AI Headshot Generator For Linkedin

AI Headshot Generator For Linkedin — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.

GPTs

GPTs are custom versions of ChatGPT with added instructions and extra knowledge. GPTs can be used and created from the GPT Store. Any user can easily create them without any programming knowledge. GPTs can be tailored for specific writing styles, topics, or tasks. The ability to create GPTs was introduced in November 2023, and by January 2024, more than 3 million GPTs had been published. == Features and uses == GPTs can be configured to answer complex questions in specific fields, solve problems, provide image-based information, or create digital content. They can be programmed as educational tools, purchasing guides, or technical advisors, as well as for many others applications. GPTs are accessed from the GPT Store section of the ChatGPT web page. The “Explore GPT” link opens the store where the most popular GPTs in each section are highlighted. The GPTs are organized by categories. The store also uses a rating system based on user experiences similar to that used by other app stores such as Apple's App Store or Google Play. Those with the best ratings appear at the top of each category. According to La Vanguardia, the most popular categories are: Personal assistants Learning to program Image generation Creative writing Gaming Entertainment It is expected that in the future the creators of GPTs will be able to monetize them. Companies like Moderna are using GPTs to assist in various specific business tasks. The company has created 750 GPTs for its own internal use. == Configuration == Creating GPTs does not require prior programming knowledge. Free users can use existing GPTs but cannot create their own. Paying subscribers can use the editor on the ChatGPT site to configure the GPT's name, image and description, instructions and access to APIs, along with visibility options. == Criticism == The implementation and use of GPTs has not been without criticism. The GPT Store has been criticized for the proliferation of low-quality GPTs and spam due to a lack of effective moderation. There are also concerns about data privacy and security, as GPTs may collect and use personal information in ways that are not always transparent to users.
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Data set (IBM mainframe)

In the context of IBM mainframe computers in the IBM System/360 line and its successors, a data set (IBM preferred) or dataset is a computer file having a record organization. Use of this term began with, e.g., DOS/360 and OS/360, and is still used by their successors, including the current VSE and z/OS. Documentation for these systems historically preferred this term rather than file. A data set is typically stored on a direct access storage device (DASD) or magnetic tape, however unit record devices, such as punch card readers, card punches, line printers and page printers can provide input/output (I/O) for a data set (file). Data sets are not unstructured streams of bytes, but rather are organized in various logical record and block structures determined by the DSORG (data set organization), RECFM (record format), and other parameters. These parameters are specified at the time of the data set allocation (creation), for example with Job Control Language DD statements. Within a running program they are stored in the Data Control Block (DCB) or Access Control Block (ACB), which are data structures used to access data sets using access methods. Records in a data set may be fixed, variable, or “undefined” length. == Data set organization == For OS/360, the DCB's DSORG parameter specifies how the data set is organized. It may be CQ Queued Telecommunications Access Method (QTAM) in Message Control Program (MCP) CX Communications line group DA Basic Direct Access Method (BDAM) GS Graphics device for Graphics Access Method(GAM) IS Indexed Sequential Access Method (ISAM) MQ QTAM message queue in application PO Partitioned Organization PS Physical Sequential among others. Data sets on tape may only be DSORG=PS. The choice of organization depends on how the data is to be accessed, and in particular, how it is to be updated. Programmers utilize various access methods (such as QSAM or VSAM) in programs for reading and writing data sets. Access method depends on the given data set organization. == Record format (RECFM) == Regardless of organization, the physical structure of each record is essentially the same, and is uniform throughout the data set. This is specified in the DCB RECFM parameter. RECFM=F means that the records are of fixed length, specified via the LRECL parameter. RECFM=V specifies a variable-length record. V records when stored on media are prefixed by a Record Descriptor Word (RDW) containing the integer length of the record in bytes and flag bits. With RECFM=FB and RECFM=VB, multiple logical records are grouped together into a single physical block on tape or DASD. FB and VB are fixed-blocked, and variable-blocked, respectively. RECFM=U (undefined) is also variable length, but the length of the record is determined by the length of the block rather than by a control field. The BLKSIZE parameter specifies the maximum length of the block. RECFM=FBS could be also specified, meaning fixed-blocked standard, meaning all the blocks except the last one were required to be in full BLKSIZE length. RECFM=VBS, or variable-blocked spanned, means a logical record could be spanned across two or more blocks, with flags in the RDW indicating whether a record segment is continued into the next block and/or was continued from the previous one. This mechanism eliminates the need for using any "delimiter" byte value to separate records. Thus data can be of any type, including binary integers, floating-point, or characters, without introducing a false end-of-record condition. The data set is an abstraction of a collection of records, in contrast to files as unstructured streams of bytes. == Partitioned data set == A partitioned data set (PDS) is a data set containing multiple members, each of which holds a separate sub-data set, similar to a directory in other types of file systems. This type of data set is often used to hold load modules (old format bound executable programs), source program libraries (especially Assembler macro definitions), ISPF screen definitions, and Job Control Language. A PDS may be compared to a Zip file or COM Structured Storage. A Partitioned Data Set can only be allocated on a single volume and have a maximum size of 65,535 tracks. Besides members, a PDS contains also a directory. Each member can be accessed indirectly via the directory structure. Once a member is located, the data stored in that member are handled in the same manner as a PS (sequential) data set. Whenever a member is deleted, the space it occupied is unusable for storing other data. Likewise, if a member is re-written, it is stored in a new spot at the back of the PDS and leaves wasted “dead” space in the middle. The only way to recover “dead” space is to perform file compression. Compression, which is done using the IEBCOPY utility, moves all members to the front of the data space and leaves free usable space at the back. (Note that in modern parlance, this kind of operation might be called defragmentation or garbage collection; data compression nowadays refers to a different, more complicated concept.) PDS files can only reside on DASD, not on magnetic tape, in order to use the directory structure to access individual members. Partitioned data sets are most often used for storing multiple job control language files, utility control statements, and executable modules. An improvement of this scheme is a Partitioned Data Set Extended (PDSE or PDS/E, sometimes just libraries) introduced with DFSMSdfp for MVS/XA and MVS/ESA systems. A PDS/E library can store program objects or other types of members, but not both. BPAM cannot process a PDS/E containing program objects. PDS/E structure is similar to PDS and is used to store the same types of data. However, PDS/E files have a better directory structure which does not require pre-allocation of directory blocks when the PDS/E is defined (and therefore does not run out of directory blocks if not enough were specified). Also, PDS/E automatically stores members in such a way that compression operation is not needed to reclaim "dead" space. PDS/E files can only reside on DASD in order to use the directory structure to access individual members. == Generation Data Group == A Generation Data Group (GDG) is a group of non-VSAM data sets that are successive generations of historically-related data stored on an IBM mainframe (running OS/360 and its successors or DOS/360 and its successors). A GDG is usually cataloged. An individual member of the GDG collection is called a "Generation Data Set." The latter may be identified by an absolute number, ACCTG.OURGDG(1234), or a relative number: (-1) for the previous generation, (0) for the current one, and (+1) the next generation. A GDG specifies how many generations of a data set are to be kept and at what age a generation will be deleted. Whenever a new generation is created, the system checks whether one or more obsolete generations are to be deleted. The purpose of GDGs is to automate archival, using the command language JCL, the data set name given is generic. When DSN appears, the GDG data set appears along with the history number, where (0) is the most recent version (-1), (-2), ... are previous generations (+1) a new generation (see DD) Another use of GDGs is to be able to address all generations simultaneously within a JCL script without having to know the number of currently available generations. To do this, you have to omit the parentheses and the generation number in the JCL when specifying the dataset. === GDG JCL & features === Generation Data Groups are defined using either the BLDG statement of the IEHPROGM utility or the DEFINE GENERATIONGROUP statement of the newer IDCAMS utility, which allows setting various parameters. LIMIT(10) would limit the number of generations limit to 10. SCRATCH FOR (91) would retain each member, up to the limited#generations, at least 91 days. IDCAMS can also delete (and optionally uncatalog) a GDG. ==== Example ==== Creation of a standard GDG for five safety scopes, each at least 35 days old: Delete a standard GDG:
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Interplanetary Internet

The interplanetary Internet is a conceived computer network in space, consisting of a set of network nodes that can communicate with each other. These nodes are the planet's orbiters and landers, and the Earth ground stations. For example, the orbiters collect the scientific data from the Curiosity rover on Mars through near-Mars communication links, transmit the data to Earth through direct links from the Mars orbiters to the Earth ground stations via the NASA Deep Space Network, and finally the data routed through Earth's internal internet. Interplanetary communication is greatly delayed by interplanetary distances, as data transmission can only go as fast as the speed of light, so a new set of protocols and technologies that are tolerant to large delays and errors are required. The interplanetary Internet has been envisioned as a store and forward network of internets that is often disconnected, has a wireless backbone fraught with error-prone links and delays ranging from tens of minutes to even hours, even when there is a connection. As of 2024 agencies and companies working towards bringing the network to fruition include NASA, ESA, SpaceX and Blue Origin. == Challenges and reasons == In the core implementation of Interplanetary Internet, satellites orbiting a planet communicate to other planet's satellites. Simultaneously, these planets revolve around the Sun with long distances, and thus many challenges face the communications. The reasons and the resultant challenges are: The motion and long distances between planets: The interplanetary communication is greatly delayed due to the interplanetary distances and the motion of the planets. The delay is variable and long, ranging from a couple of minutes (Earth-to-Mars), to a couple of hours (Pluto-to-Earth), depending on their relative positions. The interplanetary communication also suspends due to the solar conjunction, when the sun's radiation hinders the direct communication between the planets. As such, the communication characterizes lossy links and intermittent link connectivity. Low embeddable payload: Satellites can only carry a small payload, which poses challenges to the power, mass, size, and cost for communication hardware design. An asymmetric bandwidth would be the result of this limitation. This asymmetry reaches ratios up to 1000:1 as downlink:uplink bandwidth portion. Absence of fixed infrastructure: The graph of participating nodes in a specific planet-to-planet communication keeps changing over time, due to the constant motion. The routes of the planet-to-planet communication are planned and scheduled rather than being opportunistic. The Interplanetary Internet design must address these challenges to operate successfully and achieve good communication with other planets. It also must use the few available resources efficiently in the system. == Development == Space communication technology has steadily evolved from expensive, one-of-a-kind point-to-point architectures, to the re-use of technology on successive missions, to the development of standard protocols agreed upon by space agencies of many countries. This last phase has gone on since 1982 through the efforts of the Consultative Committee for Space Data Systems (CCSDS), a body composed of the major space agencies of the world. It has 11 member agencies, 32 observer agencies, and over 119 industrial associates. The evolution of space data system standards has gone on in parallel with the evolution of the Internet, with conceptual cross-pollination where fruitful, but largely as a separate evolution. Since the late 1990s, familiar Internet protocols and CCSDS space link protocols have integrated and converged in several ways; for example, the successful FTP file transfer to Earth-orbiting STRV 1B on January 2, 1996, which ran FTP over the CCSDS IPv4-like Space Communications Protocol Specifications (SCPS) protocols. Internet Protocol use without CCSDS has taken place on spacecraft, e.g., demonstrations on the UoSAT-12 satellite, and operationally on the Disaster Monitoring Constellation. Having reached the era where networking and IP on board spacecraft have been shown to be feasible and reliable, a forward-looking study of the bigger picture was the next phase. The Interplanetary Internet study at NASA's Jet Propulsion Laboratory (JPL) was started by a team of scientists at JPL led by internet pioneer Vinton Cerf and the late Adrian Hooke. Cerf was appointed as a distinguished visiting scientist at JPL in 1998, while Hooke was one of the founders and directors of CCSDS. While IP-like SCPS protocols are feasible for short hops, such as ground station to orbiter, rover to lander, lander to orbiter, probe to flyby, and so on, delay-tolerant networking is needed to get information from one region of the Solar System to another. It becomes apparent that the concept of a region is a natural architectural factoring of the Interplanetary Internet. A region is an area where the characteristics of communication are the same. Region characteristics include communications, security, the maintenance of resources, perhaps ownership, and other factors. The Interplanetary Internet is a "network of regional internets". What is needed then, is a standard way to achieve end-to-end communication through multiple regions in a disconnected, variable-delay environment using a generalized suite of protocols. Examples of regions might include the terrestrial Internet as a region, a region on the surface of the Moon or Mars, or a ground-to-orbit region. The recognition of this requirement led to the concept of a "bundle" as a high-level way to address the generalized Store-and-Forward problem. Bundles are an area of new protocol development in the upper layers of the OSI model, above the Transport Layer with the goal of addressing the issue of bundling store-and-forward information so that it can reliably traverse radically dissimilar environments constituting a "network of regional internets". Delay-tolerant networking (DTN) was designed to enable standardized communications over long distances and through time delays. At its core is the Bundle Protocol (BP), which is similar to the Internet Protocol, or IP, that serves as the heart of the Internet here on Earth. The big difference between the regular Internet Protocol (IP) and the Bundle Protocol is that IP assumes a seamless end-to-end data path, while BP is built to account for errors and disconnections — glitches that commonly plague deep-space communications. Bundle Service Layering, implemented as the Bundling protocol suite for delay-tolerant networking, will provide general-purpose delay-tolerant protocol services in support of a range of applications: custody transfer, segmentation and reassembly, end-to-end reliability, end-to-end security, and end-to-end routing among them. The Bundle Protocol was first tested in space on the UK-DMC satellite in 2008. An example of one of these end-to-end applications flown on a space mission is the CCSDS File Delivery Protocol (CFDP), used on the Deep Impact comet mission. CFDP is an international standard for automatic, reliable file transfer in both directions. CFDP should not be confused with Coherent File Distribution Protocol, which has the same acronym and is an IETF-documented experimental protocol for rapidly deploying files to multiple targets in a highly networked environment. In addition to reliably copying a file from one entity (such as a spacecraft or ground station) to another entity, CFDP has the capability to reliably transmit arbitrarily small messages defined by the user, in the metadata accompanying the file, and to reliably transmit commands relating to file system management that are to be executed automatically on the remote end-point entity (such as a spacecraft) upon successful reception of a file. == Protocol == The Consultative Committee for Space Data Systems (CCSDS) packet telemetry standard defines the protocol used for the transmission of spacecraft instrument data over the deep-space channel. Under this standard, an image or other data sent from a spacecraft instrument is transmitted using one or more packets. === CCSDS packet definition === A packet is a block of data with length that can vary between successive packets, ranging from 7 to 65,542 bytes, including the packet header. Packetized data is transmitted via frames, which are fixed-length data blocks. The size of a frame, including frame header and control information, can range up to 2048 bytes. Packet sizes are fixed during the development phase. Because packet lengths are variable but frame lengths are fixed, packet boundaries usually do not coincide with frame boundaries. === Telecom processing notes === Data in a frame is typically protected from channel errors by error-correcting codes. Even when the channel errors exceed the correction capability of the error-correcting code, the presence of errors is nearly always detected by the e
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Pivot to video

"Pivot to video" is a phrase referring to the trend, starting in 2015, of media publishing companies cutting staff resources for written content (generally published on their own web sites) in favor of short-form video content (often published on third-party platforms such as Facebook, Instagram, Twitter, YouTube, Snapchat, and TikTok). These moves were generally presented by publishers as a response to changes in social media traffic or to changes in the media consumption habits of younger audiences. However, many media commentators have argued that this shift was primarily motivated by advertising revenue, and that only advertisers, not consumers, prefer video over text. The pivot's contribution to job loss in the media industry has given the phrase "pivot to video" an association with decline, especially in a business context. Commentators have also noted a lack of transparency and accuracy in the viewership metrics reported by platforms such as Facebook, pointing out that abrupt shifts in platforms' proprietary algorithms can have devastating effects on publishers' viewership, traffic, and revenue. Following a scandal in which Facebook revealed it had artificially inflated numbers to its advertisers about how long viewers watched ads, many journalists and industry analysts concluded that the shift to video was based on such misleading or inaccurate metrics, which created a false impression that there was customer demand for additional video content. == History == Streaming media technology has been available since the early 1990s, though it was relatively low-fidelity and not widely available until the mid-2000s. In 2007, traditional media publishers including the New York Times, Washington Post and Time Inc. created new divisions to develop web videos, and Facebook launched its video platform. Twitter purchased micro-video service Vine in October 2012, began adding native video streaming in late 2014, and acquired video-streaming service Periscope in January 2015. An August 2014 profile on BuzzFeed noted the publisher's large investment into video production, and observed that "the future of BuzzFeed may not even be on BuzzFeed.com. One of the company’s nascent ideas, BuzzFeed Distributed, will be a team of 20 people producing content that lives entirely on other popular platforms, like Tumblr, Instagram or Snapchat." On 7 January 2015, Facebook issued a statement about "the shift to video," reporting that "since June 2014, Facebook has averaged more than 1 billion video views every day." Media critic John Herrman argued that "What the shift to Facebook video means is that Facebook is more interested in hosting the things media companies make than just spreading them, that it views links to outside pages as a problem to be solved, and that it sees Facebook-hosted video as an example of the solution." In February 2015, the digital video-journalism publisher NowThis announced that it would operate without a home page, producing content to be published directly on social media platforms. In April 2016, Mashable fired much of its editorial staff, attempting to pivot away from hard news coverage while "growing Mashable across every platform" and doubling down on branded content and video. By December 2017, following a sale to Ziff Davis, Mashable retreated from this focus on video; Bernard Gershon, president of GershonMedia, said that the announcement of many such "pivots" were actually aimed primarily at investors. By 2017, "advertiser interest in video [was] insatiable... Any CFO is going to say 'How can we get more video?'" according to an executive of the publishers' trade association Digital Content Next. Publishers such as Vanity Fair, the Washington Post, and Sports Illustrated began adapting their own articles into cheap video content, either dictated by a newsreader or animated as a slideshow with captions, which could be shared on social platforms or even played alongside the articles themselves. June 2017 saw numerous high-profile pivots to video. Vocativ laid off at least 20 staff, including its entire newsroom, explaining that "as the industry evolves, we are undertaking a strategic shift to focus exclusively on video content that will be distributed via social media and other platforms." Fox Sports eliminated its entire writing staff to focus on creating "premium video across all platforms." And MTV News announced a restructuring that would cut its writing team. Less than two years earlier, MTV News had hired Grantland co-founder Dan Fierman to lead a significant investment in "longform" political and cultural reporting, but Fierman left in April 2017, and in June MTV announced it was "shifting resources into short-form video content more in line with young people's media consumption habits." In July, Vice Media laid off at least 60 employees, including the editor-in-chief of Vice Sports, while expanding video production. August 2017 saw Mic cut ten writers and directed the remainder of the newsroom to generate videos for social platforms. CEO Chris Altchek said "When you think about how many hours people spend watching video versus reading, the audience has already spoken." The move was ultimately unsuccessful, and Mic laid off the majority of its staff a year later before being sold to Bustle Media Group for a fraction of its former value. In September 2017, the for-profit wiki-hosting company Fandom began adding commercially produced videos to its otherwise user-generated wiki subdomains, explicitly citing the need to "keep up with user and advertiser expectations" by "diversifying our content," claiming without substantiation that "consumer patterns are changing," necessitating the addition of "complementary video" to accommodate that supposed need. Objection to the content in these videos and its sharp contrast against the content of the wiki sites to which they were applied led to vocal user backlash, leading Fandom CCO Dorth Raphaely to offer the following non-committal response: "I agree that with these videos in particular we did not deliver the right type of content experience." Movie Pilot CEO Tobi Bauckhage explained his company's fall 2017 layoffs as part of moving "from a text-based publishing model to video... a reaction to the fact that Facebook has changed their algorithms in favor of video instead of referral traffic over the last 12 months and we were losing money in the publishing bit of our business." As part of the company's change in direction, the majority of its staff was laid off and its parent company was sold to Webedia. In November 2017, magazine publisher Condé Nast cut jobs, reduced the frequency of several magazines, and shut down the print edition of Teen Vogue, then invested significant new resources in video production, with a senior executive saying "In the next 24 months, I hope that video is half our business... It’s critical. It’s the macro trend of content consumption." In February 2018, Vox Media cut approximately 50 employees, primarily those assigned to "social video," as Vox CEO Jim Bankoff admitted that those efforts were not "viable audience or revenue growth drivers." In August 2020, Facebook Inc. (now Meta Platforms) pivoted Instagram to video in an effort to replicate the success of TikTok and appeal to a younger audience, introducing "reels" as a form of video and promoting them aggressively. Reels accounted more than half the 20 most-viewed posts on Facebook; however, most of these reels were anonymous aggregations of content from TikTok. Elon Musk declared in early 2024 that X (formerly Twitter) was now a "video-first platform", which has been described by critics as a "pivot to video". == As euphemism == In 2017, Journalist Brian Feldman said that "'Pivoting to video' has become a business strategy for digital publishers common enough in recent months to be a kind of cliché — a slick way to describe something else: layoffs." In response, writers use the phrase as gallows humor shorthand for death or cancellation, as in "how do i tell my bf i want our relationship to pivot to video" (SkyNews' Mollie Goodfellow) or "Horse broke its leg, so we had to take it out back and help it 'pivot to video'" (blogger Anil Dash). == Facebook metrics controversy == In September 2016, Facebook admitted that it had reported artificially inflated numbers to its advertisers about how long viewers watched ads leading to an overestimation of 60-80%. Plaintiffs in a later court case allege the discrepancy was as high as 150-900%. Facebook apologized in an official statement and in multiple staff appearances at New York Advertising Week. Two months later, Facebook disclosed additional discrepancies in audience metrics. In October 2018, a California federal court unsealed the text of a class action lawsuit filed by advertisers against Facebook, alleging that Facebook had known since 2015 that its viewership numbers were highly inflated, that internal records showed it "was far from an hon
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IMazing

iMazing is mobile device management software that allows users to transfer files and data between iOS devices (iPhone, iPad and iPod Touch) and macOS or Windows computers, in addition to many other features beyond the scope of what Apple's own tools enable. == History == Developed by DigiDNA, iMazing was initially released in 2008 as DiskAid, enabling users to transfer data and files from the iPhone or iPod Touch to Mac or Windows computers. DiskAid was renamed iMazing in 2014. Version 2.0 was released on September 13, 2016. In August 2021, version 2.14 of iMazing added a spyware detection feature. The feature is based on Amnesty International’s Mobile Verification Toolkit to detect Pegasus Spyware following the publication of Pegasus Project. == Description == With iMazing, an iPhone or iPad can be used similarly to an external hard drive. It performs tasks that iTunes doesn’t offer, including incremental backups of iOS devices, browsing and exporting text and voicemail messages, managing apps, encryption, and migrating data from an old phone to a new one. The menu bar app iMazing Mini enables automatic, wireless and encrypted backups of iPhones. The iMazing HEIC Converter is a free desktop app for Mac and PC that lets users convert photos from HEIC format to JPG or PNG.
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Data stream management system

A data stream management system (DSMS) is a computer software system to manage continuous data streams. It is similar to a database management system (DBMS), which is, however, designed for static data in conventional databases. A DBMS also offers a flexible query processing so that the information needed can be expressed using queries. However, in contrast to a DBMS, a DSMS executes a continuous query that is not only performed once, but is permanently installed. Therefore, the query is continuously executed until it is explicitly uninstalled. Since most DSMS are data-driven, a continuous query produces new results as long as new data arrive at the system. This basic concept is similar to complex event processing so that both technologies are partially coalescing. == Functional principle == One important feature of a DSMS is the possibility to handle potentially infinite and rapidly changing data streams by offering flexible processing at the same time, although there are only limited resources such as main memory. The following table provides various principles of DSMS and compares them to traditional DBMS. == Processing and streaming models == One of the biggest challenges for a DSMS is to handle potentially infinite data streams using a fixed amount of memory and no random access to the data. There are different approaches to limit the amount of data in one pass, which can be divided into two classes. For the one hand, there are compression techniques that try to summarize the data and for the other hand there are window techniques that try to portion the data into (finite) parts. === Synopses === The idea behind compression techniques is to maintain only a synopsis of the data, but not all (raw) data points of the data stream. The algorithms range from selecting random data points called sampling to summarization using histograms, wavelets or sketching. One simple example of a compression is the continuous calculation of an average. Instead of memorizing each data point, the synopsis only holds the sum and the number of items. The average can be calculated by dividing the sum by the number. However, it should be mentioned that synopses cannot reflect the data accurately. Thus, a processing that is based on synopses may produce inaccurate results. === Windows === Instead of using synopses to compress the characteristics of the whole data streams, window techniques only look on a portion of the data. This approach is motivated by the idea that only the most recent data are relevant. Therefore, a window continuously cuts out a part of the data stream, e.g. the last ten data stream elements, and only considers these elements during the processing. There are different kinds of such windows like sliding windows that are similar to FIFO lists or tumbling windows that cut out disjoint parts. Furthermore, the windows can also be differentiated into element-based windows, e.g., to consider the last ten elements, or time-based windows, e.g., to consider the last ten seconds of data. There are also different approaches to implementing windows. There are, for example, approaches that use timestamps or time intervals for system-wide windows or buffer-based windows for each single processing step. Sliding-window query processing is also suitable to being implemented in parallel processors by exploiting parallelism between different windows and/or within each window extent. == Query processing == Since there are a lot of prototypes, there is no standardized architecture. However, most DSMS are based on the query processing in DBMS by using declarative languages to express queries, which are translated into a plan of operators. These plans can be optimized and executed. A query processing often consists of the following steps. === Formulation of continuous queries === The formulation of queries is mostly done using declarative languages like SQL in DBMS. Since there are no standardized query languages to express continuous queries, there are a lot of languages and variations. However, most of them are based on SQL, such as the Continuous Query Language (CQL), StreamSQL and ESP. There are also graphical approaches where each processing step is a box and the processing flow is expressed by arrows between the boxes. The language strongly depends on the processing model. For example, if windows are used for the processing, the definition of a window has to be expressed. In StreamSQL, a query with a sliding window for the last 10 elements looks like follows: This stream continuously calculates the average value of "price" of the last 10 tuples, but only considers those tuples whose prices are greater than 100.0. In the next step, the declarative query is translated into a logical query plan. A query plan is a directed graph where the nodes are operators and the edges describe the processing flow. Each operator in the query plan encapsulates the semantic of a specific operation, such as filtering or aggregation. In DSMSs that process relational data streams, the operators are equal or similar to the operators of the Relational algebra, so that there are operators for selection, projection, join, and set operations. This operator concept allows the very flexible and versatile processing of a DSMS. === Optimization of queries === The logical query plan can be optimized, which strongly depends on the streaming model. The basic concepts for optimizing continuous queries are equal to those from database systems. If there are relational data streams and the logical query plan is based on relational operators from the Relational algebra, a query optimizer can use the algebraic equivalences to optimize the plan. These may be, for example, to push selection operators down to the sources, because they are not so computationally intensive like join operators. Furthermore, there are also cost-based optimization techniques like in DBMS, where a query plan with the lowest costs is chosen from different equivalent query plans. One example is to choose the order of two successive join operators. In DBMS this decision is mostly done by certain statistics of the involved databases. But, since the data of a data streams is unknown in advance, there are no such statistics in a DSMS. However, it is possible to observe a data stream for a certain time to obtain some statistics. Using these statistics, the query can also be optimized later. So, in contrast to a DBMS, some DSMS allows to optimize the query even during runtime. Therefore, a DSMS needs some plan migration strategies to replace a running query plan with a new one. === Transformation of queries === Since a logical operator is only responsible for the semantics of an operation but does not consist of any algorithms, the logical query plan must be transformed into an executable counterpart. This is called a physical query plan. The distinction between a logical and a physical operator plan allows more than one implementation for the same logical operator. The join, for example, is logically the same, although it can be implemented by different algorithms like a Nested loop join or a Sort-merge join. Notice, these algorithms also strongly depend on the used stream and processing model. Finally, the query is available as a physical query plan. === Execution of queries === Since the physical query plan consists of executable algorithms, it can be directly executed. For this, the physical query plan is installed into the system. The bottom of the graph (of the query plan) is connected to the incoming sources, which can be everything like connectors to sensors. The top of the graph is connected to the outgoing sinks, which may be for example a visualization. Since most DSMSs are data-driven, a query is executed by pushing the incoming data elements from the source through the query plan to the sink. Each time when a data element passes an operator, the operator performs its specific operation on the data element and forwards the result to all successive operators. == Examples == AURORA, StreamBase Systems, Inc. Archived 23 March 2009 at the Wayback Machine Hortonworks DataFlow IBM Streams NIAGARA Query Engine NiagaraST: A Research Data Stream Management System at Portland State University Odysseus, an open source Java-based framework for Data Stream Management Systems Pipeline DB PIPES Archived 24 December 2016 at the Wayback Machine, webMethods Business Events QStream SAS Event Stream Processing SQLstream STREAM StreamGlobe StreamInsight TelegraphCQ WSO2 Stream Processor
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SIPRNet

The Secret Internet Protocol Router Network (SIPRNet) is "a system of interconnected computer networks used by the U.S. Department of Defense and the U.S. Department of State to transmit classified information (up to and including information classified SECRET) by packet switching over the 'completely secure' environment". It also provides services such as hypertext document access and electronic mail. SIPRNet is a component of the Defense Information Systems Network. Other components handle communications with other security needs, such as the NIPRNet, which is used for nonsecure communications, and the Joint Worldwide Intelligence Communications System (JWICS), which is used for Top Secret communications. == Access == According to the U.S. Department of State Web Development Handbook, domain structure and naming conventions are the same as for the open internet, except for the addition of a second-level domain, like, e.g., "sgov" between state and gov: openforum.state.sgov.gov. Files originating from SIPRNet are marked by a header tag "SIPDIS" (SIPrnet DIStribution). A corresponding second-level domain smil.mil exists for DoD users. Access is also available to a "...small pool of trusted allies, including Australia, Canada, the United Kingdom and New Zealand...". This group (including the US) is known as the Five Eyes. SIPRNet was one of the networks accessed by Chelsea Manning, convicted of leaking the video used in WikiLeaks' "Collateral Murder" release as well as the source of the US diplomatic cables published by WikiLeaks in November 2010. == Alternate names == SIPRNet and NIPRNet are referred to colloquially as SIPPERnet and NIPPERnet (or simply sipper and nipper), respectively.
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Dashboard (computing)

In computer information systems, a dashboard is a type of graphical user interface which often provides at-a-glance views of data relevant to a particular objective or process through a combination of visualizations and summary information. In other usage, "dashboard" is another name for "progress report" or "report" and is considered a form of data visualization. The dashboard is often accessible by a web browser and is typically linked to regularly updating data sources. Dashboards are often interactive and facilitate users to explore the data themselves, usually by clicking into elements to view more detailed information. The term dashboard originates from the automobile dashboard where drivers monitor the major functions at a glance via the instrument panel. == History == The idea of digital dashboards followed the study of decision support systems in the 1970s. Early predecessors of the modern business dashboard were first developed in the 1980s in the form of Executive Information Systems (EISs). Due to problems primarily with data refreshing and handling, it was soon realized that the approach wasn't practical as information was often incomplete, unreliable, and spread across too many disparate sources. Thus, EISs hibernated until the 1990s when the information age quickened pace and data warehousing, and online analytical processing (OLAP) allowed dashboards to function adequately. Despite the availability of enabling technologies, the dashboard use didn't become popular until later in that decade, with the rise of key performance indicators (KPIs), and the introduction of Robert S. Kaplan and David P. Norton's balanced scorecard. In the late 1990s, Microsoft promoted a concept known as the Digital Nervous System and "digital dashboards" were described as being one leg of that concept. Today, the use of dashboards forms an important part of Business Performance Management (BPM). Initially dashboards were used for monitoring purposes, now with the advancement of technology, dashboards are being used for more analytical purposes. The use of dashboards has now been incorporating; scenario analysis, drill down capabilities, and presentation format flexibility. == Benefits == Digital dashboards allow managers to monitor the contribution of the various departments in their organization. In addition, they enable “rolling up” of information to present a consolidated view across an organization. To gauge exactly how well an organization is performing overall, digital dashboards allow you to capture and report specific data points from each department within the organization, thus providing a "snapshot" of performance. Benefits of using digital dashboards include: Visual presentation of performance measures Ability to identify and correct negative trends Measure efficiencies/inefficiencies Ability to generate detailed reports showing new trends Ability to make more informed decisions based on collected business intelligence Dashboards offers a holistic view of the entire business as it gives the manager a bird's eye view into the performance of sales, data inventory, web traffic, social media analytics and other associated data that is visually presented on a single dashboard. Dashboards lead to better management of marketing/financial strategies as a dashboard for the display of marketing data makes the process of marketing easier and more reliable as compared to doing it manually. Web analytics play a crucial role in shaping the marketing strategy of many businesses. Dashboards also facilitate for better tracking of sales and financial reporting as the data is more precise and in one area. Lastly, dashboards offer for better customer service through monitoring because they keep both the managers and the clients updated on the project progress through automated emails and notifications. == Align strategies and organizational goals == Gain total visibility of all systems instantly Quick identification of data outliers and correlations Consolidated reporting into one location Available on mobile devices to quickly access metrics == Classification == Dashboards can be broken down according to role and are either strategic, analytical, operational, or informational. Dashboards are the 3rd step on the information ladder, demonstrating the conversion of data to increasingly valuable insights. Strategic dashboards support managers at any level in an organization and provide the quick overview that decision-makers need to monitor the health and opportunities of the business. Dashboards of this type focus on high-level measures of performance and forecasts. Strategic dashboards benefit from static snapshots of data (daily, weekly, monthly, and quarterly) that are not constantly changing from one moment to the next. Dashboards for analytical purposes often include more context, comparisons, and history, along with subtler performance evaluators. In addition, analytical dashboards typically support interactions with the data, such as drilling down into the underlying details. Dashboards for monitoring operations are often designed differently from those that support strategic decision making or data analysis and often require monitoring of activities and events that are constantly changing and might require attention and response at a moment's notice. == Types of dashboards == Digital dashboards may be laid out to track the flows inherent in the business processes that they monitor. Graphically, users may see the high-level processes and then drill down into low-level data. This level of detail is often buried deep within the corporate enterprise and otherwise unavailable to the senior executives. Three main types of digital dashboards dominate the market today: desktop software applications, web-browser-based applications, and desktop applications are also known as desktop widgets. The last are driven by a widget engine. Both Desktop and Browser-based providers enable the distribution of dashboards via a web browser. An example of the latter is web-based-browser Asana, which helps teams orchestrate their work, from daily tasks to strategic cross-functional initiatives. With it, teams can manage everything from company objectives to digital transformation to product launches and marketing campaigns. Specialized dashboards may track all corporate functions. Examples include human resources, recruiting, sales, operations, security, information technology, project management, customer relationship management, digital marketing and many more departmental dashboards. For a smaller organization like a startup a compact startup scorecard dashboard tracks important activities across lot of domains ranging from social media to sales. Digital dashboard projects involve business units as the driver and the information technology department as the enabler. Therefore, the success of dashboard projects depends on the relevancy/importance of information provided within the dashboard. This includes the metrics chosen to monitor and the timeliness of the data forming those metrics; data must be up to date and accurate. Key performance indicators, balanced scorecards, and sales performance figures are some of the content appropriate on business dashboards. === Performance Dashboards === Dashboards involve the combination of visual and functional features. This combination of features helps improve cognition and interpretation. A performance dashboard sits at the intersection of two powerful disciplines: business intelligence and performance management. Therefore, there are different users who could use these dashboards for different reasons. For example, a level of workers could look at monitoring inventory while those in more managerial roles can look at lagging measure. Then executives could utilize the dashboard to evaluate strategic performance against objectives. == Dashboards and scorecards == Balanced scorecards and dashboards have been linked together as if they were interchangeable. However, although both visually display critical information, the difference is in the format: Scorecards can open the quality of an operation while dashboards provide calculated direction. A balanced scorecard has what they called a "prescriptive" format. It should always contain these components: Perspectives – group Objectives – verb-noun phrases pulled from a strategy plan Measures – also called metric or key performance indicators (KPIs) Spotlight indicators – red, yellow, or green symbols that provide an at-a-glance view of a measure's performance. Each of these sections ensures that a Balanced Scorecard is essentially connected to the businesses critical strategic needs. The design of a dashboard is more loosely defined. Dashboards are usually a series of graphics, charts, gauges and other visual indicators that can be monitored and interpreted. Even when there is a strategic link, on a dashboard, it may not be noticed as such since objectives are not normally pre
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ImHex

ImHex is a free cross-platform hex editor available on Windows, macOS, and Linux. ImHex is used by programmers and reverse engineers to view and analyze binary data. == History == The initial release of the project in November 2020, saw significant interest on GitHub. == Features == Features include: Hex editor Custom pattern matching and analysis scripting language Visual, node based data pre-processor Disassembler Running and visualizing of YARA rules Bookmarks Binary data diffing Additional Tools MSVC, Itanium, D and Rust name demangler ASCII table Calculator Base converter File utilities IEEE 754 floating point decoder Division by invariant multiplication calculator TCP/IP client and server Support for: Data importing and exporting ASCII string, Unicode string, numeric, hexadecimal and regular expressions search Byte manipulation File hashing Plug-ins
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Key Transparency

Key Transparency allows communicating parties to verify public keys used in end-to-end encryption. In many end-to-end encryption services, to initiate communication a user will reach out to a central server and request the public keys of the user with which they wish to communicate. If the central server is malicious or becomes compromised, a man-in-the-middle attack can be launched through the issuance of incorrect public keys. The communications can then be intercepted and manipulated. Additionally, legal pressure could be applied by surveillance agencies to manipulate public keys and read messages. With Key Transparency, public keys are posted to a public log that can be universally audited. Communicating parties can verify public keys used are accurate.
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HKDF

HKDF is a multi-purpose key derivation function (KDF) based on the HMAC message authentication code. HKDF follows "extract-then-expand" paradigm, where the KDF logically consists of two modules: the first stage takes the input keying material and "extracts" from it a fixed-length pseudorandom key, and then the second stage "expands" this key into several additional, independent pseudorandom keys as the output of the KDF. == Mechanism == HKDF is the composition of two functions, HKDF-Extract and HKDF-Expand: HKDF(salt, IKM, info, length) = HKDF-Expand(HKDF-Extract(salt, IKM), info, length) === HKDF-Extract === HKDF-Extract (XTR) takes "input key material" or "source key material" (IKM or SKM) such as a shared secret generated using Diffie-Hellman; an optional, non-secret, random or pseudorandom salt (r); and generates a cryptographic key called the PRK ("pseudorandom key"). HKDF-Extract acts as a "randomness extractor", specifically a "computational extractor", taking a potentially non-uniform value of sufficient min-entropy and generating a value indistinguishable from a uniform random value (pseudorandom). Computational extractors assume attackers are computationally bounded and source entropy may only exist in a computational sense. Such extractors can be built using cryptographic functions under suitable assumptions, modeled as universal hash function (in the generic case) or a random oracle (in constrained scenarios like sources with weak entropy). Salt (r) acts as a "source-independent extractor", strengthening HKDF's security guarantees. Using a fixed public r is safe for multiple invocations of HKDF (on "independent" but secret IKMs which may or may not be derived from the same source), provided r isn't chosen or manipulated by an attacker. Ideally, r is a random string of hash function's output length. Even low quality r (weak entropy or shorter length) is recommended as they contribute "significantly" to the security of the OKM. Without or with a low-entropy, non-secret r, if an attacker can influence the IKMs source in a way that specifically exploits HKDF-Extract's underlying hash function (finding a collision or a specific bias), XTR provides no protection. A random r, even if fixed by the application (for example, random number generators using r as seed), would strengthen protections for that specific extractor session. In such a setting, sufficiently long IKMs also provide better entropy extraction. However, allowing the attacker to influence enough of the IKM after seeing r may result in a completely insecure KDF. HKDF-Extract is the result of HMAC with r as the key (all zeros up to length of the underlying extractor hash function, if not provided) and the IKM as the message. The underlying hash function used for HKDF-Extract step may be different to the one used by HKDF-Expand. It is recommended that HKDF-Extract uses strongest hash function available to the application, as it "concentrates" the entropy already present in IKM but may not necessarily "add" to it. Truncated output from a stronger underlying hash function for XTR (for example, SHA512/256) offers stronger extraction properties. The attacker is assumed to have partial knowledge about IKM (publicly known values in the case of Diffie-Hellman) or partial control over it (entropy pools). HKDF-Extract may be skipped if the IKM is itself a cryptographically strong key (and hence can assume the role of PRK), though it is recommended that HKDF-Extract be applied for the sake of compatibility with the general case, especially if r is available to the application. === HKDF-Expand === HKDF-Expand (PRF) takes the PRK (or any random key-derivation key if HKDF-Extract step is skipped), optional info (CTXinfo), and a length (L), to generate output key material (OKM) of length L. Multiple OKMs can be generated from a single PRK by using different values for CTXinfo, which must be "independent" of the IKM passed in HKDF-Extract. Even if an attacker, who knows r and some auxillary information about the secret IKM, can force the use of the same IKM (and PRK, by extension), in two or more HKDF-Expand contexts (represented by CTXinfo), the OKMs output are computationally independent (leak no useful information on each other). HKDF-Expand, acting as a variable-output-length pseudorandom function (PRF) keyed on PRK, calls HMAC on CTXinfo as the message (empty string, if unspecified) appended to a 8-bit counter i initialized to 1. Subsequent calls to HMAC are chained in "feedback mode" by prepending the previous HMAC output to CTXinfo and incrementing i. OKM is a function of the output size (k bits) of HMAC's underlying hash function; i.e., SHA-256 outputs OKM in segments of k=256 bits for up to a maximum of length i × k bits (255 × 256 bits = 8160 bytes) truncated to desired length L. HKDF-Expand may be skipped if PRK is at least desired length L, though it is recommended that HKDF-Expand be applied for additional "smoothing" of the OKM. == Standardization == HKDF was proposed as a building block in various protocols and applications, as well as to discourage the proliferation of multiple KDF mechanisms by its authors. It is formally described in RFC 5869 with detailed analysis in a paper published in 2010. NIST SP800-56Cr2 specifies a parameterizable extract-then-expand scheme, noting that RFC 5869 HKDF is a version of it and citing its paper for the rationale for the recommendations' extract-and-expand mechanisms. == Applications == HKDF is used in the Signal Protocol for end-to-end encrypted messaging where it generates the message keys, in conjunction with the triple Elliptic-curve Diffie-Hellman handshake (X3DH) key agreement protocol. Signal's "Secure Value Recovery" and "Sealed Sender" are based on HKDF. HKDF is a main component in the Noise Protocol Framework, Message Layer Security, and is used in widely deployed protocols like IPsec Internet Key Exchange and TLS 1.3. The "multi-purpose" nature of HKDF is meant to serve applications that require key extraction, key expansion, and key hierarchies in key wrapping, key exchange, PRNG, and password-based key derivation schemes. == Implementations == There are implementations of HKDF for C#, Go, Java, JavaScript, Perl, PHP, Python, Ruby, Rust, and other programming languages. RFC6234 lays out a reference C implementation of HKDF based on the Secure Hash Standard. === Example in Python ===
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Data verification

Data verification is a process in which different types of data are checked for accuracy and inconsistencies after data migration is done. In some domains it is referred to Source Data Verification (SDV), such as in clinical trials. Data verification helps to determine whether data was accurately translated when data is transferred from one source to another, is complete, and supports processes in the new system. During verification, there may be a need for a parallel run of both systems to identify areas of disparity and forestall erroneous data loss. Methods for data verification include double data entry, proofreading and automated verification of data. Proofreading data involves someone checking the data entered against the original document. This is also time-consuming and costly. Automated verification of data can be achieved using one way hashes locally or through use of a SaaS based service such as Q by SoLVBL to provide immutable seals to allow verification of the original data.
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Insider threat

An insider threat is a perceived threat to an organization that comes from people within the organization, such as employees, former employees, contractors or business associates, who have inside information concerning the organization's security practices, data and computer systems. The threat may involve fraud, the theft of confidential or commercially valuable information, the theft of intellectual property, or the sabotage of computer systems. == Overview == Insiders may have accounts giving them legitimate access to computer systems, with this access originally having been given to them to serve in the performance of their duties; these permissions could be abused to harm the organization. Insiders are often familiar with the organization's data and intellectual property as well as the methods that are in place to protect them. This makes it easier for the insider to circumvent any security controls of which they are aware. Physical proximity to data means that the insider does not need to hack into the organizational network through the outer perimeter by traversing firewalls; rather they are in the building already, often with direct access to the organization's internal network. Insider threats are harder to defend against than attacks from outsiders, since the insider already has legitimate access to the organization's information and assets. An insider may attempt to steal property or information for personal gain or to benefit another organization or country. The threat to the organization could also be through malicious software left running on its computer systems by former employees, a so-called logic bomb. == Research == Insider threat is an active area of research in academia and government. The CERT Coordination Center at Carnegie-Mellon University maintains the CERT Insider Threat Center, which includes a database of more than 850 cases of insider threats, including instances of fraud, theft and sabotage; the database is used for research and analysis. CERT's Insider Threat Team also maintains an informational blog to help organizations and businesses defend themselves against insider crime. The Threat Lab and Defense Personnel and Security Research Center (DOD PERSEREC) has also recently emerged as a national resource within the United States of America. The Threat Lab hosts an annual conference, the SBS Summit. They also maintain a website that contains resources from this conference. Complimenting these efforts, a companion podcast was created, Voices from the SBS Summit. In 2022, the Threat Lab created an interdisciplinary journal, Counter Insider Threat Research and Practice (CITRAP) which publishes research on insider threat detection. === Findings === In the 2022 Data Breach Investigations Report (DBIR), Verizon found that 82% of breaches involved the human element, noting that employees continue to play a leading role in cybersecurity incidents and breaches. According to the UK Information Commissioners Office, 90% of all breaches reported to them in 2019 were the result of mistakes made by end users. This was up from 61% and 87% over the previous two years. A 2018 whitepaper reported that 53% of companies surveyed had confirmed insider attacks against their organization in the previous 12 months, with 27% saying insider attacks have become more frequent. A report published in July 2012 on the insider threat in the U.S. financial sector gives some statistics on insider threat incidents: 80% of the malicious acts were committed at work during working hours; 81% of the perpetrators planned their actions beforehand; 33% of the perpetrators were described as "difficult" and 17% as being "disgruntled". The insider was identified in 74% of cases. Financial gain was a motive in 81% of cases, revenge in 23% of cases, and 27% of the people carrying out malicious acts were in financial difficulties at the time. The US Department of Defense Personnel Security Research Center published a report that describes approaches for detecting insider threats. Earlier it published ten case studies of insider attacks by information technology professionals. Cybersecurity experts believe that 38% of negligent insiders are victims of a phishing attack, whereby they receive an email that appears to come from a legitimate source such as a company. These emails normally contain malware in the form of hyperlinks. == Typologies and ontologies == Multiple classification systems and ontologies have been proposed to classify insider threats. Traditional models of insider threat identify three broad categories: Malicious insiders, which are people who take advantage of their access to inflict harm on an organization; Negligent insiders, which are people who make errors and disregard policies, which place their organizations at risk; and Infiltrators, who are external actors that obtain legitimate access credentials without authorization. == Criticisms == Insider threat research has been criticized. Critics have argued that insider threat is a poorly defined concept. Forensically investigating insider data theft is notoriously difficult, and requires novel techniques such as stochastic forensics. Data supporting insider threat is generally proprietary (i.e., encrypted data). Theoretical/conceptual models of insider threat are often based on loose interpretations of research in the behavioral and social sciences, using "deductive principles and intuitions of subject matter expert." Adopting sociotechnical approaches, researchers have also argued for the need to consider insider threat from the perspective of social systems. Jordan Schoenherr said that "surveillance requires an understanding of how sanctioning systems are framed, how employees will respond to surveillance, what workplace norms are deemed relevant, and what ‘deviance’ means, e.g., deviation for a justified organization norm or failure to conform to an organizational norm that conflicts with general social values." By treating all employees as potential insider threats, organizations might create conditions that lead to insider threats. == Sector-specific concerns == === Healthcare === The healthcare industry faces particularly acute insider threat risks due to the large number of workforce members who require access to sensitive patient records for legitimate clinical purposes. The U.S. Department of Health and Human Services has identified unauthorized access by insiders, including workforce snooping on patient records and theft of protected health information for identity fraud, as a persistent enforcement concern. The Health Insurance Portability and Accountability Act (HIPAA) Security Rule addresses insider threats through several administrative safeguards, including workforce security procedures requiring covered entities to implement policies for authorizing and supervising workforce members who work with electronic protected health information, as well as termination procedures to revoke access when employment ends (45 CFR 164.308(a)(3)). The rule also requires audit controls to record and examine information system activity (45 CFR 164.312(b)), enabling detection of unauthorized access by insiders. The December 2024 Notice of proposed rulemaking (NPRM) to overhaul the HIPAA Security Rule would strengthen insider threat defenses by mandating role-based access controls, requiring notification of relevant workforce members within 24 hours of any changes to access privileges, and requiring regular review of audit logs to detect anomalous access patterns.
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Factorization of polynomials over finite fields

In mathematics and computer algebra the factorization of a polynomial consists of decomposing it into a product of irreducible factors. This decomposition is theoretically possible and is unique for polynomials with coefficients in any field, but rather strong restrictions on the field of the coefficients are needed to allow the computation of the factorization by means of an algorithm. In practice, algorithms have been designed only for polynomials with coefficients in a finite field, in the field of rationals or in a finitely generated field extension of one of them. All factorization algorithms, including the case of multivariate polynomials over the rational numbers, reduce the problem to this case; see polynomial factorization. It is also used for various applications of finite fields, such as coding theory (cyclic redundancy codes and BCH codes), cryptography (public key cryptography by the means of elliptic curves), and computational number theory. As the reduction of the factorization of multivariate polynomials to that of univariate polynomials does not have any specificity in the case of coefficients in a finite field, only polynomials with one variable are considered in this article. == Background == === Finite field === The theory of finite fields, whose origins can be traced back to the works of Gauss and Galois, has played a part in various branches of mathematics. Due to the applicability of the concept in other topics of mathematics and sciences like computer science there has been a resurgence of interest in finite fields and this is partly due to important applications in coding theory and cryptography. Applications of finite fields introduce some of these developments in cryptography, computer algebra and coding theory. A finite field or Galois field is a field with a finite order (number of elements). The order of a finite field is always a prime or a power of prime. For each prime power q = pr, there exists exactly one finite field with q elements, up to isomorphism. This field is denoted GF(q) or Fq. If p is prime, GF(p) is the prime field of order p; it is the field of residue classes modulo p, and its p elements are denoted 0, 1, ..., p−1. Thus a = b in GF(p) means the same as a ≡ b (mod p). === Irreducible polynomials === Let F be a finite field. As for general fields, a non-constant polynomial f in F[x] is said to be irreducible over F if it is not the product of two polynomials of positive degree. A polynomial of positive degree that is not irreducible over F is called reducible over F. Irreducible polynomials allow us to construct the finite fields of non-prime order. In fact, for a prime power q, let Fq be the finite field with q elements, unique up to isomorphism. A polynomial f of degree n greater than one, which is irreducible over Fq, defines a field extension of degree n which is isomorphic to the field with qn elements: the elements of this extension are the polynomials of degree lower than n; addition, subtraction and multiplication by an element of Fq are those of the polynomials; the product of two elements is the remainder of the division by f of their product as polynomials; the inverse of an element may be computed by the extended GCD algorithm (see Arithmetic of algebraic extensions). It follows that, to compute in a finite field of non prime order, one needs to generate an irreducible polynomial. For this, the common method is to take a polynomial at random and test it for irreducibility. For sake of efficiency of the multiplication in the field, it is usual to search for polynomials of the shape xn + ax + b. Irreducible polynomials over finite fields are also useful for pseudorandom number generators using feedback shift registers and discrete logarithm over F2n. The number of irreducible monic polynomials of degree n over Fq is the number of aperiodic necklaces, given by Moreau's necklace-counting function Mq(n). The closely related necklace function Nq(n) counts monic polynomials of degree n which are primary (a power of an irreducible); or alternatively irreducible polynomials of all degrees d which divide n. === Example === The polynomial P = x4 + 1 is irreducible over Q but not over any finite field. On any field extension of F2, P = (x + 1)4. On every other finite field, at least one of −1, 2 and −2 is a square, because the product of two non-squares is a square and so we have If − 1 = a 2 , {\displaystyle -1=a^{2},} then P = ( x 2 + a ) ( x 2 − a ) . {\displaystyle P=(x^{2}+a)(x^{2}-a).} If 2 = b 2 , {\displaystyle 2=b^{2},} then P = ( x 2 + b x + 1 ) ( x 2 − b x + 1 ) . {\displaystyle P=(x^{2}+bx+1)(x^{2}-bx+1).} If − 2 = c 2 , {\displaystyle -2=c^{2},} then P = ( x 2 + c x − 1 ) ( x 2 − c x − 1 ) . {\displaystyle P=(x^{2}+cx-1)(x^{2}-cx-1).} === Complexity === Polynomial factoring algorithms use basic polynomial operations such as products, divisions, gcd, powers of one polynomial modulo another, etc. A multiplication of two polynomials of degree at most n can be done in O(n2) operations in Fq using "classical" arithmetic, or in O(nlog(n) log(log(n)) ) operations in Fq using "fast" arithmetic. A Euclidean division (division with remainder) can be performed within the same time bounds. The cost of a polynomial greatest common divisor between two polynomials of degree at most n can be taken as O(n2) operations in Fq using classical methods, or as O(nlog2(n) log(log(n)) ) operations in Fq using fast methods. For polynomials h, g of degree at most n, the exponentiation hq mod g can be done with O(log(q)) polynomial products, using exponentiation by squaring method, that is O(n2log(q)) operations in Fq using classical methods, or O(nlog(q)log(n) log(log(n))) operations in Fq using fast methods. In the algorithms that follow, the complexities are expressed in terms of number of arithmetic operations in Fq, using classical algorithms for the arithmetic of polynomials. == Factoring algorithms == Many algorithms for factoring polynomials over finite fields include the following three stages: Square-free factorization Distinct-degree factorization Equal-degree factorization An important exception is Berlekamp's algorithm, which combines stages 2 and 3. === Berlekamp's algorithm === Berlekamp's algorithm is historically important as being the first factorization algorithm which works well in practice. However, it contains a loop on the elements of the ground field, which implies that it is practicable only over small finite fields. For a fixed ground field, its time complexity is polynomial, but, for general ground fields, the complexity is exponential in the size of the ground field. === Square-free factorization === The algorithm determines a square-free factorization for polynomials whose coefficients come from the finite field Fq of order q = pm with p a prime. This algorithm firstly determines the derivative and then computes the gcd of the polynomial and its derivative. If it is not one then the gcd is again divided into the original polynomial, provided that the derivative is not zero (a case that exists for non-constant polynomials defined over finite fields). This algorithm uses the fact that, if the derivative of a polynomial is zero, then it is a polynomial in xp, which is, if the coefficients belong to Fp, the pth power of the polynomial obtained by substituting x by x1/p. If the coefficients do not belong to Fp, the pth root of a polynomial with zero derivative is obtained by the same substitution on x, completed by applying the inverse of the Frobenius automorphism to the coefficients. This algorithm works also over a field of characteristic zero, with the only difference that it never enters in the blocks of instructions where pth roots are computed. However, in this case, Yun's algorithm is much more efficient because it computes the greatest common divisors of polynomials of lower degrees. A consequence is that, when factoring a polynomial over the integers, the algorithm which follows is not used: one first computes the square-free factorization over the integers, and to factor the resulting polynomials, one chooses a p such that they remain square-free modulo p. Algorithm: SFF (Square-Free Factorization) Input: A monic polynomial f in Fq[x] where q = pm Output: Square-free factorization of f R ← 1 # Make w be the product (without multiplicity) of all factors of f that have # multiplicity not divisible by p c ← gcd(f, f′) w ← f/c # Step 1: Identify all factors in w i ← 1 while w ≠ 1 do y ← gcd(w, c) fac ← w / y R ← R · faci w ← y; c ← c / y; i ← i + 1 end while # c is now the product (with multiplicity) of the remaining factors of f # Step 2: Identify all remaining factors using recursion # Note that these are the factors of f that have multiplicity divisible by p if c ≠ 1 then c ← c1/p R ← R·SFF(c)p end if Output(R) The idea is to identify the product of all irreducible factors of f with the same multiplicity. This is done in two steps. The first step uses the formal d
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Brooklyn Bridge (software)

The Brooklyn Bridge from White Crane Systems was a data transfer enabler. Although it came with some hardware, it was the software which was the basis of the product. It also could transform the data's format. == Overview == The New York Times described its category as being among "communications packages used to transfer files." In an era of 300 baud, Brooklyn Bridge operated at "115,200 baud" so that a transfer which "at 300 baud took 4 minutes and 36 seconds" only needed 5 seconds. Unlike some communications packages, this one retains the original version-date, so as not to alarm people when they seem to have what looks like an update, when it's not. == Description == Once the software is installed, users comfortable with typing the word "COPY" can do so as readily as they sneakernet. An earlier review described it as "less cumbersome than conventional communications software" The use of neither specialized hardware nor specialized software is ideal in an era when this can be done using online or other "outside" services.
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