Jean Véronis (3 June 1955 – 8 September 2013) was a French linguist, computer scientist and blogger, and a research professor at Aix-Marseille University. His research interests included natural language processing, text mining and standardisation. He was a founder of the field that is now called digital humanities. In 2006, his blog was listed among the 15 most influential by Le Monde.
Circular convolution
Circular convolution, also known as cyclic convolution, is a special case of periodic convolution, which is the convolution of two periodic functions that have the same period. Periodic convolution arises, for example, in the context of the discrete-time Fourier transform (DTFT). In particular, the DTFT of the product of two discrete sequences is the periodic convolution of the DTFTs of the individual sequences. And each DTFT is a periodic summation of a continuous Fourier transform function (see Discrete-time Fourier transform § Relation to Fourier Transform). Although DTFTs are usually continuous functions of frequency, the concepts of periodic and circular convolution are also directly applicable to discrete sequences of data. In that context, circular convolution plays an important role in maximizing the efficiency of a certain kind of common filtering operation. == Definitions == The periodic convolution of two T-periodic functions, h T ( t ) {\displaystyle h_{_{T}}(t)} and x T ( t ) {\displaystyle x_{_{T}}(t)} can be defined as: ∫ t o t o + T h T ( τ ) ⋅ x T ( t − τ ) d τ , {\displaystyle \int _{t_{o}}^{t_{o}+T}h_{_{T}}(\tau )\cdot x_{_{T}}(t-\tau )\,d\tau ,} where t o {\displaystyle t_{o}} is an arbitrary parameter. An alternative definition, in terms of the notation of normal linear or aperiodic convolution, follows from expressing h T ( t ) {\displaystyle h_{_{T}}(t)} and x T ( t ) {\displaystyle x_{_{T}}(t)} as periodic summations of aperiodic components h {\displaystyle h} and x {\displaystyle x} , i.e.: h T ( t ) ≜ ∑ k = − ∞ ∞ h ( t − k T ) = ∑ k = − ∞ ∞ h ( t + k T ) . {\displaystyle h_{_{T}}(t)\ \triangleq \ \sum _{k=-\infty }^{\infty }h(t-kT)=\sum _{k=-\infty }^{\infty }h(t+kT).} Then: Both forms can be called periodic convolution. The term circular convolution arises from the important special case of constraining the non-zero portions of both h {\displaystyle h} and x {\displaystyle x} to the interval [ 0 , T ] . {\displaystyle [0,T].} Then the periodic summation becomes a periodic extension, which can also be expressed as a circular function: x T ( t ) = x ( t m o d T ) , t ∈ R {\displaystyle x_{_{T}}(t)=x(t_{\mathrm {mod} \ T}),\quad t\in \mathbb {R} \,} (any real number) And the limits of integration reduce to the length of function h {\displaystyle h} : ( h ∗ x T ) ( t ) = ∫ 0 T h ( τ ) ⋅ x ( ( t − τ ) m o d T ) d τ . {\displaystyle (hx_{_{T}})(t)=\int _{0}^{T}h(\tau )\cdot x((t-\tau )_{\mathrm {mod} \ T})\ d\tau .} == Discrete sequences == Similarly, for discrete sequences, and a parameter N, we can write a circular convolution of aperiodic functions h {\displaystyle h} and x {\displaystyle x} as: ( h ∗ x N ) [ n ] ≜ ∑ m = − ∞ ∞ h [ m ] ⋅ x N [ n − m ] ⏟ ∑ k = − ∞ ∞ x [ n − m − k N ] {\displaystyle (hx_{_{N}})[n]\ \triangleq \ \sum _{m=-\infty }^{\infty }h[m]\cdot \underbrace {x_{_{N}}[n-m]} _{\sum _{k=-\infty }^{\infty }x[n-m-kN]}} This function is N-periodic. It has at most N unique values. For the special case that the non-zero extent of both x and h are ≤ N, it is reducible to matrix multiplication where the kernel of the integral transform is a circulant matrix. == Example == A case of great practical interest is illustrated in the figure. The duration of the x sequence is N (or less), and the duration of the h sequence is significantly less. Then many of the values of the circular convolution are identical to values of x∗h, which is actually the desired result when the h sequence is a finite impulse response (FIR) filter. Furthermore, the circular convolution is very efficient to compute, using a fast Fourier transform (FFT) algorithm and the circular convolution theorem. There are also methods for dealing with an x sequence that is longer than a practical value for N. The sequence is divided into segments (blocks) and processed piecewise. Then the filtered segments are carefully pieced back together. Edge effects are eliminated by overlapping either the input blocks or the output blocks. To help explain and compare the methods, we discuss them both in the context of an h sequence of length 201 and an FFT size of N = 1024. === Overlapping input blocks === This method uses a block size equal to the FFT size (1024). We describe it first in terms of normal or linear convolution. When a normal convolution is performed on each block, there are start-up and decay transients at the block edges, due to the filter latency (200-samples). Only 824 of the convolution outputs are unaffected by edge effects. The others are discarded, or simply not computed. That would cause gaps in the output if the input blocks are contiguous. The gaps are avoided by overlapping the input blocks by 200 samples. In a sense, 200 elements from each input block are "saved" and carried over to the next block. This method is referred to as overlap-save, although the method we describe next requires a similar "save" with the output samples. When an FFT is used to compute the 824 unaffected DFT samples, we don't have the option of not computing the affected samples, but the leading and trailing edge-effects are overlapped and added because of circular convolution. Consequently, the 1024-point inverse FFT (IFFT) output contains only 200 samples of edge effects (which are discarded) and the 824 unaffected samples (which are kept). To illustrate this, the fourth frame of the figure at right depicts a block that has been periodically (or "circularly") extended, and the fifth frame depicts the individual components of a linear convolution performed on the entire sequence. The edge effects are where the contributions from the extended blocks overlap the contributions from the original block. The last frame is the composite output, and the section colored green represents the unaffected portion. === Overlapping output blocks === This method is known as overlap-add. In our example, it uses contiguous input blocks of size 824 and pads each one with 200 zero-valued samples. Then it overlaps and adds the 1024-element output blocks. Nothing is discarded, but 200 values of each output block must be "saved" for the addition with the next block. Both methods advance only 824 samples per 1024-point IFFT, but overlap-save avoids the initial zero-padding and final addition.
Technical data management system
A technical data management system (TDMS) is a document management system (DMS) pertaining to the management of technical and engineering drawings and documents. Often the data are contained in 'records' of various forms, such as on paper, microfilms or digital media. Hence technical data management is also concerned with record management involving technical data. Technical document management systems are used within large organisations with large scale projects involving engineering. For example, a TDMS can be used for integrated steel plants (ISP), automobile factories, aero-space facilities, infrastructure companies, city corporations, research organisations, etc. In such organisations, technical archives or technical documentation centres are created as central facilities for effective management of technical data and records. TDMS functions are similar to that of conventional archive functions in concepts, except that the archived materials in this case are essentially engineering drawings, survey maps, technical specifications, plant and equipment data sheets, feasibility reports, project reports, operation and maintenance manuals, standards, etc. Document registration, indexing, repository management, reprography, etc. are parts of TDMS. Various kinds of sophisticated technologies such as document scanners, microfilming and digitization camera units, wide format printers, digital plotters, software, etc. are available, making TDMS functions an easier process than previous times. == Constituents of a technical data management system == Technical data refers to both scientific and technical information recorded and presented in any form or manner (excluding financial and management information). A Technical Data Management System is created within an organisation for archiving and sharing information such as technical specifications, datasheets and drawings. Similar to other types of data management system, a Technical Data Management System consists of the 4 crucial constituents mentioned below. === Data planning === Data plans (long-term or short-term) are constructed as the first essential step of a proper and complete TDMS. It is created to ultimately help with the 3 other constituents, data acquisition, data management and data sharing. A proper data plan should not exceed 2 pages and should address the following basics: Types of data (samples, experiment results, reports, drawings, etc.) and metadata (data that summarizes and describes other data. In this case, it refers to details such as sample sizes, experiment conditions and procedures, dates of reports, explanations of drawings, etc.) Means of researches and collections of data (field works, experiments in production lines, etc.) Costs of researches Policies for access, sharing (re-use within the organisation and re-distribution to the public) Proposals for archiving data and maintaining access to it === Data acquisition === Raw data is collected from primary sites of the organisations through the use of modern technologies. Please reference the table below for examples. The data collected is then transferred to technical data centres for data management. === Data management === After data acquisition, data is sorted out, whilst useful data is archived, unwanted data is disposed. When managing and archiving data, the features below of the data are considered. Names, labels, values and descriptions for variables and records. (In the case of TDMS, one example is names of equipments on an equipment datasheet) Derived data from the original data, with code, algorithm or command file used to create them. (In the case of TDMS, one example is an expectation report derived from the analysis of an equipment datasheet) Metadata associates with the data being archived === Data sharing === Archived and managed data are accessible to rightful entities. A proper and complete TDMS should share data to a suitable extent, under suitable security, in order to achieve optimal usage of data within the organisation. It aims for easy access when reused by other researchers and hence it enhances other research processes. Data is often referred in other tests and technical specifications, where new analysis is generated, managed and archived again. As a result, data is flowing within the organisation under effective management through the use of TDMS. == Advantages and disadvantages of usage of technical data management systems == There are strengths and weakness when using technical data management systems (TDMS) to archive data. Some of the advantages and disadvantages are listed below. === Advantages === ==== 1. Faster and easier data management ==== Since TDMS is integrated into the organisation's systems, whenever workers develop data files (SolidWorks, AutoCAD, Microsoft Word, etc.), they can also archive and manage data, linking what they need to their current work, at the same time they can also update the archives with useful data. This speeds up working processes and makes them more efficient. ==== 2. Increased security ==== All data files are centralized, hence internal and external data leakages are less likely to happen, and the data flow is more closely monitored. As a result, data in the organisation is more secured. ==== 3. Increased collaboration within the organisation ==== Since the data files are centralized and the data flow within the organisation increases, researchers and workers within the organisation are able to work on joint projects. More complex tasks can be performed for higher yields. ==== 4. Compatible to various formats of data ==== TDMS is compatible to many formats of data, from basic data like Microsoft Words to complex data like voice data. This enhances the quality of the management of data archived. === Disadvantages === ==== 1. Higher financial costs ==== Implementing TDMS into the organisation's systems involves monetary costs. Maintenance costs certain amount of human resources and money as well. These resources involve opportunity costs as they can be utilized in other aspects. ==== 2. Lower stability ==== Since TDMS manages and centralizes all the data the organisation processes, it links the working processes within the whole organisation together. It also increases the vulnerability of the organisation data network. If TDMS is not stable enough or when it is exposed to hacker and virus attacks, the organisation's data flow might shut down completely, affecting the work in an organisation-wide scale and leading to a lower stability as results. == Comparison between traditional data management approaches and technical data management systems == Test engineers and researchers are facing great challenges in turning complex test results and simulation data into usable information for higher yields of firms. These challenges are listed below. Increase in complication of designs Reduced in time and budgets available Higher quality is demanded === Traditional data management approaches === Many organisations are still applying the conventional file management systems, due to the difficulty in building a proper and complete archives for data management. The first approach is the simple file-folder system. This costs the problem of ineffectiveness as workers and researchers have to manually go through numerous layers of systems and files for the target data. Moreover, the target data may contain files with different formats and these files may not be stored in the same machine. These files are also easily lost if renamed or moved to another location. The second approach is conventional databases such as Oracle. These databases are capable of enabling easy search and access of data. However, a great drawback is that huge effort for preparing and modeling the data is required. For large-scale projects, huge monetary costs are induced, and extra IT human resources must be employed for constant handling, expanding and maintaining the inflexible system, which is custom for specific tasks, instead of all tasks. In the long-term, it is not cost-effective. === Technical data management systems (TDMS) === TDMS is developed based on 3 principles, flexible and organized file storage, self-scaling hybrid data index, and an interactive post-processing environment. The system in practical, mainly consists of 3 components, data files with essential and relevant Metadata, data finders for organizing and managing data regardless of files formats, and, a software of searching, analyzing and reporting. With metadata attached to original data files, the data finder can identify different related data files during searches, even if they are in different file formats. TDMS hence allows researchers to search for data like browsing the Internet. Last but not least, it can adapt to changes and update itself according to the changes, unlike databases. == Comparison between strong information systems and weak information systems == Complex organizations may need large amounts
Parchive
Parchive (a portmanteau of parity archive, and formally known as Parity Volume Set Specification) is an erasure code system that produces par files for checksum verification of data integrity, with the capability to perform data recovery operations that can repair or regenerate corrupted or missing data. Parchive was originally written to solve the problem of reliable file sharing on Usenet, but it can be used for protecting any kind of data from data corruption, disc rot, bit rot, and accidental or malicious damage. Despite the name, Parchive uses more advanced techniques (specifically error correction codes) than simplistic parity methods of error detection. As of 2015, PAR1 is obsolete, PAR2 is mature for widespread use, and PAR3 is a discontinued experimental version developed by MultiPar author Yutaka Sawada. The original SourceForge Parchive project has been inactive since April 30, 2015. A new PAR3 specification has been worked on since April 28, 2019 by PAR2 specification author Michael Nahas. An alpha version of the PAR3 specification has been published on January 29, 2022 while the program itself is being developed. == History == Parchive was intended to increase the reliability of transferring files via Usenet newsgroups. Usenet was originally designed for informal conversations, and the underlying protocol, NNTP was not designed to transmit arbitrary binary data. Another limitation, which was acceptable for conversations but not for files, was that messages were normally fairly short in length and limited to 7-bit ASCII text. Various techniques were devised to send files over Usenet, such as uuencoding and Base64. Later Usenet software allowed 8 bit Extended ASCII, which permitted new techniques like yEnc. Large files were broken up to reduce the effect of a corrupted download, but the unreliable nature of Usenet remained. With the introduction of Parchive, parity files could be created that were then uploaded along with the original data files. If any of the data files were damaged or lost while being propagated between Usenet servers, users could download parity files and use them to reconstruct the damaged or missing files. Parchive included the construction of small index files (.par in version 1 and .par2 in version 2) that do not contain any recovery data. These indexes contain file hashes that can be used to quickly identify the target files and verify their integrity. Because the index files were so small, they minimized the amount of extra data that had to be downloaded from Usenet to verify that the data files were all present and undamaged, or to determine how many parity volumes were required to repair any damage or reconstruct any missing files. They were most useful in version 1 where the parity volumes were much larger than the short index files. These larger parity volumes contain the actual recovery data along with a duplicate copy of the information in the index files (which allows them to be used on their own to verify the integrity of the data files if there is no small index file available). In July 2001, Tobias Rieper and Stefan Wehlus proposed the Parity Volume Set specification, and with the assistance of other project members, version 1.0 of the specification was published in October 2001. Par1 used Reed–Solomon error correction to create new recovery files. Any of the recovery files can be used to rebuild a missing file from an incomplete download. Version 1 became widely used on Usenet, but it did suffer some limitations: It was restricted to handle at most 255 files. The recovery files had to be the size of the largest input file, so it did not work well when the input files were of various sizes. (This limited its usefulness when not paired with the proprietary RAR compression tool.) The recovery algorithm had a bug, due to a flaw in the academic paper on which it was based. It was strongly tied to Usenet and it was felt that a more general tool might have a wider audience. In January 2002, Howard Fukada proposed that a new Par2 specification should be devised with the significant changes that data verification and repair should work on blocks of data rather than whole files, and that the algorithm should switch to using 16 bit numbers rather than the 8 bit numbers that PAR1 used. Michael Nahas and Peter Clements took up these ideas in July 2002, with additional input from Paul Nettle and Ryan Gallagher (who both wrote Par1 clients). Version 2.0 of the Parchive specification was published by Michael Nahas in September 2002. Peter Clements then went on to write the first two Par2 implementations, QuickPar and par2cmdline. Abandoned since 2004, Paul Houle created phpar2 to supersede par2cmdline. Yutaka Sawada created MultiPar to supersede QuickPar. MultiPar uses par2j.exe (which is partially based on par2cmdline's optimization techniques) to use as MultiPar's backend engine. == Versions == Versions 1 and 2 of the file format are incompatible. (However, many clients support both.) === Par1 === For Par1, the files f1, f2, ..., fn, the Parchive consists of an index file (f.par), which is CRC type file with no recovery blocks, and a number of "parity volumes" (f.p01, f.p02, etc.). Given all of the original files except for one (for example, f2), it is possible to create the missing f2 given all of the other original files and any one of the parity volumes. Alternatively, it is possible to recreate two missing files from any two of the parity volumes and so forth. Par1 supports up to a total of 256 source and recovery files. === Par2 === Par2 files generally use this naming/extension system: filename.vol000+01.PAR2, filename.vol001+02.PAR2, filename.vol003+04.PAR2, filename.vol007+06.PAR2, etc. The number after the "+" in the filename indicates how many blocks it contains, and the number after "vol" indicates the number of the first recovery block within the PAR2 file. If an index file of a download states that 4 blocks are missing, the easiest way to repair the files would be by downloading filename.vol003+04.PAR2. However, due to the redundancy, filename.vol007+06.PAR2 is also acceptable. There is also an index file filename.PAR2, it is identical in function to the small index file used in PAR1. Par2 specification supports up to 32,768 source blocks and up to 65,535 recovery blocks. Input files are split into multiple equal-sized blocks so that recovery files do not need to be the size of the largest input file. Although Unicode is mentioned in the PAR2 specification as an option, most PAR2 implementations do not support Unicode. Directory support is included in the PAR2 specification, but most or all implementations do not support it. === Par3 === The Par3 specification was originally planned to be published as an enhancement over the Par2 specification. However, to date, it has remained closed source by specification owner Yutaka Sawada. A discussion on a new format started in the GitHub issue section of the maintained fork par2cmdline on January 29, 2019. The discussion led to a new format which is also named as Par3. The new Par3 format's specification is published on GitHub, but remains being an alpha draft as of January 28, 2022. The specification is written by Michael Nahas, the author of Par2 specification, with the help from Yutaka Sawada, animetosho and malaire. The new format claims to have multiple advantages over the Par2 format, including support for: More than 216 files and more than 216 blocks. Packing small files into one block, as well as deduplication when a block appears in multiple files. UTF-8 file names. File permissions, hard links, symbolic/soft links, and empty directories. Embedding PAR data inside other formats, like ZIP archives or ISO disk images. "Incremental backups", where a user creates recovery files for some file or folder, change some data, and create new recovery files reusing some of the older files. More error correction code algorithms (such as LDPC and sparse random matrix). BLAKE3 hashes, dropping support for the MD5 hashes used in PAR2. == Software == === Multi-platform === par2+tbb (GPLv2) — a concurrent (multithreaded) version of par2cmdline 0.4 using TBB. Only compatible with x86 based CPUs. It is available in the FreeBSD Ports system as par2cmdline-tbb. Original par2cmdline — (obsolete). Available in the FreeBSD Ports system as par2cmdline. par2cmdline maintained fork by BlackIkeEagle. par2cmdline-mt is another multithreaded version of par2cmdline using OpenMP, GPLv2, or later. Currently merged into BlackIkeEagle's fork and maintained there. ParPar (CC0) is a high performance, multithreaded PAR2 client and Node.js library. Does not support verifying or repair, it can currently only create PAR2 archives. par2deep (LGPL-3.0) — Produce, verify and repair par2 files recursively, both on the command line as well as with the aid of a graphical user interface. It is available in the Python Package Index system as par2deep. par2cron (MIT License) is an o
Master data management
Master data management (MDM) is a discipline in which business and information technology collaborate to ensure the uniformity, accuracy, stewardship, semantic consistency, and accountability of the enterprise's official shared master data assets. == Reasons for master data management == Data consistency and accuracy: MDM ensures that the organization's critical data is consistent and accurate across all systems, reducing discrepancies and errors caused by multiple, siloed copies of the same data. Improved decision-making: By providing a single version of the truth (SVOT), MDM enables organizations to deliver the right data to decision makers, allowing them to clearly understand business performance and make informed, data-driven decisions. Operational efficiency: With the consistent and accurate data provided by an MDM, operational processes such as reporting and inventory management can be automated to improve efficiency. Employee learning, onboarding, and customer service also become more efficient, as MDM data facilitates rapid, accurate, and thorough information retrieval, permitting more employee time to be spent on work. Regulatory compliance: MDM tries to help organizations comply with industry standards and regulations by ensuring that master data is accurately recorded, maintained, and audited. However, issues with data quality, classification, and reconciliation may require data transformation. As with other Extract, Transform, Load-based data movements, these processes are expensive and inefficient, reducing return on investment for a project. == Business unit and product line segmentation == As a result of business unit and product line segmentation, the same entity (whether a customer, supplier, or product) will be included in different product lines. This leads to data redundancy and even confusion. For example, a customer takes out a mortgage at a bank. If the marketing and customer service departments have separate databases, advertisements might still be sent to the customer, even though they've already signed up. The two parts of the bank are unaware, and the customer is sent irrelevant communications. Record linkage can associate different records corresponding to the same entity, mitigating this issue. == Mergers and acquisitions == One of the most common problems for master data management is company growth through mergers or acquisitions. Reconciling these separate master data systems can present difficulties, as existing applications have dependencies on the master databases. Ideally, database administrators resolve this problem through deduplication of the master data as part of the merger. Over time, as further mergers and acquisitions occur, the problem can multiply. Data reconciliation processes can become extremely complex or even unreliable. Some organizations end up with 10, 15, or even 100 separate and poorly integrated master databases. This can cause serious problems in customer satisfaction, operational efficiency, decision support, and regulatory compliance. Another problem involves determining the proper degrees of detail and normalization to include in the master data schema. For example, in a federated Human Resources environment, the enterprise software may focus on storing people's data as current status, adding a few fields to identify the date of hire, date of last promotion, etc. However, this simplification can introduce business-impacting errors into dependent systems for planning and forecasting. The stakeholders of such systems may be forced to build a parallel network of new interfaces to track the onboarding of new hires, planned retirements, and divestment, which works against one of the aims of master data management. == People, processes and technology == Master data management is enabled by technology, but is more than the technologies that enable it. An organization's master data management capability will also include people and processes in its definition. === People === Several roles should be staffed within MDM. Most prominently, the Data Owner and the Data Steward. Several people would likely be allocated to each role and each person responsible for a subset of Master Data (e.g. one data owner for employee master data, another for customer master data). The Data Owner is responsible for the requirements for data definition, data quality, data security, etc. as well as for compliance with data governance and data management procedures. The Data Owner should also be funding improvement projects in case of deviations from the requirements. The Data Steward is running the master data management on behalf of the data owner and probably also being an advisor to the Data Owner. === Processes === Master data management can be viewed as a "discipline for specialized quality improvement" defined by the policies and procedures put in place by a data governance organization. It has the objective of providing processes for collecting, aggregating, matching, consolidating, quality-assuring, persisting and distributing master data throughout an organization to ensure a common understanding, consistency, accuracy and control, in the ongoing maintenance and application use of that data. Processes commonly seen in master data management include source identification, data collection, data transformation, normalization, rule administration, error detection and correction, data consolidation, data storage, data distribution, data classification, taxonomy services, item master creation, schema mapping, product codification, data enrichment, hierarchy management, business semantics management and data governance. === Technology === A master data management tool can be used to support master data management by removing duplicates, standardizing data (mass maintaining), and incorporating rules to eliminate incorrect data from entering the system to create an authoritative source of master data. Master data are the products, accounts, and parties for which the business transactions are completed. Where the technology approach produces a "golden record" or relies on a "source of record" or "system of record", it is common to talk of where the data is "mastered". This is accepted terminology in the information technology industry, but care should be taken, both with specialists and with the wider stakeholder community, to avoid confusing the concept of "master data" with that of "mastering data". ==== Implementation models ==== There are several models for implementing a technology solution for master data management. These depend on an organization's core business, its corporate structure, and its goals. These include: Source of record Registry Consolidation Coexistence Transaction/centralized ===== Source of record ===== This model identifies a single application, database, or simpler source (e.g. a spreadsheet) as being the "source of record" (or "system of record" where solely application databases are relied on). The benefit of this model is its conceptual simplicity, but it may not fit with the realities of complex master data distribution in large organizations. The source of record can be federated, for example by groups of attributes (so that different attributes of a master data entity may have different sources of record) or geographically (so that different parts of an organization may have different master sources). Federation is only applicable in certain use cases, where there is a clear delineation of which subsets of records will be found in which sources. The source of record model can be applied more widely than simply to master data, for example to reference data. ==== Transmission of master data ==== There are several ways in which master data may be collated and distributed to other systems. This includes: Data consolidation – The process of capturing master data from multiple sources and integrating it into a single hub (operational data store) for replication to other destination systems. Data federation – The process of providing a single virtual view of master data from one or more sources to one or more destination systems. Data propagation – The process of copying master data from one system to another, typically through point-to-point interfaces in legacy systems. == Change management in implementation == Challenges in adopting master data management within large organizations often arise when stakeholders disagree on a "single version of the truth" concept is not affirmed by stakeholders, who believe that their local definition of the master data is necessary. For example, the product hierarchy used to manage inventory may be entirely different from the product hierarchies used to support marketing efforts or pay sales representatives. It is above all necessary to identify if different master data is genuinely required. If it is required, then the solution implemented (technology and process) must be able to allow multiple versions of the truth to exist but will prov
Wumpus world
Wumpus world is a simple world use in artificial intelligence for which to represent knowledge and to reason. Wumpus world was introduced by Michael Genesereth, and is discussed in the Russell-Norvig Artificial Intelligence book Artificial Intelligence: A Modern Approach. Wumpus World is loosely inspired by the 1972 video game Hunt the Wumpus. == Problem description == In Artificial Intelligence: A Modern Approach, the wumpus world features a 4x4 grid, containing a monster called a wumpus, multiple bottomless pits and hidden gold. The agent starts at (1,1) and has to find the gold and return to the starting position. The agent loses 1 point for every move and gains 1000 points for bringing the gold to the starting position. The agent can sense pits by a breeze, stench indicates a wumpus, and sparkle indicates gold. The wumpus can be killed by an arrow but costs 10 points.
Generalized distributive law
The generalized distributive law (GDL) is a generalization of the distributive property which gives rise to a general message passing algorithm. It is a synthesis of the work of many authors in the information theory, digital communications, signal processing, statistics, and artificial intelligence communities. The law and algorithm were introduced in a semi-tutorial by Srinivas M. Aji and Robert J. McEliece with the same title. == Introduction == "The distributive law in mathematics is the law relating the operations of multiplication and addition, stated symbolically, a ∗ ( b + c ) = a ∗ b + a ∗ c {\displaystyle a(b+c)=ab+ac} ; that is, the monomial factor a {\displaystyle a} is distributed, or separately applied, to each term of the binomial factor b + c {\displaystyle b+c} , resulting in the product a ∗ b + a ∗ c {\displaystyle ab+ac} " – Britannica. As it can be observed from the definition, application of distributive law to an arithmetic expression reduces the number of operations in it. In the previous example the total number of operations reduced from three (two multiplications and an addition in a ∗ b + a ∗ c {\displaystyle ab+ac} ) to two (one multiplication and one addition in a ∗ ( b + c ) {\displaystyle a(b+c)} ). Generalization of distributive law leads to a large family of fast algorithms. This includes the FFT and Viterbi algorithm. This is explained in a more formal way in the example below: α ( a , b ) = d e f ∑ c , d , e ∈ A f ( a , c , b ) g ( a , d , e ) {\displaystyle \alpha (a,\,b){\stackrel {\mathrm {def} }{=}}\displaystyle \sum \limits _{c,d,e\in A}f(a,\,c,\,b)\,g(a,\,d,\,e)} where f ( ⋅ ) {\displaystyle f(\cdot )} and g ( ⋅ ) {\displaystyle g(\cdot )} are real-valued functions, a , b , c , d , e ∈ A {\displaystyle a,b,c,d,e\in A} and | A | = q {\displaystyle |A|=q} (say) Here we are "marginalizing out" the independent variables ( c {\displaystyle c} , d {\displaystyle d} , and e {\displaystyle e} ) to obtain the result. When we are calculating the computational complexity, we can see that for each q 2 {\displaystyle q^{2}} pairs of ( a , b ) {\displaystyle (a,b)} , there are q 3 {\displaystyle q^{3}} terms due to the triplet ( c , d , e ) {\displaystyle (c,d,e)} which needs to take part in the evaluation of α ( a , b ) {\displaystyle \alpha (a,\,b)} with each step having one addition and one multiplication. Therefore, the total number of computations needed is 2 ⋅ q 2 ⋅ q 3 = 2 q 5 {\displaystyle 2\cdot q^{2}\cdot q^{3}=2q^{5}} . Hence the asymptotic complexity of the above function is O ( n 5 ) {\displaystyle O(n^{5})} . If we apply the distributive law to the RHS of the equation, we get the following: α ( a , b ) = d e f ∑ c ∈ A f ( a , c , b ) ⋅ ∑ d , e ∈ A g ( a , d , e ) {\displaystyle \alpha (a,\,b){\stackrel {\mathrm {def} }{=}}\displaystyle \sum \limits _{c\in A}f(a,\,c,\,b)\cdot \sum _{d,\,e\in A}g(a,\,d,\,e)} This implies that α ( a , b ) {\displaystyle \alpha (a,\,b)} can be described as a product α 1 ( a , b ) ⋅ α 2 ( a ) {\displaystyle \alpha _{1}(a,\,b)\cdot \alpha _{2}(a)} where α 1 ( a , b ) = d e f ∑ c ∈ A f ( a , c , b ) {\displaystyle \alpha _{1}(a,b){\stackrel {\mathrm {def} }{=}}\displaystyle \sum \limits _{c\in A}f(a,\,c,\,b)} and α 2 ( a ) = d e f ∑ d , e ∈ A g ( a , d , e ) {\displaystyle \alpha _{2}(a){\stackrel {\mathrm {def} }{=}}\displaystyle \sum \limits _{d,\,e\in A}g(a,\,d,\,e)} Now, when we are calculating the computational complexity, we can see that there are q 3 {\displaystyle q^{3}} additions in α 1 ( a , b ) {\displaystyle \alpha _{1}(a,\,b)} and α 2 ( a ) {\displaystyle \alpha _{2}(a)} each and there are q 2 {\displaystyle q^{2}} multiplications when we are using the product α 1 ( a , b ) ⋅ α 2 ( a ) {\displaystyle \alpha _{1}(a,\,b)\cdot \alpha _{2}(a)} to evaluate α ( a , b ) {\displaystyle \alpha (a,\,b)} . Therefore, the total number of computations needed is q 3 + q 3 + q 2 = 2 q 3 + q 2 {\displaystyle q^{3}+q^{3}+q^{2}=2q^{3}+q^{2}} . Hence the asymptotic complexity of calculating α ( a , b ) {\displaystyle \alpha (a,b)} reduces to O ( n 3 ) {\displaystyle O(n^{3})} from O ( n 5 ) {\displaystyle O(n^{5})} . This shows by an example that applying distributive law reduces the computational complexity which is one of the good features of a "fast algorithm". == History == Some of the problems that used distributive law to solve can be grouped as follows: Decoding algorithms: A GDL like algorithm was used by Gallager's for decoding low density parity-check codes. Based on Gallager's work Tanner introduced the Tanner graph and expressed Gallagers work in message passing form. The tanners graph also helped explain the Viterbi algorithm. It is observed by Forney that Viterbi's maximum likelihood decoding of convolutional codes also used algorithms of GDL-like generality. Forward–backward algorithm: The forward backward algorithm helped as an algorithm for tracking the states in the Markov chain. And this also was used the algorithm of GDL like generality Artificial intelligence: The notion of junction trees has been used to solve many problems in AI. Also the concept of bucket elimination used many of the concepts. == The MPF problem == MPF or marginalize a product function is a general computational problem which as special case includes many classical problems such as computation of discrete Hadamard transform, maximum likelihood decoding of a linear code over a memory-less channel, and matrix chain multiplication. The power of the GDL lies in the fact that it applies to situations in which additions and multiplications are generalized. A commutative semiring is a good framework for explaining this behavior. It is defined over a set K {\displaystyle K} with operators " + {\displaystyle +} " and " . {\displaystyle .} " where ( K , + ) {\displaystyle (K,\,+)} and ( K , . ) {\displaystyle (K,\,.)} are a commutative monoids and the distributive law holds. Let p 1 , … , p n {\displaystyle p_{1},\ldots ,p_{n}} be variables such that p 1 ∈ A 1 , … , p n ∈ A n {\displaystyle p_{1}\in A_{1},\ldots ,p_{n}\in A_{n}} where A {\displaystyle A} is a finite set and | A i | = q i {\displaystyle |A_{i}|=q_{i}} . Here i = 1 , … , n {\displaystyle i=1,\ldots ,n} . If S = { i 1 , … , i r } {\displaystyle S=\{i_{1},\ldots ,i_{r}\}} and S ⊂ { 1 , … , n } {\displaystyle S\,\subset \{1,\ldots ,n\}} , let A S = A i 1 × ⋯ × A i r {\displaystyle A_{S}=A_{i_{1}}\times \cdots \times A_{i_{r}}} , p S = ( p i 1 , … , p i r ) {\displaystyle p_{S}=(p_{i_{1}},\ldots ,p_{i_{r}})} , q S = | A S | {\displaystyle q_{S}=|A_{S}|} , A = A 1 × ⋯ × A n {\displaystyle \mathbf {A} =A_{1}\times \cdots \times A_{n}} , and p = { p 1 , … , p n } {\displaystyle \mathbf {p} =\{p_{1},\ldots ,p_{n}\}} Let S = { S j } j = 1 M {\displaystyle S=\{S_{j}\}_{j=1}^{M}} where S j ⊂ { 1 , . . . , n } {\displaystyle S_{j}\subset \{1,...\,,n\}} . Suppose a function is defined as α i : A S i → R {\displaystyle \alpha _{i}:A_{S_{i}}\rightarrow R} , where R {\displaystyle R} is a commutative semiring. Also, p S i {\displaystyle p_{S_{i}}} are named the local domains and α i {\displaystyle \alpha _{i}} as the local kernels. Now the global kernel β : A → R {\displaystyle \beta :\mathbf {A} \rightarrow R} is defined as: β ( p 1 , . . . , p n ) = ∏ i = 1 M α ( p S i ) {\displaystyle \beta (p_{1},...\,,p_{n})=\prod _{i=1}^{M}\alpha (p_{S_{i}})} Definition of MPF problem: For one or more indices i = 1 , . . . , M {\displaystyle i=1,...\,,M} , compute a table of the values of S i {\displaystyle S_{i}} -marginalization of the global kernel β {\displaystyle \beta } , which is the function β i : A S i → R {\displaystyle \beta _{i}:A_{S_{i}}\rightarrow R} defined as β i ( p S i ) = ∑ p S i c ∈ A S i c β ( p ) {\displaystyle \beta _{i}(p_{S_{i}})\,=\displaystyle \sum \limits _{p_{S_{i}^{c}}\in A_{S_{i}^{c}}}\beta (p)} Here S i c {\displaystyle S_{i}^{c}} is the complement of S i {\displaystyle S_{i}} with respect to { 1 , . . . , n } {\displaystyle \mathbf {\{} 1,...\,,n\}} and the β i ( p S i ) {\displaystyle \beta _{i}(p_{S_{i}})} is called the i t h {\displaystyle i^{th}} objective function, or the objective function at S i {\displaystyle S_{i}} . It can observed that the computation of the i t h {\displaystyle i^{th}} objective function in the obvious way needs M q 1 q 2 q 3 ⋯ q n {\displaystyle Mq_{1}q_{2}q_{3}\cdots q_{n}} operations. This is because there are q 1 q 2 ⋯ q n {\displaystyle q_{1}q_{2}\cdots q_{n}} additions and ( M − 1 ) q 1 q 2 . . . q n {\displaystyle (M-1)q_{1}q_{2}...q_{n}} multiplications needed in the computation of the i th {\displaystyle i^{\text{th}}} objective function. The GDL algorithm which is explained in the next section can reduce this computational complexity. The following is an example of the MPF problem. Let p 1 , p 2 , p 3 , p 4 , {\displaystyle p_{1},\,p_{2},\,p_{3},\,p_{4},} and p 5 {\displaystyle p_{5}} be variables such that p 1 ∈ A 1 , p 2 ∈ A 2 , p 3 ∈ A 3 , p 4 ∈ A 4 , {\displaystyle p_{1}\in