AI Grammar Tagalog

AI Grammar Tagalog — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.

Eager learning

In artificial intelligence, eager learning is a learning method in which the system tries to construct a general, input-independent target function during training of the system, as opposed to lazy learning, where generalization beyond the training data is delayed until a query is made to the system. The main advantage gained in employing an eager learning method, such as an artificial neural network, is that the target function will be approximated globally during training, thus requiring much less space than using a lazy learning system. Eager learning systems also deal much better with noise in the training data. Eager learning is an example of offline learning, in which post-training queries to the system have no effect on the system itself, and thus the same query to the system will always produce the same result. The main disadvantage with eager learning is that it is generally unable to provide good local approximations in the target function.
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Ontology alignment

Ontology alignment, or ontology matching, is the process of determining correspondences between concepts in ontologies. A set of correspondences is also called an alignment. The phrase takes on a slightly different meaning, in computer science, cognitive science or philosophy. == Computer science == For computer scientists, concepts are expressed as labels for data. Historically, the need for ontology alignment arose out of the need to integrate heterogeneous databases, ones developed independently and thus each having their own data vocabulary. In the Semantic Web context involving many actors providing their own ontologies, ontology matching has taken a critical place for helping heterogeneous resources to interoperate. Ontology alignment tools find classes of data that are semantically equivalent, for example, "truck" and "lorry". The classes are not necessarily logically identical. According to Euzenat and Shvaiko (2007), there are three major dimensions for similarity: syntactic, external, and semantic. Coincidentally, they roughly correspond to the dimensions identified by Cognitive Scientists below. A number of tools and frameworks have been developed for aligning ontologies, some with inspiration from Cognitive Science and some independently. Ontology alignment tools have generally been developed to operate on database schemas, XML schemas, taxonomies, formal languages, entity-relationship models, dictionaries, and other label frameworks. They are usually converted to a graph representation before being matched. Since the emergence of the Semantic Web, such graphs can be represented in the Resource Description Framework line of languages by triples of the form , as illustrated in the Notation 3 syntax. In this context, aligning ontologies is sometimes referred to as "ontology matching". The problem of Ontology Alignment has been tackled recently by trying to compute matching first and mapping (based on the matching) in an automatic fashion. Systems like DSSim, X-SOM or COMA++ obtained at the moment very high precision and recall. The Ontology Alignment Evaluation Initiative aims to evaluate, compare and improve the different approaches. === Formal definition === Given two ontologies i = ⟨ C i , R i , I i , T i , V i ⟩ {\displaystyle i=\langle C_{i},R_{i},I_{i},T_{i},V_{i}\rangle } and j = ⟨ C j , R j , I j , T j , V j ⟩ {\displaystyle j=\langle C_{j},R_{j},I_{j},T_{j},V_{j}\rangle } where C {\displaystyle C} is the set of classes, R {\displaystyle R} is the set of relations, I {\displaystyle I} is the set of individuals, T {\displaystyle T} is the set of data types, and V {\displaystyle V} is the set of values, we can define different types of (inter-ontology) relationships. Such relationships will be called, all together, alignments and can be categorized among different dimensions: similarity vs logic: this is the difference between matchings (predicating about the similarity of ontology terms), and mappings (logical axioms, typically expressing logical equivalence or inclusion among ontology terms) atomic vs complex: whether the alignments we considered are one-to-one, or can involve more terms in a query-like formulation (e.g., LAV/GAV mapping) homogeneous vs heterogeneous: do the alignments predicate on terms of the same type (e.g., classes are related only to classes, individuals to individuals, etc.) or we allow heterogeneity in the relationship? type of alignment: the semantics associated to an alignment. It can be subsumption, equivalence, disjointness, part-of or any user-specified relationship. Subsumption, atomic, homogeneous alignments are the building blocks to obtain richer alignments, and have a well defined semantics in every Description Logic. Let's now introduce more formally ontology matching and mapping. An atomic homogeneous matching is an alignment that carries a similarity degree s ∈ [ 0 , 1 ] {\displaystyle s\in [0,1]} , describing the similarity of two terms of the input ontologies i {\displaystyle i} and j {\displaystyle j} . Matching can be either computed, by means of heuristic algorithms, or inferred from other matchings. Formally we can say that, a matching is a quadruple m = ⟨ i d , t i , t j , s ⟩ {\displaystyle m=\langle id,t_{i},t_{j},s\rangle } , where t i {\displaystyle t_{i}} and t j {\displaystyle t_{j}} are homogeneous ontology terms, s {\displaystyle s} is the similarity degree of m {\displaystyle m} . A (subsumption, homogeneous, atomic) mapping is defined as a pair μ = ⟨ t i , t j ⟩ {\displaystyle \mu =\langle t_{i},t_{j}\rangle } , where t i {\displaystyle t_{i}} and t j {\displaystyle t_{j}} are homogeneous ontology terms. == Cognitive science == For cognitive scientists interested in ontology alignment, the "concepts" are nodes in a semantic network that reside in brains as "conceptual systems." The focal question is: if everyone has unique experiences and thus different semantic networks, then how can we ever understand each other? This question has been addressed by a model called ABSURDIST (Aligning Between Systems Using Relations Derived Inside Systems for Translation). Three major dimensions have been identified for similarity as equations for "internal similarity, external similarity, and mutual inhibition." == Ontology alignment methods == Two sub research fields have emerged in ontology mapping, namely monolingual ontology mapping and cross-lingual ontology mapping. The former refers to the mapping of ontologies in the same natural language, whereas the latter refers to "the process of establishing relationships among ontological resources from two or more independent ontologies where each ontology is labelled in a different natural language". Existing matching methods in monolingual ontology mapping are discussed in Euzenat and Shvaiko (2007). Approaches to cross-lingual ontology mapping are presented in Fu et al. (2011).
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StoredIQ

StoredIQ was a company founded for information lifecycle management (ILM) of unstructured data. Founded in 2001 as Deepfile in Austin, Texas by Jeff Erramouspe, Jeff Bone, Russell Turpin, Rudy Rouhana, Laura Arbilla and Brett Funderburg, the company changed its name in 2005 to StoredIQ. It continued to operate successfully for over a decade until it was acquired in 2012 by IBM. It now serves as a platform for IBM's information life cycle governance, big data governance and enterprise content management technologies. StoredIQ was awarded five patents by the USPTO. The first, originally filed in 2003, enabled unstructured data in file systems to be manipulated in a similar way to information stored in databases. Subsequent patents built upon the patented actionable file system with further enhancements specific to Enterprise Policy Management and expanding the reach of StoredIQ's management capability all the way to individual desktops. In 2008 StoredIQ was recognized as "Best in Compliance" by Network Products Guide. At the same time, StoredIQ was being recognized as a "Top 5 Provider" by the prestigious Socha-Gelbmann eDiscovery survey. There were takeover negotiations with EMC Corporation, initially a strategic investor in StoredIQ, however, the company rejected the approach, leaving EMC to acquire a competitor. The company published a whitepaper titled The Truth About Big Data. This promotion combined with StoredIQ's patented technology led to IBM selecting StoredIQ as the basis for some products.
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Pointer jumping

Pointer jumping or path doubling is a design technique for parallel algorithms that operate on pointer structures, such as linked lists and directed graphs. Pointer jumping allows an algorithm to follow paths with a time complexity that is logarithmic with respect to the length of the longest path. It does this by "jumping" to the end of the path computed by neighbors. The basic operation of pointer jumping is to replace each neighbor in a pointer structure with its neighbor's neighbor. In each step of the algorithm, this replacement is done for all nodes in the data structure, which can be done independently in parallel. In the next step when a neighbor's neighbor is followed, the neighbor's path already followed in the previous step is added to the node's followed path in a single step. Thus, each step effectively doubles the distance traversed by the explored paths. Pointer jumping is best understood by looking at simple examples such as list ranking and root finding. == List ranking == One of the simpler tasks that can be solved by a pointer jumping algorithm is the list ranking problem. This problem is defined as follows: given a linked list of N nodes, find the distance (measured in the number of nodes) of each node to the end of the list. The distance d(n) is defined as follows, for nodes n that point to their successor by a pointer called next: If n.next is nil, then d(n) = 0. For any other node, d(n) = d(n.next) + 1. This problem can easily be solved in linear time on a sequential machine, but a parallel algorithm can do better: given n processors, the problem can be solved in logarithmic time, O(log N), by the following pointer jumping algorithm: The pointer jumping occurs in the last line of the algorithm, where each node's next pointer is reset to skip the node's direct successor. It is assumed, as in common in the PRAM model of computation, that memory access are performed in lock-step, so that each n.next.next memory fetch is performed before each n.next memory store; otherwise, processors may clobber each other's data, producing inconsistencies. The following diagram follows how the parallel list ranking algorithm uses pointer jumping for a linked list with 11 elements. As the algorithm describes, the first iteration starts initialized with all ranks set to 1 except those with a null pointer for next. The first iteration looks at immediate neighbors. Each subsequent iteration jumps twice as far as the previous. Analyzing the algorithm yields a logarithmic running time. The initialization loop takes constant time, because each of the N processors performs a constant amount of work, all in parallel. The inner loop of the main loop also takes constant time, as does (by assumption) the termination check for the loop, so the running time is determined by how often this inner loop is executed. Since the pointer jumping in each iteration splits the list into two parts, one consisting of the "odd" elements and one of the "even" elements, the length of the list pointed to by each processor's n is halved in each iteration, which can be done at most O(log N) time before each list has a length of at most one. == Root finding == Following a path in a graph is an inherently serial operation, but pointer jumping reduces the total amount of work by following all paths simultaneously and sharing results among dependent operations. Pointer jumping iterates and finds a successor — a vertex closer to the tree root — each time. By following successors computed for other vertices, the traversal down each path can be doubled every iteration, which means that the tree roots can be found in logarithmic time. Pointer doubling operates on an array successor with an entry for every vertex in the graph. Each successor[i] is initialized with the parent index of vertex i if that vertex is not a root or to i itself if that vertex is a root. At each iteration, each successor is updated to its successor's successor. The root is found when the successor's successor points to itself. The following pseudocode demonstrates the algorithm. algorithm Input: An array parent representing a forest of trees. parent[i] is the parent of vertex i or itself for a root Output: An array containing the root ancestor for every vertex for i ← 1 to length(parent) do in parallel successor[i] ← parent[i] while true for i ← 1 to length(successor) do in parallel successor_next[i] ← successor[successor[i]] if successor_next = successor then break for i ← 1 to length(successor) do in parallel successor[i] ← successor_next[i] return successor The following image provides an example of using pointer jumping on a small forest. On each iteration the successor points to the vertex following one more successor. After two iterations, every vertex points to its root node. == History and examples == Although the name pointer jumping would come later, JáJá attributes the first uses of the technique in early parallel graph algorithms and list ranking. The technique has been described with other names such as shortcutting, but by the 1990s textbooks on parallel algorithms consistently used the term pointer jumping. Today, pointer jumping is considered a software design pattern for operating on recursive data types in parallel. As a technique for following linked paths, graph algorithms are a natural fit for pointer jumping. Consequently, several parallel graph algorithms utilizing pointer jumping have been designed. These include algorithms for finding the roots of a forest of rooted trees, connected components, minimum spanning trees, and biconnected components. However, pointer jumping has also shown to be useful in a variety of other problems including computer vision, image compression, and Bayesian inference.
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Deep Learning Indaba

The Deep Learning Indaba is an annual conference and educational event that aims to strengthen machine learning and artificial intelligence (AI) capacity across Africa. Launched in 2017, it brings together students, researchers, industry practitioners, and policymakers from across the African continent. == History == The Deep Learning Indaba began in 2017 at the University of the Witwatersrand with over 300 participants from 23 African countries, offering tutorials in advanced AI topics and featuring notable speakers like Nando de Freitas. In 2018, it expanded to 650 delegates at Stellenbosch University, introducing parallel sessions to encourage collaboration. The 2019 edition in Nairobi, Kenya, reflected further growth, with increasing sponsorship and support from major tech companies like Google and Microsoft. === Deep Learning IndabaX ===
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Bisection (software engineering)

Bisection is a method used in software development to identify change sets that result in a specific behavior change. It is mostly employed for finding the patch that introduced a bug. Another application area is finding the patch that indirectly fixed a bug. == Overview == The process of locating the changeset that introduced a specific regression was described as "source change isolation" in 1997 by Brian Ness and Viet Ngo of Cray Research. Regression testing was performed on Cray's compilers in editions comprising one or more changesets. Editions with known regressions could not be validated until developers addressed the problem. Source change isolation narrowed the cause to a single changeset that could then be excluded from editions, unblocking them with respect to this problem, while the author of the change worked on a fix. Ness and Ngo outlined linear search and binary search methods of performing this isolation. Code bisection has the goal of minimizing the effort to find a specific change set. It employs a divide and conquer algorithm that depends on having access to the code history which is usually preserved by revision control in a code repository. == Bisection method == === Code bisection algorithm === Code history has the structure of a directed acyclic graph which can be topologically sorted. This makes it possible to use a divide and conquer search algorithm which: splits up the search space of candidate revisions tests for the behavior in question reduces the search space depending on the test result re-iterates the steps above until a range with at most one bisectable patch candidate remains === Algorithmic complexity === Bisection is in LSPACE having an algorithmic complexity of O ( log ⁡ N ) {\displaystyle O(\log N)} with N {\displaystyle N} denoting the number of revisions in the search space, and is similar to a binary search. === Desirable repository properties === For code bisection it is desirable that each revision in the search space can be built and tested independently. === Monotonicity === For the bisection algorithm to identify a single changeset which caused the behavior being tested to change, the behavior must change monotonically across the search space. For a Boolean function such as a pass/fail test, this means that it only changes once across all changesets between the start and end of the search space. If there are multiple changesets across the search space where the behavior being tested changes between false and true, then the bisection algorithm will find one of them, but it will not necessarily be the root cause of the change in behavior between the start and the end of the search space. The root cause could be a different changeset, or a combination of two or more changesets across the search space. To help deal with this problem, automated tools allow specific changesets to be ignored during a bisection search. == Automation support == Although the bisection method can be completed manually, one of its main advantages is that it can be easily automated. It can thus fit into existing test automation processes: failures in exhaustive automated regression tests can trigger automated bisection to localize faults. Ness and Ngo focused on its potential in Cray's continuous delivery-style environment in which the automatically isolated bad changeset could be automatically excluded from builds. The revision control systems Fossil, Git and Mercurial have built-in functionality for code bisection. The user can start a bisection session with a specified range of revisions from which the revision control system proposes a revision to test, the user tells the system whether the revision tested as "good" or "bad", and the process repeats until the specific "bad" revision has been identified. Other revision control systems, such as Bazaar or Subversion, support bisection through plugins or external scripts. Phoronix Test Suite can do bisection automatically to find performance regressions.
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Task Force on Process Mining

The IEEE Task Force on Process Mining (TFPM) is a non-commercial association for process mining. The IEEE (Institute of Electrical and Electronics Engineers) Task Force on Process Mining was established in October 2009 as part of the IEEE Computational Intelligence Society at the Eindhoven University of Technology. The task force is supported by over 80 organizations and has around 750 members. The main goal of the task force is to promote the research, development, education, and understanding of process mining. == About == In 2012, the IEEE World Congress on Computational Intelligence/ IEEE Congress on Evolutionary Computation held a session on Process Mining. Process mining is a type of research that is a mix of computational intelligence and data mining, as well as process modeling and analysis. === Activities and organization === The Task Force on Process Mining has a Steering Committee and an Advisory Board. The Steering Committee, was chaired by Wil van der Aalst in its inception in 2009, defined 15 action lines. These include the organization of the annual International Process Mining Conference (ICPM) series, standardization efforts leading to the IEEE XES standard for storing and exchanging event data, and the Process Mining Manifesto which was translated into 16 languages. The Task Force on Process Mining also publishes a newsletter, provides data sets, organizes workshops and competitions, and connects researchers and practitioners. In 2016, the IEEE Standards Association published the IEEE Standard for Extensible Event Stream (XES), which is a widely accepted file format by the process mining community. As of 2023, Boudewijn van Dongen serves as chair of the Steering Committee. Wil van der Aalst and Moe Wynn both serve as vice-chair of the Steering Committee.
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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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Ugly duckling theorem

The ugly duckling theorem is an argument showing that classification is not really possible without some sort of bias. More particularly, it assumes finitely many properties combinable by logical connectives, and finitely many objects; it asserts that any two different objects share the same number of (extensional) properties. The theorem is named after Hans Christian Andersen's 1843 story "The Ugly Duckling", because it shows that a duckling is just as similar to a swan as two swans are to each other. It was derived by Satosi Watanabe in 1969. == Mathematical formula == Suppose there are n things in the universe, and one wants to put them into classes or categories. One has no preconceived ideas or biases about what sorts of categories are "natural" or "normal" and what are not. So one has to consider all the possible classes that could be, all the possible ways of making a set out of the n objects. There are 2 n {\displaystyle 2^{n}} such ways, the size of the power set of n objects. One can use that to measure the similarity between two objects, and one would see how many sets they have in common. However, one cannot. Any two objects have exactly the same number of classes in common if we can form any possible class, namely 2 n − 1 {\displaystyle 2^{n-1}} (half the total number of classes there are). To see this is so, one may imagine each class is represented by an n-bit string (or binary encoded integer), with a zero for each element not in the class and a one for each element in the class. As one finds, there are 2 n {\displaystyle 2^{n}} such strings. As all possible choices of zeros and ones are there, any two bit-positions will agree exactly half the time. One may pick two elements and reorder the bits so they are the first two, and imagine the numbers sorted lexicographically. The first 2 n / 2 {\displaystyle 2^{n}/2} numbers will have bit #1 set to zero, and the second 2 n / 2 {\displaystyle 2^{n}/2} will have it set to one. Within each of those blocks, the top 2 n / 4 {\displaystyle 2^{n}/4} will have bit #2 set to zero and the other 2 n / 4 {\displaystyle 2^{n}/4} will have it as one, so they agree on two blocks of 2 n / 4 {\displaystyle 2^{n}/4} or on half of all the cases, no matter which two elements one picks. So if we have no preconceived bias about which categories are better, everything is then equally similar (or equally dissimilar). The number of predicates simultaneously satisfied by two non-identical elements is constant over all such pairs. Thus, some kind of inductive bias is needed to make judgements to prefer certain categories over others. === Boolean functions === Let x 1 , x 2 , … , x n {\displaystyle x_{1},x_{2},\dots ,x_{n}} be a set of vectors of k {\displaystyle k} booleans each. The ugly duckling is the vector which is least like the others. Given the booleans, this can be computed using Hamming distance. However, the choice of boolean features to consider could have been somewhat arbitrary. Perhaps there were features derivable from the original features that were important for identifying the ugly duckling. The set of booleans in the vector can be extended with new features computed as boolean functions of the k {\displaystyle k} original features. The only canonical way to do this is to extend it with all possible Boolean functions. The resulting completed vectors have 2 k {\displaystyle 2^{k}} features. The ugly duckling theorem states that there is no ugly duckling because any two completed vectors will either be equal or differ in exactly half of the features. Proof. Let x and y be two vectors. If they are the same, then their completed vectors must also be the same because any Boolean function of x will agree with the same Boolean function of y. If x and y are different, then there exists a coordinate i {\displaystyle i} where the i {\displaystyle i} -th coordinate of x {\displaystyle x} differs from the i {\displaystyle i} -th coordinate of y {\displaystyle y} . Now the completed features contain every Boolean function on k {\displaystyle k} Boolean variables, with each one exactly once. Viewing these Boolean functions as polynomials in k {\displaystyle k} variables over GF(2), segregate the functions into pairs ( f , g ) {\displaystyle (f,g)} where f {\displaystyle f} contains the i {\displaystyle i} -th coordinate as a linear term and g {\displaystyle g} is f {\displaystyle f} without that linear term. Now, for every such pair ( f , g ) {\displaystyle (f,g)} , x {\displaystyle x} and y {\displaystyle y} will agree on exactly one of the two functions. If they agree on one, they must disagree on the other and vice versa. (This proof is believed to be due to Watanabe.) == Discussion == A possible way around the ugly duckling theorem would be to introduce a constraint on how similarity is measured by limiting the properties involved in classification, for instance, between A and B. However Medin et al. (1993) point out that this does not actually resolve the arbitrariness or bias problem since in what respects A is similar to B: "varies with the stimulus context and task, so that there is no unique answer, to the question of how similar is one object to another". For example, "a barberpole and a zebra would be more similar than a horse and a zebra if the feature striped had sufficient weight. Of course, if these feature weights were fixed, then these similarity relations would be constrained". Yet the property "striped" as a weight 'fix' or constraint is arbitrary itself, meaning: "unless one can specify such criteria, then the claim that categorization is based on attribute matching is almost entirely vacuous". Stamos (2003) remarked that some judgments of overall similarity are non-arbitrary in the sense they are useful: "Presumably, people's perceptual and conceptual processes have evolved that information that matters to human needs and goals can be roughly approximated by a similarity heuristic... If you are in the jungle and you see a tiger but you decide not to stereotype (perhaps because you believe that similarity is a false friend), then you will probably be eaten. In other words, in the biological world stereotyping based on veridical judgments of overall similarity statistically results in greater survival and reproductive success." Unless some properties are considered more salient, or 'weighted' more important than others, everything will appear equally similar, hence Watanabe (1986) wrote: "any objects, in so far as they are distinguishable, are equally similar". In a weaker setting that assumes infinitely many properties, Murphy and Medin (1985) give an example of two putative classified things, plums and lawnmowers: "Suppose that one is to list the attributes that plums and lawnmowers have in common in order to judge their similarity. It is easy to see that the list could be infinite: Both weigh less than 10,000 kg (and less than 10,001 kg), both did not exist 10,000,000 years ago (and 10,000,001 years ago), both cannot hear well, both can be dropped, both take up space, and so on. Likewise, the list of differences could be infinite… any two entities can be arbitrarily similar or dissimilar by changing the criterion of what counts as a relevant attribute." According to Woodward, the ugly duckling theorem is related to Schaffer's Conservation Law for Generalization Performance, which states that all algorithms for learning of boolean functions from input/output examples have the same overall generalization performance as random guessing. The latter result is generalized by Woodward to functions on countably infinite domains.
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KiSAO

The Kinetic Simulation Algorithm Ontology (KiSAO) supplies information about existing algorithms available for the simulation of systems biology models, their characterization and interrelationships. KiSAO is part of the BioModels.net project and of the COMBINE initiative. == Structure == KiSAO consists of three main branches: simulation algorithm simulation algorithm characteristic simulation algorithm parameter The elements of each algorithm branch are linked to characteristic and parameter branches using has characteristic and has parameter relationships accordingly. The algorithm branch itself is hierarchically structured using relationships which denote that the descendant algorithms were derived from, or specify, more general ancestors.
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List of library and information science journals

This list covers the journals, magazines, periodicals already published and continuing in the discipline of library and information science (LIS). It doesn't include ceased titles or predatory journals. Titles listed were taken from various scholarly sources, UGC Care and Wikipedia articles. == LIS journal prestige as assessed by LIS faculty == In a 2013 article by Laura Manzari, 232 LIS faculty members from ALA-accredited information science programs ranked the most prestigious journals in library and information science. The following journals were ranked in the top ten most prestigious: Journal of the Association for Information Science and Technology The Library Quarterly Annual Review of Information Science and Technology Journal of Documentation Library Trends Library and Information Science Research Information Processing and Management Journal of Education for Library and Information Science Education College & Research Libraries First Monday (journal) A subsequent study by Safón and Docampo in 2023 identified impactful LIS journals based on their influence on papers published in other LIS publications. Journals listed in the top ten in this study that did not appear in Manzari's list include: Scientometrics International Journal of Information Management Quantitative Science Studies MIS Quarterly Information and Management Journal of the Association for Information Systems Journal of Informetrics The Journal of Academic Librarianship == India == Annals of Library and Information Studies. (Pub: CSIR-NIScPR ), Formerly: Annals of Library Science. ISSN 0003-4835. (1954-) OPEN ACCESS Collnet Journal of Scientrometrics and Information Management (Pub: Taru Publications, Online through Taylor and Francis) ISSN: 0973-7766 Online 2168-930X. College Libraries (Pub: West Bengal College Librarians’ Association (WBCLA) ISSN 0972-1975, Quarterly DESIDOC Journal of Library and Information Technology (DJLIT) (Formerly: DESIDOC Bulletin 0970-8154, DESIDOC Bulletin of Information Technology. 0971-4383/0974-0643) (Pub: Defence Scientific Information & Documentation Centre) ISSN: 0974-0643, ISSN: 0976-4658 (O), Bi-monthly, OPEN ACCESS. Grandhalaya Sarvaswam (Bilingual: Telugu & English) [Pub: Andhra Pradesh Library Association, Vijayawada, Andhra Pradesh, India] (1915–) Gyankosh: Journal of Library and Information Management. (Pub: Integrated Academy Of Management And Technology. Through: Indian Journals.Com). ISSN: 2229-4023 (P), 2249-3182. Half yearly. IASLIC Bulletin (Pub: Indian Association of Special Libraries and Information Centres) ISSN: 0018-8411. Quarterly (1956-) IASLIC Newsletter (Pub: Indian Association of Special Libraries and Information Centres. (Pub: Indian Association of Special Libraries and Information Centres) ISSN 0018-845X. Monthly. (1966-) INFLIBNET Newsletter. (Pub: INFLIBNET). Monthly. Informatics Studies. (Pub: Centre For Informatics Research And Development). Quarterly. Through: Indian journals.com. ISSN: 2583-8994 (Online), 2320-530X (Print) ISST Journal of Advances in Librarianship (Pub:Intellectuals Society for Socio-Techno Welfare) ISSN: 0976-9021. Semiannual. Journal of Advanced Research in Library and Information Science. (JALIS Publishers). 4/year. ISSN 2277-2219. Journal of Indian Library Association (Pub: Indian Library Association). ISSN (P) 2277-5145 O) 2456-513X. Quarterly. (1965-). Journal of Scientometric Research. (Pub: Phcog.Net). ISSN (P) 2321-6654, (O) 2320-0057]; Frequency : Triannual. KELPRO Bulletin (Pub: Kerala Library Professionals' Organisation - KELPRO). ISSN 0975-4911( Print),2582-497X (O).(1993-) KIIT Journal of Library and Information Management (Pub: KIIT University, online through Indian Journals.com) Half yearly. ISSN: 2348-0858. Library Herald. (Pub: Delhi Library Association - DLA). Quarterly. ISSN: 0024-2292. Library Progress (International). (Pub: Bpas Publications, Through: ). Half yearly. ISSN: 0970-1052. (O) ISSN: 2320-317X. (1981-) Pearl: A Journal of Library and Information Science. (Pub: University Library Teacher's Association of Andhra Pradesh, Hyderabad), ISSN: 0973-7081 (print), 0975-6922 (online). Quarterly. RBU Journal of Library and Information Science. (Pub: Rabindra Bharati University).ISSN: 0972-2750. Annual. SALIS Journal of Information Management and Technology - SJIMT. (Pub: Society for the Advancement of Library and Information Science). Half-yearly. ISSN 0975-4105. SALIS Journal of Library and Information Science - SJLIS: an International Journal. (Pub: Society for the Advancement of Library and Information Science). Half-yearly. ISSN: 0973-3108. SRELS journal of Information and Knowledge (Formerly: Library Science with a Slant to Documentation, ISSN: 0024-2543; Library Science with a Slant to Documentation and Information Studies ISSN: 0970-6089; SRELS Journal of Information Management ISSN: ). Quarterly. ISSN: 2583-9314 (O) World Digital Libraries. Half yearly. ISSN: 0974-567X (P), 0975-7597 (O). == Other countries == African Journal of Library, Archives and Information Science Art Libraries Journal (Cambridge University Press) Bibliothèque de l'École des Chartes Canadian Journal of Information and Library Science Cataloging & Classification Quarterly Communications in Information Literacy Cataloging & Classification Quarterly Catholic Library Association Children and Libraries Code4Lib Journal College & Research Libraries Communications in Information Literacy Disability in Library and Information Studies Electronic Journal of Academic and Special Librarianship El Profesional de la Información (es) (EPI) (Formerly Information World en Español) Evidence Based Library and Information Practice (journal) Faslname-ye Ketab Florida Libraries. Florida Library Association. Georgia Library Quarterly. Quarterly. (Pub: Georgia Library Association). Hipertext.net IFLA Journal In the Library with the Lead Pipe Information & Culture International Journal of Information Retrieval Research (IJIRR) Information Processing and Management Information Research Information Sciences (journal) Information Visualization (journal) Information, Communication & Society International Journal of Geographical Information Science Information Research: An International Electronic Journal (IR) Internet Research (journal) Issues in Science and Technology Librarianship Italian Journal of Library and Information Studies (JLIS.it) JLIS.it Journal of Documentation (JDoc) Journal of Information Ethics Journal of Information Science (JIS) Journal of Information Technology Journal of Informetrics Journal of Librarianship and Information Science Journal of Library & Information Studies - JLIS. (Pub: National Taiwan University) Journal of Library Administration Journal of Religious & Theological Information Journal of the Association for Information Science and Technology (Formerly Journal of the American Society for Information Science and Technology) (JASIST) Journal of the Medical Library Association Journal of the Canadian Health Libraries Association (Pub: Canadian Health Libraries Association). Knowledge Organization (journal) Knowledge Quest. (Pub: American Association of School Librarians) Library and Information Science Abstracts Library Literature and Information Science Library, Information Science & Technology Abstracts Library Literature and Information Science Retrospective Library Review (journal) Library Trends Libri (journal) Malaysian Journal of Library and Information Science MLA Forum New Century Library New Review of Children's Literature and Librarianship Notes (journal) Portal – Libraries and the Academy Progressive Librarian, Progressive Librarians Guild Reference and User Services Quarterly Reference Services Review Research Evaluation (journal) Scientometrics (journal) Serials Review South African Journal of Libraries and Information Science The Charleston Advisor The Christian Librarian, from the Association of Christian Librarians The Journal of Academic Librarianship The Library Quarterly (LQ) The Public-Access Computer Systems Review TripleC Webolog
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Principles for a Data Economy

The Principles for a Data Economy – Data Rights and Transactions is a transatlantic legal project carried out jointly by the American Law Institute (ALI) and the European Law Institute (ELI). The Principles for a Data Economy deals with a range of different legal questions that arise in the data economy. Since data is different from other tradeable items, the Principles draw up legal rules for data transactions and data rights that take into account the interests of different stakeholders involved in the data economy. The Principles are designed to facilitate contractual relations as well as the drafting of model agreements and can guide courts and legislators worldwide. The project proposes a set of principles that can be implemented in any legal system and is designed to work in conjunction with any kind of data privacy/data protection law, intellectual property law or trade secret law. The Principles do not address or seek to change any of the substantive rules of these bodies of law. The Project Team consists of Neil B Cohen and Christiane Wendehorst (as Project Reporters) and Lord John Thomas as well as Steven O. Weise (as Project Chairs). == Characteristics of data == The law governing trades in commerce has historically focused on trade in items that are tangible like goods or on intangible assets, such as shares or licenses. However, data does not fit into any of these traditional categories, nor does it qualify as a service. It is often unclear how traditional legal rules and doctrines can apply to data, as data is different from other assets in many ways. For example, data can be multiplied at basically no cost and can be used in parallel for a variety of different purposes by many different people at the same time (data is a “non-rivalrous” resource). Uncertainty regarding the applicable rules to govern the data economy may inhibit innovation and growth and trouble stakeholders like data-driven industries, start-ups, and consumers. == Stakeholders in the data economy == The Principles have taken the basic types of players and relations which can be found in data ecosystems as a starting point to provide guidance in different situations. The central actors in the data economy are data controllers (also called “data holders”). They are in a position to access the data and decide for which purposes and means this data should be processed. A controller may exercise control all by itself or share it with co-controllers, such as under a data pooling arrangement. Data processors provide the processing of data on a controller’s behalf as a service. Another important group of stakeholders includes those that contribute to the generation of data (e.g. data subjects). Other players in the data economy include data assemblers or data intermediaries (e.g. data trusts). == History of the project and timeline == Before the official adoption of the project by ALI and ELI bodies in 2018, the project team carried out a Feasibility Study from October 2016 to February 2018. In the following years, the project team produced a number of drafts (e.g. “Preliminary Drafts” No. 1 to 4, “Tentative Draft No. 1”) and project progress were regularly discussed with advisory bodies and members of both the ALI and the ELI. The project reporters also included feedback and insights from industry stakeholders and experts that was gained after several meetings and workshops, hosted, inter alia by UNCITRAL, UNIDROIT and several national governmental institutions. Tentative Draft No. 2 was presented at the ALI Annual Meeting in May 2021 and approved by ALI membership. The latest draft ("Final Council Draft") was also approved by the ELI Council and ELI Membership. The Principles for a Data Economy were presented at an international conference with representatives from institutions such as the Uniform Law Commission (ULC), the European Commission, UNIDROIT, the OECD, the International Chamber of Commerce (ICC) and the World Economic Forum (WEF) in October 2021. == Project structure == The current draft (“Tentative Draft No. 2”) of the Principles consists of five Parts that each governs different aspects of the data economy: General Provisions, Data Contracts, Data Rights, Third Party Aspects of Data Activities, and Multi-State Issues. === General Provisions === Part I includes general provisions that apply to all other Parts of the Principles for a Data Economy. This Part sets out the purpose of the Principles: they aim to make existing law in the field of the data economy more coherent and support the development of the law in this field by courts and legislators worldwide. It is also clarified that the Principles have a wide scope of application and can be used in a variety of ways by stakeholders in the data economy. The Principles may, for example, serve private parties as a basis for contract formation, guide the deliberations of arbitral tribunals or inspire national legislation. Part I then defines several key terms, such as ‘digital data’ and ‘data right’. The scope of the Principles is limited to matters where information is recorded as an asset, resource or tradeable commodity and where large amounts of data, rather than single pieces of information, are concerned. This Part also clarifies that remedies with respect to data contracts and data rights are left to the applicable national law. === Data Contracts === Part II lists different types of contracts that often occur in the data economy and establishes two broad categories, namely contracts for the supply and sharing of data and contracts for services with regard to data. Contracts for the supply and sharing of data include, e.g. data transfer contracts or data pooling arrangements, while contracts for services with regard to data cover contracts for the processing of data or data intermediary contracts. The Principles provide default terms for each contract type, on issues such as the manner in which data should supply or which characteristics the data supplied should meet. These default terms 'automatically' become part of the contract unless the parties agree otherwise. === Data Rights === Part III governs legally protected interests of players in the data economy that stem from the characteristics of data as a resource (e.g. its non-rivalrous nature) or from public interest considerations. Such data rights may include the right to data access, the right to require the controller to desist from data activities or to correct incorrect/incomplete data, or even to receive an economic share in profits derived from the use of data. For example, the Principles deal with data rights of stakeholders that had a share in the co-generation of data and identify different factors to be considered in determining whether to afford a party a data right. The underlying idea that parties who have contributed to the generation of data should have some rights in the utilization of the data is also recognized by governmental institutions, such as by the Japanese Ministry of Economy, Trade and Industry (METI), and the term co-generated data, which was coined by the Principles for a Data Economy, has been adopted, inter alia by the European Commission, the German Data Ethics Commission and the Global Partnership on Artificial Intelligence (GPAI). This Part also deals with data rights for the public interest, such as data sharing rights in the field of innovation. === Third Party Aspects === Part IV governs different situations in which data transactions interfere with the rights of third parties. Such rights include intellectual property rights or rights derived from data privacy or data protection law. This Part sets out under which circumstances data activities should be considered wrongful vis à vis another party. For example, a data activity (like data processing or the onward supply of data) could be considered wrongful, if a controller interferes with the rights of data subjects that are protected by data-protection law. A data activity could also be wrongful if the controller is non-compliant with contractual limitations on data activities, enforceable by the protected party (e.g. a controller may only process data for a certain purpose). If someone obtained access to data by unauthorized means (i.e. data “theft”) this could also be considered wrongful. The Part on Third-Party Aspects also takes a detailed look at the effects of the onward supply of data can have on third parties, while balancing the protection of third parties on the one hand, with the interests of data recipients and the desire to encourage data sharing on the other. === Multi-State Issues === As transactions in the data economy are international by nature and hardly occur within one legal system alone, the Part V of the Principles also briefly touches upon the applicability of the rules and doctrines of private international law to such transactions. == Links == Website of the “Principles for a Data Economy – Data Rights and Transaction
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Mobile Passport Control

Mobile Passport Control (MPC) is a mobile app that enables eligible travelers entering the United States to submit their passport information and customs declaration form to Customs and Border Protection via smartphone or tablet and go through the inspections process using an expedited lane. It is available to "U.S. citizens, U.S. lawful permanent residents, Canadian B1/B2 citizen visitors and returning Visa Waiver Program travelers with approved ESTA". The app is available on iOS and Android devices and is operational at 34 US airports, 14 international airports offering preclearance facilities, and 4 seaports. The use of Mobile Passport Control operations have increased threefold from 2016 to 2017. == History == Mobile Passport Control operations were launched in Atlanta at the Hartsfield-Jackson International Airport in 2016 and is now available at 34 U.S. airports, 14 international airports that offer preclearance and 4 U.S. cruise ports. The Mobile Passport app is authorized by CBP and sponsored by the Airports Council International-North America, Boeing, and the Port of Everglades. Airside Mobile, Inc. secured a Series A funding of $6 million in the fall of 2017. == How it works == During the customs process at the Federal Inspection Service (FIS) area of a U.S. airport, travelers arriving from international locations typically wait in long lines before presenting passports and paperwork and verbally answering questions made by CBP officials. Eligible travelers who have downloaded the Mobile Passport app can expedite this process by submitting information regarding their passport and trip details, and a newly-taken selfie, via their mobile device to CBP officials, then access an expedited line. Mobile Passport Control users will be required to show their physical passport(s) and briefly talk to a CBP officer. == Locations == === US airports === Atlanta (ATL) Baltimore (BWI) Boston (BOS) Charlotte (CLT) Chicago (ORD) Dallas/Ft Worth (DFW) Denver (DEN) Detroit (DTW) as of 7/2024 Ft. Lauderdale (FLL) Honolulu (HNL) Houston (HOU and IAH) Kansas City (MCI) Las Vegas (LAS) Los Angeles (LAX) Miami (MIA) Minneapolis (MSP) New York (JFK) Newark (EWR) Oakland (OAK) Orlando (MCO) Palm Beach (PBI) Philadelphia (PHL) Phoenix (PHX) Pittsburgh (PIT) Portland (PDX) Sacramento (SMF) San Diego (SAN) San Francisco (SFO) San Jose (SJC) San Juan (SJU) Seattle (SEA) Tampa (TPA) Washington Dulles (IAD) === International Preclearance locations === Abu Dhabi (AUH) Aruba (AUA) Bermuda (BDA) Calgary (YYC) Dublin (DUB) Edmonton (YEG) Halifax (YHZ) Montreal (YUL) Nassau (NAS) Ottawa (YOW) Shannon (SNN) Toronto (YYZ) Vancouver (YVR) Winnipeg (YWG) Sepinggan (BPN) === Seaports === Fort Lauderdale (PEV) Miami (MSE) San Juan (PUE) West Palm Beach (WPB)
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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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Communication-avoiding algorithm

Communication-avoiding algorithms minimize movement of data within a memory hierarchy for improving its running-time and energy consumption. These minimize the total of two costs (in terms of time and energy): arithmetic and communication. Communication, in this context refers to moving data, either between levels of memory or between multiple processors over a network. It is much more expensive than arithmetic. == Formal theory == === Two-level memory model === A common computational model in analyzing communication-avoiding algorithms is the two-level memory model: There is one processor and two levels of memory. Level 1 memory is infinitely large. Level 0 memory ("cache") has size M {\displaystyle M} . In the beginning, input resides in level 1. In the end, the output resides in level 1. Processor can only operate on data in cache. The goal is to minimize data transfers between the two levels of memory. === Matrix multiplication === Corollary 6.2: More general results for other numerical linear algebra operations can be found in. The following proof is from. == Motivation == Consider the following running-time model: Measure of computation = Time per FLOP = γ Measure of communication = No. of words of data moved = β ⇒ Total running time = γ·(no. of FLOPs) + β·(no. of words) From the fact that β >> γ as measured in time and energy, communication cost dominates computation cost. Technological trends indicate that the relative cost of communication is increasing on a variety of platforms, from cloud computing to supercomputers to mobile devices. The report also predicts that gap between DRAM access time and FLOPs will increase 100× over coming decade to balance power usage between processors and DRAM. Energy consumption increases by orders of magnitude as we go higher in the memory hierarchy. United States president Barack Obama cited communication-avoiding algorithms in the FY 2012 Department of Energy budget request to Congress: New Algorithm Improves Performance and Accuracy on Extreme-Scale Computing Systems. On modern computer architectures, communication between processors takes longer than the performance of a floating-point arithmetic operation by a given processor. ASCR researchers have developed a new method, derived from commonly used linear algebra methods, to minimize communications between processors and the memory hierarchy, by reformulating the communication patterns specified within the algorithm. This method has been implemented in the TRILINOS framework, a highly-regarded suite of software, which provides functionality for researchers around the world to solve large scale, complex multi-physics problems. == Objectives == Communication-avoiding algorithms are designed with the following objectives: Reorganize algorithms to reduce communication across all memory hierarchies. Attain the lower-bound on communication when possible. The following simple example demonstrates how these are achieved. === Matrix multiplication example === Let A, B and C be square matrices of order n × n. The following naive algorithm implements C = C + A B: for i = 1 to n for j = 1 to n for k = 1 to n C(i,j) = C(i,j) + A(i,k) B(k,j) Arithmetic cost (time-complexity): n2(2n − 1) for sufficiently large n or O(n3). Rewriting this algorithm with communication cost labelled at each step for i = 1 to n {read row i of A into fast memory} - n2 reads for j = 1 to n {read C(i,j) into fast memory} - n2 reads {read column j of B into fast memory} - n3 reads for k = 1 to n C(i,j) = C(i,j) + A(i,k) B(k,j) {write C(i,j) back to slow memory} - n2 writes Fast memory may be defined as the local processor memory (CPU cache) of size M and slow memory may be defined as the DRAM. Communication cost (reads/writes): n3 + 3n2 or O(n3) Since total running time = γ·O(n3) + β·O(n3) and β >> γ the communication cost is dominant. The blocked (tiled) matrix multiplication algorithm reduces this dominant term: ==== Blocked (tiled) matrix multiplication ==== Consider A, B and C to be n/b-by-n/b matrices of b-by-b sub-blocks where b is called the block size; assume three b-by-b blocks fit in fast memory. for i = 1 to n/b for j = 1 to n/b {read block C(i,j) into fast memory} - b2 × (n/b)2 = n2 reads for k = 1 to n/b {read block A(i,k) into fast memory} - b2 × (n/b)3 = n3/b reads {read block B(k,j) into fast memory} - b2 × (n/b)3 = n3/b reads C(i,j) = C(i,j) + A(i,k) B(k,j) - {do a matrix multiply on blocks} {write block C(i,j) back to slow memory} - b2 × (n/b)2 = n2 writes Communication cost: 2n3/b + 2n2 reads/writes << 2n3 arithmetic cost Making b as large possible: 3b2 ≤ M we achieve the following communication lower bound: 31/2n3/M1/2 + 2n2 or Ω (no. of FLOPs / M1/2) == Previous approaches for reducing communication == Most of the approaches investigated in the past to address this problem rely on scheduling or tuning techniques that aim at overlapping communication with computation. However, this approach can lead to an improvement of at most a factor of two. Ghosting is a different technique for reducing communication, in which a processor stores and computes redundantly data from neighboring processors for future computations. Cache-oblivious algorithms represent a different approach introduced in 1999 for fast Fourier transforms, and then extended to graph algorithms, dynamic programming, etc. They were also applied to several operations in linear algebra as dense LU and QR factorizations. The design of architecture specific algorithms is another approach that can be used for reducing the communication in parallel algorithms, and there are many examples in the literature of algorithms that are adapted to a given communication topology.
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