programmableanalog ics,IEEE Transactions on Nanotechnology10(2)(2011)266–274.[34]Y.Pershin,M.Di Ventra,Practical approach to programmable analogcircuits with memristors,IEEE Transactions on Circuits and Systems I: Regular Papers57(8)(2010)1857–1864.[35]Y.V.Pershin, Fontaine,M.Di Ventra,Memristive model of amoebalearning,Physical Review E80(2)(2009)021926.[36]S.Jo,T.Chang,I.Ebong,B.Bhadviya,P.Mazumder,W.Lu,Nanoscalememristor device as synapse in neuromorphic systems,Nano letters10(4) (2010)1297–1301.[37]M.Kryder,C.Kim,After hard drives-what comes next?,IEEE Transac-tions on Magnetics45(10)(2009)3406–3413.[38] F.Miao,J.P.Strachan,J.J.Yang,M.-X.Zhang,I.Goldfarb,A.C.Tor-rezan,P.Eschbach,R.D.Kelley,G.Medeiros-Ribeiro,R.S.Williams, Anatomy of a nanoscale conduction channel reveals the mechanism of a high-performance memristor,Advanced Materials23(2011)5633–5640.[39]Elpida Memory develops resistance RAM prototype.URL /en/news/2012/01-24r.html [40]L.Chua,Resistance switching memories are memristors,Applied PhysicsA:Materials Science&Processing102(4)(2011)765–783.[41] D.Manners,IEF2011:HP to replaceflash and SSD in2013,ElectronicsWeekly(2011).[42]G.Rose,Overview:Memristive devices,circuits and systems,in:IEEEInternational Symposium on Circuits and Systems(ISCAS’10),2010,pp.1955–1958.[43]S.-M.Kang,Y.Leblebici,CMOS Digital Integrated Circuits Analysis&Design,McGraw-Hill,2007.[44]W.Fei,H.Yu,W.Zhang,K.Yeo,Design exploration of hybrid cmos andmemristor circuit by new modified nodal analysis,IEEE Transactions on Very Large Scale Integration(VLSI)Systems(99)(2011)1–15.[45] B.Mouttet,Programmable crossbar signal processor,US Patent7,302,513(2007).[46]S.Kim,H.Jeong,S.Kim,S.Choi,K.Lee,Flexible memristive memoryarray on plastic substrates,Nano Letters11(12)(2011)5438–5442. [47] C.Jung,J.Choi,K.Min,Two-step write scheme for reducing sneak-path leakage in complementary memristor array,IEEE Transactions on Nanotechnology11(3)(2012)611–618.[48]J.J.Yang,M.-X.Zhang,M.D.Pickett,F.Miao,J.P.Strachan,W.-D.Li,W.Yi,D.A.A.Ohlberg,B.J.Choi,W.Wu,J.H.Nickel,G.Medeiros-Ribeiro,R.S.Williams,Engineering nonlinearity into memristors for passive crossbar applications,Applied Physics Letters100(11)(2012) 113501.[49]M.Qureshi,W.Yi,G.Medeiros-Ribeiro,R.Williams,AC sense tech-nique for memristor crossbar,Electronics letters48(13)(2012)757–758.[50] B.Widrow,Adaptive“adaline”neuron using chemical“memistors”,Tech.rep.,Stanford University(1960).[51]H.Kim,S.Adhikari,Memistor is not memristor,IEEE Circuits and Sys-tems Magazine12(1)(2012)75–78.。
引用电脑各种错误英语提示信息的意思一、BIOS中的提示信息提示信息说明Drive A error 驱动器A错误System halt 系统挂起Keyboard controller error 键盘控制器错误Keyboard error or no keyboard present 键盘错误或者键盘不存在BIOS ROM checksum error BIOS ROM 校验错误Single hardisk cable fail 当硬盘使用Cable选项时硬盘安装位置不正确FDD Controller Failure BIOS 软盘控制器错误HDD Controller Failure BIOS 硬盘控制器错误Driver Error 驱动器错误Cache Memory Bad, Do not Enable Cache 高速缓存Cache损坏,不能使用Error: Unable to control A20 line 错误提示:不能使用A20地址控制线Memory write/Read failure 内存读写失败Memory allocation error 内存定位错误CMOS Battery state Low CMOS没电了Keyboard interface error 键盘接口错误Hard disk drive failure 加载硬盘失败Hard disk not present 硬盘不存在Floppy disk(s) fail (40) 软盘驱动器加载失败,一般是数据线插反,电源线没有插接,CMOS 内部软驱设置错误CMOS checksum error-efaults loaded. CMOS校验错误,装入缺省(默认)设置二、BIOS刷新失败后,Bootblock启动时出现的提示信息提示信息说明Detecting floppy drive A media... 检测软驱A的格式Drive media is : 1.44Mb1.2Mb 720Kb 360K 驱动器格式是1.44Mb、12Mb、720kb、360kb 的一种DISK BOOT FAILURE, INSERT SYSTEM DISK AND PRESS ENTER 磁盘引导失败,插入系统盘后按任意键继续三、MBR主引导区提示信息提示信息说明Invalid partition table 无效的分区表Error loading operating sy stem 不能装入引导系统Missing operating system 系统引导文件丢失说明:如果在计算机启动过程中,在硬件配置清单下方(也就时在平时正常启动时出现Starting Windows 98…的地方)出现不可识别字符,此时可判断硬盘分区表损坏。
Memory-Based and Disk-Based Algorithms for Very HighDegree Permutation GroupsGene Cooperman∗College of Computer Science Northeastern University Boston,MA 02115/USA gene@Eric RobinsonCollege of Computer Science Northeastern University Boston,MA 02115/USAtivadar@ABSTRACTGroup membership is a fundamental algorithm,upon which most other algorithms of computational group theory de-pend.Until now,group membership for permutation groups has been limited to ten million points or less.We extend the applicability of group membership algorithms to permuta-tion groups acting on more than 100,000,000points.As an example,we experimentally construct a group membership data structure for Thompson’s group,acting on 143,127,000points,in 36minutes.More significantly,we require approx-imately 10GB of RAM for the computation —even though a single permutation of Thompson’s group already requires half a gigabyte of storage.In addition,we propose a disk-based group membership algorithm with the promise of extending group membership to well over one billion (1,000,000,000)points.Such a disk-based algorithm has formerly been impossible,due in part to the lack of a practical disk-based algorithm for multiplying and taking inverses of such large permutations.Random access to disk is prohibitively expensive.We demonstrate the first practical disk-based implementation of the basic permutation operations.We also propose a disk-based ar-chitecture for group membership data structures.Categories and Subject DescriptorsI.1.2[Symbolic and Algebraic Manipulation ]:Algo-rithms—algebraic algorithmsGeneral TermsAlgorithms,ExperimentationKeywordspermutation groups,group membership,permutation mul-tiplication,disk-based methods,Thompson’s groupoffinding the order of such constructed permutation groups by a single,uniform set of heuristics.In extending group membership to higher degrees,we modify the randomized Schreier-Sims group membership al-gorithm of Sims[35].One variation is more space-efficient. Another variation adds additional pseudo-random group el-ements by applying the shallow Schreier trees of Cooperman and Finkelstein[13,12].Shallow Schreier trees were also the key to the nearly linear time algorithms of Babai,Cooper-man,Finkelstein and Seress[3]for small base groups.A further enhancement uses a new heuristic,called powerlev-elling(see Section3.1.2).A key to the success of the new algorithm is the use of a high quality random word generator.Several algo-rithms for random generation are available,including those of Babai[1],Celler et al.[7],and Cooperman[8].Although the theoretical complexity guarantees are far from satisfac-tory,current implementations make random generation of group elements quite practical.Babai’s method was thefirst polynomial time method,op-erating in O∼(n6)time.The product replacement method of Celler et al.was shown by Pak[33]to run in at most O∼(n10)time,although in implementations it is the most practical and most widely used of the three methods.The method of Celler et al.is particularly impressive in that after its initialization,it can produce a new,high quality pseudo-random element with only one group multiplication. Cooperman’s method operates in O∼(n3)time.A variation of Cooperman’s method is used here,for the sake of its abil-ity to compactly represent pseudo-random group elements by a vector of0/1exponents with respect to afixed straight line program.Section2provides the background and a review of the Schreier-Sims group membership algorithm.Section3de-scribes a space-efficient group membership algorithm for a permutation representation of Thompson’s group,acting on 143,127,000million points.Thompson’s group is a sporadic simple group of order90,745,943,887,872,000.Section4de-scribes a proposed efficient disk-based version of the algo-rithm.Of particular interest is Section4.1,which describes a practical algorithm for disk-based permutation multiplica-tion and permutation inverse,along with timings.1.1Previous LiteratureThe need for analysis of very high degree permutation groups has a long history.Almost ten years ago,Cooper-man et al.[15,14]produced a permutation representation of degree9,606,125for Lyons’group acting on a conjugacy class of subgroups of order three.The representation was found,using the matrix representation of Wilson[39]as a starting point.The representation was verified in a Monte Carlo manner by computing its order through ad hoc meth-ods.Gollan then began his work on a revised existence proof of Lyons’group[23,24,25].As one part of that work,he deterministically verified the order of the permutation repre-sentation through the“double coset trick”,an independent rediscovery of an unpublished Verify algorithm of Sims. Later,a coset enumeration of Lyons’group yielded a per-mutation action on8,835,156points,based on Sims’origi-nal unpublished presentation.The coset enumeration was executed in two different ways.It was carried out as a par-allel enumeration by Cooperman and Havas[17](described therein as part of the future work).It was also demonstrated as a sequential coset enumeration by Havas and Sims[27]. That presentation was verified as producing Lyons’group by Gollan and Havas[26].Later work produced large permutation representations for Thompson’s group acting on143,127,000and for Janko’s group J4acting on173,067,389points.A permutation rep-resentation was implicit in the condensation computation for Thompson’s group of Cooperman et al.[18,21].Weller[38] carried out a direct computation at approximately the same time.Havas et al.[28]produced a presentation for Thomp-son’s group,and also a permutation representation thereof through coset enumeration.Weller[36,37]did the same for Janko’s group,using some of the hashing techniques of[14, 15]and the double coset trick of[23,25].That work was used in a revised existence proof for Janko’s group[19]. Finally,the matrix recognition project[30,31]expects to reduce certain matrix group recognition problems to the base case of the simple groups,which then require other methods for analysis.The methods of this paper provide a useful alternative in this setting,since they allow the well-developed computational methods for permutation groups to be applied.Note,for example,that any group with a representation in GL(30,2)(the group of matrices of dimen-sion30over thefinitefield with two elements)has a permu-tation representation on at most230,or approximately one billion points.The proposed disk-based algorithm grew out of work by Cooperman and Grinberg[16]in which a shared memory coset enumeration algorithm was found to be memory-bound. The result was a new faster algorithm for memory-based per-mutation multiplication by Cooperman and Ma[20].That algorithm has been retargeted here to provide the missing link in a disk-based group membership algorithm.2.BACKGROUNDA group membership algorithm takes as input a permu-tation,g,on n points,and a set of permutations,S,on n points,which generate a group G= S .The member-ship algorithm decides if g∈G.The original group membership algorithm by Sims[35] began a long period of new algorithmic research in permu-tation group algorithms.It works by divide-and-conquer. 2.1NotationDenote the points on which G acts by the integersΩ= {1,2,...,n}.For i∈Ωand g∈G,let i g denote the action of the permutation g on the point i.(Hence,i gh=(i g)h for g,h∈G.)Let e be the identity element of G.Let H≤G denote that H is a subgroup of G,and H<G that H is a proper subgroup of G.Define the point stabilizer subgroup G(i)={g:g∈G,∀j<i,j g=j}, sometimes called“G move i”(and moving all the points larger than i).Note that this yields a point stabilizer sub-group chainG=G(1)≥G(2)≥···G(n)={e}for e the identity.Let G/H={Hg:g∈G}be the set of cosets of H in G (where Hg={hg:h∈H}).Note that i G(i+1)g=i g for g∈G(where i G(i+1)g=(i G(i+1))g).So,for h∈G(i)g,i h isa signature of G(i)g.In other words,∀h1,h2∈G(i),i h1=i h2⇔G(i)h1=G(i)h2.A transversal of G(i)/G(i+1),T(i)is defined as a set of representatives of cosets of G(i+1)in G(i).So,|T(i)|=|G(i)/G(i+1)|.Further,a transversal T(i)satisfies∀j∈Ω,i g=j⇐⇒∃t,T(i)∩G(i+1)g={t}with i g=i t.2.2Review of Schreier-Sims RandomizedGroup Membership AlgorithmThis section describes a variation of the Schreier-Sims al-gorithm that forms the basis for the algorithmic work of this paper.The goal of the algorithm is to construct transver-sals T(i)for all i≥1.Once T(i)is constructed,the group membership algorithm for g∈G is solved,as seen below: ALGORITHM A:INPUT:permutation group G,transversals{T(i)},permutation g on{1,2,...,n}Let g1←gLOOP:For i=1,...,nIf T(i)∩G(i+1)g i=∅,then stop and return NOT MEMBER Otherwise,let t i∈T(i)be the unique elementsuch that T(i)∩G(i+1)g i={t i}Set g i+1←g i t−1iNote that g i+1∈G(i+1)and that g i=g i+1t iIf g i+1=e,then goto LOOPReturn g=g1←t i t i−1···t iIt also follows that any element g∈G can be uniquely represented asg=t n−1t n−2···t1for t i∈T(i).Hence,|G|=|T(n−1)||T(n−2)|···|T(1)|.This solves the problem of computing the group order.In order to construct T(i)for all i,two problems must be solved.P1:Given a random element of G(i),find a random element of G(i+1).P2:Given either generators or random elements of G(i), construct a transversal,T(i).The solution to Problem P1follows by noting that any random element g i∈G(i)has a unique representation g i= t n−1t n−2···t i for appropriate t j∈T(j)for j≥i.Fur-ther,the randomness of g i implies that each t j is as if cho-sen randomly from T(j).As in Algorithm A,one can de-termine from g i the unique t i and g i+1such that g i+1= t n−1t n−2···t i+1=g i t−1i.The randomness of the t j then imply that g i+1is random in G(i+1).The solution to Problem P2follows from simple search algorithms,such as breadth-first search.Given sufficient random elements of G(i),they are guaranteed to generate G(i).Let S(i)be the generating set of G(i).Initialize a reachability set R⊆Ωto R={(i,e)}.ALGORITHM B:INPUT:generating set S(i)for G(i)While there exists g∈S(i)and j∈R with j g/∈R do Add the pair(j g,g)to RThe data structure described in Algorithm B is called a Schreier tree.Next,if g∈G(i),then one canfind the unique t such that G(i)g∩T(i)as follows.Initialize t←e and initialize j←i g.LOOP:If j=i,then stop and return tOtherwise,let(j,h)∈R satisfy i t=jSet t←ht and set j←j g−1Goto LOOPAt termination,i t=i g and hence we have constructed the element t∈T(i).2.3Shallow Schreier TreesShallow Schreier trees were developed by Cooperman and Finkelstein[13,12].The primary result on shallow Schreier tree follows.Theorem2.1([12,Theorem3.5](paraphrased)). Forδ≥1,let d=⌈20δlog2|G(i)/G(i+1)|⌉.Then d random group elements suffice for a Monte Carlo algorithm to build a new Schreier tree for G(i)/G(i+1)of depth d.The proba-bility of error is less than|G(i)/G(i+1)|−δ.Intuitively,the theorem says that for a transversal of size T,20log2T random elements suffice to build a Schreier tree.Further,the tree will have depth at most20log2T. The probability of failing to construct the tree within the stated bounds is less than1/T.The proof of the theorem uses a very conservative algorithm.We apply a more ag-gressive heuristic to reduce the constant20.2.4Generation of Random ElementsA random subproduct on elements(h1,...,h k),is defined asg1···g i−1The chosen algorithm for random elements is purely heuris-tic,since the theoretical guarantees for currently known random generation algorithms are much too coarse.The algorithm is suggested by the more theoretical method of Cooperman[8].Random subproducts were used earlier by Cooperman and Finkelstein[10,11]in the context of a sim-ple O(n4)randomized group membership algorithm for large base groups.Intuitively,if a distribution of random group elements covers a set that is close to a subgroup,then the result of Cooperman and Finkelstein shows that a random subproduct will produce a new random element that escapes from that set.The motivation for our choice of heuristic is two-fold.Our first goal is to generate reasonably short words representing a random element of the permutation group.This saves space and time.In experiments,product replacement and Cooperman’s method both satisfy thefirst goal.The second goal is that the each random element be rep-resentable as a subproduct of afixed,short word in the group generators.A word w is a subword of g1···g k if w=g e11···g e kkfor some choice of e i∈{0,1}.(We de-fine g1i=g i and g0i to be the identity.)This is especiallydesirable for the disk-based version of the algorithm(see Section4).When the group is given on two generators,the second goal is easy to achieve by many heuristics.One can choose a word wℓ=aba−1b−1aba−1b−1···ab of length4ℓfor gener-ators a and b,and any word of lengthℓin those generators can be represented as a subword of wℓ.This second goal is harder to achieve when the group is given by more than two generators.The stated heuristic is one of many that allow the group membership algorithm to perform in reasonable time.Fur-ther research is required to determine the best heuristic. 3.MEMORY-BASED GROUPMEMBERSHIPThe algorithm proceeds as in Section2.2.The most im-portant and memory intensive portion of the algorithm is the computation of a transversal for G(1)/G(2).First,the method by which the transversal for G(1)/G(2)is computed and stored will be illustrated,and then it will be shown that this method can be easily extended to calculate transversals for G(i)/G(i+1)for i>1.Since for small base groups,the size of the transversal tends to decrease rapidly with increas-ing i,the remaining transversals are computed in a fraction of the space needed for G(1)/G(2).3.1Building the First Schreier TreeWe tried two methods for computing the transversal for G(1)/G(2).Thefirst was a standard Schreier tree.The sec-ond method introduced additional random group elements to guarantee a shallow Schreier tree.3.1.1Method1A modified Schreier vector representation is used,but without backpointers.A separate bit vector for the 143,127,000nodes records if a node has been seen before. The Schreier tree is explored in breadth-first order.New nodes in the Schreier tree are appended to the Schreier vec-tor as a pair consisting of a string of bits representing a word in the generators,and the image of the point1under that word.Once the Schreier vector is complete,it is sorted based on image points.At the end,each vector location at index i stores a string of bits representing a word in the generators mapping1to i.The storage to represent the word on original generators is not much more than the storage for a“backpointer”to the parent node in the Schreier tree.Storing the string directly tends to be more CPU efficient,by avoiding cache misses as one traces backpointers.The Thompson group had a maximum depth of72and an average depth of59for the transversal elements discovered and the mapping was complete(a mapping was discovered from the orbit to all of the other locations).3.1.2Method2The second method works harder to ensure an acceptably shallow Schreier tree.There is a tension between using many pseudo-random group elements as generators to reduce the Schreier tree depth and few generators so as to minimize storage requirements.This method does use backpointers to indicate the parent node of a given node in the Schreier tree.Initially,a subtree of the Schreier tree for G(1)/G(2)is built to a specified depth (depth20in the case of Thompson’s group).At this depth, we reached138,000points using the two original generators. Random elements are then used to extend the initial sub-tree.Since our random elements are always subwords of a fixed word,we save storage by storing them as bit represen-tations indicating the exponents relative to thefixed word. For Thompson’s group,35bits suffice.Our random word is produced as g k for k=9,based on Section2.4.The average length of g k as a word in the original generators is15,and words longer than length30are rejected.Each successive pass applies a new random element to each of the138,000nodes of the initial subtree.Further-more,for each new node discovered by application of that random group element,the tree is extended by a subtree rooted at the newly discovered node.The subtree extension is built using only only the original group generators.A good depth for the subtree was found to be20.This method guarantees that all transversal elements are expressible as words in at most one random element.This is done because the random group elements are much more expensive to apply than group generators.This process con-tinues until the number of nodes gained per pass through the tree is reduced to some specified percentage of the permuta-tion degree.A good percentage for Thompson’s group was found to be0.5%.At this point,a computational method,which we call pow-erlevelling,begins.A powerlevel is the application of all of the original generators to every node in the tree.If any of these applications discovers a new node,the tree is extended by a subtree rooted at the new node.For Thompson’s group, a depth of30for this subtree was used.Powerlevelling is then recursively applied to all nodes of the new subtree.If at any point during the powerlevelling process there are no new nodes gained by passing through the tree,the Schreier tree is complete.The depth of the Schreier tree was bounded above by 101:applications of original generators to depth20;appli-cations of approximately15random elements to each node of the subtree;application of original generators for an ad-ditional incremental depth of20;and a powerlevelling phase incrementally increasing the depth by30+30=60.Since a transversal element,expressed as a word,could include a random element,and since a random element was expressed as a word of length up to30,the transversal element was expressible as a word of length at most131.3.2Finding a Small SuborbitA suborbit is an orbit of the point stabilizer subgroup. The transversal of G(2)/G(3)is a suborbit.A small transver-sal greatly reduces the computation time for computing the transversal of G(2)/G(3).The initial suborbit on the point2 was of length35million,which made the computation time too long.Notwithstanding this consideration,if the transver-sal of G(2)/G(3)is too small,then|G(3)/G(4)|becomes com-parable to|G(2)/G(3)|,and the random words used to com-pute the transversal for|G(2)/G(3)|become very long.For balance,we use a heuristic that searched for a subor-bit of size approximately0.6%of the full permutation de-gree or smaller.The heuristic uses the incremental rate R at which new elements of the transversal are found in order to decide when to stop exploring the current suborbit,and choose a suborbit with a different initial random point.Iff is the number of points found andτthe desired suborbit size,then the heuristic rejects a suborbit if0.5f+fR>τ. Since initial random points are more often found in larger suborbits,the search is biased toward large suborbits sat-isfying0.5f+fR≤τ.The suborbit found is somewhat smaller(of size179,712),but suitable.3.3Building the Remaining Schreier Trees The remaining two levels were discovered by applying ran-dom elements to build a tree(see Section2.3).The quality of the random element was found to be very important.For a Schreier tree of depth d,random elements from words sig-nificantly longer than d were needed.3.4Experimental ResultsFigure1shows the breakdown of CPU times for Thomp-son’s putation of the second transversal requires 8random group elements,while the third transversal re-quires5random group elements.The computation used the first method(Section3.1.1)to compute the Schreier tree of thefirst transversal.The15minutes divides into7min-utes tofind all transversal elements and then8minutes to sort the Schreier vector based on image points.The second method was also tried,and required20minutes.For com-parison,the entire computation for Lyons’group acting on 9,606,125points completed in less than one minute.Preprocessing3minutesTransversal1(143,127,000points)15minutesFinding small suborbit(28tries)11minutesTransversal2(179,712points)5minutesTransversal3(3,528points)2minutesFor multiplication by permutation inverse,one follows thetwo phase algorithm as described for permutation inverses.However,one employs the pair(Y[i],X[i])instead of thepair(i,X[i]).Hence,for the pair(a,b)∈B[j],the secondphase computation,Z[b]←a,becomes Z[X[i]]=Y[i].Experimental times for permutation multiplication areshown below.The corresponding times for a disk-basedalgorithm based on the traditional permutation algorithm(with random access)is not shown.Such random accesswould likely require days to complete in all cases.Computer b(blocksize,bytes)(s)16MB17Pentium II/RAID-51MB64MB108Pentium II/RAID-51MBPentium II/RAID-51MB64MB118Pentium II/RAID-54MBPentium II/RAID-52MB64MB409.0800MHz AMD2MBw.Hence,we produce a set of random words,W,based on thefixedwordw =g 1···g k ,we proceed as described ear-lier.Let the word v ′s =g e 11···g e s −1s −1for exponents {e 1,...,e s −1}⊆{0,1}corresponds to a prefix of v .At step s ,for each element v ∈W ,we maintain an orderedset {(r i ,r v ′s i ):1≤i ≤ℓ}.If e s =1,then v ′s participates instep s and we will compute v ′s +1=v ′s g s .In that case,we will compute {(r i ,r v ′sg +1i ):1≤i ≤ℓ},and maintain it as an ordered set.We execute step s by scanning R simulta-neously with each ordered set {(r i ,r v ′s i ):1≤i ≤ℓ}that is participating in step s .4.3ExtensionsThe permutation operations and external sorting were both required as algorithmic disk-based subroutines.Both algorithms are limited as the size of the data grows compared to the size of main memory.This is because both algorithms require holding buffers for many streams of data simultane-ously in memory.For example,in the case of permutation multiplication,these are the data blocks B[j].The size of a data block B[j]is limited to approximately half of the size of main memory.The number of buffers is proportional to the quotient of the size of data by the size of a buffer for a single data block B[j].As the size of the data grows,not all of the buffers can simultaneously fit in main memory.In both cases,the algorithms are extended by taking a block B[j]as being larger than main memory.This keeps the number of buffers at a manageable level.In the case of external sort,this trick is well-known.In the case of the permutation multiplication algorithm of Section 4.1,at step 2one is required to permute data from a segment of the Y array and store it in a B[j]buffer.This is effectively an example of a permutation multiplication problem,and one applies the disk-based permutation multiplication re-cursively to solve it.Similar ideas are used for permutation inverse and multiplication by the permutation inverse.Many of the other algorithms of computational permuta-tion group theory can also be extended to disk-based algo-rithms using the methodology outlined in this section.In particular,this include verification of group membership.5.COMPACT REPRESENTATION OF SCHREIER TREESAn important consideration is the space storage for the representation of the Schreier trees.A natural representa-tion requires a pointer from each node to its parent,along with a label indicating which group element maps the par-ent to the child.A pointer typically requires four bytes,and upon breaking the 4GB barrier,it requires eight bytes.The method of Cooperman and Finkelstein for Schreier coset graphs [9]shows how to encode both the pointer and the label in a data structure that takes two bits or less of storage per node.That method depends on having a perfect hash encoding of the cosets.Such a perfect hash encoding exists,since for h ∈G (i )g ,i h is a signature of G (i )g ,as noted in Section 2.1.A future implementation will use this more compact stor-age method.This re-design of the Schreier tree data struc-ture is likely to reduce the overall storage requirements of the group membership application for Thompson’s group to well under 4GB.Because of this intended re-design,we didnot take as much care in minimizing the storage require-ments of this preliminary version.6.CONCLUSIONComputational permutation group algorithms and heuris-tics for very high degree permutation groups are a missing link in the ability to analyze the large group representations being produced today.Such large permutation represen-tations arise both from presentations of groups and from matrix representations.In this paper,we have raised the limits for what permutation degrees are practical by one or two powers of ten.For the future,we expect disk-based methods to raise the limits still further.Applying such disk-based methods will depend on the availability of disks with high data transfer rates.Such technology is available both through disk strip-ing (e.g.RAID-0and RAID-3)and through the use of clus-ters with many local disks and a high bandwidth local area network.Implementing the disk-based algorithm closer to this “bleeding edge”of technology will require further work.For today,the memory-based algorithm presented here is eminently practical.Although the storage requirements for Thompson’s group for this preliminary implementation were approximately 10GB,the methods of Section 5will likely reduce the memory requirements to under 4GB.7.ACKNOWLEDGEMENTSWe are grateful to Michael Weller for providing us with the large permutation representations that formed the basis of these experiments,and for describing his own experiences with such large computations.The generators for Thomp-son’s group are standard generators in the sense of Wilson,and were generated by Weller from one of Wilson’s matrix representations [39].We thank Xiaoqin Ma and Viet Ha Nguyen for discussions about issues of random and sequen-tial access in RAM.We also thank the Mariner Project at Boston University for providing the experimental facilities.8.REFERENCES[1]L.Babai.Local expansion of vertex-transitive graphsand random generation in finite groups.In Theory of Computing ,pages 164–174,New York,1991.(LosAngeles,1991),Association for Computing Machinery.[2]L.Babai,G.Cooperman,L.Finkelstein,E.M.Luks,and A.Seress.Fast Monte Carlo algorithms forpermutation p.Syst.Sci.,50:296–308,1995.[3]L.Babai,G.Cooperman,L.Finkelstein,andA.Seress.Nearly linear time algorithms forpermutation groups with a small base.In Proc.of International Symposium on Symbolic and Algebraic Computation ISSAC ’91,pages 200–209.(Bonn),ACM Press,1991.[4]L.Babai,E.M.Luks,and A.Seress.Fastmanagement of permutation groups I.SIAM puting ,26:1310–1342,1997.[5]W.Bosma,J.Cannon,and C.Playoust.The magmaalgebra system i:The user language.J.Symbolic Comput.,24:235–265,1997.[6]G.Butler and puting inpermutation and matrix groups I:Normal closure,commutator subgroups,p.,39:663–670,1982.[7]F.Celler,C.R.Leedham-Green,S.H.Murray,A.C.Niemeyer,and E.O’Brien.Generating randomelements of afinite m.Algebra,23:4931–4948,1995.[8]G.Cooperman.Towards a practical,theoreticallysound algorithm for random generation infinitegroups.arXiv:math.PR/0205203,/abs/math.PR/0205203.[9]G.Cooperman and L.Finkelstein.New methods forusing cayley graphs in interconnection networks.Discrete Applied Mathematics,37/38:95–118,1992.(special issue on Interconnection Networks).[10]G.Cooperman and L.Finkelstein.Randomizedalgorithms for permutation groups.CentrumWissenschaft Institut Quarterly(CWI),pages107–125,June1992.[11]G.Cooperman and binatorialtools for computational group theory.In Groups andComputation,volume11of Amer.Math.Soc.DIMACS Series,pages53–86.(DIMACS,1991),1993.[12]G.Cooperman and L.Finkelstein.A random basechange algorithm for permutation groups.J.Symbolic Comput.,17:513–528,1994.[13]G.Cooperman,L.Finkelstein,and N.Sarawagi.Arandom base change algorithm for permutationgroups.In Proc.of International Symposium onSymbolic and Algebraic Computation ISSAC’90,pages161–168,Tokyo,Japan,1990.[14]G.Cooperman,L.Finkelstein,M.Tselman,andB.York.Constructing permutation representations formatrix groups.J.Symbolic Comput.,1997.[15]G.Cooperman,L.Finkelstein,B.York,andM.Tselman.Constructing permutationrepresentations for large matrix groups.In Proceedings of International Symposium on Symbolic andAlgebraic Computation ISSAC’94,pages134–138,New York,1994.(Oxford),ACM Press.[16]G.Cooperman and V.Grinberg.Scalable parallelcoset enumeration:Bulk definition and the memorywall.J.Symbolic Comput.,33:563–585,2002.[17]G.Cooperman and G.Havas.Practical parallel cosetenumeration.In Workshop on High PerformanceComputing and Gigabit Local Area Networks,volume226of Lecture Notes in Control and InformationSciences,pages15–27,1997.[18]G.Cooperman,G.Hiss,K.Lux,and J.M¨u ller.TheBrauer tree of the principal19-block of the sporadicsimple thompson group.J.Experimental Math.,6:293–300,1997.[19]G.Cooperman,W.Lempken,G.Michler,andM.Weller.A new existence proof of Janko’s simplegroup J4.In Computational Methods forRepresentations of Groups and Algebras,volume173of Progress in Mathematics,pages161–175,1999. [20]G.Cooperman and X.Ma.Overcoming the memorywall in symbolic algebra:A faster permutationalgorithm(formally reviewed communication).SIGSAM Bulletin,36:1–4,Dec.2002.[21]G.Cooperman and M.Tselman.New sequential andparallel algorithms for generating high dimensionHecke algebras using the condensation technique.InProc.of International Symposium on Symbolic andAlgebraic Computation(ISSAC’96),pages155–160.ACM Press,1996.[22]The GAP Group.GAP—Groups,Algorithms,andProgramming,Version4.3,2002..[23]H.Gollan.A new existence proof for Ly,the sporadicsimple group of R.Lyons.Preprint30,1995.[24]H.Gollan.A contribution to the revision project ofthe sporadic groups:Lyons’simple group Ly.Vorlesungen aus dem FB Mathematik,26,1997. [25]H.Gollan.A new existence proof for Ly,the sporadicsimple group of R.Lyons.J.Symbolic Comput.,31:203–209,2001.[26]H.Gollan and G.Havas.On Sims’presentation forLyons’simple group.In Computational Methods forRepresentations of Groups and Algebras,volume173of Progress in Mathematics,pages235–240,1999. [27]G.Havas and C.Sims.A presentation for the Lyonssimple group.In Computational Methods forRepresentations of Groups and Algebras,volume173of Progress in Mathematics,pages241–249,1999. [28]G.Havas,L.Soicher,and R.Wilson.A presentationfor the Thompson sporadic simple group.In Groupsand Computation III,pages193–200,New York,2001.(Ohio,1999),de Gruyter.[29]W.M.Kantor.Sylow’s theorem in polynomial time.J.Comp.Syst.Sci.,30:359–394,1985.[30]C.Leedham-Green.The computational matrix groupproject.In Groups and Computation III,pages229–248,New York,2001.(Ohio,1999),de Gruyter.[31]C.Leedham-Green,E.O’Brien,and C.Praeger.Recognising matrix groups.In J.Grabmeier,E.Kaltofen,and V.Weispfenning,editors,ComputerAlgebra Handbook,pages474–475,2003.[32]puting the composition factors of apermutation group in polynomial time.Combinatorica,7:87–99,1987.[33]I.Pak.The product replacement algorithm ispolynomial.In Proc.41st IEEE Symposium onFoundations of Computer Science(FOCS),pages476–485.IEEE Press,2000.[34]R.Ramakrishnan and J.Gehrke.DatabaseManagement Systems.McGrawHill,second edition,2000.[35]putation with permutation groups.InProc.Second Symp.on Symbolic and AlgebraicManipulation.ACM Press,1971.[36]M.Weller.Construction of large permutationrepresentations for matrix groups.In W.J.E.Krause, editor,High Performance Computing in Science andEngineering’98,pages430–.Springer,1999.[37]M.Weller.Construction of large permutationrepresentations for matrix groups ii.ApplicableAlgebra in Engineering,Communication andComputing,11:463–488,2001.[38]puter aided existence proof ofThompson’s sporadic simple group.manuscript,2003.[39]R.Wilson.Atlas offinite group representations./atlas.。