AI Chatbot Q

AI Chatbot Q — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.

• 

  Clef (app)

  Clef was a San Francisco-based technology company, known for developing a mobile app that created a two-factor authentication for websites. It allowed users to access sites with a single login password management service which stores encrypted passwords in private accounts. It had a standard verification method that requires access to data on the mobile phone to confirm the user's identity. The application required a Wi-Fi or mobile network, and the user could log in by scanning the computer screen with their phone. == History == Clef was founded in 2013 by Mark Hudnall, B. Byrne and Jesse Pollak. It raised $1.6 million in seed funding in November 2014. Clef integrated with many websites and applications, including WordPress. On March 17, 2017, Clef announced they would no longer support the plugin after June 6, 2017; Clef was acquired by Authy, another 2FA service, which later got acquired by Twilio.

  Read more →
• 

  Bibliometrician

  A bibliometrician is a researcher or a specialist in bibliometrics. It is near-synonymous with an informetrican (who studies informetrics), a scientometrican (who study scientometrics) and a webometrician, who study webometrics. == Notable bibliometricians == Christine L. Borgman Samuel C. Bradford Blaise Cronin Margaret Elizabeth Egan Eugene Garfield (developer of the Science Citation Index and the Impact factor) Jorge E. Hirsch (developer of the h-index) Alfred J. Lotka Vasily Nalimov Derek J. de Solla Price Ronald Rousseau George Kingsley Zipf

  Read more →
• 

  Divide-and-conquer algorithm

  In computer science, divide and conquer is an algorithm design paradigm. A divide-and-conquer algorithm recursively breaks down a problem into two or more sub-problems of the same or related type, until these become simple enough to be solved directly. The solutions to the sub-problems are then combined to give a solution to the original problem. The divide-and-conquer technique is the basis of efficient algorithms for many problems, such as sorting (e.g., quicksort, merge sort), multiplying large numbers (e.g., the Karatsuba algorithm), finding the closest pair of points, syntactic analysis (e.g., top-down parsers), SAT solving, and computing the discrete Fourier transform (FFT). Designing efficient divide-and-conquer algorithms can be difficult. As in mathematical induction, it is often necessary to generalize the problem to make it amenable to a recursive solution. The correctness of a divide-and-conquer algorithm is usually proved by mathematical induction, and its computational cost is often determined by solving recurrence relations. == Divide and conquer == The divide-and-conquer paradigm is often used to find an optimal solution of a problem. Its basic idea is to decompose a given problem into two or more similar, but simpler, subproblems, to solve them in turn, and to compose their solutions to solve the given problem. Problems of sufficient simplicity are solved directly. For example, to sort a given list of n natural numbers, split it into two lists of about n/2 numbers each, sort each of them in turn, and interleave both results appropriately to obtain the sorted version of the given list (see the picture). This approach is known as the merge sort algorithm. The name "divide and conquer" is sometimes applied to algorithms that reduce each problem to only one sub-problem, such as the binary search algorithm for finding a record in a sorted list (or its analogue in numerical computing, the bisection algorithm for root finding). These algorithms can be implemented more efficiently than general divide-and-conquer algorithms; in particular, if they use tail recursion, they can be converted into simple loops. Under this broad definition, however, every algorithm that uses recursion or loops could be regarded as a "divide-and-conquer algorithm". Therefore, some authors consider that the name "divide and conquer" should be used only when each problem may generate two or more subproblems. The name decrease and conquer has been proposed instead for the single-subproblem class. An important application of divide and conquer is in optimization, where if the search space is reduced ("pruned") by a constant factor at each step, the overall algorithm has the same asymptotic complexity as the pruning step, with the constant depending on the pruning factor (by summing the geometric series); this is known as prune and search. == Early historical examples == Early examples of these algorithms are primarily decrease and conquer – the original problem is successively broken down into single subproblems, and indeed can be solved iteratively. Binary search, a decrease-and-conquer algorithm where the subproblems are of roughly half the original size, has a long history. While a clear description of the algorithm on computers appeared in 1946 in an article by John Mauchly, the idea of using a sorted list of items to facilitate searching dates back at least as far as Babylonia in 200 BC. Another ancient decrease-and-conquer algorithm is the Euclidean algorithm to compute the greatest common divisor of two numbers by reducing the numbers to smaller and smaller equivalent subproblems, which dates to several centuries BC. An early example of a divide-and-conquer algorithm with multiple subproblems is Gauss's 1805 description of what is now called the Cooley–Tukey fast Fourier transform (FFT) algorithm, although he did not analyze its operation count quantitatively, and FFTs did not become widespread until they were rediscovered over a century later. An early two-subproblem D&C algorithm that was specifically developed for computers and properly analyzed is the merge sort algorithm, invented by John von Neumann in 1945. Another notable example is the algorithm invented by Anatolii A. Karatsuba in 1960 that could multiply two n-digit numbers in O ( n log 2 ⁡ 3 ) {\displaystyle O(n^{\log _{2}3})} operations (in Big O notation). This algorithm disproved Andrey Kolmogorov's 1956 conjecture that Ω ( n 2 ) {\displaystyle \Omega (n^{2})} operations would be required for that task. As another example of a divide-and-conquer algorithm that did not originally involve computers, Donald Knuth gives the method a post office typically uses to route mail: letters are sorted into separate bags for different geographical areas, each of these bags is itself sorted into batches for smaller sub-regions, and so on until they are delivered. This is related to a radix sort, described for punch-card sorting machines as early as 1929. == Advantages == === Solving difficult problems === Divide and conquer is a powerful tool for solving conceptually difficult problems: all it requires is a way of breaking the problem into sub-problems, of solving the trivial cases, and of combining sub-problems to the original problem. Similarly, decrease and conquer only requires reducing the problem to a single smaller problem, such as the classic Tower of Hanoi puzzle, which reduces moving a tower of height n {\displaystyle n} to move a tower of height n − 1 {\displaystyle n-1} . === Algorithm efficiency === The divide-and-conquer paradigm often helps in the discovery of efficient algorithms. It was the key, for example, to Karatsuba's fast multiplication method, the quicksort and mergesort algorithms, the Strassen algorithm for matrix multiplication, and fast Fourier transforms. In all these examples, the D&C approach led to an improvement in the asymptotic cost of the solution. For example, if (a) the base cases have constant-bounded size, the work of splitting the problem and combining the partial solutions is proportional to the problem's size n {\displaystyle n} , and (b) there is a bounded number p {\displaystyle p} of sub-problems of size ~ n p {\displaystyle {\frac {n}{p}}} at each stage, then the cost of the divide-and-conquer algorithm will be O ( n log p ⁡ n ) {\displaystyle O(n\log _{p}n)} . For other types of divide-and-conquer approaches, running times can also be generalized. For example, when a) the work of splitting the problem and combining the partial solutions take c n {\displaystyle cn} time, where n {\displaystyle n} is the input size and c {\displaystyle c} is some constant; b) when n < 2 {\displaystyle n<2} , the algorithm takes time upper-bounded by c {\displaystyle c} , and c) there are q {\displaystyle q} subproblems where each subproblem has size ~ n 2 {\displaystyle {\frac {n}{2}}} . Then, the running times are as follows: if the number of subproblems q > 2 {\displaystyle q>2} , then the divide-and-conquer algorithm's running time is bounded by O ( n log 2 ⁡ q ) {\displaystyle O(n^{\log _{2}q})} . if the number of subproblems is exactly one, then the divide-and-conquer algorithm's running time is bounded by O ( n ) {\displaystyle O(n)} . If, instead, the work of splitting the problem and combining the partial solutions take c n 2 {\displaystyle cn^{2}} time, and there are 2 subproblems where each has size n 2 {\displaystyle {\frac {n}{2}}} , then the running time of the divide-and-conquer algorithm is bounded by O ( n 2 ) {\displaystyle O(n^{2})} . === Parallelism === Divide-and-conquer algorithms are naturally adapted for execution in multi-processor machines, especially shared-memory systems where the communication of data between processors does not need to be planned in advance because distinct sub-problems can be executed on different processors. === Memory access === Divide-and-conquer algorithms naturally tend to make efficient use of memory caches. The reason is that once a sub-problem is small enough, it and all its sub-problems can, in principle, be solved within the cache, without accessing the slower main memory. An algorithm designed to exploit the cache in this way is called cache-oblivious, because it does not contain the cache size as an explicit parameter. Moreover, D&C algorithms can be designed for important algorithms (e.g., sorting, FFTs, and matrix multiplication) to be optimal cache-oblivious algorithms–they use the cache in a probably optimal way, in an asymptotic sense, regardless of the cache size. In contrast, the traditional approach to exploiting the cache is blocking, as in loop nest optimization, where the problem is explicitly divided into chunks of the appropriate size—this can also use the cache optimally, but only when the algorithm is tuned for the specific cache sizes of a particular machine. The same advantage exists with regards to other hierarchical storage systems, such as NUMA or virtual memory, as well as for multip

  Read more →
• 

  Schema crosswalk

  A schema crosswalk is a table that shows equivalent elements (or "fields") in more than one database schema. It maps the elements in one schema to the equivalent elements in another. Crosswalk tables are often employed within or in parallel to enterprise systems, especially when multiple systems are interfaced or when the system includes legacy system data. In the context of Interfaces, they function as an internal extract, transform, load (ETL) mechanism. For example, this is a metadata crosswalk from MARC standards to Dublin Core: Crosswalks show people where to put the data from one scheme into a different scheme. They are often used by libraries, archives, museums, and other cultural institutions to translate data to or from MARC standards, Dublin Core, Text Encoding Initiative (TEI), and other metadata schemes. For example, an archive has a MARC record in its catalog describing a manuscript. Suppose the archive makes a digital copy of that manuscript and wants to display it on the web along with the information from the catalog. In that case, it will have to translate the data from the MARC catalog record into a different format, such as Metadata Object Description Schema, that is viewable on a webpage. Because MARC has various fields than MODS, decisions must be made about where to put the data into MODS. This type of "translating" from one format to another is often called "metadata mapping" or "field mapping," and is related to "data mapping", and "semantic mapping". Crosswalks also have several technical capabilities. They help databases using different metadata schemes to share information. They help metadata harvesters create union catalogs. They enable search engines to search multiple databases simultaneously with a single query. == Challenges for crosswalks == One of the biggest challenges for crosswalks is that no two metadata schemes are 100% equivalent. One scheme may have a field that doesn't exist in another scheme or a field that is split into two different fields in another scheme; this is why data is often lost when mapping from a complex scheme to a simpler one. For example, when mapping from MARC to Simple Dublin Core, the distinction between types of titles is lost: Simple Dublin Core only has one "Title" element, so all of the different types of MARC titles get lumped together without further distinctions. A future attempt to convert the metadata back into MARC would enter the information in the basic MARC 245 Title Statement field, with none of the original distinctions. This is why crosswalks are said to be "lateral" (one-way) mappings from one scheme to another. Separate crosswalks would be required to map from scheme A to scheme B and from scheme B to scheme A. === Difficulties in mapping === Other mapping problems arise when: One scheme has one element that needs to be split up with different parts of it placed in multiple other elements in the second scheme ("one-to-many" mapping) One scheme allows an element to be repeated more than once while another only allows that element to appear once with multiple terms in it Schemes have different data formats (e.g. John Doe or Doe, John) An element in one scheme is indexed, but the equivalent element in the other scheme is not Schemes may use different controlled vocabularies Schemes change their standards over time Some of these problems are not fixable. As Karen Coyle says in "Crosswalking Citation Metadata: The University of California's Experience," "The more metadata experience we have, the more it becomes clear that metadata perfection is not attainable, and anyone who attempts it will be sorely disappointed. When metadata is crosswalked between two or more unrelated sources, there will be data elements that cannot be reconciled in an ideal manner. The key to a successful metadata crosswalk is intelligent flexibility. It is essential to focus on the important goals and be willing to compromise to reach a practical conclusion to projects."

  Read more →
• 

  Artificial intelligence of things

  Artificial Intelligence of Things (AIoT) is the combination of artificial intelligence (AI) technologies with the Internet of things (IoT) infrastructure to create systems capable of sensing, learning, and acting on data without continuous human intervention. While IoT focuses on connectivity and sensor data collection, AI enables IoT devices to analyse data in real time and produce actionable outputs, including automated decisions at the edge. == Applications == === Manufacturing and predictive maintenance === Manufacturing accounts for the largest share of AIoT adoption by industry vertical. A common application is predictive maintenance, where sensors measuring vibration, temperature, current draw, and acoustic emissions feed machine learning models trained to detect signatures that precede equipment failure. These systems can flag developing faults weeks or months in advance, and in more advanced deployments can autonomously adjust machine parameters such as motor speed or cooling cycles to delay or prevent failure. === Other industries === In healthcare, AIoT enables remote patient monitoring through wearable devices that collect vital signs and apply AI models to detect anomalies or predict deterioration. In logistics, GPS and telematics sensors combined with AI models support real-time route optimisation, vehicle maintenance prediction, and fuel cost forecasting. Smart building systems use occupancy, temperature, and energy sensors with AI to dynamically adjust HVAC and lighting, reducing energy consumption. == Architecture == AIoT systems typically operate across three layers: a device layer of sensors and actuators that collect data, a connectivity layer that transmits data via protocols such as MQTT or HTTP, and a compute layer where AI models process the data either in the cloud or at the edge. The trend toward edge-based processing, where inference runs on low-cost processors near the data source rather than in a centralised cloud, has accelerated as hardware costs have fallen and applications increasingly require sub-second response times. == Market == Market sizing estimates for AIoT vary significantly depending on scope and definition. Fortune Business Insights valued the AIoT market at USD 35.65 billion in 2023, projecting growth to USD 253.86 billion by 2030 at a compound annual growth rate of 32.4%. Grand View Research estimated the broader market at USD 171.4 billion in 2024 with a CAGR of 31.7% through 2030, reflecting a wider definition that includes AI-integrated hardware components. North America accounted for approximately 40% of global market share in 2024, with the Asia-Pacific region projected as the fastest-growing market.

  Read more →
• 

  Systematic review

  A systematic review is a scholarly synthesis of the evidence on a clearly presented topic using critical methods to identify, define and assess research on the topic. A systematic review extracts and interprets data from published studies on the topic (in the scientific literature), then analyzes, describes, critically appraises and summarizes interpretations into a refined evidence-based conclusion. For example, a systematic review of randomized controlled trials is a way of summarizing and implementing evidence-based medicine. Systematic reviews, sometimes along with meta-analyses, are generally considered the highest level of evidence in medical research. While a systematic review may be applied in the biomedical or health care context, it may also be used where an assessment of a precisely defined subject can advance understanding in a field of research. A systematic review may examine clinical tests, public health interventions, environmental interventions, social interventions, adverse effects, qualitative evidence syntheses, methodological reviews, policy reviews, and economic evaluations. Systematic reviews are closely related to meta-analyses, and often the same instance will combine both (being published with a subtitle of "a systematic review and meta-analysis"). The distinction between the two is that a meta-analysis uses statistical methods to induce a single number from the pooled data set (such as an effect size), whereas the strict definition of a systematic review excludes that step. However, in practice, when one is mentioned, the other may often be involved, as it takes a systematic review to assemble the information that a meta-analysis analyzes, and people sometimes refer to an instance as a systematic review, even if it includes the meta-analytical component. An understanding of systematic reviews and how to implement them in practice is common for professionals in health care, public health, and public policy. Systematic reviews contrast with a type of review often called a narrative review. Systematic reviews and narrative reviews both review the literature (the scientific literature), but the term literature review without further specification refers to a narrative review. == Characteristics == A systematic review can be designed to provide a thorough summary of current literature relevant to a research question. A systematic review uses a rigorous and transparent approach for research synthesis, with the aim of assessing and, where possible, minimizing bias in the findings. While many systematic reviews are based on an explicit quantitative meta-analysis of available data, there are also qualitative reviews and other types of mixed-methods reviews that adhere to standards for gathering, analyzing, and reporting evidence. Systematic reviews of quantitative data or mixed-method reviews sometimes use statistical techniques (meta-analysis) to combine results of eligible studies. Scoring levels are sometimes used to rate the quality of the evidence depending on the methodology used, although this is discouraged by the Cochrane Library. As evidence rating can be subjective, multiple people may be consulted to resolve any scoring differences between how evidence is rated. The EPPI-Centre, Cochrane, and the Joanna Briggs Institute have been influential in developing methods for combining both qualitative and quantitative research in systematic reviews. Several reporting guidelines exist to standardise reporting about how systematic reviews are conducted. Such reporting guidelines are not quality assessment or appraisal tools. The Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) statement suggests a standardized way to ensure a transparent and complete reporting of systematic reviews, and is now required for this kind of research by more than 170 medical journals worldwide. The latest version of this commonly used statement corresponds to PRISMA 2020 (the respective article was published in 2021). Several specialized PRISMA guideline extensions have been developed to support particular types of studies or aspects of the review process, including PRISMA-P for review protocols and PRISMA-ScR for scoping reviews. A list of PRISMA guideline extensions is hosted by the EQUATOR (Enhancing the QUAlity and Transparency Of health Research) Network. However, the PRISMA guidelines have been found to be limited to intervention research and the guidelines have to be changed in order to fit non-intervention research. As a result, Non-Interventional, Reproducible, and Open (NIRO) Systematic Reviews was created to counter this limitation. For qualitative reviews, reporting guidelines include ENTREQ (Enhancing transparency in reporting the synthesis of qualitative research) for qualitative evidence syntheses; RAMESES (Realist And MEta-narrative Evidence Syntheses: Evolving Standards) for meta-narrative and realist reviews; and eMERGe (Improving reporting of Meta-Ethnography) for meta-ethnograph. Developments in systematic reviews during the 21st century included realist reviews and the meta-narrative approach, both of which addressed problems of variation in methods and heterogeneity existing on some subjects. == Types == There are over 30 types of systematic review and Table 1 below non-exhaustingly summarises some of these. There is not always consensus on the boundaries and distinctions between the approaches described below. === Scoping reviews === Scoping reviews are distinct from systematic reviews in several ways. A scoping review is an attempt to search for concepts by mapping the language and data which surrounds those concepts and adjusting the search method iteratively to synthesize evidence and assess the scope of an area of inquiry. This can mean that the concept search and method (including data extraction, organisation and analysis) are refined throughout the process, sometimes requiring deviations from any protocol or original research plan. A scoping review may often be a preliminary stage before a systematic review, which 'scopes' out an area of inquiry and maps the language and key concepts to determine if a systematic review is possible or appropriate, or to lay the groundwork for a full systematic review. The goal can be to assess how much data or evidence is available regarding a certain area of interest. This process is further complicated if it is mapping concepts across multiple languages or cultures. As a scoping review should be systematically conducted and reported (with a transparent and repeatable method), some academic publishers categorize them as a kind of 'systematic review', which may cause confusion. Scoping reviews are helpful when it is not possible to carry out a systematic synthesis of research findings, for example, when there are no published clinical trials in the area of inquiry. Scoping reviews are helpful when determining if it is possible or appropriate to carry out a systematic review, and are a useful method when an area of inquiry is very broad, for example, exploring how the public are involved in all stages systematic reviews. There is still a lack of clarity when defining the exact method of a scoping review as it is both an iterative process and is still relatively new. There have been several attempts to improve the standardisation of the method, for example via a Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) guideline extension for scoping reviews (PRISMA-ScR). PROSPERO (the International Prospective Register of Systematic Reviews) does not permit the submission of protocols of scoping reviews, although some journals will publish protocols for scoping reviews. == Stages == While there are multiple kinds of systematic review methods, the main stages of a review can be summarised as follows: === Defining the research question === Some reported that the 'best practices' involve 'defining an answerable question' and publishing the protocol of the review before initiating it to reduce the risk of unplanned research duplication and to enable transparency and consistency between methodology and protocol. Clinical reviews of quantitative data are often structured using the mnemonic PICO, which stands for 'Population or Problem', 'Intervention or Exposure', 'Comparison', and 'Outcome', with other variations existing for other kinds of research. For qualitative reviews, PICo is 'Population or Problem', 'Interest', and 'Context'. === Searching for sources === Relevant criteria can include selecting research that is of good quality and answers the defined question. The search strategy should be designed to retrieve literature that matches the protocol's specified inclusion and exclusion criteria. The methodology section of a systematic review should list all of the databases and citation indices that were searched. The titles and abstracts of identified articles can be checked against predetermined criteria for eligibility and r

  Read more →
• 

  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

  Read more →
• 

  Mobile content management system

  A mobile content management system (MCMs) is a type of content management system (CMS) capable of storing and delivering content and services to mobile devices, such as mobile phones, smart phones, and PDAs. Mobile content management systems may be discrete systems, or may exist as features, modules or add-ons of larger content management systems capable of multi-channel content delivery. Mobile content delivery has unique, specific constraints including widely variable device capacities, small screen size, limitations on wireless bandwidth, sometimes small storage capacity, and (for some devices) comparatively weak device processors. Demand for mobile content management increased as mobile devices became increasingly ubiquitous and sophisticated. MCMS technology initially focused on the business to consumer (B2C) mobile market place with ringtones, games, text-messaging, news, and other related content. Since, mobile content management systems have also taken root in business-to-business (B2B) and business-to-employee (B2E) situations, allowing companies to provide more timely information and functionality to business partners and mobile workforces in an increasingly efficient manner. A 2008 estimate put global revenue for mobile content management at US$8 billion. == Key features == === Multi-channel content delivery === Multi-channel content delivery capabilities allow users not to manage a central content repository while simultaneously delivering that content to mobile devices such as mobile phones, smartphones, tablets and other mobile devices. Content can be stored in a raw format (such as Microsoft Word, Excel, PowerPoint, PDF, Text, HTML etc.) to which device-specific presentation styles can be applied. === Content access control === Access control includes authorization, authentication, access approval to each content. In many cases the access control also includes download control, wipe-out for specific user, time specific access. For the authentication, MCM shall have basic authentication which has user ID and password. For higher security many MCM supports IP authentication and mobile device authentication. === Specialized templating system === While traditional web content management systems handle templates for only a handful of web browsers, mobile CMS templates must be adapted to the very wide range of target devices with different capacities and limitations. There are two approaches to adapting templates: multi-client and multi-site. The multi-client approach makes it possible to see all versions of a site at the same domain (e.g. sitename.com), and templates are presented based on the device client used for viewing. The multi-site approach displays the mobile site on a targeted sub-domain (e.g. mobile.sitename.com). === Location-based content delivery === Location-based content delivery provides targeted content, such as information, advertisements, maps, directions, and news, to mobile devices based on current physical location. Currently, GPS (global positioning system) navigation systems offer the most popular location-based services. Navigation systems are specialized systems, but incorporating mobile phone functionality makes greater exploitation of location-aware content delivery possible.

  Read more →
• 

  AZFinText

  Arizona Financial Text System (AZFinText) is a textual-based quantitative financial prediction system written by Robert P. Schumaker of University of Texas at Tyler and Hsinchun Chen of the University of Arizona. == System == This system differs from other systems in that it uses financial text as one of its key means of predicting stock price movement. This reduces the information lag-time problem evident in many similar systems where new information must be transcribed (e.g., such as losing a costly court battle or having a product recall), before the quant can react appropriately. AZFinText overcomes these limitations by utilizing the terms used in financial news articles to predict future stock prices twenty minutes after the news article has been released. It is believed that certain article terms can move stocks more than others. Terms such as factory exploded or workers strike will have a depressing effect on stock prices whereas terms such as earnings rose will tend to increase stock prices. The AZFinText system analyzes financial news to identify the patterns in how investors react to such specific information. It uses methods like sentiment analysis and term weighting to examine the text of news articles. This system is designed to find price differences that occur when the market responds to news stories. This approach provides an alternative and easier method for predicting stock market movements. == Overview of research == The foundation of AZFinText can be found in the ACM TOIS article. Within this paper, the authors tested several different prediction models and linguistic textual representations. From this work, it was found that using the article terms and the price of the stock at the time the article was released was the most effective model and using proper nouns was the most effective textual representation technique. Combining the two, AZFinText netted a 2.84% trading return over the five-week study period. AZFinText was then extended to study what combination of peer organizations help to best train the system. Using the premise that IBM has more in common with Microsoft than GM, AZFinText studied the effect of varying peer-based training sets. To do this, AZFinText trained on the various levels of GICS and evaluated the results. It was found that sector-based training was most effective, netting an 8.50% trading return, outperforming Jim Cramer, Jim Jubak and DayTraders.com during the study period. AZFinText was also compared against the top 10 quantitative systems and outperformed 6 of them. A third study investigated the role of portfolio building in a textual financial prediction system. From this study, Momentum and Contrarian stock portfolios were created and tested. Using the premise that past winning stocks will continue to win and past losing stocks will continue to lose, AZFinText netted a 20.79% return during the study period. It was also noted that traders were generally overreacting to news events, creating the opportunity of abnormal returns. A fourth study looked into using author sentiment as an added predictive variable. Using the premise that an author can unwittingly influence market trades simply by the terms they use, AZFinText was tested using tone and polarity features. It was found that Contrarian activity was occurring within the market, where articles of a positive tone would decrease in price and articles of a negative tone would increase in price. A further study investigated what article verbs have the most influence on stock price movement. From this work, it was found that planted, announcing, front, smaller and crude had the highest positive impact on stock price. == Notable publicity == AZFinText has been the topic of discussion by numerous media outlets. Some of the more notable ones include The Wall Street Journal, MIT's Technology Review, Dow Jones Newswire, WBIR in Knoxville, TN, Slashdot and other media outlets.

  Read more →
• 

  March algorithm

  The March algorithm is a widely used algorithm that tests SRAM memory by filling all its entries test patterns. It carries out several passes through an SRAM checking the patterns and writing new patterns. The SRAM read and write operations performed on each pass are called a March element and each element is repeated for each entry. The March algorithm is often used to find functional faults in SRAM during testing such as: Stuck-at Faults (SAFs) Transition Faults (TFs) Address Decoder Faults (AFs) Coupling Faults (CFs), such as Inversion (CFin), Idempotent (CFid), and State (CFst) coupling faults It has been suggested to test SRAM modules using the algorithm before sale using a built-in self-test mechanism. == Notation == Each pass in a test sequence is represented by an "element". An element consists of a vertical arrow to indicate the direction in which the memory is scanned followed by a list of read/write operations to be applied to each memory cell. Multiple elements can be listed, separated by semicolons, to form a "test". For example, { ⇕ ( w 0 ) ; ⇑ ( r 0 , w 1 ) ; ⇓ ( r 1 , w 0 , r 0 ) } {\displaystyle \{\Updownarrow (w0);\Uparrow (r0,w1);\Downarrow (r1,w0,r0)\}} specifies to: Scan in both directions, writing 0. Scan from lowest to highest address, reading 0 and writing 1. Scan from highest to lowest address, reading 1, writing 0 and reading 0. == Variants == Many variants of the March algorithm exist with different sequences of tests. Each variant makes a different tradeoff between what faults it can detect and the complexity of the algorithm. Several variants have been given names:

  Read more →
• 

  Magic Quadrant

  Magic Quadrant (MQ) is a series of market research reports published by research and advisory firm Gartner that rely on proprietary qualitative data analysis methods to demonstrate market trends, such as direction, maturity, and participants. Their analyses are conducted for several specific technology industries and are updated every 1–2 years: once an updated report has been published, its predecessor is "retired". == Rating == Gartner rates vendors upon two criteria: completeness of vision and ability to execute. Completeness of vision – Reflects the vendor's innovation, and whether the vendor drives or follows the market. Ability to execute – Summarizes factors such as the vendor's financial viability, market responsiveness, product development, sales channels and customer base. The two component scores lead to a vendor position in one of four quadrants: === Leaders === Vendors in the "Leaders" quadrant have the highest composite scores for their completeness of vision and ability to execute. A vendor in the Leaders quadrant has the market share, credibility, and marketing & sales capabilities needed to drive the acceptance of new technologies. These vendors demonstrate a clear understanding of market needs, they are innovators and thought leaders, and they have well-articulated plans that customers and prospects can use when designing their infrastructures and strategies. In addition, they have a presence in the five major geographical regions, consistent financial performance, and broad platform support. === Challengers === Vendors in the "Challengers" quadrant have high scores mainly for their ability to execute. They both participate in the market and execute well enough to be a serious threat to vendors in the "Leaders" quadrant. They have strong products, as well as sufficiently credible market position and resources to sustain continued growth. Financial viability is not an issue for vendors in the "Challengers" quadrant, but they lack the size and influence of vendors in the "Leaders" quadrant due to their relative lack of vision. === Visionaries === Vendors in the "Visionaries" quadrant have high scores mainly for their completeness of vision. They deliver innovative products that address operationally or financially important end-user problems at a broad scale, but have not yet demonstrated the ability to capture market share or maintain sustainable levels of profitability. Visionary vendors are frequently privately held companies and acquisition targets for larger, established companies. The likelihood of acquisition often reduces the risks associated with installing their systems. === Niche Players === Vendors in the "Niche Players" quadrant have relatively low scores for both their ability to execute and their completeness of vision. They are often narrowly focused on specific market or vertical segments. This quadrant often also includes vendors that are adapting their existing products to enter the market under consideration, or larger vendors having difficulty developing and executing on their vision. == Gartner Critical Capabilities == Gartner Critical Capabilities complement Magic Quadrant analysis to offer deeper insight into the products and services offered by multiple vendors by a comparative analysis that scores competing products or services against a set of critical differentiators identified by Gartner. Gartner has periodically ended Magic Quadrant listings for IT Service Management, Web Content Management, and other industries as those markets have fully matured or other factors rendered the analytic framework inapplicable. == Criticism == The Magic Quadrant, and analysts in general, skew the market: according to research, by applying their methodologies to describe a market, they change that marketplace to fit their tools. Another criticism is that open source vendors are not considered sufficiently by analysts like Gartner, as has been published in an online discussion between a VP from Talend and a German Research VP from Gartner. On May 29, 2009 (2009-05-29), software vendor ZL Technologies filed a federal lawsuit against Gartner that challenged the "legitimacy" of Gartner's Magic Quadrant rating system. Gartner filed a motion to dismiss by claiming First Amendment protection since it contends that its MQ reports contain "pure opinion", which legally means opinions that are not based on fact. The court threw out the ZL case because it lacked a specific complaint. The decision was upheld on appeal.

  Read more →
• 

  Enterprise data planning

  Enterprise data planning is the starting point for enterprise wide change. It states the destination and describes how you will get there. It defines benefits, costs and potential risks. It provides measures to be used along the way to judge progress and adjust the journey according to changing circumstances. Data is fundamental to investment enterprises. Effective, economic management of data underpins operations and enables transformations needed to satisfy customer demands, competition and regulation. Data warehouse(s) and other aspects of the overall data architecture are critical to the enterprise. EDMworks has created a strategic data planning approach for the Investment Sector. It consists of a planning process, planning intranets, templates and training materials. EDMworks planning process is based on the belief that extensive domain knowledge significantly shortens planning iterations and enables progressively higher quality plans to be produced and implemented. This approach drives the development of an effective and economic enterprise data architecture. Enterprise data planning is based on proven business disciplines. Key architectural layers for data and applications are then added in order to provide an enterprise wide understanding of the uses and interdependencies of data. This enables the definition of the core components of the EDM plan: Industry structure and business objectives Assessment of systems and services Target architecture for applications, data and infrastructure Target organization structures Systems, database, infrastructure and organizational plans Business case, costs, benefits, results and risks. EDMworks uses several components from the Open Systems Group TOGAF enterprise systems planning process. TOGAF acts as an extension to good business planning methods to provide a framework for the development of the systems and data architectural components. == History == James Martin was one of the pathfinders in data planning methodologies. He was one of the first to identify data as being an enterprise wide asset that required management. He developed a series of tools and methods to support that process. Most of the large consulting firms developed their own methods to address the same basic issue. Frequently, their approaches were incorporated into their own branded system development methodologies that encompassed the complete systems development life-cycle. Others, such as Ed Tozer, developed more focused offerings that dealt with the complexities of extracting key business needs from senior management and then defining relevant architectural visions for the specific enterprise. From these various sources, the concepts of Business, Data, Applications and Technology Architectures emerged. The Open Group Architectural Framework (TOGAF) has taken this work forward and has established a sound method in TOGAF version 9. EDMworks approach is to adopt these planning and architectural practices as a basis and then add two additional dimensions to the planning and implementation focus: Domain knowledge of the Investments sector. Investments is a complex global industry with a common set of characteristics about clients, information vendors, competition and regulation. Domain knowledge significantly improves the quality of the planning and implementation processes Development of people and teams. Change is a major feature of in any Enterprise Data Management program and people and teams both need development in order to make EDM effective throughout an organization.

  Read more →
• 

  Behavior-based robotics

  Behavior-based robotics (BBR) or behavioral robotics is an approach in robotics that focuses on robots that are able to exhibit complex-appearing behaviors despite little internal variable state to model its immediate environment, mostly gradually correcting its actions via sensory-motor links. == Principles == Behavior-based robotics sets itself apart from traditional artificial intelligence by using biological systems as a model. Classic artificial intelligence typically uses a set of steps to solve problems, it follows a path based on internal representations of events compared to the behavior-based approach. Rather than use preset calculations to tackle a situation, behavior-based robotics relies on adaptability. This advancement has allowed behavior-based robotics to become commonplace in researching and data gathering. Most behavior-based systems are also reactive, which means they need no programming of what a chair looks like, or what kind of surface the robot is moving on. Instead, all the information is gleaned from the input of the robot's sensors. The robot uses that information to gradually correct its actions according to the changes in immediate environment. Behavior-based robots (BBR) usually show more biological-appearing actions than their computing-intensive counterparts, which are very deliberate in their actions. A BBR often makes mistakes, repeats actions, and appears confused, but can also show the anthropomorphic quality of tenacity. Comparisons between BBRs and insects are frequent because of these actions. BBRs are sometimes considered examples of weak artificial intelligence, although some have claimed they are models of all intelligence. == Features == Most behavior-based robots are programmed with a basic set of features to start them off. They are given a behavioral repertoire to work with dictating what behaviors to use and when, obstacle avoidance and battery charging can provide a foundation to help the robots learn and succeed. Rather than build world models, behavior-based robots simply react to their environment and problems within that environment. They draw upon internal knowledge learned from their past experiences combined with their basic behaviors to resolve problems. == History == The school of behavior-based robots owes much to work undertaken in the 1980s at the Massachusetts Institute of Technology by Rodney Brooks, who with students and colleagues built a series of wheeled and legged robots utilizing the subsumption architecture. Brooks' papers, often written with lighthearted titles such as "Planning is just a way of avoiding figuring out what to do next", the anthropomorphic qualities of his robots, and the relatively low cost of developing such robots, popularized the behavior-based approach. Brooks' work builds—whether by accident or not—on two prior milestones in the behavior-based approach. In the 1950s, W. Grey Walter, an English scientist with a background in neurological research, built a pair of vacuum tube-based robots that were exhibited at the 1951 Festival of Britain, and which have simple but effective behavior-based control systems. The second milestone is Valentino Braitenberg's 1984 book, "Vehicles – Experiments in Synthetic Psychology" (MIT Press). He describes a series of thought experiments demonstrating how simply wired sensor/motor connections can result in some complex-appearing behaviors such as fear and love. Later work in BBR is from the BEAM robotics community, which has built upon the work of Mark Tilden. Tilden was inspired by the reduction in the computational power needed for walking mechanisms from Brooks' experiments (which used one microcontroller for each leg), and further reduced the computational requirements to that of logic chips, transistor-based electronics, and analog circuit design. A different direction of development includes extensions of behavior-based robotics to multi-robot teams. The focus in this work is on developing simple generic mechanisms that result in coordinated group behavior, either implicitly or explicitly.

  Read more →
• 

  Algorithms and Combinatorics

  Algorithms and Combinatorics (ISSN 0937-5511) is a book series in mathematics, and particularly in combinatorics and the design and analysis of algorithms. It is published by Springer Science+Business Media, and was founded in 1987. == Books == The books published in this series include: The Simplex Method: A Probabilistic Analysis (Karl Heinz Borgwardt, 1987, vol. 1) Geometric Algorithms and Combinatorial Optimization (Martin Grötschel, László Lovász, and Alexander Schrijver, 1988, vol. 2; 2nd ed., 1993) Systems Analysis by Graphs and Matroids (Kazuo Murota, 1987, vol. 3) Greedoids (Bernhard Korte, László Lovász, and Rainer Schrader, 1991, vol. 4) Mathematics of Ramsey Theory (Jaroslav Nešetřil and Vojtěch Rödl, eds., 1990, vol. 5) Matroid Theory and its Applications in Electric Network Theory and in Statics (Andras Recszki, 1989, vol. 6) Irregularities of Partitions: Papers from the meeting held in Fertőd, July 7–11, 1986 (Gábor Halász and Vera T. Sós, eds., 1989, vol. 8) Paths, Flows, and VLSI-Layout: Papers from the meeting held at the University of Bonn, Bonn, June 20–July 1, 1988 (Bernhard Korte, László Lovász, Hans Jürgen Prömel, and Alexander Schrijver, eds., 1990, vol. 9) New Trends in Discrete and Computational Geometry (János Pach, ed., 1993, vol. 10) Discrete Images, Objects, and Functions in Z n {\displaystyle \mathbb {Z} ^{n}} (Klaus Voss, 1993, vol. 11) Linear Optimization and Extensions (Manfred Padberg, 1999, vol. 12) The Mathematics of Paul Erdős I (Ronald Graham and Jaroslav Nešetřil, eds., 1997, vol. 13) The Mathematics of Paul Erdős II (Ronald Graham and Jaroslav Nešetřil, eds., 1997, vol. 14) Geometry of Cuts and Metrics (Michel Deza and Monique Laurent, 1997, vol. 15) Probabilistic Methods for Algorithmic Discrete Mathematics (M. Habib, C. McDiarmid, J. Ramirez-Alfonsin, and B. Reed, 1998, vol. 16) Modern Cryptography, Probabilistic Proofs and Pseudorandomness (Oded Goldreich, 1999, vol. 17) Geometric Discrepancy: An Illustrated Guide (Jiří Matoušek, 1999, vol. 18) Applied Finite Group Actions (Adalbert Kerber, 1999, vol. 19) Matrices and Matroids for Systems Analysis (Kazuo Murota, 2000, vol. 20; corrected ed., 2010) Combinatorial Optimization (Bernhard Korte and Jens Vygen, 2000, vol. 21; 5th ed., 2012) The Strange Logic of Random Graphs (Joel Spencer, 2001, vol. 22) Graph Colouring and the Probabilistic Method (Michael Molloy and Bruce Reed, 2002, Vol. 23) Combinatorial Optimization: Polyhedra and Efficiency (Alexander Schrijver, 2003, vol. 24. In three volumes: A. Paths, flows, matchings; B. Matroids, trees, stable sets; C. Disjoint paths, hypergraphs) Discrete and Computational Geometry: The Goodman-Pollack Festschrift (B. Aronov, S. Basu, J. Pach, and M. Sharir, eds., 2003, vol. 25) Topics in Discrete Mathematics: Dedicated to Jarik Nešetril on the Occasion of his 60th birthday (M. Klazar, J. Kratochvíl, M. Loebl, J. Matoušek, R. Thomas, and P. Valtr, eds., 2006, vol. 26) Boolean Function Complexity: Advances and Frontiers (Stasys Jukna, 2012, Vol. 27) Sparsity: Graphs, Structures, and Algorithms (Jaroslav Nešetřil and Patrice Ossona de Mendez, 2012, vol. 28) Optimal Interconnection Trees in the Plane (Marcus Brazil and Martin Zachariasen, 2015, vol. 29) Combinatorics and Complexity of Partition Functions (Alexander Barvinok, 2016, vol. 30)

  Read more →
• 

  In-place algorithm

  In computer science, an in-place algorithm is an algorithm that operates directly on the input data structure without requiring extra space proportional to the input size. In other words, it modifies the input in place, without creating a separate copy of the data structure. An algorithm which is not in-place is sometimes called not-in-place or out-of-place. In-place can have slightly different meanings. In its strictest form, the algorithm can only have a constant amount of extra space, counting everything including function calls and pointers. However, this form is very limited as simply having an index to a length n array requires O(log n) bits. More broadly, in-place means that the algorithm does not use extra space for manipulating the input but may require a small though non-constant extra space for its operation. Usually, this space is O(log n), though sometimes anything in o(n) is allowed. Note that space complexity also has varied choices in whether or not to count the index lengths as part of the space used. Often, the space complexity is given in terms of the number of indices or pointers needed, ignoring their length. In this article, we refer to total space complexity (DSPACE), counting pointer lengths. Therefore, the space requirements here have an extra log n factor compared to an analysis that ignores the lengths of indices and pointers. An algorithm may or may not count the output as part of its space usage. Since in-place algorithms usually overwrite their input with output, no additional space is needed. When writing the output to write-only memory or a stream, it may be more appropriate to only consider the working space of the algorithm. In theoretical applications such as log-space reductions, it is more typical to always ignore output space (in these cases it is more essential that the output is write-only). == Examples == Given an array a of n items, suppose we want an array that holds the same elements in reversed order and to dispose of the original. One seemingly simple way to do this is to create a new array of equal size, fill it with copies from a in the appropriate order and then delete a. function reverse(a[0..n - 1]) allocate b[0..n - 1] for i from 0 to n - 1 b[n − 1 − i] := a[i] return b Unfortunately, this requires O(n) extra space for having the arrays a and b available simultaneously. Also, allocation and deallocation are often slow operations. Since we no longer need a, we can instead overwrite it with its own reversal using this in-place algorithm which will only need constant number (2) of integers for the auxiliary variables i and tmp, no matter how large the array is. function reverse_in_place(a[0..n-1]) for i from 0 to floor((n-2)/2) tmp := a[i] a[i] := a[n − 1 − i] a[n − 1 − i] := tmp As another example, many sorting algorithms rearrange arrays into sorted order in-place, including: bubble sort, comb sort, selection sort, insertion sort, heapsort, and Shell sort. These algorithms require only a few pointers, so their space complexity is O(log n). Quicksort operates in-place on the data to be sorted. However, quicksort requires O(log n) stack space pointers to keep track of the subarrays in its divide and conquer strategy. Consequently, quicksort needs O(log2 n) additional space. Although this non-constant space technically takes quicksort out of the in-place category, quicksort and other algorithms needing only O(log n) additional pointers are usually considered in-place algorithms. Most selection algorithms are also in-place, although some considerably rearrange the input array in the process of finding the final, constant-sized result. Some text manipulation algorithms such as trim and reverse may be done in-place. == In computational complexity == In computational complexity theory, the strict definition of in-place algorithms includes all algorithms with O(1) space complexity, the class DSPACE(1). This class is very limited; it equals the regular languages. In fact, it does not even include any of the examples listed above. Algorithms are usually considered in L, the class of problems requiring O(log n) additional space, to be in-place. This class is more in line with the practical definition, as it allows numbers of size n as pointers or indices. This expanded definition still excludes quicksort, however, because of its recursive calls. Identifying the in-place algorithms with L has some interesting implications; for example, it means that there is a (rather complex) in-place algorithm to determine whether a path exists between two nodes in an undirected graph, a problem that requires O(n) extra space using typical algorithms such as depth-first search (a visited bit for each node). This in turn yields in-place algorithms for problems such as determining if a graph is bipartite or testing whether two graphs have the same number of connected components. == Role of randomness == In many cases, the space requirements of an algorithm can be drastically cut by using a randomized algorithm. For example, if one wishes to know if two vertices in a graph of n vertices are in the same connected component of the graph, there is no known simple, deterministic, in-place algorithm to determine this. However, if we simply start at one vertex and perform a random walk of about 20n3 steps, the chance that we will stumble across the other vertex provided that it is in the same component is very high. Similarly, there are simple randomized in-place algorithms for primality testing such as the Miller–Rabin primality test, and there are also simple in-place randomized factoring algorithms such as Pollard's rho algorithm. == In functional programming == Functional programming languages often discourage or do not support explicit in-place algorithms that overwrite data, since this is a type of side effect; instead, they only allow new data to be constructed. However, good functional language compilers will often recognize when an object very similar to an existing one is created and then the old one is thrown away, and will optimize this into a simple mutation "under the hood". Note that it is possible in principle to carefully construct in-place algorithms that do not modify data (unless the data is no longer being used), but this is rarely done in practice.

  Read more →