In computer science, a pointer algorithm (sometimes called a pointer machine, or a reference machine; see the article Pointer machine for a close but non-identical concept) is a type of algorithm that manages a linked data structure. This concept is used as a model for lower-bound proofs and specific restrictions on the linked data structure and on the algorithm's access to the structure vary. This model has been used extensively with problems related to the disjoint-set data structure. Thus, Tarjan and La Poutré used this model to prove lower bounds on the amortized complexity of a disjoint-set data structure (La Poutré also addressed the interval split-find problem). Blum used this model to prove a lower bound on the single operation worst-case time of disjoint set data structure. Blum and Rochow proved a worst-case lower bound for the interval union-find problem. == Example == In Tarjan's lower bound for the disjoint set union problem, the assumptions on the algorithm are: The algorithm maintains a linked structure of nodes. Each element of the problem is associated with a node. Each set is represented by a node. The nodes of each set constitute a distinct connected component in the structure (this property is called separability). The find operation is performed by following links from the element node to the set node. Under these assumptions, the lower bound of Ω ( m α ( m , n ) ) {\displaystyle \Omega (m\alpha (m,n))} on the cost of a sequence of m operations is proven.
Elements (toolchain)
RemObjects Elements is a toolchain for software development, comprising six programming languages: C#, Swift, Go, Java, Oxygene (a form of modern Object Pascal), and Visual Basic .NET. All languages interoperate, meaning a single project can use any combination of languages, and they can all be compiled to .NET, the JVM, native, or WebAssembly. Elements supports Microsoft Windows, all Apple Inc. platforms (including iOS, visionOS and watchOS), Android, and Linux. Elements also supports language conversion, allowing source code in one language to be rewritten in another. Elements is supported in Visual Studio, but RemObjects also makes their own IDEs, Fire (on MacOS) and Water (on Windows.) == Background == RemObjects began in 2002, creating software for Delphi, but in 2005 in response to the growth of .NET and that Delphi was targeting only native Windows, they released Oxygene (known as Chrome at the time) as a new version of Object Pascal, with more modern syntax as well as being .NET-native. Since then, five other languages have been added to the suite, as well as compiling for the web via WebAssembly and to native architectures (eg Intel 32/64 or ARM64). Elements is primarily intended for developers who want to pull together libraries and codebases written in multiple languages, including legacy codebases in older languages while modernizing either with newer syntax and features or by adding in the use of newer or more popular languages. Because of the Oxygene flavour of Object Pascal, supporting Delphi apps is a primary focus, including allowing Pascal to be compiled for other architectures or providing language features that match other prominent languages. == Approach == New versions of the Elements come out approximately every week. RemObjects names its programming languages after chemical elements, sometimes with poetic or musical spelling, rather than referring to them directly. They are: C#: Hydrogene Object Pascal: Oxygene Java: Iodine Visual Basic: Mercury Go: Gold Swift: Silver == History == The Elements compiler was first introduced with version 1.0 in 2005 under the name "Chrome", with support for only the Oxygene language on the .NET platform, primarily as a response to the then-new and not well-received Delphi .NET compiler from Embarcadero. Chrome saw updates to version 1.5 'Floorshow' and Chrome 2.0 'Joyride' over the next few years, moving in parallel with major advancements on the .NET platform for .NET 2.0 (Generics) and .NET 3.x (LINQ), respectively. With the release of version 3.0 (code-named Oxygène after the Jean-Michel Jarre album of the same name) Chrome was rebranded to Oxygene in 2008, and also shipped co-branded by Embarcadero as Delphi Prism (later just Prism) as part of RAD Studio, replacing Embarcadero's own and now-defunct Delphi.NET compiler. 2010 saw the release of Oxygene 4 ("Echoes"), the last version to focus on just a single language and platform. With Oxygene 5 in 2011 and Oxygene 6 in 2013, RemObjects introduced new platform support for Java/Android (code-name "Cooper") and then Cocoa, the Apple development platform (code-name "Toffee"). Elements 7.0 was released at the beginning of 2014, adding the second programming language, C# to the compiler, and delegating Oxygene from the product name to merely branding the Object Pascal-based language. Over the subsequent years, Elements gained support for additional languages, with Apple Swift in 2015, Java in 2017, and subsequently Google's Go and Mercury, a revitalized Visual Basic.NET. Elements also gained support for its fourth target platform, "Island", for CPU-native compilation for Windows, Linux, and WebAssembly. In addition to the chemical elements-based names for the different languages, the "Elements" concept was carried on with the introduction of dedicated development environments alchemically named Fire (for the Mac, in 2015) and Water (for Windows, in 2018). == Fire and Water (IDEs) == Fire and Water are integrated development environments developed by RemObjects Software. They are designed specifically for use with the Elements Compiler. Fire is the version developed for macOS, while Water is intended for Microsoft Windows. Both IDEs are designed to work closely with the Elements compiler and are primarily intended for developers using the RemObjects language ecosystem. They support software development across multiple platforms, including .NET, Android, iOS, macOS, Windows, Linux, and WebAssembly. The IDEs include standard development tools such as syntax highlighting, code completion, debugging, and project navigation. Build operations are managed using a custom system known as EBuild, which is part of the broader Elements toolchain. The IDEs are distributed as part of the RemObjects Elements package and are updated in coordination with the compiler itself. == In media == Oxygene has been mentioned several times by Verity Stob in their Chronicles of Delphi series, currently living at The Register.
Artificial intelligence in industry
Industrial artificial intelligence, or industrial AI, refers to the application of artificial intelligence to industrial business processes. Unlike general artificial intelligence which is a frontier research discipline to build computerized systems that perform tasks requiring human intelligence, industrial AI is more concerned with the application of such technologies to address industrial pain-points for customer value creation, productivity improvement, cost reduction, site optimization, predictive analysis and insight discovery. Artificial intelligence and machine learning have become key enablers to leverage data in production in recent years due to a number of different factors: More affordable sensors and the automated process of data acquisition; More powerful computation capability of computers to perform more complex tasks at a faster speed with lower cost; Faster connectivity infrastructure and more accessible cloud services for data management and computing power outsourcing. == Categories == Possible applications of industrial AI and machine learning in the production domain can be divided into seven application areas: Market and trend analysis Machinery and equipment Intralogistics Production process Supply chain Building Product Each application area can be further divided into specific application scenarios that describe concrete AI/ML scenarios in production. While some application areas have a direct connection to production processes, others cover production adjacent fields like logistics or the factory building. An example from the application scenario Process Design & Innovation are collaborative robots. Collaborative robotic arms are able to learn the motion and path demonstrated by human operators and perform the same task. Predictive and preventive maintenance through data-driven machine learning are application scenarios from the Machinery & Equipment application area. == Challenges == In contrast to entirely virtual systems, in which ML applications are already widespread today, real-world production processes are characterized by the interaction between the virtual and the physical world. Data is recorded using sensors and processed on computational entities and, if desired, actions and decisions are translated back into the physical world via actuators or by human operators. This poses major challenges for the application of ML in production engineering systems. These challenges are attributable to the encounter of process, data and model characteristics: The production domain's high reliability requirements, high risk and loss potential, the multitude of heterogeneous data sources and the non-transparency of ML model functionality impede a faster adoption of ML in real-world production processes. In particular, production data comprises a variety of different modalities, semantics and quality. Furthermore, production systems are dynamic, uncertain and complex, and engineering and manufacturing problems are data-rich but information-sparse. Besides that, due to the variety of use cases and data characteristics, problem-specific data sets are required, which are difficult to acquire, hindering both practitioners and academic researchers in this domain. === Process and industry characteristics === The domain of production engineering can be considered as a rather conservative industry when it comes to the adoption of advanced technology and their integration into existing processes. This is due to high demands on reliability of the production systems resulting from the potentially high economic harm of reduced process effectiveness due to e.g., additional unplanned downtime or insufficient product qualities. In addition, the specifics of machining equipment and products prevent area-wide adoptions across a variety of processes. Besides the technical reasons, the reluctant adoption of ML is fueled by a lack of IT and data science expertise across the domain. === Data characteristics === The data collected in production processes mainly stem from frequently sampling sensors to estimate the state of a product, a process, or the environment in the real world. Sensor readings are susceptible to noise and represent only an estimate of the reality under uncertainty. Production data typically comprises multiple distributed data sources resulting in various data modalities (e.g., images from visual quality control systems, time-series sensor readings, or cross-sectional job and product information). The inconsistencies in data acquisition lead to low signal-to-noise ratios, low data quality and great effort in data integration, cleaning and management. In addition, as a result from mechanical and chemical wear of production equipment, process data is subject to various forms of data drifts. === Machine learning model characteristics === ML models are considered as black-box systems given their complexity and intransparency of input-output relation. This reduces the comprehensibility of the system behavior and thus also the acceptance by plant operators. Due to the lack of transparency and the stochasticity of these models, no deterministic proof of functional correctness can be achieved, complicating the certification of production equipment. Given their inherent unrestricted prediction behavior, ML models are vulnerable against erroneous or manipulated data, further risking the reliability of the production system because of lacking robustness and safety. In addition to high development and deployment costs, the data drifts cause high maintenance costs, which is disadvantageous compared to purely deterministic programs. == Standard processes for data science in production == The development of ML applications – starting with the identification and selection of the use case and ending with the deployment and maintenance of the application – follows dedicated phases that can be organized in standard process models. The process models assist in structuring the development process and defining requirements that must be met in each phase to enter the next phase. The standard processes can be classified into generic and domain-specific ones. Generic standard processes (e.g., CRISP-DM, ASUM-DM, or knowledge discovery in databases (KDD)) describe a generally valid methodology and are thus independent of individual domains. Domain-specific processes on the other hand consider specific peculiarities and challenges of special application areas. The Machine Learning Pipeline in Production is a domain-specific data science methodology that is inspired by the CRISP-DM model and was specifically designed to be applied in fields of engineering and production technology. To address the core challenges of ML in engineering – process, data, and model characteristics – the methodology especially focuses on use-case assessment, achieving a common data and process understanding data integration, data preprocessing of real-world production data and the deployment and certification of real-world ML applications. == Industrial data sources == The foundation of most artificial intelligence and machine learning applications in industrial settings are comprehensive datasets from the respective fields. Those datasets act as the basis for training the employed models. In other domains, like computer vision, speech recognition or language models, extensive reference datasets (e.g. ImageNet, Librispeech, The People's Speech) and data scraped from the open internet are frequently used for this purpose. Such datasets rarely exist in the industrial context because of high confidentiality requirements and high specificity of the data. Industrial applications of artificial intelligence are therefore often faced with the problem of data availability. For these reasons, existing open datasets applicable to industrial applications, often originate from public institutions like governmental agencies or universities and data analysis competitions hosted by companies. In addition to this, data sharing platforms exist. However, most of these platforms have no industrial focus and offer limited filtering abilities regarding industrial data sources.
List of library and information science journals
This list covers the journals, magazines, periodicals already published and continuing in the discipline of library and information science (LIS). It doesn't include ceased titles or predatory journals. Titles listed were taken from various scholarly sources, UGC Care and Wikipedia articles. == LIS journal prestige as assessed by LIS faculty == In a 2013 article by Laura Manzari, 232 LIS faculty members from ALA-accredited information science programs ranked the most prestigious journals in library and information science. The following journals were ranked in the top ten most prestigious: Journal of the Association for Information Science and Technology The Library Quarterly Annual Review of Information Science and Technology Journal of Documentation Library Trends Library and Information Science Research Information Processing and Management Journal of Education for Library and Information Science Education College & Research Libraries First Monday (journal) A subsequent study by Safón and Docampo in 2023 identified impactful LIS journals based on their influence on papers published in other LIS publications. Journals listed in the top ten in this study that did not appear in Manzari's list include: Scientometrics International Journal of Information Management Quantitative Science Studies MIS Quarterly Information and Management Journal of the Association for Information Systems Journal of Informetrics The Journal of Academic Librarianship == India == Annals of Library and Information Studies. (Pub: CSIR-NIScPR ), Formerly: Annals of Library Science. ISSN 0003-4835. (1954-) OPEN ACCESS Collnet Journal of Scientrometrics and Information Management (Pub: Taru Publications, Online through Taylor and Francis) ISSN: 0973-7766 Online 2168-930X. College Libraries (Pub: West Bengal College Librarians’ Association (WBCLA) ISSN 0972-1975, Quarterly DESIDOC Journal of Library and Information Technology (DJLIT) (Formerly: DESIDOC Bulletin 0970-8154, DESIDOC Bulletin of Information Technology. 0971-4383/0974-0643) (Pub: Defence Scientific Information & Documentation Centre) ISSN: 0974-0643, ISSN: 0976-4658 (O), Bi-monthly, OPEN ACCESS. Grandhalaya Sarvaswam (Bilingual: Telugu & English) [Pub: Andhra Pradesh Library Association, Vijayawada, Andhra Pradesh, India] (1915–) Gyankosh: Journal of Library and Information Management. (Pub: Integrated Academy Of Management And Technology. Through: Indian Journals.Com). ISSN: 2229-4023 (P), 2249-3182. Half yearly. IASLIC Bulletin (Pub: Indian Association of Special Libraries and Information Centres) ISSN: 0018-8411. Quarterly (1956-) IASLIC Newsletter (Pub: Indian Association of Special Libraries and Information Centres. (Pub: Indian Association of Special Libraries and Information Centres) ISSN 0018-845X. Monthly. (1966-) INFLIBNET Newsletter. (Pub: INFLIBNET). Monthly. Informatics Studies. (Pub: Centre For Informatics Research And Development). Quarterly. Through: Indian journals.com. ISSN: 2583-8994 (Online), 2320-530X (Print) ISST Journal of Advances in Librarianship (Pub:Intellectuals Society for Socio-Techno Welfare) ISSN: 0976-9021. Semiannual. Journal of Advanced Research in Library and Information Science. (JALIS Publishers). 4/year. ISSN 2277-2219. Journal of Indian Library Association (Pub: Indian Library Association). ISSN (P) 2277-5145 O) 2456-513X. Quarterly. (1965-). Journal of Scientometric Research. (Pub: Phcog.Net). ISSN (P) 2321-6654, (O) 2320-0057]; Frequency : Triannual. KELPRO Bulletin (Pub: Kerala Library Professionals' Organisation - KELPRO). ISSN 0975-4911( Print),2582-497X (O).(1993-) KIIT Journal of Library and Information Management (Pub: KIIT University, online through Indian Journals.com) Half yearly. ISSN: 2348-0858. Library Herald. (Pub: Delhi Library Association - DLA). Quarterly. ISSN: 0024-2292. Library Progress (International). (Pub: Bpas Publications, Through: ). Half yearly. ISSN: 0970-1052. (O) ISSN: 2320-317X. (1981-) Pearl: A Journal of Library and Information Science. (Pub: University Library Teacher's Association of Andhra Pradesh, Hyderabad), ISSN: 0973-7081 (print), 0975-6922 (online). Quarterly. RBU Journal of Library and Information Science. (Pub: Rabindra Bharati University).ISSN: 0972-2750. Annual. SALIS Journal of Information Management and Technology - SJIMT. (Pub: Society for the Advancement of Library and Information Science). Half-yearly. ISSN 0975-4105. SALIS Journal of Library and Information Science - SJLIS: an International Journal. (Pub: Society for the Advancement of Library and Information Science). Half-yearly. ISSN: 0973-3108. SRELS journal of Information and Knowledge (Formerly: Library Science with a Slant to Documentation, ISSN: 0024-2543; Library Science with a Slant to Documentation and Information Studies ISSN: 0970-6089; SRELS Journal of Information Management ISSN: ). Quarterly. ISSN: 2583-9314 (O) World Digital Libraries. Half yearly. ISSN: 0974-567X (P), 0975-7597 (O). == Other countries == African Journal of Library, Archives and Information Science Art Libraries Journal (Cambridge University Press) Bibliothèque de l'École des Chartes Canadian Journal of Information and Library Science Cataloging & Classification Quarterly Communications in Information Literacy Cataloging & Classification Quarterly Catholic Library Association Children and Libraries Code4Lib Journal College & Research Libraries Communications in Information Literacy Disability in Library and Information Studies Electronic Journal of Academic and Special Librarianship El Profesional de la Información (es) (EPI) (Formerly Information World en Español) Evidence Based Library and Information Practice (journal) Faslname-ye Ketab Florida Libraries. Florida Library Association. Georgia Library Quarterly. Quarterly. (Pub: Georgia Library Association). Hipertext.net IFLA Journal In the Library with the Lead Pipe Information & Culture International Journal of Information Retrieval Research (IJIRR) Information Processing and Management Information Research Information Sciences (journal) Information Visualization (journal) Information, Communication & Society International Journal of Geographical Information Science Information Research: An International Electronic Journal (IR) Internet Research (journal) Issues in Science and Technology Librarianship Italian Journal of Library and Information Studies (JLIS.it) JLIS.it Journal of Documentation (JDoc) Journal of Information Ethics Journal of Information Science (JIS) Journal of Information Technology Journal of Informetrics Journal of Librarianship and Information Science Journal of Library & Information Studies - JLIS. (Pub: National Taiwan University) Journal of Library Administration Journal of Religious & Theological Information Journal of the Association for Information Science and Technology (Formerly Journal of the American Society for Information Science and Technology) (JASIST) Journal of the Medical Library Association Journal of the Canadian Health Libraries Association (Pub: Canadian Health Libraries Association). Knowledge Organization (journal) Knowledge Quest. (Pub: American Association of School Librarians) Library and Information Science Abstracts Library Literature and Information Science Library, Information Science & Technology Abstracts Library Literature and Information Science Retrospective Library Review (journal) Library Trends Libri (journal) Malaysian Journal of Library and Information Science MLA Forum New Century Library New Review of Children's Literature and Librarianship Notes (journal) Portal – Libraries and the Academy Progressive Librarian, Progressive Librarians Guild Reference and User Services Quarterly Reference Services Review Research Evaluation (journal) Scientometrics (journal) Serials Review South African Journal of Libraries and Information Science The Charleston Advisor The Christian Librarian, from the Association of Christian Librarians The Journal of Academic Librarianship The Library Quarterly (LQ) The Public-Access Computer Systems Review TripleC Webolog
Algorithm characterizations
Algorithm characterizations are attempts to formalize the word algorithm. Algorithm does not have a generally accepted formal definition. Researchers are actively working on this problem. This article will present some of the "characterizations" of the notion of "algorithm" in more detail. == The problem of definition == Over the last 200 years, the definition of the algorithm has become more complicated and detailed as researchers have tried to pin down the term. Indeed, there may be more than one type of "algorithm". But most agree that algorithm has something to do with defining generalized processes for the creation of "output" integers from other "input" integers – "input parameters" arbitrary and infinite in extent, or limited in extent but still variable—by the manipulation of distinguishable symbols (counting numbers) with finite collections of rules that a person can perform with paper and pencil. The most common number-manipulation schemes—both in formal mathematics and in routine life—are: (1) the recursive functions calculated by a person with paper and pencil, and (2) the Turing machine or its Turing equivalents—the primitive register-machine or "counter-machine" model, the random-access machine model (RAM), the random-access stored-program machine model (RASP) and its functional equivalent "the computer". When we are doing "arithmetic" we are really calculating by the use of "recursive functions" in the shorthand algorithms we learned in grade school, for example, adding and subtracting. The proofs that every "recursive function" we can calculate by hand we can compute by machine and vice versa—note the usage of the words calculate versus compute—is remarkable. But this equivalence together with the thesis (unproven assertion) that this includes every calculation/computation indicates why so much emphasis has been placed upon the use of Turing-equivalent machines in the definition of specific algorithms, and why the definition of "algorithm" itself often refers back to "the Turing machine". This is discussed in more detail under Stephen Kleene's characterization. The following are summaries of the more famous characterizations (Kleene, Markov, Knuth) together with those that introduce novel elements—elements that further expand the definition or contribute to a more precise definition. [ A mathematical problem and its result can be considered as two points in a space, and the solution consists of a sequence of steps or a path linking them. Quality of the solution is a function of the path. There might be more than one attribute defined for the path, e.g. length, complexity of shape, an ease of generalizing, difficulty, and so on. ] == Chomsky hierarchy == There is more consensus on the "characterization" of the notion of "simple algorithm". All algorithms need to be specified in a formal language, and the "simplicity notion" arises from the simplicity of the language. The Chomsky (1956) hierarchy is a containment hierarchy of classes of formal grammars that generate formal languages. It is used for classifying of programming languages and abstract machines. From the Chomsky hierarchy perspective, if the algorithm can be specified on a simpler language (than unrestricted), it can be characterized by this kind of language, else it is a typical "unrestricted algorithm". Examples: a "general purpose" macro language, like M4 is unrestricted (Turing complete), but the C preprocessor macro language is not, so any algorithm expressed in C preprocessor is a "simple algorithm". See also Relationships between complexity classes. == Features of a good algorithm == The following are desirable features of a well-defined algorithm, as discussed in Scheider and Gersting (1995): Unambiguous Operations: an algorithm must have specific, outlined steps. The steps should be exact enough to precisely specify what to do at each step. Well-Ordered: The exact order of operations performed in an algorithm should be concretely defined. Feasibility: All steps of an algorithm should be possible (also known as effectively computable). Input: an algorithm should be able to accept a well-defined set of inputs. Output: an algorithm should produce some result as an output, so that its correctness can be reasoned about. Finiteness: an algorithm should terminate after a finite number of instructions. Properties of specific algorithms that may be desirable include space and time efficiency, generality (i.e. being able to handle many inputs), or determinism. == 1881 John Venn's negative reaction to W. Stanley Jevons's Logical Machine of 1870 == In early 1870 W. Stanley Jevons presented a "Logical Machine" (Jevons 1880:200) for analyzing a syllogism or other logical form e.g. an argument reduced to a Boolean equation. By means of what Couturat (1914) called a "sort of logical piano [,] ... the equalities which represent the premises ... are "played" on a keyboard like that of a typewriter. ... When all the premises have been "played", the panel shows only those constituents whose sum is equal to 1, that is, ... its logical whole. This mechanical method has the advantage over VENN's geometrical method..." (Couturat 1914:75). For his part John Venn, a logician contemporary to Jevons, was less than thrilled, opining that "it does not seem to me that any contrivances at present known or likely to be discovered really deserve the name of logical machines" (italics added, Venn 1881:120). But of historical use to the developing notion of "algorithm" is his explanation for his negative reaction with respect to a machine that "may subserve a really valuable purpose by enabling us to avoid otherwise inevitable labor": (1) "There is, first, the statement of our data in accurate logical language", (2) "Then secondly, we have to throw these statements into a form fit for the engine to work with – in this case the reduction of each proposition to its elementary denials", (3) "Thirdly, there is the combination or further treatment of our premises after such reduction," (4) "Finally, the results have to be interpreted or read off. This last generally gives rise to much opening for skill and sagacity." He concludes that "I cannot see that any machine can hope to help us except in the third of these steps; so that it seems very doubtful whether any thing of this sort really deserves the name of a logical engine."(Venn 1881:119–121). == 1943, 1952 Stephen Kleene's characterization == This section is longer and more detailed than the others because of its importance to the topic: Kleene was the first to propose that all calculations/computations—of every sort, the totality of—can equivalently be (i) calculated by use of five "primitive recursive operators" plus one special operator called the mu-operator, or be (ii) computed by the actions of a Turing machine or an equivalent model. Furthermore, he opined that either of these would stand as a definition of algorithm. A reader first confronting the words that follow may well be confused, so a brief explanation is in order. Calculation means done by hand, computation means done by Turing machine (or equivalent). (Sometimes an author slips and interchanges the words). A "function" can be thought of as an "input-output box" into which a person puts natural numbers called "arguments" or "parameters" (but only the counting numbers including 0—the nonnegative integers) and gets out a single nonnegative integer (conventionally called "the answer"). Think of the "function-box" as a little man either calculating by hand using "general recursion" or computing by Turing machine (or an equivalent machine). "Effectively calculable/computable" is more generic and means "calculable/computable by some procedure, method, technique ... whatever...". "General recursive" was Kleene's way of writing what today is called just "recursion"; however, "primitive recursion"—calculation by use of the five recursive operators—is a lesser form of recursion that lacks access to the sixth, additional, mu-operator that is needed only in rare instances. Thus most of life goes on requiring only the "primitive recursive functions." === 1943 "Thesis I", 1952 "Church's Thesis" === In 1943 Kleene proposed what has come to be known as Church's thesis: "Thesis I. Every effectively calculable function (effectively decidable predicate) is general recursive" (First stated by Kleene in 1943 (reprinted page 274 in Davis, ed. The Undecidable; appears also verbatim in Kleene (1952) p.300) In a nutshell: to calculate any function the only operations a person needs (technically, formally) are the 6 primitive operators of "general" recursion (nowadays called the operators of the mu recursive functions). Kleene's first statement of this was under the section title "12. Algorithmic theories". He would later amplify it in his text (1952) as follows: "Thesis I and its converse provide the exact definition of the notion of a calculation (decision) procedure or algorithm, for the
PDE surface
PDE surfaces are used in geometric modelling and computer graphics for creating smooth surfaces conforming to a given boundary configuration. PDE surfaces use partial differential equations to generate a surface which usually satisfy a mathematical boundary value problem. PDE surfaces were first introduced into the area of geometric modelling and computer graphics by two British mathematicians, Malcolm Bloor and Michael Wilson. == Technical details == The PDE method involves generating a surface for some boundary by means of solving an elliptic partial differential equation of the form ( ∂ 2 ∂ u 2 + a 2 ∂ 2 ∂ v 2 ) 2 X ( u , v ) = 0. {\displaystyle \left({\frac {\partial ^{2}}{\partial u^{2}}}+a^{2}{\frac {\partial ^{2}}{\partial v^{2}}}\right)^{2}X(u,v)=0.} Here X ( u , v ) {\displaystyle X(u,v)} is a function parameterised by the two parameters u {\displaystyle u} and v {\displaystyle v} such that X ( u , v ) = ( x ( u , v ) , y ( u , v ) , z ( u , v ) ) {\displaystyle X(u,v)=(x(u,v),y(u,v),z(u,v))} where x {\displaystyle x} , y {\displaystyle y} and z {\displaystyle z} are the usual cartesian coordinate space. The boundary conditions on the function X ( u , v ) {\displaystyle X(u,v)} and its normal derivatives ∂ X / ∂ n {\displaystyle \partial {X}/\partial {n}} are imposed at the edges of the surface patch. With the above formulation it is notable that the elliptic partial differential operator in the above PDE represents a smoothing process in which the value of the function at any point on the surface is, in some sense, a weighted average of the surrounding values. In this way, a surface is obtained as a smooth transition between the chosen set of boundary conditions. The parameter a {\displaystyle a} is a special design parameter which controls the relative smoothing of the surface in the u {\displaystyle u} and v {\displaystyle v} directions. When a = 1 {\displaystyle a=1} , the PDE is the biharmonic equation: X u u u u + 2 X u u v v + X v v v v = 0 {\displaystyle X_{uuuu}+2X_{uuvv}+X_{vvvv}=0} . The biharmonic equation is the equation produced by applying the Euler-Lagrange equation to the simplified thin plate energy functional X u u 2 + 2 X u v 2 + X v v 2 {\displaystyle X_{uu}^{2}+2X_{uv}^{2}+X_{vv}^{2}} . So solving the PDE with a = 1 {\displaystyle a=1} is equivalent to minimizing the thin plate energy functional subject to the same boundary conditions. == Applications == PDE surfaces can be used in many application areas. These include computer-aided design, interactive design, parametric design, computer animation, computer-aided physical analysis and design optimisation. == Related publications == M.I.G. Bloor and M.J. Wilson, Generating Blend Surfaces using Partial Differential Equations, Computer Aided Design, 21(3), 165–171, (1989). H. Ugail, M.I.G. Bloor, and M.J. Wilson, Techniques for Interactive Design Using the PDE Method, ACM Transactions on Graphics, 18(2), 195–212, (1999). J. Huband, W. Li and R. Smith, An Explicit Representation of Bloor-Wilson PDE Surface Model by using Canonical Basis for Hermite Interpolation, Mathematical Engineering in Industry, 7(4), 421-33 (1999). H. Du and H. Qin, Direct Manipulation and Interactive Sculpting of PDE surfaces, Computer Graphics Forum, 19(3), C261-C270, (2000). H. Ugail, Spine Based Shape Parameterisations for PDE surfaces, Computing, 72, 195–204, (2004). L. You, P. Comninos, J.J. Zhang, PDE Blending Surfaces with C2 Continuity, Computers and Graphics, 28(6), 895–906, (2004).
Applied Information Science in Economics
The Applied Information Science in Economics (Russian: Прикладная информатика в Экономике) or Applied Computer Science in Economics is a professional qualification generally awarded in Russian Federation. The degree inherited from the U.S.S.R. education system also known as Specialist degree. The degree is awarded after five years of full-time study and includes several internships, course-works, thesis writing and defense. The degree has similarities with German Magister Artium or Diplom degree. However, due to the Bologna Process number of such degrees are declining. Degree focuses on applying mathematical methods in economics involving maximum information technology. It is very close to applied mathematics, but includes also major part of computer science. == List of specialty codes in the education system == 080801 - Applied computer science in economics 351400 - Applied computer science == Fields of activity == Organization and management; Project design; Experimental research; Marketing; Consulting; Operational and Maintenance. == Major == Information Science and Programming. High Level Methods of Information Science and Programming. Information Technologies in Economics. Computer Systems, Networks and Telecommunications Services. Operational Environments, Systems and Shells. Architecture and Design of Information Systems for Companies. Data Bases. Information security. Information Management. Imitative Simulation.