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"Cardinality-Union and intersection-If A and B are disjoint sets, then |A\u222aB|=|A|+|B|.\nFrom this, one can show that in general, the cardinalities of unions and intersections are related by the following equation: |C\u222aD|+|C\u2229D|=|C|+|D|."
large_corpus_distillation
of information by a protocol to the network should be intentional, performed with the agreement of both recipient and sender, authenticated to the degree possible and necessary, only acted upon to the degree of its trustworthiness, and minimised and provided to a minimum number of entities.Active use of extension point...
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"Actor model-Message-passing semantics-Actor creation plus addresses in messages means variable topology A natural development of the actor model was to allow addresses in messages. Influenced by packet switched networks [1961 and 1964], Hewitt proposed the development of a new model of concurrent computation in which ...
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"Hash function-Properties-Variable range In many applications, the range of hash values may be different for each run of the program or may change along the same run (for instance, when a hash table needs to be expanded). In those situations, one needs a hash function which takes two parameters\u2014the input data z, a...
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"X Toolkit Intrinsics-X Toolkit Intrinsics-X Toolkit Intrinsics (also known as Xt, for X toolkit) is a library that implements an API to facilitate the development of programs with a graphical user interface (GUI) for the X Window System. It can be used in the C or C++ languages.\nThe low-level library Xlib is the clie...
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"Aitken's delta-squared process-Example pseudocode for Aitken extrapolation-This pseudo code also computes the Aitken approximation to f\u2032(\u03b1) . The Aitken extrapolates will be denoted by aitkenX. During the computation of the extrapolate, it is important to check if the denominator becomes too small, which co...
large_corpus_distillation
"Trait (computer programming)-Rationale-In object-oriented programming, behavior is sometimes shared between classes which are not related to each other. For example, many unrelated classes may have methods to serialize objects to JSON. Historically, there have been several approaches to solve this without duplicating ...
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"PDP-14-Hardware-JMR \u2013 JuMp to RETURN from a subroutine, to ADDRESS+1 of the most recent JMS.effectively, in modern terminology, JMS pushed the current instruction address onto a \"stack\"and JMR popped the return address.In effect, JMR is actually a specific TRR in which PC2 is transferred to PC1. SKP \u2013 SKi...
large_corpus_distillation
"Lottery wheeling-Purpose-If the lottery is pick 6, then a wheeling system can be used in playing with 7 or more numbers. If the lottery is pick 5, then a wheeling system can be used in playing with 6 or more numbers. For example, in a pick 5 lottery, a lottery system can have 9 numbers and a guarantee of 3 if 3, meani...
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thresholds, let J be the smallest value of n for which either\nS n \u2265\u03b1 or S n \u2264\u03b2. Let {S n \u2217;n\u22651} be the stopped random walk; i.e., S n \u2217=S n for n\u2264J and S n \u2217=S J for n>J. Let\n\u03c0\u2217\ni\n=Pr{S\nJ\n=i}.\na) Consider a Markov chain in which this stopped random walk is r...
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that implies that the orbit length is a divisor of the group order."
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performed the best in classifying humous clay and peat, while the Decision Trees performed the best in classifying clayey peat. The classification by this method is able to reach very high accuracy, even for the most complex problem, its accuracy was 83%, and the incorrectly classified class was a geologically neighbou...
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"K-means clustering-Algorithms-Standard algorithm (naive k-means) The most common algorithm uses an iterative refinement technique. Due to its ubiquity, it is often called \"the k-means algorithm\"; it is also referred to as Lloyd's algorithm, particularly in the computer science community. It is sometimes also referre...
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"HAL (software)-Rationale-Traditionally, the operating system kernel was responsible for providing an abstract interface to the hardware the system ran on. Applications used the system call interface, or performed file I/O on device nodes in order to communicate with hardware through these abstractions. This sufficed f...
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"Branch (computer science)-Improving performance by reducing stalls from branches-Several techniques improve speed by reducing stalls from conditional branches."
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"Upstream (software development)-Examples-A patch sent upstream is offered to the original authors or maintainers of the software. If accepted, the authors or maintainers will include the patch in their software, either immediately or in a future release. If rejected, the person who submitted the patch will have to mai...
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"Principles of Model Checking-Synopsis-The introduction and first chapter outline the field of model checking: a model of a machine or process can be analysed to see if desirable properties hold. For instance, a vending machine might satisfy the property \"the balance can never fall below \u20ac0,00\". A video game mig...
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"Content validity-Measurement-One widely used method of measuring content validity was developed by C. H. Lawshe. It is essentially a method for gauging agreement among raters or judges regarding how essential a particular item is. In an article regarding pre-employment testing, Lawshe (1975) proposed that each of the...
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"Traitor tracing-Traitor tracing-Traitor tracing schemes are ineffective if the traitor rebroadcasts the entire (decrypted) original content."
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fee to 0.3% on consumer credit cards, and 0.2% on debit cards.Merchants are also required to lease or purchase processing equipment, in some cases, this equipment is provided free of charge by the processor. Merchants must also satisfy data security compliance standards which are highly technical and complicated. In ma...
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the store or area.\nIf the reception procedure takes several stages, or if additional waiting time is necessary before the provision of the service can be concluded, it should be possible to place visitors on hold for subsequent treatment."
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remains in their system for 48 hours or until they molt (shed)."
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"Glossary of computer science-B-Boolean algebra In mathematics and mathematical logic, the branch of algebra in which the values of the variables are the truth values true and false, usually denoted 1 and 0, respectively. Contrary to elementary algebra, where the values of the variables are numbers and the prime operat...
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if implemented, will result in 8\u201312 bytes per code point (about 10 bytes in average), namely for BMP, each code point will occupy exactly 6 bytes more than the same code in quoted-printable/UTF-16. Base64/UTF-32 gets 5+1\u20443 bytes for any code point.\nAn ASCII control character under quoted-printable or UTF-7 m...
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"Multiple subset sum-Multiple knapsack problem-The knapsack problem is a special case of MKP in which m=1.\nThe subset-sum problem is a special case of MKP in which both the value of each item equals its weight, and m=1.The MKP has a Polynomial-time approximation scheme."
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"Segment descriptor-Structure-The x86 and x86-64 segment descriptor has the following form: Where the fields stand for: Base Address Starting memory address of the segment. Its length is 32 bits and it is created from the lower part bits 16 to 31, and the upper part bits 0 to 7, followed by bits 24 to 31."
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"Structured encryption-Description-STE schemes with a variety of leakage profiles have been designed for a wide array of abstract data types and data structures including arrays, multi-maps, dictionaries and graphs.STE is closely related to but different than searchable symmetric encryption. The purpose of SSE is to en...
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"Edge recombination operator-Algorithm-Then, to create a path K, the following algorithm is employed: algorithm ero is let K be the empty list let N be the first node of a random parent."
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"Fundamental theorem on homomorphisms-Fundamental theorem on homomorphisms-In abstract algebra, the fundamental theorem on homomorphisms, also known as the fundamental homomorphism theorem, or the first isomorphism theorem, relates the structure of two objects between which a homomorphism is given, and of the kernel an...
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"MapReduce-Logical view-As another example, imagine that for a database of 1.1 billion people, one would like to compute the average number of social contacts a person has according to age. In SQL, such a query could be expressed as: Using MapReduce, the K1 key values could be the integers 1 through 1100, each represen...
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where inspecting differences between versions is essential."
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separate lists to better organize them and easily send an email to all the members of that list.\nAbility to export contact lists to file Calendar It is now possible to copy and paste events between the various days of the calendar.\nFiles New Quick Actions on a file allow the user to convert an image to another format...
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"Extraposition-Clause bound-A further widely acknowledged fact about extraposition is that it is clause-bound. This aspect of extraposition is known as the Right Roof Constraint. There is a \"right roof\" above which extraposition cannot occur. In other words, extraposition cannot occur out of an embedded clause: a. Th...
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"Hybrid electric vehicle-Technology-Diesel The most prominent example of a full hybrid diesel system is the HYbrid4 by PSA Peugeot-Citro\u00ebn. It was discontinued in 2016, following the decline in diesel popularity following the VW Dieselgate scandal."
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"Laser cutting-Machine configurations-Five and six-axis machines also permit cutting formed workpieces. In addition, there are various methods of orienting the laser beam to a shaped workpiece, maintaining a proper focus distance and nozzle standoff, etc.\nPulsing Pulsed lasers which provide a high-power burst of energ...
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"Process (computing)-History-Programs consist of sequences of instructions for processors. A single processor can run only one instruction at a time: it is impossible to run more programs at the same time. A program might need some resource, such as an input device, which has a large delay, or a program might start som...
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"P-adic number-Modular properties-The quotient ring Zp/pnZp may be identified with the ring Z/pnZ of the integers modulo pn.\nThis can be shown by remarking that every p-adic integer, represented by its normalized p-adic series, is congruent modulo pn with its partial sum {\\textstyle \\sum _{i=0}^{n-1}a_{i}p^{i},...
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could also be solved in polynomial time, and one would have P = NP. As of 2017 it is generally conjectured that P \u2260 NP, with the practical implication that the worst cases of NP problems are intrinsically difficult to solve, i.e., take longer than any reasonable time span (decades!) for interesting lengths of inpu...
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"Key size-Effect of quantum computing attacks on key strength-Mainstream symmetric ciphers (such as AES or Twofish) and collision resistant hash functions (such as SHA) are widely conjectured to offer greater security against known quantum computing attacks. They are widely thought most vulnerable to Grover's algorithm...
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"Stream processing-Comparison to prior parallel paradigms-As the computing needs of the world evolved, the amount of data to be managed increased very quickly. It was obvious that the sequential programming model could not cope with the increased need for processing power. Various efforts have been spent on finding alt...
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"Coding conventions-Software maintenance-Even for the original author, consistently coded software eases maintainability. There is no guarantee that an individual will remember the precise rationale for why a particular piece of code was written in a certain way long after the code was originally written. Coding conven...
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"Kraft\u2013McMillan inequality-Kraft\u2013McMillan inequality-In coding theory, the Kraft\u2013McMillan inequality gives a necessary and sufficient condition for the existence of a prefix code (in Leon G. Kraft's version) or a uniquely decodable code (in Brockway McMillan's version) for a given set of codeword lengths...
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"Runtime error detection-Runtime error detection-Runtime error detection can identify defects that manifest themselves only at runtime (for example, file overwrites) and zeroing in on the root causes of the application crashing, running slowly, or behaving unpredictably. Defects commonly detected by runtime error detec...
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"Interlock protocol-How it works-The Interlock protocol works roughly as follows: Alice encrypts her message with Bob's key, then sends half her encrypted message to Bob.\nBob encrypts his message with Alice's key and sends half of his encrypted message to Alice."
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"Construction grammar-Concepts-The semantic meaning of a grammatical construction is made up of conceptual structures postulated in cognitive semantics: image-schemas, frames, conceptual metaphors, conceptual metonymies, prototypes of various kinds, mental spaces, and bindings across these (called \"blends\"). Pragmati...
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"Encryption software-Classification-Symmetric key ciphers can be further divided into stream ciphers and block ciphers. Stream ciphers typically encrypt plaintext a bit or byte at a time, and are most commonly used to encrypt real-time communications, such as audio and video information. The key is used to establish th...
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"Average absolute deviation-Measures of dispersion-The term \"average absolute deviation\" does not uniquely identify a measure of statistical dispersion, as there are several measures that can be used to measure absolute deviations, and there are several measures of central tendency that can be used as well. Thus, to ...
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"Canonical commutation relation-The Weyl relations-It is important to note that for technical reasons, the Weyl relations are not strictly equivalent to the canonical commutation relation [x^,p^]=i\u210f . If x^ and p^ were bounded operators, then a special case of the Baker\u2013Campbell\u2013Hausdorff formula woul...
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"Grammatical relation-Defining the grammatical relations-This third strategy is tacitly preferred by most work in theoretical syntax. All those theories of syntax that avoid providing concrete definitions of the grammatical relations but yet reference them often are (perhaps unknowingly) pursuing an approach in terms o...
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"Half-precision floating-point format-IEEE 754 half-precision binary floating-point format: binary16-The IEEE 754 standard specifies a binary16 as having the following format: Sign bit: 1 bit Exponent width: 5 bits Significand precision: 11 bits (10 explicitly stored)The format is laid out as follows: The format is ass...
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trading rule. This intends to increase the robustness of the model and its ability to adapt to changing market circumstances.To avoid overfitting (or curve-fitting) to historical data - and unlike many other techniques used in trading software such as optimizing of trading rules by repeated backtesting, genetic algorit...
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criticism holds that this model can explain the Dunning\u2013Kruger effect only when the self-assessment is measured relative to one's peer group. But it may fail when it is measured relative to absolute standards."
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"Polling (computer science)-Description-Polling has the disadvantage that if there are too many devices to check, the time required to poll them can exceed the time available to service the I/O device.\nAlgorithm Polling can be described in the following steps: Host actions: The host repeatedly reads the busy bit of th...
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"Jaccard index-Tanimoto similarity and distance-Various forms of functions described as Tanimoto similarity and Tanimoto distance occur in the literature and on the Internet. Most of these are synonyms for Jaccard similarity and Jaccard distance, but some are mathematically different. Many sources cite an IBM Technical...
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"Theory of descriptions-Criticism of Russell's analysis-Keith Donnellan According to Keith Donnellan, there are two distinct ways we may use a definite description such as \"the current Emperor of Kentucky is gray\", and thus makes his distinction between the referential and the attributive use of a definite descriptio...
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"Garden-path sentence-Parsing-Serial parsing is where the reader makes one interpretation of the ambiguity and continues to parse the sentence in the context of that interpretation. The reader will continue to use the initial interpretation as reference for future parsing until disambiguating information is given.Paral...
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"UTF-16-Description-Examples To encode U+10437 (\ud801\udc37) to UTF-16: Subtract 0x10000 from the code point, leaving 0x0437.\nFor the high surrogate, shift right by 10 (divide by 0x400), then add 0xD800, resulting in 0x0001 + 0xD800 = 0xD801.\nFor the low surrogate, take the low 10 bits (remainder of dividing by 0x40...
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"Reduced instruction set computer-Characteristics and design philosophy-Yet another impetus of both RISC and other designs came from practical measurements on real-world programs. Andrew Tanenbaum summed up many of these, demonstrating that processors often had oversized immediates. For instance, he showed that 98% of ...
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"Matrix ring-Properties-The matrix ring Mn(R) is commutative if and only if n = 0, R = 0, or R is commutative and n = 1. In fact, this is true also for the subring of upper triangular matrices. Here is an example showing two upper triangular 2 \u00d7 2 matrices that do not commute, assuming 1 \u2260 0: [1000][1100]=[11...
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"Reservation ALOHA-Reservation ALOHA-ALOHAnet became operational in June 1971, providing the first public demonstration of a wireless packet data network.ALOHA was subsequently employed in the Ethernet cable based network in the 1970s, and following regulatory developments in the early 1980s it became possible to use t...
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"Normal number-Properties and examples-The set of non-normal numbers, despite being \"large\" in the sense of being uncountable, is also a null set (as its Lebesgue measure as a subset of the real numbers is zero, so it essentially takes up no space within the real numbers). Also, the non-normal numbers (as well as the...
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"Web Ontology Language-Terminology-Example Let's call human the class of all humans in the world is a subclass of owl:thing. The class of all women (say woman) in the world is a subclass of human.\nThen we have owl:Nothing woman human owl:Thing The membership of some individual to a class could be noted ClassAssertion...
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"Fril-Prolog and Fril comparison-Syntax Prolog has a syntax with a typical amount of punctuation, whereas Fril has an extremely simple syntax similar to that of Lisp. A (propositional) clause is a list consisting of a predicate followed by its arguments (if any). Among the types of top-level constructs are rules and di...
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"Surrogate alcohol-Common surrogate alcohols-Many alcoholic liquids contain alcohol but are not meant to be ingested in the same way as alcoholic beverages. Typical surrogate alcohols include: Hand sanitizer Mouthwash Aftershave or cologne Cooking wine Cleaning fluids such as Windex Extracts Charcoal lighter fluid Rubb...
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"Software testing-Testing types, techniques and tactics-Property testing libraries allow the user to control the strategy by which random inputs are constructed, to ensure coverage of degenerate cases, or inputs featuring specific patterns that are needed to fully exercise aspects of the implementation under test.\nPro...
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"Xtend-Semantics-Instead of using the imperative for-loop, one could use a functional style lambda expression in square brackets and call the higher-order function forEach in extension syntax on the list: Note that the lambda's parameter, if not specified, is called it, which can be skipped like this in Java. Its type ...
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[present participial after present indicative]) [\u0280\u026at\u0361\u026c\u02bc\u0251k\u02bce\u0280\u026at\u02b0\u0251b\u025bl\u025bh\u028ab\u0251\u026c\u028al\u0251] re tla ke re thabele ho ba hlola ('we will definitely be happy to defeat them' [present-future subjunctive after future indicative]) Group V contains se...
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"Algebraic number field-Examples-The Gaussian rationals, denoted Q(i) (read as \" Q adjoined i \"), form the first (historically) non-trivial example of a number field. Its elements are elements of the form where both a and b are rational numbers and i is the imaginary unit. Such expressions may be added, subtracted,...
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"Electronic business-Concerns-Digital signatures A final way to secure information online would be to use a digital signature. If a document has a digital signature on it, no one else is able to edit the information without being detected. That way if it is edited, it may be adjusted for reliability after the fact. In ...
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theory, and value/equality. Bruno Nettl has noted as recently as 2003 that comparative study seems to have fallen in and out of style, noting that although it can supply conclusions about the organization of musicological data, reflections on history or the nature of music as a cultural artifact, or understanding some ...
large_corpus_distillation
"Page table-Page table-A page table is the data structure used by a virtual memory system in a computer operating system to store the mapping between virtual addresses and physical addresses. Virtual addresses are used by the program executed by the accessing process, while physical addresses are used by the hardware, ...
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or more simply (q\u222bR|g(y)|qdy)1/q\u2264(p\u222bR|f(x)|pdx)1/p."
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"Madryga-The algorithm-The key schedule is very simple. To start with, the entire key is XORed with a random constant of the same length as the key, then rotated to the left by 3 bits. It is rotated again after each iteration of rotation and XOR. The rightmost byte of it is used in each iteration to XOR with the rightm...
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is not indifferent to\nthe measure we use. Mirror descent accomplishes this.\n2.4.1 Bregman Projections\nDefinition: If k\u00b7k is some norm on IRd, then k\u00b7k is its dual norm.\n\u2217\nExample: If dual norm of the \u2113 norm k\u00b7k is the \u2113 norm k\u00b7k , then 1 + 1 = 1. This is the\np p q q p q\nlimitin...
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"Complexity class-Properties of complexity classes-Completeness If a problem X is hard for C and is also in C, then X is said to be complete for C. This means that X is the hardest problem in C (since there could be many problems that are equally hard, more precisely X is as hard as the hardest problems in C). Of ...
large_corpus_distillation
"Zipping (computer science)-In programming languages-Zip functions are often available in programming languages, often referred to as zip. In Lisp-dialects one can simply map the desired function over the desired lists, map is variadic in Lisp so it can take an arbitrary number of lists as argument. An example from Clo...
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"Multiplication algorithm-Computational complexity of multiplication-A line of research in theoretical computer science is about the number of single-bit arithmetic operations necessary to multiply two n -bit integers. This is known as the computational complexity of multiplication. Usual algorithms done by hand have ...
large_corpus_distillation
When the income (or wealth) distribution is given as a continuous probability density function p(x), the Gini coefficient is again half of the relative mean absolute difference: G=12\u03bc\u222b\u2212\u221e\u221e\u222b\u2212\u221e\u221ep(x)p(y)|x\u2212y|dxdy where \u03bc=\u222b\u2212\u221e\u221exp(x)dx is the mean of ...
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"Multi-stage continuous integration-Recommended practices-Recommended practice #2 For multi-stage continuous integration, each team must have its own branch."
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"Birthday problem-Calculating the probability-From a permutations perspective, let the event A be the probability of finding a group of 23 people without any repeated birthdays. Where the event B is the probability of finding a group of 23 people with at least two people sharing same birthday, P(B) = 1 \u2212 P(A). P(A...
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"Lempel\u2013Ziv\u2013Markov chain algorithm-Compression algorithm details-To find matches of length N or higher, a search is started using the N-sized hash table, and continued using the hash chain array; the search stop after a pre-defined number of hash chain nodes has been traversed, or when the hash chains \"wraps...
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"Jordan normal form-Generalized eigenvectors-A proof We give a proof by induction that any complex-valued square matrix A may be put in Jordan normal form. Since the underlying vector space can be shown to be the direct sum of invariant subspaces associated with the eigenvalues, A can be assumed to have just one eigenv...
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"14.R: Chapter 14 Review Exercises\nFor the following exercises, determine whether the statement is true or false. Justify your answer with a proof or a\ncounterexample.\n1. The domain of f(x,y)=x3arcsin(y) is {(x,y)|x\u2208R and \u2212\u03c0\u2264y\u2264\u03c0}.\n2. If the function f(x,y) is continuous everywhere, the...
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representation in terms of indicator variables. The exchangeable property is an important tool in this section.\nE(I )= 1 j\u2208{1,2,\u2026,n}\nj n for .\nProof\nX D j P(I =1)=P(X =x)= 1\nj is uniformly distributed on n for each so j j n .\nE(N )=1 n\nn for each\nProof\nThis follows from the previous result and basic ...
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(6) use the encryption key to authenticate the StingRay to the service provider as being the target device, and (7) forward signals between the target device and the legitimate cell site while decrypting and recording communications content."
large_corpus_distillation
"XOR gate-Alternatives-An XOR gate circuit can be made from four NAND gates. In fact, both NAND and NOR gates are so-called \"universal gates\" and any logical function can be constructed from either NAND logic or NOR logic alone. If the four NAND gates are replaced by NOR gates, this results in an XNOR gate, which can...
large_corpus_distillation
"Polyalphabetic cipher-History-The work of Al-Qalqashandi (1355\u20131418), based on the earlier work of Ibn al-Durayhim (1312\u20131359), contained the first published discussion of the substitution and transposition of ciphers, as well as the first description of a polyalphabetic cipher, in which each plaintext lette...
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for all v.\nThen E=\u03bc(K), the group of all roots of unity of K.\nIn particular it is finite and cyclic.Proof. All roots of unity of K have absolute value 1 so \u03bc(K)\u2282E.\nFor converse note that Lemma 1 with c=C=1 and any P implies E is finite. Moreover E\u2282E(P) for each finite set of places P\u...
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"193 (number)-In mathematics-193 is the number of compositions of 14 into distinct parts. In decimal, it is the seventeenth full repetend prime, or long prime."
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"Cryptanalysis-Asymmetric ciphers-Asymmetric cryptography (or public-key cryptography) is cryptography that relies on using two (mathematically related) keys; one private, and one public. Such ciphers invariably rely on \"hard\" mathematical problems as the basis of their security, so an obvious point of attack is to d...
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"Online machine learning-Statistical view of online learning-As an example, consider the case of online least squares linear regression. Here, the weight vectors come from the convex set S=Rd , and nature sends back the convex loss function vt(w)=(\u27e8w,xt\u27e9\u2212yt)2 . Note here that yt is implicitly sent wit...
large_corpus_distillation
"6.867 Machine learning, lecture 17 (Jaakkola) 6\na)\n1\nx\nx 3\nb)\n1\nx\nx 3\nc)\n1\nx\nx 3\n2 x x 4 2 x x 4 2 x x 4\nd) 1 2 3 4\nFigure 2: a-c) successive merging of clusters in a hierarchical clustering algorithm and d)\nthe resulting cluster hierarchy.\nIt is often a good idea to normalize the documents so they ha...
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to predicting exam scores for students\nin a particular year (we didn\u2019t assume that all the students had the same type). We also\nmake the same assumption about user types, i.e., that the type is sampled from the \u201cbag\u201d\nfor each rating, resulting potentially in different types for different movies. Since...
large_corpus_distillation
"Substitution cipher-Types-The book cipher is a type of homophonic cipher, one example being the Beale ciphers. This is a story of buried treasure that was described in 1819\u201321 by use of a ciphered text that was keyed to the Declaration of Independence. Here each ciphertext character was represented by a number. T...
large_corpus_distillation
"Canadian online media-Types of online media-News and magazines As information is increasingly going digital, the Newspaper Audience Databank (NADbank) claims online readership for most Canadian newspapers have surpassed the numbers in print readership. However, there is also lack of evidence that newspapers are coming...
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but the life calculation is based on an industry standard when calculating actual life. See the Hoists Manufacturers Institute site for true life calculation, which is based on load and hours used. In today's modern world for the North American market, there are a few governing bodies for the industry. The Overhead All...
large_corpus_distillation
"Secure access service edge-Characteristics-SASE principal elements are: Convergence of WAN and network security functions.\nA cloud-native architecture delivering converged WAN and security as a service that offers the scalability, elasticity, adaptability and self-healing typical of all cloud services.\nGlobally dist...
large_corpus_distillation
"C syntax-Control structures-A function returns to its caller by the return statement. When return is followed by an expression, the value is returned to the caller as the value of the function. Encountering the end of the function is equivalent to a return with no expression. In that case, if the function is declared ...
large_corpus_distillation
on injective modules below.\nIn a commutative Noetherian ring, there are only finitely many minimal prime ideals. Also, the descending chain condition holds on prime ideals.\nIn a commutative Noetherian domain R, every element can be factorized into irreducible elements (in short, R is a factorization domain). Thus, if...
large_corpus_distillation
function calls, whereas modern versions of the Windows API support thousands. However, in general, the interface remained fairly consistent, and an old Windows 1.0 application will still look familiar to a programmer who is used to the modern Windows API.Microsoft has made an effort to maintain backward compatibility. ...
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