AI Chatbot Rankings

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

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  Wavelet noise

  Wavelet noise is an alternative to Perlin noise which reduces the problems of aliasing and detail loss that are encountered when Perlin noise is summed into a fractal. == Algorithm detail == The basic algorithm for 2-dimensional wavelet noise is as follows: Create an image, R {\displaystyle R} , filled with uniform white noise. Downsample R {\displaystyle R} to half-size to create R ↓ {\displaystyle R^{\downarrow }} , then upsample it back up to full size to create R ↓↑ {\displaystyle R^{\downarrow \uparrow }} . Subtract R ↓↑ {\displaystyle R^{\downarrow \uparrow }} from R {\displaystyle R} to create the end result, N {\displaystyle N} . This results in an image that contains all the information that cannot be represented at half-scale. From here, N {\displaystyle N} can be used similarly to Perlin noise to create fractal patterns.

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  Upper ontology

  In information science, an upper ontology (also known as a top-level ontology, upper model, or foundation ontology) is an ontology (in the sense used in information science) that consists of very general terms (such as "object", "property", "relation") that are common across all domains. An important function of an upper ontology is to support broad semantic interoperability among a large number of domain-specific ontologies by providing a common starting point for the formulation of definitions. Terms in the domain ontology are ranked under the terms in the upper ontology, e.g., the upper ontology classes are superclasses or supersets of all the classes in the domain ontologies. A number of upper ontologies have been proposed, each with its own proponents. Library classification systems predate upper ontology systems. Though library classifications organize and categorize knowledge using general concepts that are the same across all knowledge domains, neither system is a replacement for the other. == Development == Any standard foundational ontology is likely to be contested among different groups, each with its own idea of "what exists". One factor exacerbating the failure to arrive at a common approach has been the lack of open-source applications that would permit the testing of different ontologies in the same computational environment. The differences have thus been debated largely on theoretical grounds, or are merely the result of personal preferences. Foundational ontologies can however be compared on the basis of adoption for the purposes of supporting interoperability across domain ontologies. No particular upper ontology has yet gained widespread acceptance as a de facto standard. Different organizations have attempted to define standards for specific domains. The 'Process Specification Language' (PSL) created by the National Institute of Standards and Technology (NIST) is one example. Another important factor leading to the absence of wide adoption of any existing upper ontology is the complexity. Some upper ontologies—Cyc is often cited as an example in this regard—are very large, ranging up to thousands of elements (classes, relations), with complex interactions among them and with a complexity similar to that of a human natural language, and the learning process can be even longer than for a natural language because of the unfamiliar format and logical rules. The motivation to overcome this learning barrier is largely absent because of the paucity of publicly accessible examples of use. As a result, those building domain ontologies for local applications tend to create the simplest possible domain-specific ontology, not related to any upper ontology. Such domain ontologies may function adequately for the local purpose, but they are very time-consuming to relate accurately to other domain ontologies. To solve this problem, some genuinely top level ontologies have been developed, which are deliberately designed to have minimal overlap with any domain ontologies. Examples are Basic Formal Ontology and the DOLCE (see below). === Arguments for the infeasibility of an upper ontology === Historically, many attempts in many societies have been made to impose or define a single set of concepts as more primal, basic, foundational, authoritative, true or rational than all others. A common objection to such attempts points out that humans lack the sort of transcendent perspective — or God's eye view — that would be required to achieve this goal. Humans are bound by language or culture, and so lack the sort of objective perspective from which to observe the whole terrain of concepts and derive any one standard. Thomasson, under the headline "1.5 Skepticism about Category Systems", wrote: "category systems, at least as traditionally presented, seem to presuppose that there is a unique true answer to the question of what categories of entity there are – indeed the discovery of this answer is the goal of most such inquiries into ontological categories. [...] But actual category systems offered vary so much that even a short survey of past category systems like that above can undermine the belief that such a unique, true and complete system of categories may be found. Given such a diversity of answers to the question of what the ontological categories are, by what criteria could we possibly choose among them to determine which is uniquely correct?" Another objection is the problem of formulating definitions. Top level ontologies are designed to maximize support for interoperability across a large number of terms. Such ontologies must therefore consist of terms expressing very general concepts, but such concepts are so basic to our understanding that there is no way in which they can be defined, since the very process of definition implies that a less basic (and less well understood) concept is defined in terms of concepts that are more basic and so (ideally) more well understood. Very general concepts can often only be elucidated, for example by means of examples, or paraphrase. There is no self-evident way of dividing the world up into concepts, and certainly no non-controversial one There is no neutral ground that can serve as a means of translating between specialized (or "lower" or "application-specific") ontologies Human language itself is already an arbitrary approximation of just one among many possible conceptual maps. To draw any necessary correlation between English words and any number of intellectual concepts, that we might like to represent in our ontologies, is just asking for trouble. (WordNet, for instance, is successful and useful, precisely because it does not pretend to be a general-purpose upper ontology; rather, it is a tool for semantic / syntactic / linguistic disambiguation, which is richly embedded in the particulars and peculiarities of the English language.) Any hierarchical or topological representation of concepts must begin from some ontological, epistemological, linguistic, cultural, and ultimately pragmatic perspective. Such pragmatism does not allow for the exclusion of politics between persons or groups, indeed it requires they be considered as perhaps more basic primitives than any that are represented. Those who doubt the feasibility of general purpose ontologies are more inclined to ask "what specific purpose do we have in mind for this conceptual map of entities and what practical difference will this ontology make?" This pragmatic philosophical position surrenders all hope of devising the encoded ontology version of "The world is everything that is the case." (Wittgenstein, Tractatus Logico-Philosophicus). Finally, there are objections similar to those against artificial intelligence. Technically, the complex concept acquisition and the social / linguistic interactions of human beings suggest any axiomatic foundation of "most basic" concepts must be cognitive biological or otherwise difficult to characterize since we don't have axioms for such systems. Ethically, any general-purpose ontology could quickly become an actual tyranny by recruiting adherents into a political program designed to propagate it and its funding means, and possibly defend it by violence. Historically, inconsistent and irrational belief systems have proven capable of commanding obedience to the detriment or harm of persons both inside and outside a society that accepts them. How much more harmful would a consistent rational one be, were it to contain even one or two basic assumptions incompatible with human life? === Arguments for the feasibility of an upper ontology === Many of those who doubt the possibility of developing wide agreement on a common upper ontology fall into one of two traps: they assert that there is no possibility of universal agreement on any conceptual scheme; but they argue that a practical common ontology does not need to have universal agreement, it only needs a large enough user community (as is the case for human languages) to make it profitable for developers to use it as a means to general interoperability, and for third-party developer to develop utilities to make it easier to use; and they point out that developers of data schemes find different representations congenial for their local purposes; but they do not demonstrate that these different representations are in fact logically inconsistent. In fact, different representations of assertions about the real world (though not philosophical models), if they accurately reflect the world, must be logically consistent, even if they focus on different aspects of the same physical object or phenomenon. If any two assertions about the real world are logically inconsistent, one or both must be wrong, and that is a topic for experimental investigation, not for ontological representation. In practice, representations of the real world are created as and known to be approximations to the basic reality, and their use is circumscribed by the limits of e

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  Ecoinformatics

  Ecoinformatics, or ecological informatics, is the science of information in ecology and environmental science. It integrates environmental and information sciences to define entities and natural processes with language common to both humans and computers. However, this is a rapidly developing area in ecology and there are alternative perspectives on what constitutes ecoinformatics. A few definitions have been circulating, mostly centered on the creation of tools to access and analyze natural system data. However, the scope and aims of ecoinformatics are certainly broader than the development of metadata standards to be used in documenting datasets. Ecoinformatics aims to facilitate environmental research and management by developing ways to access, integrate databases of environmental information, and develop new algorithms enabling different environmental datasets to be combined to test ecological hypotheses. Ecoinformatics is related to the concept of ecosystem services. Ecoinformatics characterize the semantics of natural system knowledge. For this reason, much of today's ecoinformatics research relates to the branch of computer science known as knowledge representation, and active ecoinformatics projects are developing links to activities such as the Semantic Web. Current initiatives to effectively manage, share, and reuse ecological data are indicative of the increasing importance of fields like ecoinformatics to develop the foundations for effectively managing ecological information. Examples of these initiatives are National Science Foundation Datanet projects, DataONE, Data Conservancy, and Artificial Intelligence for Environment & Sustainability. == Software Development Lifecycle == Central to the concept of ecoinformatics is the Software Development Lifecycle (SDLC), a systematic framework for writing, implementing, and maintaining software products. Typically in Ecoinformatics projects, the development pipeline includes data collection, usually from several different environmental data sources, then integrating these data sources together, and then analyzing the data. Here, each step of the SDLC is described in the context of ecoinformatics, per Michener et al. It is important to note that the plan, collect, assure, describes and preserve steps refer to the data collection entity, which can be individual researchers or large data-collection networks, while the discover, integrate, and analyze steps typically refer to the individual researcher. Plan: Ecoinformatics projects require data from several databases. Each database holds different data, and therefore researchers should identify what types of environmental or ecological data they will need to answer their research question. Collect: Data is collected in several different ways. In ecoinformatics, this is usually restricted to manually entering data into a spreadsheet, and parsing data from an existing database. The growth of relational databases has made it easier for ecologists to download relevant data and integrate datasets together Assure: Data entries should be checked thoroughly to validate their accuracy and usability, such as to check for outliers and erroneous points. The same principle applies to data downloaded from datasets. This responsibility falls on both the ecologist downloading the data, and the entity that sets up the data collection system. Describe: An accurate description of the metadata of a dataset that is used in a study should include enough information to deduce the data collection and processing methodology, when the data were collected, why the data were collected, and how the data were stored. This is important for reproducibility, especially for projects that build on each other and may recycle data Preserve: After data is collected by an institutional entity, it should be archived such that it is easily accessible. Ideally, this is in databases that are maintained and not at risk of deprecation Discover: While there are good practices for discovering data to start a research project, this process is often marred by a lack of usable, published data, as researchers may collect data specific to their study, but may not publish this data for wider use. On the data collection end, this can be addressed by better data-sharing practices, such as by linking datasets when publishing papers or studies. On the data procurement end, this can be addressed by more precise data searching, such as using key words to find relevant datasets. Integrate: Synthesizing datasets together can be difficult and labor-intensive, largely due to the methodological differences in data collection. There are several approaches to this, but the best practices typically involve computational approaches, namely using R or Python, to automate the processes and prevent errors Analyze: Data analysis can take several forms, and should be tailored to the specific ecological project. However, all data analysis methods should be well-documented, including the procedure for analysis, justification for analysis methods, and any shortcomings in a specific approach. == Applications of Ecoinformatics Across Ecology == === Ecosystem Ecology === Source: Ecosystem studies, by definition, encompass interactions across the entire life sciences spectrum, from microscopic biochemical reactions to large-scale geological phenomena. As a result, big databases may not be designed specifically for any particular research question, but should be inclusive enough to support most studies. Since ecosystem-level questions require a broad perspective, data-related ecosystem projects would likely incorporate data from several databases. A common framework for incorporating data into ecosystem-level studies is the network science model, in which data collection mechanisms and resources are treated like a large, interconnected network instead of individual entities. The network may include several data collection stations within one databases, or may span across multiple databases. Currently there are several large-scale networks, but they do not generate data on the scale to consider ecology as a big data science. A current challenge for ecoinformatics in ecosystem ecology is that most funding is prioritized for generating new data rather than maintaining existing data infrastructures. Integrating data across the different spatial scales can also be difficult, since each dataset may hold different types of data. === Urban Ecology === Source: The current push for smart cities, and sensor network integration into infrastructure, has positioned as a major source of data for ecological studies. Typical urban ecology questions address the effects of urbanization on the local ecosystem, and how to drive future development to promote urban biodiversity. While sensor networks in cities typically collect environmental data to optimize city processes, they may also be used for ecological initiatives, especially with respect to understanding the complex, multi-layered relationship between cities and their local ecosystem. It can also be used to better understand the current landscape of cities, and identify avenues for rewinding of cities. For example, analyzing mobility patterns can identify areas that may lend themselves well to building parks and green spaces. Bird watching data can also be used to identify the types of bird species in a local area. === Infectious Disease === Source: Like other disciplines of ecology, emerging infectious disease and epidemiology span multiple scales, from understanding the genetics that drive disease trends to large-scale spatiotemporal analyses. As a result, infectious disease studies can incorporate everything from bioinformatics, genetic sequences, amino acid sequences, and environmental observation data. On the micro-scale, these data can then be used to predict infectivity/transmissibility, drug resistance, drug candidates, and mutation sites. On the macro-scale, it can be used to identify societal trends or environmental factors that lend themselves to spillover, locations of infection, and practices that cause disease transmission. == Databases == Source: USGS National Streamflow sensor network GBIF Neotoma Paleobiology database European Vegetation Archive USDA Forest Inventory Analysis TRY BIEN AmeriFlux TEAM iNaturalist NEON GLEON LTER CZO TERN SAEON

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  Kleene's algorithm

  In theoretical computer science, in particular in formal language theory, Kleene's algorithm transforms a given nondeterministic finite automaton (NFA) into a regular expression. Together with other conversion algorithms, it establishes the equivalence of several description formats for regular languages. Alternative presentations of the same method include the "elimination method" attributed to Brzozowski and McCluskey, the algorithm of McNaughton and Yamada, and the use of Arden's lemma. == Algorithm description == According to Gross and Yellen (2004), the algorithm can be traced back to Kleene (1956). A presentation of the algorithm in the case of deterministic finite automata (DFAs) is given in Hopcroft and Ullman (1979). The presentation of the algorithm for NFAs below follows Gross and Yellen (2004). Given a nondeterministic finite automaton M = (Q, Σ, δ, q0, F), with Q = { q0,...,qn } its set of states, the algorithm computes the sets Rkij of all strings that take M from state qi to qj without going through any state numbered higher than k. Here, "going through a state" means entering and leaving it, so both i and j may be higher than k, but no intermediate state may. Each set Rkij is represented by a regular expression; the algorithm computes them step by step for k = -1, 0, ..., n. Since there is no state numbered higher than n, the regular expression Rn0j represents the set of all strings that take M from its start state q0 to qj. If F = { q1,...,qf } is the set of accept states, the regular expression Rn01 | ... | Rn0f represents the language accepted by M. The initial regular expressions, for k = -1, are computed as follows for i≠j: R−1ij = a1 | ... | am where qj ∈ δ(qi,a1), ..., qj ∈ δ(qi,am) and as follows for i=j: R−1ii = a1 | ... | am | ε where qi ∈ δ(qi,a1), ..., qi ∈ δ(qi,am) In other words, R−1ij mentions all letters that label a transition from i to j, and we also include ε in the case where i=j. After that, in each step the expressions Rkij are computed from the previous ones by Rkij = Rk-1ik (Rk-1kk) Rk-1kj | Rk-1ij Another way to understand the operation of the algorithm is as an "elimination method", where the states from 0 to n are successively removed: when state k is removed, the regular expression Rk-1ij, which describes the words that label a path from state i>k to state j>k, is rewritten into Rkij so as to take into account the possibility of going via the "eliminated" state k. By induction on k, it can be shown that the length of each expression Rkij is at most ⁠1/3⁠(4k+1(6s+7) - 4) symbols, where s denotes the number of characters in Σ. Therefore, the length of the regular expression representing the language accepted by M is at most ⁠1/3⁠(4n+1(6s+7)f - f - 3) symbols, where f denotes the number of final states. This exponential blowup is inevitable, because there exist families of DFAs for which any equivalent regular expression must be of exponential size. In practice, the size of the regular expression obtained by running the algorithm can be very different depending on the order in which the states are considered by the procedure, i.e., the order in which they are numbered from 0 to n. == Example == The automaton shown in the picture can be described as M = (Q, Σ, δ, q0, F) with the set of states Q = { q0, q1, q2 }, the input alphabet Σ = { a, b }, the transition function δ with δ(q0,a)=q0, δ(q0,b)=q1, δ(q1,a)=q2, δ(q1,b)=q1, δ(q2,a)=q1, and δ(q2,b)=q1, the start state q0, and set of accept states F = { q1 }. Kleene's algorithm computes the initial regular expressions as After that, the Rkij are computed from the Rk-1ij step by step for k = 0, 1, 2. Kleene algebra equalities are used to simplify the regular expressions as much as possible. Step 0 Step 1 Step 2 Since q0 is the start state and q1 is the only accept state, the regular expression R201 denotes the set of all strings accepted by the automaton.

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  Residual neural network

  A residual neural network (also referred to as a residual network or ResNet) is a deep learning architecture in which the layers learn residual functions with reference to the layer inputs. It was developed in 2015 for image recognition, and won the ImageNet Large Scale Visual Recognition Challenge (ILSVRC) of that year. As a point of terminology, "residual connection" refers to the specific architectural motif of x ↦ f ( x ) + x {\displaystyle x\mapsto f(x)+x} , where f {\displaystyle f} is an arbitrary neural network module. The motif had been used previously (see §History for details). However, the publication of ResNet made it widely popular for feedforward networks, appearing in neural networks that are seemingly unrelated to ResNet. The residual connection stabilizes the training and convergence of deep neural networks with hundreds of layers, and is a common motif in deep neural networks, such as transformer models (e.g., BERT, and GPT models such as ChatGPT), the AlphaGo Zero system, the AlphaStar system, and the AlphaFold system. == Mathematics == === Residual connection === In a multilayer neural network model, consider a (non-residual) subnetwork with a certain number of stacked layers (e.g., 2 or 3). Let H ( x ; α ) {\displaystyle H(x;\alpha )} denote the subnetwork. Suppose H ∗ {\displaystyle H^{}} is the desired optimal output of this subnetwork. Residual learning simply adds x {\displaystyle x} directly to the output, such that the optimal learned output now becomes be H ∗ − x {\displaystyle H^{}-x} , which is interpreted as a "residual" with respect to x {\displaystyle x} . The operation of "adding x {\displaystyle x} " is implemented via a "skip connection" that performs an identity mapping to connect the input of the subnetwork with its output. This connection is referred to as a "residual connection" in later work. Let F ( x ; α ) = H ( x ; a ) + x {\displaystyle F(x;\alpha )=H(x;a)+x} . The function F {\displaystyle F} is often represented by matrix multiplication interlaced with activation functions and normalization operations (e.g., batch normalization or layer normalization). As a whole, one of these subnetworks is referred to as a "residual block". A deep residual network is constructed by simply stacking these blocks. Long short-term memory (LSTM) has a memory mechanism that serves as a residual connection. In an LSTM without a forget gate, an input x t {\displaystyle x_{t}} is processed by a function F {\displaystyle F} and added to a memory cell c t {\displaystyle c_{t}} , resulting in c t + 1 = c t + F ( x t ) {\displaystyle c_{t+1}=c_{t}+F(x_{t})} . An LSTM with a forget gate essentially functions as a highway network. To stabilize the variance of the layers' inputs, it is recommended to replace the residual connections x + f ( x ) {\displaystyle x+f(x)} with x / L + f ( x ) {\displaystyle x/L+f(x)} , where L {\displaystyle L} is the total number of residual layers. === Projection connection === If the function F {\displaystyle F} is of type F : R n → R m {\displaystyle F:\mathbb {R} ^{n}\to \mathbb {R} ^{m}} where n ≠ m {\displaystyle n\neq m} , then F ( x ) + x {\displaystyle F(x)+x} is undefined. To handle this special case, a projection connection is used: y = F ( x ) + P ( x ) {\displaystyle y=F(x)+P(x)} where P {\displaystyle P} is typically a linear projection, defined by P ( x ) = M x {\displaystyle P(x)=Mx} where M {\displaystyle M} is a m × n {\displaystyle m\times n} matrix. The matrix is trained via backpropagation, as is any other parameter of the model. === Signal propagation === The introduction of identity mappings facilitates signal propagation in both forward and backward paths. ==== Forward propagation ==== If the output of the ℓ {\displaystyle \ell } -th residual block is the input to the ( ℓ + 1 ) {\displaystyle (\ell +1)} -th residual block (assuming no activation function between blocks), then the ( ℓ + 1 ) {\displaystyle (\ell +1)} -th input is: x ℓ + 1 = F ( x ℓ ) + x ℓ {\displaystyle x_{\ell +1}=F(x_{\ell })+x_{\ell }} Applying this formulation recursively, e.g.: x ℓ + 2 = F ( x ℓ + 1 ) + x ℓ + 1 = F ( x ℓ + 1 ) + F ( x ℓ ) + x ℓ {\displaystyle {\begin{aligned}x_{\ell +2}&=F(x_{\ell +1})+x_{\ell +1}\\&=F(x_{\ell +1})+F(x_{\ell })+x_{\ell }\end{aligned}}} yields the general relationship: x L = x ℓ + ∑ i = ℓ L − 1 F ( x i ) {\displaystyle x_{L}=x_{\ell }+\sum _{i=\ell }^{L-1}F(x_{i})} where L {\textstyle L} is the index of a residual block and ℓ {\textstyle \ell } is the index of some earlier block. This formulation suggests that there is always a signal that is directly sent from a shallower block ℓ {\textstyle \ell } to a deeper block L {\textstyle L} . ==== Backward propagation ==== The residual learning formulation provides the added benefit of mitigating the vanishing gradient problem to some extent. However, it is crucial to acknowledge that the vanishing gradient issue is not the root cause of the degradation problem, which is tackled through the use of normalization. To observe the effect of residual blocks on backpropagation, consider the partial derivative of a loss function E {\displaystyle {\mathcal {E}}} with respect to some residual block input x ℓ {\displaystyle x_{\ell }} . Using the equation above from forward propagation for a later residual block L > ℓ {\displaystyle L>\ell } : ∂ E ∂ x ℓ = ∂ E ∂ x L ∂ x L ∂ x ℓ = ∂ E ∂ x L ( 1 + ∂ ∂ x ℓ ∑ i = ℓ L − 1 F ( x i ) ) = ∂ E ∂ x L + ∂ E ∂ x L ∂ ∂ x ℓ ∑ i = ℓ L − 1 F ( x i ) {\displaystyle {\begin{aligned}{\frac {\partial {\mathcal {E}}}{\partial x_{\ell }}}&={\frac {\partial {\mathcal {E}}}{\partial x_{L}}}{\frac {\partial x_{L}}{\partial x_{\ell }}}\\&={\frac {\partial {\mathcal {E}}}{\partial x_{L}}}\left(1+{\frac {\partial }{\partial x_{\ell }}}\sum _{i=\ell }^{L-1}F(x_{i})\right)\\&={\frac {\partial {\mathcal {E}}}{\partial x_{L}}}+{\frac {\partial {\mathcal {E}}}{\partial x_{L}}}{\frac {\partial }{\partial x_{\ell }}}\sum _{i=\ell }^{L-1}F(x_{i})\end{aligned}}} This formulation suggests that the gradient computation of a shallower layer, ∂ E ∂ x ℓ {\textstyle {\frac {\partial {\mathcal {E}}}{\partial x_{\ell }}}} , always has a later term ∂ E ∂ x L {\textstyle {\frac {\partial {\mathcal {E}}}{\partial x_{L}}}} that is directly added. Even if the gradients of the F ( x i ) {\displaystyle F(x_{i})} terms are small, the total gradient ∂ E ∂ x ℓ {\textstyle {\frac {\partial {\mathcal {E}}}{\partial x_{\ell }}}} resists vanishing due to the added term ∂ E ∂ x L {\textstyle {\frac {\partial {\mathcal {E}}}{\partial x_{L}}}} . == Variants of residual blocks == === Basic block === A basic block is the simplest building block studied in the original ResNet. This block consists of two sequential 3x3 convolutional layers and a residual connection. The input and output dimensions of both layers are equal. === Bottleneck block === A bottleneck block consists of three sequential convolutional layers and a residual connection. The first layer in this block is a 1×1 convolution for dimension reduction (e.g., to 1/2 of the input dimension); the second layer performs a 3×3 convolution; the last layer is another 1×1 convolution for dimension restoration. The models of ResNet-50, ResNet-101, and ResNet-152 are all based on bottleneck blocks. === Pre-activation block === The pre-activation residual block applies activation functions before applying the residual function F {\displaystyle F} . Formally, the computation of a pre-activation residual block can be written as: x ℓ + 1 = F ( ϕ ( x ℓ ) ) + x ℓ {\displaystyle x_{\ell +1}=F(\phi (x_{\ell }))+x_{\ell }} where ϕ {\displaystyle \phi } can be any activation (e.g. ReLU) or normalization (e.g. LayerNorm) operation. This design reduces the number of non-identity mappings between residual blocks, and allows an identity mapping directly from the input to the output. This design was used to train models with 200 to over 1000 layers, and was found to consistently outperform variants where the residual path is not an identity function. The pre-activation ResNet with 200 layers took 3 weeks to train for ImageNet on 8 GPUs in 2016. Since GPT-2, transformer blocks have been mostly implemented as pre-activation blocks. This is often referred to as "pre-normalization" in the literature of transformer models. == Applications == Originally, ResNet was designed for computer vision. All transformer architectures include residual connections. Indeed, very deep transformers cannot be trained without them. The original ResNet paper made no claim on being inspired by biological systems. However, later research has related ResNet to biologically-plausible algorithms. A study published in Science in 2023 disclosed the complete connectome of an insect brain (specifically that of a fruit fly larva). This study discovered "multilayer shortcuts" that resemble the skip connections in artificial neural networks, including ResNets. == History == === Previous work === Residual connections were noticed in neu

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  Environmental informatics

  Environmental informatics is the science of information applied to environmental science. As such, it provides the information processing and communication infrastructure to the interdisciplinary field of environmental sciences aiming at data, information and knowledge integration, the application of computational intelligence to environmental data as well as the identification of environmental impacts of information technology. Environmental informatics thus acts as a bridge, providing an interdisciplinary means of analysing, describing and understanding the complex interactions between humans, nature and technology. Since each field of applied computer science has its own subject matter, terminology and methods, specialised disciplines, such as environmental, bio- and geoinformatics have emerged, each of which combines computer science with a specific field of application such as environmental, bio- or geosciences. Environmental informatics, bioinformatics and geoinformatics all deal with computer-based processing of environmental phenomena. However, environmental informatics is the only field that pursues normative goals (e.g., political goals of environmental protection, environmental planning, and sustainability). This also influences the choice of methods. This also distinguishes it from application areas such as numerical weather prediction, which is considered an early and important example of computer simulation of environmental phenomena. The UK Natural Environment Research Council defines environmental informatics as the "research and system development focusing on the environmental sciences relating to the creation, collection, storage, processing, modelling, interpretation, display and dissemination of data and information." Kostas Karatzas defined environmental informatics as the "creation of a new 'knowledge-paradigm' towards serving environmental management needs." Karatzas argued further that environmental informatics "is an integrator of science, methods and techniques and not just the result of using information and software technology methods and tools for serving environmental engineering needs." Environmental informatics emerged in early 1990 in Central Europe. Current initiatives to effectively manage, share, and reuse environmental and ecological data are indicative of the increasing importance of fields like environmental informatics and ecoinformatics to develop the foundations for effectively managing ecological information. Examples of these initiatives are National Science Foundation Datanet projects, DataONE and Data Conservancy. == Subject matter and objectives == The subject of environmental informatics are environmental information systems (EIS). An EIS 'is a computer-based system that integrates and stores data collected about the natural environment and provides powerful methods for accessing and evaluating it.' This allows environmental data to be processed by computers for environmental protection, planning, research and technology. According to Jaeschke and Bossel, environmental informatics has three interrelated objectives: Environmental informatics serves to procure data and information for describing the state and development of the environment. Of particular importance is information that is needed to prevent or limit undesirable changes and to support desirable changes. Based on the evaluation and analysis of data, environmental informatics improves our understanding of the environment and the interactions between nature, technology and society. It thus supports environmentally relevant decisions. This enables the influence of development (system correction), the assessment of the effects and side effects of potential measures, and the creation of tools for the routine planning, implementation and monitoring of measures. == History == The simulation model World3, which formed the basis of the highly acclaimed study The Limits to Growth, is considered the starting point of environmental informatics. It incorporated environmental information, among other things, to calculate scenarios for global development. In the mid-1980s, interest grew in structuring environmental protection as an area of application for computer science. One of the first publications in German was the book Informatik im Umweltschutz. Anwendungen und Perspektiven (Computer science in environmental protection. Applications and perspectives) from 1986. The term 'environmental informatics' did not appear until around 1993, which is why the development of environmental informatics is usually referred to as having taken place in the 1990s. In 1993, the first university chair for environmental informatics was established in Cottbus. In 1994, the anthology Umweltinformatik. Informatikmethoden für Umweltschutz und Umweltforschung (Environmental Informatics: Informatics Methods for Environmental Protection and Environmental Research) was published. The development of environmental informatics was 'primarily initiated by German computer science.' In the English-speaking world, the volume Environmental Informatics was published in 1995, mainly based on the German anthology of 1994. An article in the conference proceedings of the World Computer Congress of the International Federation for Information Processing (IFIP) in Hamburg in 1994 describes the initial situation of environmental informatics as follows: 'On the one hand, we suffer from the huge amount of available data – people sometimes speak of data graveyards – on the other hand, the really relevant data may still be missing.' This statement indicates the need that led to the emergence of environmental informatics as a specialised discipline of applied computer science. Furthermore, the specific characteristics and processing requirements of environmental data necessitated the emergence of environmental informatics. The special features of environmental data include: The data structures required are highly heterogeneous due to specific processes and differing perspectives on environmental aspects (e.g., water protection, emission control, hazardous substances). In addition to the heterogeneity of the data, heterogeneous databases also play a role, as environmental data is often obtained and presented in an interdisciplinary manner. Obligations change frequently as a result of new legislation, whether regional (e.g. state regulations on water protection), national (e.g. federal emission control regulations) or international (e.g. Registration, Evaluation, Authorisation and Restriction of Chemicals|REACH). The objects represented are often multidimensional and, therefore, require complex geometric representation using curves or polygons. It is often necessary to process uncertain, imprecise or incomplete data, which is, for example, the result of extrapolations or forecasts. A new "knowledge paradigm" has emerged to meet the requirements of environmental management. Environmental informatics produces its own concepts, methods and techniques and is not merely the result of using information and communication technology methods and tools to meet environmental requirements. The development of environmental informatics since the 1990s has been significantly influenced by the newly established conferences EnviroInfo, ISESS and ITEE and is documented in the respective proceedings. Aspects of sustainability and sustainable development were increasingly integrated into environmental informatics after 2000, thereby expanding the field. In 2004, the Working Group on Sustainable Information Society of the Gesellschaft für Informatik e. V. (German Informatics Society, GI) published the Memorandum on a Sustainable Information Society, which formulates recommendations for an information society that is compatible with human, social and natural needs. Since 2007, environmental informatics has often been described in more detail as informatics for environmental protection, sustainable development and risk management. The increased focus on sustainability has also contributed to the formation of the research focus Information and Communications Technology for Sustainability (ICT4S) and to the emergence of the international conference ICT4S in 2013. ICT-ENSURE, the European Commission's funding measure for the establishment of a European research area on "ICT for Environmental Sustainability Research" (2008–2010), has also contributed to the structuring of environmental informatics. == Environmental informatics and sustainable development == Efforts to place environmental informatics within the context of sustainable development have been growing since 2000 and were significantly influenced by the Memorandum on a Sustainable Information Society. According to this Memorandum, the information society offers great but unevenly distributed opportunities for education, participation and intercultural understanding. In addition, the Memorandum highlighted the material and energy consumption of inf

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  FAIR data

  FAIR data is data which meets the 2016 FAIR principles of findability, accessibility, interoperability, and reusability (FAIR). The FAIR principles emphasize machine-actionability (i.e., the capacity of computational systems to find, access, interoperate, and reuse data with none or minimal human intervention) because humans increasingly rely on computational support to deal with data as a result of the increase in the volume, complexity, and rate of production of data. The abbreviation FAIR/O data is sometimes used to indicate that the dataset or database in question complies with the FAIR principles and also carries an explicit data‑capable open license. == FAIR principles published by GO FAIR == Findable The first step in (re)using data is to find them. Metadata and data should be easy to find for both humans and computers. Machine-readable metadata are essential for automatic discovery of datasets and services, so this is an essential component of the FAIRification process. F1. (Meta)data are assigned a globally unique and persistent identifier F2. Data are described with rich metadata (defined by R1 below) F3. Metadata clearly and explicitly include the identifier of the data they describe F4. (Meta)data are registered or indexed in a searchable resource Accessible Once the user finds the required data, they need to know how they can be accessed, possibly including authentication and authorisation. A1. (Meta)data are retrievable by their identifier using a standardised communications protocol A1.1 The protocol is open, free, and universally implementable A1.2 The protocol allows for an authentication and authorisation procedure, where necessary A2. Metadata are accessible, even when the data are no longer available Interoperable The data usually need to be integrated with other data. In addition, the data need to interoperate with applications or workflows for analysis, storage, and processing. I1. (Meta)data use a formal, accessible, shared, and broadly applicable language for knowledge representation I2. (Meta)data use vocabularies that follow FAIR principles I3. (Meta)data include qualified references to other (meta)data Reusable The ultimate goal of FAIR is to optimise the reuse of data. To achieve this, metadata and data should be well-described so that they can be replicated and/or combined in different settings. R1. (Meta)data are richly described with a plurality of accurate and relevant attributes R1.1. (Meta)data are released with a clear and accessible data usage license R1.2. (Meta)data are associated with detailed provenance R1.3. (Meta)data meet domain-relevant community standards The principles refer to three types of entities: data (or any digital object), metadata (information about that digital object), and infrastructure. For instance, principle F4 defines that both metadata and data are registered or indexed in a searchable resource (the infrastructure component). === Acceptance and implementation === Before FAIR, a 2007 OECD report was the most influential paper discussing similar ideas related to data accessibility. In January 2014, the Lorentz Centre at Leiden University hosted a workshop entitled "Jointly designing a data FAIRPORT" where the participants first formulated the FAIR principles. After further discussions, they were published in the March 2016 issue of Scientific Data. At the 2016 G20 Hangzhou summit, the G20 leaders issued a statement endorsing the application of FAIR principles to research. Also in 2016, a group of Australian organisations developed a Statement on FAIR Access to Australia's Research Outputs, which aimed to extend the principles to research outputs more generally. In 2017, Germany, Netherlands and France agreed to establish an international office to support the FAIR initiative, the GO FAIR International Support and Coordination Office. Other international organisations active in the research data ecosystem, such as CODATA or Research Data Alliance (RDA) also support FAIR implementations by their communities. FAIR principles implementation assessment is being explored by FAIR Data Maturity Model Working Group of RDA, CODATA's strategic Decadal Programme "Data for Planet: Making data work for cross-domain challenges" mentions FAIR data principles as a fundamental enabler of data driven science. The Association of European Research Libraries recommends the use of FAIR principles. A 2017 paper by advocates of FAIR data reported that awareness of the FAIR concept was increasing among various researchers and institutes, but also, understanding of the concept was becoming confused as different people apply their own differing perspectives to it. Guides on implementing FAIR data practices state that the cost of a data management plan in compliance with FAIR data practices should be 5% of the total research budget. In 2019 the Global Indigenous Data Alliance (GIDA) released the CARE Principles for Indigenous Data Governance as a complementary guide. The CARE principles extend principles outlined in FAIR data to include Collective benefit, Authority to control, Responsibility, and Ethics to ensure data guidelines address historical contexts and power differentials. The CARE Principles for Indigenous Data Governance were drafted at the International Data Week and Research Data Alliance Plenary co-hosted event, "Indigenous Data Sovereignty Principles for the Governance of Indigenous Data Workshop", held 8 November 2018, in Gaborone, Botswana. The lack of information on how to implement the guidelines have led to inconsistent interpretations of them. In January 2020, representatives of nine groups of universities around the world produced the Sorbonne declaration on research data rights, which included a commitment to FAIR data, and called on governments to provide support to enable it. In 2021, researchers identified the FAIR principles as a conceptual component of data catalog software tools, with the other components being metadata management, business context and data responsibility roles. In April 2022, Matthias Scheffler and colleagues argued in Nature that FAIR principles are "a must" so that data mining and artificial intelligence can extract useful scientific information from the data. There have been moves in the geosciences to establish FAIR data by use of decimal georeferencing However, making data (and research outcomes) FAIR is a challenging task, and it is challenging to assess the FAIRness. In 2020, the FAIR Data Maturity Model Working Group published a set of guidelines for assessing "FAIRness".

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  Anyword

  Anyword is a technology company that offers an artificial intelligence platform, using natural language processing to generate and optimize marketing text for websites, social media, email, and ads. The company also offers a complete managed service to publishers and brands to help them increase their revenue through social ads. It is used by National Geographic, Red Bull, The New York Times, BBC, Ted Baker, etc. The company has an office in New York, and Tel Aviv. == History == It was founded in 2013 — its original name was Keywee Inc. In March 2015, Anyword received $9.1 million in the Series A funding round led by a notable group of investors. In July 2016, the company was selected as an official Facebook Marketing Partner. In August 2019, Anyword was named Best Content Marketing Platform in the Digiday Technology Award winners. In November 2021, it raised $21 million in its Series B funding round.

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  Cloud-based integration

  Cloud-based integration is a form of systems integration business delivered as a cloud computing service that addresses data, process, service-oriented architecture (SOA) and application integration. == Description == Integration platform as a service (iPaaS) is a suite of cloud services enabling customers to develop, execute and govern integration flows between disparate applications. Under the cloud-based iPaaS integration model, customers drive the development and deployment of integrations without installing or managing any hardware or middleware. The iPaaS model allows businesses to achieve integration without big investment into skills or licensed middleware software. iPaaS used to be regarded primarily as an integration tool for cloud-based software applications, used mainly by small to mid-sized business. Over time, a hybrid type of iPaaS—hybrid-IT iPaaS—that connects cloud to on-premises, is becoming increasingly popular. Additionally, large enterprises are exploring new ways of integrating iPaaS into their existing IT infrastructures. Cloud integration was created to break down the data silos, improve connectivity and optimize the business process. Cloud integration has increased in popularity as the usage of Software as a Service solutions has grown. Prior to the emergence of cloud computing in the early 2000s, integration could be categorized as either internal or business to business (B2B). Internal integration requirements were serviced through an on-premises middleware platform and typically utilized a service bus to manage exchange of data between systems. B2B integration was serviced through EDI gateways or value-added network (VAN). The advent of SaaS applications created a new kind of demand which was met through cloud-based integration. Since their emergence, many such services have also developed the capability to integrate legacy or on-premises applications, as well as function as EDI gateways. The following essential features were proposed by one marketing company: Deployed on a multi-tenant, elastic cloud infrastructure Subscription model pricing (operating expense, not capital expenditure) No software development (required connectors should already be available) Users do not perform deployment or manage the platform itself Presence of integration management and monitoring features The emergence of this sector led to new cloud-based business process management tools that do not need to build integration layers - since those are now a separate service. Drivers of growth include the need to integrate mobile app capabilities with proliferating API publishing resources and the growth in demand for the Internet of things functionalities as more 'things' connect to the Internet.

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  Least-squares spectral analysis

  Least-squares spectral analysis (LSSA) is a class of methods for estimating a frequency spectrum by fitting sinusoids to data using a least-squares fit. Unlike Fourier analysis, the most widely used spectral method in science, data need not be equally spaced to use LSSA. Furthermore, while Fourier analysis generally amplifies long-period noise in long or gapped records, LSSA mitigates such problems. The first strictly least-squares LSSA method was developed in 1969 and 1971, and is known as the Vaníček method or the Gauss–Vaniček method, after its inventor Petr Vaníček and Carl Friedrich Gauss, the inventor of the least-squares method for error minimization. A widely known LSSA variant is the Lomb method or the Lomb–Scargle periodogram, based on dated computational simplifications of the Vaníček method introduced in the 1970s and 1980s, first by Nicholas R. Lomb and later by Jeffrey D. Scargle. Other LSSA variants have been subsequently developed. == Historical background == The close connections between Fourier analysis, the periodogram, and the least-squares fitting of sinusoids have been known for a long time. However, most developments are restricted to complete data sets of equally spaced samples. In 1963, Freek J. M. Barning of Mathematisch Centrum, Amsterdam, handled unequally spaced data by similar techniques, including both a periodogram analysis equivalent to what nowadays is called the Lomb method and least-squares fitting of selected frequencies of sinusoids determined from such periodograms — and connected by a procedure known today as the matching pursuit with post-back fitting or the orthogonal matching pursuit. Petr Vaníček, a Canadian geophysicist and geodesist of the University of New Brunswick, proposed in 1969 also the matching-pursuit approach for equally and unequally spaced data, which he called "successive spectral analysis" and the result a "least-squares periodogram". He generalized this method to account for any systematic components beyond a simple mean, such as a "predicted linear (quadratic, exponential, ...) secular trend of unknown magnitude", and applied it to a variety of samples, in 1971. Vaníček's strictly least-squares method was then simplified in 1976 by Nicholas R. Lomb of the University of Sydney, who pointed out its close connection to periodogram analysis. Subsequently, the definition of a periodogram of unequally spaced data was modified and analyzed by Jeffrey D. Scargle of NASA Ames Research Center, who showed that, with minor changes, it becomes identical to Lomb's least-squares formula for fitting individual sinusoid frequencies. Scargle states that his paper "does not introduce a new detection technique, but instead studies the reliability and efficiency of detection with the most commonly used technique, the periodogram, in the case where the observation times are unevenly spaced," and further points out regarding least-squares fitting of sinusoids compared to periodogram analysis, that his paper "establishes, apparently for the first time, that (with the proposed modifications) these two methods are exactly equivalent." Press summarizes the development this way: A completely different method of spectral analysis for unevenly sampled data, one that mitigates these difficulties and has some other very desirable properties, was developed by Lomb, based in part on earlier work by Barning and Vanicek, and additionally elaborated by Scargle. In 1989, Michael J. Korenberg of Queen's University in Kingston, Ontario, developed the "fast orthogonal search" method of more quickly finding a near-optimal decomposition of spectra or other problems, similar to the technique that later became known as the orthogonal matching pursuit. == Development of LSSA and variants == === The Vaníček method === In the Vaníček method, a discrete data set is approximated by a weighted sum of sinusoids of progressively determined frequencies using a standard linear regression or least-squares fit. The frequencies are chosen using a method similar to Barning's, but going further in optimizing the choice of each successive new frequency by picking the frequency that minimizes the residual after least-squares fitting (equivalent to the fitting technique now known as matching pursuit with pre-backfitting). The number of sinusoids must be less than or equal to the number of data samples (counting sines and cosines of the same frequency as separate sinusoids). The relationship between the DFT and the approximation of trigonometric functions using the least-squares method is well explained in (Strutz, 2017). A data vector Φ is represented as a weighted sum of sinusoidal basis functions, tabulated in a matrix A by evaluating each function at the sample times, with weight vector x: ϕ ≈ A x , {\displaystyle \phi \approx {\textbf {A}}x,} where the weights vector x is chosen to minimize the sum of squared errors in approximating Φ. The solution for x is closed-form, using standard linear regression: x = ( A T A ) − 1 A T ϕ . {\displaystyle x=({\textbf {A}}^{\mathrm {T} }{\textbf {A}})^{-1}{\textbf {A}}^{\mathrm {T} }\phi .} Here the matrix A can be based on any set of functions mutually independent (not necessarily orthogonal) when evaluated at the sample times; functions used for spectral analysis are typically sines and cosines evenly distributed over the frequency range of interest. If we choose too many frequencies in a too-narrow frequency range, the functions will be insufficiently independent, the matrix ill-conditioned, and the resulting spectrum meaningless. When the basis functions in A are orthogonal (that is, not correlated, meaning the columns have zero pair-wise dot products), the matrix ATA is diagonal; when the columns all have the same power (sum of squares of elements), then that matrix is an identity matrix times a constant, so the inversion is trivial. The latter is the case when the sample times are equally spaced and sinusoids chosen as sines and cosines equally spaced in pairs on the frequency interval 0 to a half cycle per sample (spaced by 1/N cycles per sample, omitting the sine phases at 0 and maximum frequency where they are identically zero). This case is known as the discrete Fourier transform, slightly rewritten in terms of measurements and coefficients. x = A T ϕ {\displaystyle x={\textbf {A}}^{\mathrm {T} }\phi } — DFT case for N equally spaced samples and frequencies, within a scalar factor. === The Lomb method === Trying to lower the computational burden of the Vaníček method in 1976 (no longer an issue), Lomb proposed using the above simplification in general, except for pair-wise correlations between sine and cosine bases of the same frequency, since the correlations between pairs of sinusoids are often small, at least when they are not tightly spaced. This formulation is essentially that of the traditional periodogram but adapted for use with unevenly spaced samples. The vector x is a reasonably good estimate of an underlying spectrum, but since we ignore any correlations, Ax is no longer a good approximation to the signal, and the method is no longer a least-squares method — yet in the literature continues to be referred to as such. Rather than just taking dot products of the data with sine and cosine waveforms directly, Scargle modified the standard periodogram formula so to find a time delay τ {\displaystyle \tau } first, such that this pair of sinusoids would be mutually orthogonal at sample times t j {\displaystyle t_{j}} and also adjusted for the potentially unequal powers of these two basis functions, to obtain a better estimate of the power at a frequency. This procedure made his modified periodogram method exactly equivalent to Lomb's method. Time delay τ {\displaystyle \tau } by definition equals to tan ⁡ 2 ω τ = ∑ j sin ⁡ 2 ω t j ∑ j cos ⁡ 2 ω t j . {\displaystyle \tan {2\omega \tau }={\frac {\sum _{j}\sin 2\omega t_{j}}{\sum _{j}\cos 2\omega t_{j}}}.} Then the periodogram at frequency ω {\displaystyle \omega } is estimated as: P x ( ω ) = 1 2 [ [ ∑ j X j cos ⁡ ω ( t j − τ ) ] 2 ∑ j cos 2 ⁡ ω ( t j − τ ) + [ ∑ j X j sin ⁡ ω ( t j − τ ) ] 2 ∑ j sin 2 ⁡ ω ( t j − τ ) ] , {\displaystyle P_{x}(\omega )={\frac {1}{2}}\left[{\frac {\left[\sum _{j}X_{j}\cos \omega (t_{j}-\tau )\right]^{2}}{\sum _{j}\cos ^{2}\omega (t_{j}-\tau )}}+{\frac {\left[\sum _{j}X_{j}\sin \omega (t_{j}-\tau )\right]^{2}}{\sum _{j}\sin ^{2}\omega (t_{j}-\tau )}}\right],} which, as Scargle reports, has the same statistical distribution as the periodogram in the evenly sampled case. At any individual frequency ω {\displaystyle \omega } , this method gives the same power as does a least-squares fit to sinusoids of that frequency and of the form: ϕ ( t ) = A sin ⁡ ω t + B cos ⁡ ω t . {\displaystyle \phi (t)=A\sin \omega t+B\cos \omega t.} In practice, it is always difficult to judge if a given Lomb peak is significant or not, especially when the nature of the noise is unknown, so for example a false-alarm spectr

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  Bartels–Stewart algorithm

  In numerical linear algebra, the Bartels–Stewart algorithm is used to numerically solve the Sylvester matrix equation A X − X B = C {\displaystyle AX-XB=C} . Developed by R.H. Bartels and G.W. Stewart in 1971, it was the first numerically stable method that could be systematically applied to solve such equations. The algorithm works by using the real Schur decompositions of A {\displaystyle A} and B {\displaystyle B} to transform A X − X B = C {\displaystyle AX-XB=C} into a triangular system that can then be solved using forward or backward substitution. In 1979, G. Golub, C. Van Loan and S. Nash introduced an improved version of the algorithm, known as the Hessenberg–Schur algorithm. It remains a standard approach for solving Sylvester equations when X {\displaystyle X} is of small to moderate size. == The algorithm == Let X , C ∈ R m × n {\displaystyle X,C\in \mathbb {R} ^{m\times n}} , and assume that the eigenvalues of A {\displaystyle A} are distinct from the eigenvalues of B {\displaystyle B} . Then, the matrix equation A X − X B = C {\displaystyle AX-XB=C} has a unique solution. The Bartels–Stewart algorithm computes X {\displaystyle X} by applying the following steps: 1.Compute the real Schur decompositions R = U T A U , {\displaystyle R=U^{T}AU,} S = V T B T V . {\displaystyle S=V^{T}B^{T}V.} The matrices R {\displaystyle R} and S {\displaystyle S} are block-upper triangular matrices, with diagonal blocks of size 1 × 1 {\displaystyle 1\times 1} or 2 × 2 {\displaystyle 2\times 2} . 2. Set F = U T C V . {\displaystyle F=U^{T}CV.} 3. Solve the simplified system R Y − Y S T = F {\displaystyle RY-YS^{T}=F} , where Y = U T X V {\displaystyle Y=U^{T}XV} . This can be done using forward substitution on the blocks. Specifically, if s k − 1 , k = 0 {\displaystyle s_{k-1,k}=0} , then ( R − s k k I ) y k = f k + ∑ j = k + 1 n s k j y j , {\displaystyle (R-s_{kk}I)y_{k}=f_{k}+\sum _{j=k+1}^{n}s_{kj}y_{j},} where y k {\displaystyle y_{k}} is the k {\displaystyle k} th column of Y {\displaystyle Y} . When s k − 1 , k ≠ 0 {\displaystyle s_{k-1,k}\neq 0} , columns [ y k − 1 ∣ y k ] {\displaystyle [y_{k-1}\mid y_{k}]} should be concatenated and solved for simultaneously. 4. Set X = U Y V T . {\displaystyle X=UYV^{T}.} === Computational cost === Using the QR algorithm, the real Schur decompositions in step 1 require approximately 10 ( m 3 + n 3 ) {\displaystyle 10(m^{3}+n^{3})} flops, so that the overall computational cost is 10 ( m 3 + n 3 ) + 2.5 ( m n 2 + n m 2 ) {\displaystyle 10(m^{3}+n^{3})+2.5(mn^{2}+nm^{2})} . === Simplifications and special cases === In the special case where B = − A T {\displaystyle B=-A^{T}} and C {\displaystyle C} is symmetric, the solution X {\displaystyle X} will also be symmetric. This symmetry can be exploited so that Y {\displaystyle Y} is found more efficiently in step 3 of the algorithm. == The Hessenberg–Schur algorithm == The Hessenberg–Schur algorithm replaces the decomposition R = U T A U {\displaystyle R=U^{T}AU} in step 1 with the decomposition H = Q T A Q {\displaystyle H=Q^{T}AQ} , where H {\displaystyle H} is an upper-Hessenberg matrix. This leads to a system of the form H Y − Y S T = F {\displaystyle HY-YS^{T}=F} that can be solved using forward substitution. The advantage of this approach is that H = Q T A Q {\displaystyle H=Q^{T}AQ} can be found using Householder reflections at a cost of ( 5 / 3 ) m 3 {\displaystyle (5/3)m^{3}} flops, compared to the 10 m 3 {\displaystyle 10m^{3}} flops required to compute the real Schur decomposition of A {\displaystyle A} . == Software and implementation == The subroutines required for the Hessenberg-Schur variant of the Bartels–Stewart algorithm are implemented in the SLICOT library. These are used in the MATLAB control system toolbox. == Alternative approaches == For large systems, the O ( m 3 + n 3 ) {\displaystyle {\mathcal {O}}(m^{3}+n^{3})} cost of the Bartels–Stewart algorithm can be prohibitive. When A {\displaystyle A} and B {\displaystyle B} are sparse or structured, so that linear solves and matrix vector multiplies involving them are efficient, iterative algorithms can potentially perform better. These include projection-based methods, which use Krylov subspace iterations, methods based on the alternating direction implicit (ADI) iteration, and hybridizations that involve both projection and ADI. Iterative methods can also be used to directly construct low rank approximations to X {\displaystyle X} when solving A X − X B = C {\displaystyle AX-XB=C} .

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  Hindley–Milner type system

  A Hindley–Milner (HM) type system is a classical type system for the lambda calculus with parametric polymorphism. It is also known as Damas–Milner or Damas–Hindley–Milner. It was first described by J. Roger Hindley and later rediscovered by Robin Milner. Luis Damas contributed a close formal analysis and proof of the method in his PhD thesis. Among HM's more notable properties are its completeness and its ability to infer the most general type of a given program without programmer-supplied type annotations or other hints. Algorithm W is an efficient type inference method in practice and has been successfully applied on large code bases, although it has a high theoretical complexity. HM is preferably used for functional programming languages. It was first implemented as part of the type system of the programming language ML. Since then, HM has been extended in various ways, most notably with type class constraints like those in Haskell. == Introduction == As a type inference method, Hindley–Milner is able to deduce the types of variables, expressions and functions from programs written in an entirely untyped style. Being scope sensitive, it is not limited to deriving the types only from a small portion of source code, but rather from complete programs or modules. Being able to cope with parametric types, too, it is core to the type systems of many functional programming languages. It was first applied in this manner in the ML programming language. The origin is the type inference algorithm for the simply typed lambda calculus that was devised by Haskell Curry and Robert Feys in 1958. In 1969, J. Roger Hindley extended this work and proved that their algorithm always inferred the most general type. In 1978, Robin Milner, independently of Hindley's work, provided an equivalent algorithm, Algorithm W. In 1982, Luis Damas finally proved that Milner's algorithm is complete and extended it to support systems with polymorphic references. === Monomorphism vs. polymorphism === In the simply typed lambda calculus, types T are either atomic type constants or function types of form T → T {\displaystyle T\rightarrow T} . Such types are monomorphic. Typical examples are the types used in arithmetic values: 3 : N u m b e r a d d 3 4 : N u m b e r a d d : N u m b e r → N u m b e r → N u m b e r {\displaystyle {\begin{array}{ll}3&:{\mathtt {Number}}\\{\mathtt {add}}\ 3\ 4&:{\mathtt {Number}}\\{\mathtt {add}}&:{\mathtt {Number}}\rightarrow {\mathtt {Number}}\rightarrow {\mathtt {Number}}\end{array}}} Contrary to this, the untyped lambda calculus is neutral to typing at all, and many of its functions can be meaningfully applied to all type of arguments. The trivial example is the identity function i d ≡ λ x . x {\displaystyle {\mathtt {id}}\equiv \lambda x.x} which simply returns whatever value it is applied to. Less trivial examples include parametric types like lists. While polymorphism in general means that operations accept values of more than one type, the polymorphism used here is parametric. One finds the notation of type schemes in the literature, too, emphasizing the parametric nature of the polymorphism. Additionally, constants may be typed with (quantified) type variables. For example, the following type schemes quantify universally over α {\displaystyle \alpha } , meaning that they are true for all possible α {\displaystyle \alpha } : c o n s : ∀ α . α → L i s t α → L i s t α n i l : ∀ α . L i s t α i d : ∀ α . α → α {\displaystyle {\begin{array}{ll}{\mathtt {cons}}&:\forall \alpha .\alpha \rightarrow {\mathtt {List}}\ \alpha \rightarrow {\mathtt {List}}\ \alpha \\{\mathtt {nil}}&:\forall \alpha .{\mathtt {List}}\ \alpha \\{\mathtt {id}}&:\forall \alpha .\alpha \rightarrow \alpha \end{array}}} Polymorphic types can become monomorphic by consistent substitution of their variables. Examples of monomorphic instances are: i d ′ : S t r i n g → S t r i n g n i l ′ : L i s t N u m b e r {\displaystyle {\begin{array}{ll}{\mathtt {id}}'&:{\mathtt {String}}\rightarrow {\mathtt {String}}\\{\mathtt {nil}}'&:{\mathtt {List}}\ {\mathtt {Number}}\end{array}}} More generally, types are polymorphic when they contain type variables, while types without them are monomorphic. Contrary to the type systems used for example in Pascal (1970) or C (1972), which only support monomorphic types, HM is designed with emphasis on parametric polymorphism. The successors of the languages mentioned, like C++ (1985), focused on different types of polymorphism, namely subtyping in connection with object-oriented programming and overloading. While subtyping is incompatible with HM, a variant of systematic overloading is available in the HM-based type system of Haskell. === Let-polymorphism === When extending the type inference for the simply-typed lambda calculus towards polymorphism, one has to decide whether assigning a polymorphic type not only as type of an expression, but also as the type of a λ-bound variable is admissible. This would allow the generic identity type to be assigned to the variable 'id' in: (λ id . ... (id 3) ... (id "text") ... ) (λ x . x) Allowing this gives rise to the polymorphic lambda calculus; however, type inference in this system is not decidable. Instead, HM distinguishes variables that are immediately bound to an expression from more general λ-bound variables, calling the former let-bound variables, and allows polymorphic types to be assigned only to these. This leads to let-polymorphism where the above example takes the form let id = λ x . x in ... (id 3) ... (id "text") ... which can be typed with a polymorphic type for 'id'. As indicated, the expression syntax is extended to make the let-bound variables explicit, and by restricting the type system to allow only let-bound variable to have polymorphic types, while the parameters in lambda-abstractions must get a monomorphic type, type inference becomes decidable. == Overview == The remainder of this article proceeds as follows: The HM type system is defined. This is done by describing a deduction system that makes precise what expressions have what type, if any. From there, it works towards an implementation of the type inference method. After introducing a syntax-driven variant of the above deductive system, it sketches an efficient implementation (algorithm J), appealing mostly to the reader's metalogical intuition. Because it remains open whether algorithm J indeed realises the initial deduction system, a less efficient implementation (algorithm W), is introduced and its use in a proof is hinted. Finally, further topics related to the algorithm are discussed. The same description of the deduction system is used throughout, even for the two algorithms, to make the various forms in which the HM method is presented directly comparable. == The Hindley–Milner type system == The type system can be formally described by syntax rules that fix a language for the expressions, types, etc. The presentation here of such a syntax is not too formal, in that it is written down not to study the surface grammar, but rather the depth grammar, and leaves some syntactical details open. This form of presentation is usual. Building on this, typing rules are used to define how expressions and types are related. As before, the form used is a bit liberal. === Syntax === The expressions to be typed are exactly those of the lambda calculus extended with a let-expression as shown in the adjacent table. Parentheses can be used to disambiguate an expression. The application is left-binding and binds stronger than abstraction or the let-in construct. Types are syntactically split into two groups, monotypes and polytypes. ==== Monotypes ==== Monotypes always designate a particular type. Monotypes τ {\displaystyle \tau } are syntactically represented as terms. Examples of monotypes include type constants like i n t {\displaystyle {\mathtt {int}}} or s t r i n g {\displaystyle {\mathtt {string}}} , and parametric types like M a p ( S e t s t r i n g ) i n t {\displaystyle {\mathtt {Map\ (Set\ string)\ int}}} . The latter types are examples of applications of type functions, for example, from the set { M a p 2 , S e t 1 , s t r i n g 0 , i n t 0 , → 2 } {\displaystyle \{{\mathtt {Map^{2},\ Set^{1},\ string^{0},\ int^{0}}},\ \rightarrow ^{2}\}} , where the superscript indicates the number of type parameters. The complete set of type functions C {\displaystyle C} is arbitrary in HM, except that it must contain at least → 2 {\displaystyle \rightarrow ^{2}} , the type of functions. It is often written in infix notation for convenience. For example, a function mapping integers to strings has type i n t → s t r i n g {\displaystyle {\mathtt {int}}\rightarrow {\mathtt {string}}} . Again, parentheses can be used to disambiguate a type expression. The application binds stronger than the infix arrow, which is right-binding. Type variables are admitted as monotypes. Monotypes are not to be confused with monomorphic types, which exc

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  Adobe InDesign

  Adobe InDesign is a desktop publishing and page layout designing software application produced by Adobe and first released in 1999. It can be used to create works such as posters, flyers, brochures, magazines, newspapers, presentations, books and ebooks. InDesign can also publish content suitable for tablet devices in conjunction with Adobe Digital Publishing Suite. Graphic designers and production artists are the principal users. InDesign is the successor to PageMaker, which Adobe acquired by buying Aldus Corporation in late 1994. (Freehand, Aldus's competitor to Adobe Illustrator, was licensed from Altsys, the maker of Fontographer.) By 1998, PageMaker had lost much of the professional market to the comparatively feature-rich QuarkXPress version 3.3, released in 1992, and version 4.0, released in 1996. In 1999, Quark announced its offer to buy Adobe and to divest the combined company of PageMaker to avoid problems under United States antitrust law. Adobe declined Quark's offer and continued to develop a new desktop publishing application. Aldus had begun developing a successor to PageMaker, code-named "Shuksan". Later, Adobe code-named the project "K2", and Adobe released InDesign 1.0 in 1999. InDesign exports documents in Adobe's Portable Document Format (PDF) and supports multiple languages. It was the first DTP application to support Unicode character sets, advanced typography with OpenType fonts, advanced transparency features, layout styles, optical margin alignment, and cross-platform scripting with JavaScript. Later versions of the software introduced new file formats. To support the new features, especially typography, introduced with InDesign CS, the program and its document format are not backward-compatible. Instead, InDesign CS2 introduced the INX (.inx) format, an XML-based document representation, to allow backward compatibility with future versions. InDesign CS versions updated with the 3.1 April 2005 update can read InDesign CS2-saved files exported to the .inx format. The InDesign Interchange format does not support versions earlier than InDesign CS. With InDesign CS4, Adobe replaced INX with InDesign Markup Language (IDML), another XML-based document representation. InDesign was the first native Mac OS X publishing software. With the third major version, InDesign CS, Adobe increased InDesign's distribution by bundling it with Adobe Photoshop, Adobe Illustrator, and Adobe Acrobat in Adobe Creative Suite. Adobe developed InDesign CS3 (and Creative Suite 3) as universal binary software compatible with native Intel and PowerPC Macs in 2007, two years after the announced 2005 schedule, inconveniencing early adopters of Intel-based Macs. Adobe CEO Bruce Chizen said, "Adobe will be first with a complete line of universal applications." == File format == The MIME type is not official File Open formats: indd, indl, indt, indb, inx, idml, pmd, xqx New File formats: indd, indl, indb File Save As formats: indd, indt Save file format for InCopy: icma (Assignment file) icml (Content file, Exported file) icap (Package for InCopy) idap (Package for InDesign) File Export formats: pdf, idml, icml, eps, jpg, txt, XML, rtf == Versions == Newer versions can, as a rule, open files created by older versions, but the reverse is not true. Current versions can export the InDesign file as an IDML file (InDesign Markup Language), which can be opened by InDesign versions from CS4 upwards; older versions from CS4 down can export to an INX file (InDesign Interchange format). === Server version === In October 2005, Adobe released InDesign Server CS2, a modified version of InDesign (without a user interface) for Windows and Macintosh server platforms. It does not provide any editing client; rather, it is for use by developers in creating client-server solutions with the InDesign plug-in technology. In March 2007 Adobe officially announced Adobe InDesign CS3 Server as part of the Adobe InDesign family. == Features == Paragraph styles are an essential tool for designers when working with text in Adobe InDesign. Despite their menacing appearance, they are straightforward to operate. Other features that make InDesign a good tool for working with text and paragraphs include: Creating frames and shapes Aligning objects with grids and guides Manipulating objects Organizing objects Importing text Formatting text Spell checking Importing images Parent pages (formerly master pages) Paragraph styles == Internationalization and localization == InDesign Middle Eastern editions have unique settings for laying out Arabic or Hebrew text. They feature: Text settings: Special settings for laying out Arabic or Hebrew text, such as: Ability to use Arabic, Persian or Hindi digits; Use kashidas for letter spacing and full justification; Ligature option; Adjust the position of diacritics, such as vowels of the Arabic script; Justify text in three possible ways: Standard, Arabic, Naskh; Option to insert special characters, including Geresh, Gershayim, Maqaf for Hebrew and Kashida for Arabic texts; Apply standard, Arabic, or Hebrew styles for page, paragraph, and footnote numbering. Bi-directional text flow: Right-to-left behavior applies to several objects: Story, paragraph, character, and table. It allows mixing right-to-left and left-to-right words, paragraphs, and stories in a document. Changing the direction of neutral characters (e.g., / or ?) is possible according to the user's keyboard language. Table of contents: Provides a table of contents titles, one for each supported language. This table is sorted according to the chosen language. InDesign CS4 Middle Eastern versions allow users to select the language of the index title and cross-references. Indices: This allows the creation of a simple keyword index or a somewhat more detailed index of the information in the text using embedded indexing codes. Unlike more sophisticated programs, InDesign cannot insert character style information as part of an index entry (e.g., when indexing book, journal, or movie titles). Indices are limited to four levels (the top level and three sub-levels). Like tables of contents, indices can be sorted according to the selected language. Importing and exporting: Can import QuarkXPress files up to version 4.1 (1999), even using Arabic XT, Arabic Phonyx, or Hebrew XPressWay fonts, retaining the layout and content. Includes 50 import/export filters, including a Microsoft Word 97-98-2000 import filter and a plain text import filter. Exports IDML files can be read by QuarkXPress 2017. Reverse layout: Include a reverse layout feature to reverse the layout of a document when converting a left-to-right document to a right-to-left one or vice versa. Complex script rendering: InDesign supports Unicode character encoding, and Middle Eastern editions support complex text layouts for Arabic and Hebrew complex scripts. The underlying Arabic and Hebrew support is present in the Western editions of InDesign CS4, CS5, CS5.5, and CS6, but the user interface is not exposed, making it difficult to access.

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  Physical schema

  A physical data model (or database design) is a representation of a data design as implemented, or intended to be implemented, in a database management system. In the lifecycle of a project it typically derives from a logical data model, though it may be reverse-engineered from a given database implementation. A complete physical data model will include all the database artifacts required to create relationships between tables or to achieve performance goals, such as indexes, constraint definitions, linking tables, partitioned tables or clusters. Analysts can usually use a physical data model to calculate storage estimates; it may include specific storage allocation details for a given database system. As of 2012 seven main databases dominate the commercial marketplace: Informix, Oracle, Postgres, SQL Server, Sybase, IBM Db2 and MySQL. Other RDBMS systems tend either to be legacy databases or used within academia such as universities or further education colleges. Physical data models for each implementation would differ significantly, not least due to underlying operating-system requirements that may sit underneath them. For example: SQL Server runs only on Microsoft Windows operating-systems (Starting with SQL Server 2017, SQL Server runs on Linux. It's the same SQL Server database engine, with many similar features and services regardless of your operating system), while Oracle and MySQL can run on Solaris, Linux and other UNIX-based operating-systems as well as on Windows. This means that the disk requirements, security requirements and many other aspects of a physical data model will be influenced by the RDBMS that a database administrator (or an organization) chooses to use. == Physical schema == Physical schema is a term used in data management to describe how data is to be represented and stored (files, indices, etc.) in secondary storage using a particular database management system (DBMS) (e.g., Oracle RDBMS, Sybase SQL Server, etc.). In the ANSI/SPARC Architecture three schema approach, the internal schema is the view of data that involved data management technology. This is as opposed to an external schema that reflects an individual's view of the data, or the conceptual schema that is the integration of a set of external schemas. The logical schema was the way data were represented to conform to the constraints of a particular approach to database management. At that time the choices were hierarchical and network. Describing the logical schema, however, still did not describe how physically data would be stored on disk drives. That is the domain of the physical schema. Now logical schemas describe data in terms of relational tables and columns, object-oriented classes, and XML tags. A single set of tables, for example, can be implemented in numerous ways, up to and including an architecture where table rows are maintained on computers in different countries.

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  AVT Statistical filtering algorithm

  AVT Statistical filtering algorithm is an approach to improving quality of raw data collected from various sources. It is most effective in cases when there is inband noise present. In those cases AVT is better at filtering data then, band-pass filter or any digital filtering based on variation of. Conventional filtering is useful when signal/data has different frequency than noise and signal/data is separated/filtered by frequency discrimination of noise. Frequency discrimination filtering is done using Low Pass, High Pass and Band Pass filtering which refers to relative frequency filtering criteria target for such configuration. Those filters are created using passive and active components and sometimes are implemented using software algorithms based on Fast Fourier transform (FFT). AVT filtering is implemented in software and its inner working is based on statistical analysis of raw data. When signal frequency/(useful data distribution frequency) coincides with noise frequency/(noisy data distribution frequency) we have inband noise. In this situations frequency discrimination filtering does not work since the noise and useful signal are indistinguishable and where AVT excels. To achieve filtering in such conditions there are several methods/algorithms available which are briefly described below. == Averaging algorithm == Collect n samples of data Calculate average value of collected data Present/record result as actual data == Median algorithm == Collect n samples of data Sort the data in ascending or descending order. Note that order does not matter Select the data that happen to be in n/2 position and present/record it as final result representing data sample == AVT algorithm == AVT algorithm stands for Antonyan Vardan Transform and its implementation explained below. Collect n samples of data Calculate the standard deviation and average value Drop any data that is greater or less than average ± one standard deviation Calculate average value of remaining data Present/record result as actual value representing data sample This algorithm is based on amplitude discrimination and can easily reject any noise that is not like actual signal, otherwise statistically different than 1 standard deviation of the signal. Note that this type of filtering can be used in situations where the actual environmental noise is not known in advance. Notice that it is preferable to use the median in above steps than average. Originally the AVT algorithm used average value to compare it with results of median on the data window. == Filtering algorithms comparison == Using a system that has signal value of 1 and has noise added at 0.1% and 1% levels will simplify quantification of algorithm performance. The R script is used to create pseudo random noise added to signal and analyze the results of filtering using several algorithms. Please refer to "Reduce Inband Noise with the AVT Algorithm" article for details. This graphs show that AVT algorithm provides best results compared with Median and Averaging algorithms while using data sample size of 32, 64 and 128 values. Note that this graph was created by analyzing random data array of 10000 values. Sample of this data is graphically represented below. From this graph it is apparent that AVT outperforms other filtering algorithms by providing 5% to 10% more accurate data when analyzing same datasets. Considering random nature of noise used in this numerical experiment that borderlines worst case situation where actual signal level is below ambient noise the precision improvements of processing data with AVT algorithm are significant. == AVT algorithm variations == === Cascaded AVT === In some situations better results can be obtained by cascading several stages of AVT filtering. This will produce singular constant value which can be used for equipment that has known stable characteristics like thermometers, thermistors and other slow acting sensors. === Reverse AVT === Collect n samples of data Calculate the standard deviation and average value Drop any data that is within one standard deviation ± average band Calculate average value of remaining data Present/record result as actual data This is useful for detecting minute signals that are close to background noise level. == Possible applications and uses == Use to filter data that is near or below noise level Used in planet detection to filter out raw data from the Kepler space telescope Filter out noise from sound sources where all other filtering methods (Low-pass filter, High-pass filter, Band-pass filter, Digital filter) fail. Pre-process scientific data for data analysis (Smoothness) before plotting see (Plot (graphics)) Used in SETI (Search for extraterrestrial intelligence) for detecting/distinguishing extraterrestrial signals from cosmic background Use AVT as image filtering algorithm to detect altered images. This image of Jupiter generated from this program, detecting alterations in original picture that was modified to be visually appealing by applying filters. Another version of this comparison is the Reverse AVT filter applied to the same original Jupiter Image, where we only see that altered portion as Noise that was eliminated by AVT algorithm. Use AVT as image filtering algorithm to estimate data density from images. Picture of Pillars of Creation Nebula shows data density in filtered images from Hubble and Webb. Note that image on the left has big patches of missing data marked with simpler color patterns.

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