In machine learning, the term tensor informally refers to two different concepts: (i) a way of organizing data and (ii) a multilinear (tensor) transformation. Data may be organized in a multidimensional array (M-way array), informally referred to as a "data tensor"; however, in the strict mathematical sense, a tensor is a multilinear mapping over a set of domain vector spaces to a range vector space. Observations, such as images, movies, volumes, sounds, and relationships among words and concepts, stored in an M-way array ("data tensor"), may be analyzed either by artificial neural networks or tensor methods. Tensor decomposition factors data tensors into smaller tensors. Operations on data tensors can be expressed in terms of matrix multiplication and the Kronecker product. The computation of gradients, a crucial aspect of backpropagation, can be performed using software libraries such as PyTorch and TensorFlow. Computations are often performed on graphics processing units (GPUs) using CUDA, and on dedicated hardware such as Google's Tensor Processing Unit or Nvidia's Tensor core. These developments have greatly accelerated neural network architectures, and increased the size and complexity of models that can be trained. == History == A tensor is by definition a multilinear map. In mathematics, this may express a multilinear relationship between sets of algebraic objects. In physics, tensor fields, considered as tensors at each point in space, are useful in expressing mechanics such as stress or elasticity. In machine learning, the exact use of tensors depends on the statistical approach being used. In 2001, the field of signal processing and statistics were making use of tensor methods. Pierre Comon surveys the early adoption of tensor methods in the fields of telecommunications, radio surveillance, chemometrics and sensor processing. Linear tensor rank methods (such as, Parafac/CANDECOMP) analyzed M-way arrays ("data tensors") composed of higher order statistics that were employed in blind source separation problems to compute a linear model of the data. He noted several early limitations in determining the tensor rank and efficient tensor rank decomposition. In the early 2000s, multilinear tensor methods crossed over into computer vision, computer graphics and machine learning with papers by Vasilescu or in collaboration with Terzopoulos, such as Human Motion Signatures, TensorFaces TensorTextures and Multilinear Projection. Multilinear algebra, the algebra of higher-order tensors, is a suitable and transparent framework for analyzing the multifactor structure of an ensemble of observations and for addressing the difficult problem of disentangling the causal factors based on second order or higher order statistics associated with each causal factor. Tensor (multilinear) factor analysis disentangles and reduces the influence of different causal factors with multilinear subspace learning. When treating an image or a video as a 2- or 3-way array, i.e., "data matrix/tensor", tensor methods reduce spatial or time redundancies as demonstrated by Wang and Ahuja. Yoshua Bengio, Geoff Hinton and their collaborators briefly discuss the relationship between deep neural networks and tensor factor analysis beyond the use of M-way arrays ("data tensors") as inputs. One of the early uses of tensors for neural networks appeared in natural language processing. A single word can be expressed as a vector via Word2vec. Thus a relationship between two words can be encoded in a matrix. However, for more complex relationships such as subject-object-verb, it is necessary to build higher-dimensional networks. In 2009, the work of Sutskever introduced Bayesian Clustered Tensor Factorization to model relational concepts while reducing the parameter space. From 2014 to 2015, tensor methods become more common in convolutional neural networks (CNNs). Tensor methods organize neural network weights in a "data tensor", analyze and reduce the number of neural network weights. Lebedev et al. accelerated CNN networks for character classification (the recognition of letters and digits in images) by using 4D kernel tensors. == Definition == Let F {\displaystyle \mathbb {F} } be a field (such as the real numbers R {\displaystyle \mathbb {R} } or the complex numbers C {\displaystyle \mathbb {C} } ). A tensor T ∈ F I 1 × I 2 × … × I C {\displaystyle {\mathcal {T}}\in {\mathbb {F} }^{I_{1}\times I_{2}\times \ldots \times I_{C}}} is a multilinear transformation from a set of domain vector spaces to a range vector space: T : { F I 1 × F I 2 × … F I C } ↦ F I 0 {\displaystyle {\mathcal {T}}:\{{\mathbb {F} }^{I_{1}}\times {\mathbb {F} }^{I_{2}}\times \ldots {\mathbb {F} }^{I_{C}}\}\mapsto {\mathbb {F} }^{I_{0}}} Here, C {\displaystyle C} and I 0 , I 1 , … , I C {\displaystyle I_{0},I_{1},\ldots ,I_{C}} are positive integers, and ( C + 1 ) {\displaystyle (C+1)} is the number of modes of a tensor (also known as the number of ways of a multi-way array). The dimensionality of mode c {\displaystyle c} is I c {\displaystyle I_{c}} , for 0 ≤ c ≤ C {\displaystyle 0\leq c\leq C} . In statistics and machine learning, an image is vectorized when viewed as a single observation, and a collection of vectorized images is organized as a "data tensor". For example, a set of facial images { d i p , i e , i l , i v ∈ R I X } {\displaystyle \{{\mathbb {d} }_{i_{p},i_{e},i_{l},i_{v}}\in {\mathbb {R} }^{I_{X}}\}} with I X {\displaystyle I_{X}} pixels that are the consequences of multiple causal factors, such as a facial geometry i p ( 1 ≤ i p ≤ I P ) {\displaystyle i_{p}(1\leq i_{p}\leq I_{P})} , an expression i e ( 1 ≤ i e ≤ I E ) {\displaystyle i_{e}(1\leq i_{e}\leq I_{E})} , an illumination condition i l ( 1 ≤ i l ≤ I L ) {\displaystyle i_{l}(1\leq i_{l}\leq I_{L})} , and a viewing condition i v ( 1 ≤ i v ≤ I V ) {\displaystyle i_{v}(1\leq i_{v}\leq I_{V})} may be organized into a data tensor (ie. multiway array) D ∈ R I X × I P × I E × I L × V {\displaystyle {\mathcal {D}}\in {\mathbb {R} }^{I_{X}\times I_{P}\times I_{E}\times I_{L}\times V}} where I P {\displaystyle I_{P}} are the total number of facial geometries, I E {\displaystyle I_{E}} are the total number of expressions, I L {\displaystyle I_{L}} are the total number of illumination conditions, and I V {\displaystyle I_{V}} are the total number of viewing conditions. Tensor factorizations methods such as TensorFaces and multilinear (tensor) independent component analysis factorizes the data tensor into a set of vector spaces that span the causal factor representations, where an image is the result of tensor transformation T {\displaystyle {\mathcal {T}}} that maps a set of causal factor representations to the pixel space. Another approach to using tensors in machine learning is to embed various data types directly. For example, a grayscale image, commonly represented as a discrete 2-way array D ∈ R I R X × I C X {\displaystyle {\mathbf {D} }\in {\mathbb {R} }^{I_{RX}\times I_{CX}}} with dimensionality I R X × I C X {\displaystyle I_{RX}\times I_{CX}} where I R X {\displaystyle I_{RX}} are the number of rows and I C X {\displaystyle I_{CX}} are the number of columns. When an image is treated as 2-way array or 2nd order tensor (i.e. as a collection of column/row observations), tensor factorization methods compute the image column space, the image row space and the normalized PCA coefficients or the ICA coefficients. Similarly, a color image with RGB channels, D ∈ R N × M × 3 . {\displaystyle {\mathcal {D}}\in \mathbb {R} ^{N\times M\times 3}.} may be viewed as a 3rd order data tensor or 3-way array.-------- In natural language processing, a word might be expressed as a vector v {\displaystyle v} via the Word2vec algorithm. Thus v {\displaystyle v} becomes a mode-1 tensor v ↦ A ∈ R N . {\displaystyle v\mapsto {\mathcal {A}}\in \mathbb {R} ^{N}.} The embedding of subject-object-verb semantics requires embedding relationships among three words. Because a word is itself a vector, subject-object-verb semantics could be expressed using mode-3 tensors v a × v b × v c ↦ A ∈ R N × N × N . {\displaystyle v_{a}\times v_{b}\times v_{c}\mapsto {\mathcal {A}}\in \mathbb {R} ^{N\times N\times N}.} In practice the neural network designer is primarily concerned with the specification of embeddings, the connection of tensor layers, and the operations performed on them in a network. Modern machine learning frameworks manage the optimization, tensor factorization and backpropagation automatically. === As unit values === Tensors may be used as the unit values of neural networks which extend the concept of scalar, vector and matrix values to multiple dimensions. The output value of single layer unit y m {\displaystyle y_{m}} is the sum-product of its input units and the connection weights filtered through the activation function f {\displaystyle f} : y m = f ( ∑ n x n u m , n ) , {\displaystyle y_{m}=f\left(\sum _{n}x_{n}u_{m,n}\right),} where y m ∈ R .
IRows
iRows was a web-based spreadsheet in beta with a GUI similar to the traditional desktop-based spreadsheet applications, such as Microsoft Excel and OpenOffice.org. It was shut down on December 31, 2006, after it was announced that its two founders had been hired by Google. iRows used Ajax and XML. It was described as an example of a Web 2.0 system. iRows supported conventional spreadsheet features functions, value formatting and charts and added web oriented spreadsheet capabilities like collaboration (multiple people using a shared spreadsheet, sending a spreadsheet as a link instead of an attachment and ability to publish spreadsheets on other web pages (e.g. blogs).
UI data binding
UI data binding is a software design pattern to simplify development of GUI applications. UI data binding binds UI elements to an application domain model. Most frameworks employ the Observer pattern as the underlying binding mechanism. To work efficiently, UI data binding has to address input validation and data type mapping. A bound control is a widget whose value is tied or bound to a field in a recordset (e.g., a column in a row of a table). Changes made to data within the control are automatically saved to the database when the control's exit event triggers. == Example == == Data binding frameworks and tools == === Delphi === DSharp third-party data binding tool OpenWire Visual Live Binding - third-party visual data binding tool === Java === JFace Data Binding JavaFX Property === .NET === Windows Forms data binding overview WPF data binding overview Avalonia Unity 3D data binding framework (available in modifications for NGUI, iGUI and EZGUI libraries) === JavaScript === Angular AngularJS Backbone.js Ember.js Datum.js knockout.js Meteor, via its Blaze live update engine OpenUI5 React Vue.js
Algorithmic Puzzles
Algorithmic Puzzles is a book of puzzles based on computational thinking. It was written by computer scientists Anany and Maria Levitin, and published in 2011 by Oxford University Press. == Topics == The book begins with a "tutorial" introducing classical algorithm design techniques including backtracking, divide-and-conquer algorithms, and dynamic programming, methods for the analysis of algorithms, and their application in example puzzles. The puzzles themselves are grouped into three sets of 50 puzzles, in increasing order of difficulty. A final two chapters provide brief hints and more detailed solutions to the puzzles, with the solutions forming the majority of pages of the book. Some of the puzzles are well known classics, some are variations of known puzzles making them more algorithmic, and some are new. They include: Puzzles involving chessboards, including the eight queens puzzle, knight's tours, and the mutilated chessboard problem Balance puzzles River crossing puzzles The Tower of Hanoi Finding the missing element in a data stream The geometric median problem for Manhattan distance == Audience and reception == The puzzles in the book cover a wide range of difficulty, and in general do not require more than a high school level of mathematical background. William Gasarch notes that grouping the puzzles only by their difficulty and not by their themes is actually an advantage, as it provides readers with fewer clues about their solutions. Reviewer Narayanan Narayanan recommends the book to any puzzle aficionado, or to anyone who wants to develop their powers of algorithmic thinking. Reviewer Martin Griffiths suggests another group of readers, schoolteachers and university instructors in search of examples to illustrate the power of algorithmic thinking. Gasarch recommends the book to any computer scientist, evaluating it as "a delight".
Chinese speech synthesis
Chinese speech synthesis is the application of speech synthesis to the Chinese language (usually Standard Chinese). It poses additional difficulties due to Chinese characters frequently having different pronunciations in different contexts and the complex prosody, which is essential to convey the meaning of words, and sometimes the difficulty in obtaining agreement among native speakers concerning what the correct pronunciation is of certain phonemes. == Concatenation (Ekho and KeyTip) == Recordings can be concatenated in any desired combination, but the joins sound forced (as is usual for simple concatenation-based speech synthesis) and this can severely affect prosody; these synthesizers are also inflexible in terms of speed and expression. However, because these synthesizers do not rely on a corpus, there is no noticeable degradation in performance when they are given more unusual or awkward phrases. Ekho is an open source TTS which simply concatenates sampled syllables. It currently supports Cantonese, Mandarin, and experimentally Korean. Some of the Mandarin syllables have been pitched-normalised in Praat. A modified version of these is used in Gradint's "synthesis from partials". cjkware.com used to ship a product called KeyTip Putonghua Reader which worked similarly; it contained 120 Megabytes of sound recordings (GSM-compressed to 40 Megabytes in the evaluation version), comprising 10,000 multi-syllable dictionary words plus single-syllable recordings in 6 different prosodies (4 tones, neutral tone, and an extra third-tone recording for use at the end of a phrase). == Lightweight synthesizers (eSpeak and Yuet) == The lightweight open-source speech project eSpeak, which has its own approach to synthesis, has experimented with Mandarin and Cantonese. eSpeak was used by Google Translate from May 2010 until December 2010. The commercial product "Yuet" is also lightweight (it is intended to be suitable for resource-constrained environments like embedded systems); it was written from scratch in ANSI C starting from 2013. Yuet claims a built-in NLP model that does not require a separate dictionary; the speech synthesised by the engine claims clear word boundaries and emphasis on appropriate words. Communication with its author is required to obtain a copy. Both eSpeak and Yuet can synthesis speech for Cantonese and Mandarin from the same input text, and can output the corresponding romanisation (for Cantonese, Yuet uses Yale and eSpeak uses Jyutping; both use Pinyin for Mandarin). eSpeak does not concern itself with word boundaries when these don't change the question of which syllable should be spoken. == Corpus-based == A "corpus-based" approach can sound very natural in most cases but can err in dealing with unusual phrases if they can't be matched with the corpus. The synthesiser engine is typically very large (hundreds or even thousands of megabytes) due to the size of the corpus. === iFlyTek === Anhui USTC iFlyTek Co., Ltd (iFlyTek) published a W3C paper in which they adapted Speech Synthesis Markup Language to produce a mark-up language called Chinese Speech Synthesis Markup Language (CSSML) which can include additional markup to clarify the pronunciation of characters and to add some prosody information. The amount of data involved is not disclosed by iFlyTek but can be seen from the commercial products that iFlyTek have licensed their technology to; for example, Bider's SpeechPlus is a 1.3 Gigabyte download, 1.2 Gigabytes of which is used for the highly compressed data for a single Chinese voice. iFlyTek's synthesiser can also synthesise mixed Chinese and English text with the same voice (e.g. Chinese sentences containing some English words); they claim their English synthesis to be "average". The iFlyTek corpus appears to be heavily dependent on Chinese characters, and it is not possible to synthesize from pinyin alone. It is sometimes possible by means of CSSML to add pinyin to the characters to disambiguate between multiple possible pronunciations, but this does not always work. === NeoSpeech === There is an online interactive demonstration for NeoSpeech speech synthesis, which accepts Chinese characters and also pinyin if it's enclosed in their proprietary "VTML" markup. === Mac OS === Mac OS had Chinese speech synthesizers available up to version 9. This was removed in 10.0 and reinstated in 10.7 (Lion). === Historical corpus-based synthesizers (no longer available) === A corpus-based approach was taken by Tsinghua University in SinoSonic, with the Harbin dialect voice data taking 800 Megabytes. This was planned to be offered as a download but the link was never activated. Nowadays, only references to it can be found on Internet Archive. Bell Labs' approach, which was demonstrated online in 1997 but subsequently removed, was described in a monograph "Multilingual Text-to-Speech Synthesis: The Bell Labs Approach" (Springer, October 31, 1997, ISBN 978-0-7923-8027-6), and the former employee who was responsible for the project, Chilin Shih (who subsequently worked at the University of Illinois) put some notes about her methods on her website.
Attempto Controlled English
Attempto Controlled English (ACE) is a controlled natural language, i.e. a subset of standard English with a restricted syntax and restricted semantics described by a small set of construction and interpretation rules. It has been under development at the University of Zurich since 1995. In 2013, ACE version 6.7 was announced. ACE can serve as knowledge representation, specification, and query language, and is intended for professionals who want to use formal notations and formal methods, but may not be familiar with them. Though ACE appears perfectly natural—it can be read and understood by any speaker of English—it is in fact a formal language. ACE and its related tools have been used in the fields of software specifications, theorem proving, proof assistants, text summaries, ontologies, rules, querying, medical documentation and planning. Here are some simple examples: Every woman is a human. A woman is a human. A man tries-on a new tie. If the tie pleases his wife then the man buys it. ACE construction rules require that each noun be introduced by a determiner (a, every, no, some, at least 5, ...). Regarding the list of examples above, ACE interpretation rules decide that (1) is interpreted as universally quantified, while (2) is interpreted as existentially quantified. Sentences like "Women are human" do not follow ACE syntax and are consequently not valid. Interpretation rules resolve the anaphoric references in (3): the tie and it of the second sentence refer to a new tie of the first sentence, while his and the man of the second sentence refer to a man of the first sentence. Thus an ACE text is a coherent entity of anaphorically linked sentences. The Attempto Parsing Engine (APE) translates ACE texts unambiguously into discourse representation structures (DRS) that use a variant of the language of first-order logic. A DRS can be further translated into other formal languages, for instance AceRules with various semantics, OWL, and SWRL. Translating an ACE text into (a fragment of) first-order logic allows users to reason about the text, for instance to verify, to validate, and to query it. == Overview == As an overview of the current version 6.6 of ACE this section: Briefly describes the vocabulary Gives an account of the syntax Summarises the handling of ambiguity Explains the processing of anaphoric references. === Vocabulary === The vocabulary of ACE comprises: Predefined function words (e.g. determiners, conjunctions) Predefined phrases (e.g. "it is false that ...", "it is possible that ...") Content words (e.g. nouns, verbs, adjectives, adverbs). === Grammar === The grammar of ACE defines and constrains the form and the meaning of ACE sentences and texts. ACE's grammar is expressed as a set of construction rules. The meaning of sentences is described as a small set of interpretation rules. A Troubleshooting Guide describes how to use ACE and how to avoid pitfalls. ==== ACE texts ==== An ACE text is a sequence of declarative sentences that can be anaphorically interrelated. Furthermore, ACE supports questions and commands. ==== Simple sentences ==== A simple sentence asserts that something is the case—a fact, an event, a state. The temperature is −2 °C. A customer inserts 2 cards. A card and a code are valid. Simple ACE sentences have the following general structure: subject + verb + complements + adjuncts Every sentence has a subject and a verb. Complements (direct and indirect objects) are necessary for transitive verbs (insert something) and ditransitive verbs (give something to somebody), whereas adjuncts (adverbs, prepositional phrases) are optional. All elements of a simple sentence can be elaborated upon to describe the situation in more detail. To further specify the nouns customer and card, we could add adjectives: A trusted customer inserts two valid cards. possessive nouns and of-prepositional phrases: John's customer inserts a card of Mary. or variables as appositions: John inserts a card A. Other modifications of nouns are possible through relative sentences: A customer who is trusted inserts a card that he owns. which are described below since they make a sentence composite. We can also detail the insertion event, e.g. by adding an adverb: A customer inserts some cards manually. or, equivalently: A customer manually inserts some cards. or, by adding prepositional phrases: A customer inserts some cards into a slot. We can combine all of these elaborations to arrive at: John's customer who is trusted inserts a valid card of Mary manually into a slot A. ==== Composite sentences ==== Composite sentences are recursively built from simpler sentences through coordination, subordination, quantification, and negation. Note that ACE composite sentences overlap with what linguists call compound sentences and complex sentences. ===== Coordination ===== Coordination by and is possible between sentences and between phrases of the same syntactic type. A customer inserts a card and the machine checks the code. There is a customer who inserts a card and who enters a code. A customer inserts a card and enters a code. An old and trusted customer enters a card and a code. Note that the coordination of the noun phrases a card and a code represents a plural object. Coordination by or is possible between sentences, verb phrases, and relative clauses. A customer inserts a card or the machine checks the code. A customer inserts a card or enters a code. A customer owns a card that is invalid or that is damaged. Coordination by and and or is governed by the standard binding order of logic, i.e. and binds stronger than or. Commas can be used to override the standard binding order. Thus the sentence: A customer inserts a VisaCard or inserts a MasterCard, and inserts a code. means that the customer inserts a VisaCard and a code, or alternatively a MasterCard and a code. ===== Subordination ===== There are four constructs of subordination: relative sentences, if-then sentences, modality, and sentence subordination. Relative sentences starting with who, which, and that allow to add detail to nouns: A customer who is trusted inserts a card that he owns. With the help of if-then sentences we can specify conditional or hypothetical situations: If a card is valid then a customer inserts it. Note the anaphoric reference via the pronoun it in the then-part to the noun phrase a card in the if-part. Modality allows us to express possibility and necessity: A trusted customer can/must insert a card. It is possible/necessary that a trusted customer inserts a card. Sentence subordination comes in various forms: It is true/false that a customer inserts a card. It is not provable that a customer inserts a card. A clerk believes that a customer inserts a card. ===== Quantification ===== Quantification allows us to speak about all objects of a certain class (universal quantification), or to denote explicitly the existence of at least one object of this class (existential quantification). The textual occurrence of a universal or existential quantifier opens its scope that extends to the end of the sentence, or in coordinations to the end of the respective coordinated sentence. To express that all involved customers insert cards we can write Every customer inserts a card. This sentence means that each customer inserts a card that may, or may not, be the same as the one inserted by another customer. To specify that all customers insert the same card—however unrealistic that situation seems—we can write: A card is inserted by every customer. or, equivalently: There is a card that every customer inserts. To state that every card is inserted by a customer we write: Every card is inserted by a customer. or, somewhat indirectly: For every card there is a customer who inserts it. ===== Negation ===== Negation allows us to express that something is not the case: A customer does not insert a card. A card is not valid. To negate something for all objects of a certain class one uses no: No customer inserts more than 2 cards. or, there is no: There is no customer who inserts a card. To negate a complete statement one uses sentence negation: It is false that a customer inserts a card. These forms of negation are logical negations, i.e. they state that something is provably not the case. Negation as failure states that a state of affairs cannot be proved, i.e. there is no information whether the state of affairs is the case or not. It is not provable that a customer inserts a card. ==== Queries ==== ACE supports two forms of queries: yes/no-queries and wh-queries. Yes/no-queries ask for the existence or non-existence of a specified situation. If we specified: A customer inserts a card. then we can ask: Does a customer insert a card? to get a positive answer. Note that interrogative sentences always end with a question mark. With the help of wh-queries, i.e. queries with query words, we can interrogate a text for details of the specified situation. If we specified: A
Operational historian
In manufacturing, an operational historian is a time-series database application that is developed for operational process data. Historian software is often embedded or used in conjunction with standard DCS and PLC control systems to provide enhanced data capture, validation, compression, and aggregation capabilities. Historians have been deployed in almost every industry and contribute to functions such as supervisory control, performance monitoring, quality assurance, and, more recently, machine learning applications which can learn from vast quantities of historical data. These systems were originally developed to capture instrumentation and control data, which led many to use the term "tag" for a stream of process data, referring to the physical "tags" which had been placed on instrumentation for manually capturing data. Raw data may be accessed via OPC HDA, SQL, or REST API interfaces. == Operational Support == Operational historians are typically used within the manufacturing facility by engineers and operators for supervisory functions and analysis. An operational historian will typically capture all instrumentation and control data, whereas an enterprise historian that is deployed to support business functions will capture only a subset of the plant data. Typically, these applications offer data access through dedicated APIs (Application Programming Interfaces) and SDKs (Software Development Kits) which offer high-performance read and write operations. These operate through vendor-specific or custom applications. Front-end tools for trending process data over time are the most common interfaces to these databases. Because these applications are typically deployed next to or near the source of their process data, they are often marketed and sold as 'real-time database systems.' This distinction varies among vendors, who often have to make tradeoffs in performance between data capture and presentation, and application and analysis functionality. The following is a list of typical challenges for operational historians: data collection from instrumentation and controls storage and archiving of very large volumes of data organization of data in the form of "tags" or "points" limiting of monitoring (alarms) and validation aggregation and interpolation manual data entry (MDE) == Data access == As opposed to enterprise historians, the data access layer in the operational historian is designed to offer sophisticated data fetching modes without complex information analysis facilities. The following settings are typically available for data access operations: Data scope (single point or tag, history based on time range, history based on sample count) Request modes (raw data, last-known value, aggregation, interpolation) Sampling (single point, all points without sampling, all points with interval sampling) Data omission (based on the sample quality, based on the sample value, based on the count) Even though the operational historians are rarely relational database management systems, they often offer SQL-based interfaces to query the database. In most of such implementations, the dialect does not follow the SQL standard in order to provide syntax for specifying data access operations parameters.