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  Engineering Historical Memory

  Engineering Historical Memory (EHM) is an online database in the digital humanities, serving as an open-access research tool for primary historical materials focused on 11th to 15th century Afro-Eurasia. It adopts computational methods to make historical documents machine-understandable. EHM parses traditional artifacts such as historical maps, travel accounts, chronicles and codices into computer-readable formats, and links them to secondary multi-media references, a process referred to as the "automatic narrative generation". This approach generates cultural narratives and facilitates interaction with the historical artifacts, making them accessible to audiences from various backgrounds. == History == EHM was first theorised in 2007 by researcher Andrea Nanetti when he was a visiting scholar at Princeton University, and the preliminary test results were published between 2008 and 2011. In 2013, the EHM research team was set up in Singapore following Nanetti's professorship at Nanyang Technological University (NTU). Two years later, after receiving several Microsoft research grants, EHM went live on Microsoft Azure. In 2018, the College of Humanities, Arts and Social Sciences (CoHASS) at NTU Singapore formed the Digital Humanities Research Cluster, as part of which, EHM has been an ongoing interdisciplinary research project led by Nanetti. Partnering with international educational and cultural institutions such as Ca' Foscari University of Venice, University of Florence, Taylor & Francis Group, Delft University of Technology (TUDelft), and SenticNet, EHM has been supported by over 130 scholars and engineers. == Applications == Primary historical materials on EHM are curated into several categories, including maps, travel accounts, chronicles, codices, sites, archival documents, and paintings, such as the Morosini Codex (listed under Chronicles) and Pope Gregory X's Privilege for the Holy Monastery of St Catherine of Sinai (listed under Archival Documents). EHM has been adopted by cultural organisations as an exhibition and research tool in the digital humanities field. An example is the publication of a digital interactive edition of Fra Mauro's Map of the World on EHM, a collaboration project between NTU Singapore and the Biblioteca Nazionale Marciana of Venice. The digitisation process of the map on EHM involved transcribing and geo-referencing the textual content in the 15th-century map, followed by creating semantic annotations to connect the map's content with related secondary data sources. The e-map was subsequently adopted and launched online by Museo Galileo in March 2022 and incorporated into the virtual exhibition "Venezia and Suzhou: Water Cities along the Silk Roads" (online, September-December 2022). In 2024, the Fra Mauro's Map of the World application on EHM was awarded the Digital Humanities and Multimedia Studies Prize (DHMS) by the Medieval Academy of America. Image-Based Video Search Engine is another experimental project under the EHM scope led by the research teams at Delft University of Technology (TUDelft) and NTU Singapore. This ongoing project aims to improve the efficiency of retrieving targeted objects from audio-visuals. == Awards == In 2021, EHM won the GLAMi Awards (MuseWeb Conference - Galleries, Libraries, Archives, and Museums Innovation awards) in the "Resources for Scholars and Researchers" category. In the same year, EHM was a Falling Walls finalist for Science Breakthrough of the Year in the category Social Sciences and Humanities after nominated by the School of Advanced Study at the University of London. In April 2022, the Italian National Commission for UNESCO has selected and sent the EHM project to the organisers of the "Jikji Memory of the World" Award for final evaluation. In January 2024, the Medieval Academy of America announced its 2024 Digital Humanities and Multimedia Studies Prize (DHMS) goes to the Fra Mauro's Map of the World application on EHM.

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  Relationship square

  In statistics, the relationship square is a graphical representation for use in the factorial analysis of a table individuals x variables. This representation completes classical representations provided by principal component analysis (PCA) or multiple correspondence analysis (MCA), namely those of individuals, of quantitative variables (correlation circle) and of the categories of qualitative variables (at the centroid of the individuals who possess them). It is especially important in factor analysis of mixed data (FAMD) and in multiple factor analysis (MFA). == Definition of relationship square in the MCA frame == The first interest of the relationship square is to represent the variables themselves, not their categories, which is all the more valuable as there are many variables. For this, we calculate for each qualitative variable j {\displaystyle j} and each factor F s {\displaystyle F_{s}} ( F s {\displaystyle F_{s}} , rank s {\displaystyle s} factor, is the vector of coordinates of the individuals along the axis of rank s {\displaystyle s} ; in PCA, F s {\displaystyle F_{s}} is called principal component of rank s {\displaystyle s} ), the square of the correlation ratio between the F s {\displaystyle F_{s}} and the variable j {\displaystyle j} , usually denoted : η 2 ( j , F s ) {\displaystyle \eta ^{2}(j,F_{s})} Thus, to each factorial plane, we can associate a representation of qualitative variables themselves. Their coordinates being between 0 and 1, the variables appear in the square having as vertices the points (0,0), ( 0,1), (1,0) and (1,1). == Example in MCA == Six individuals ( i 1 , … , i 6 ) {\displaystyle i_{1},\ldots ,i_{6})} are described by three variables ( q 1 , q 2 , q 3 ) {\displaystyle (q_{1},q_{2},q_{3})} having respectively 3, 2 and 3 categories. Example : the individual i 1 {\displaystyle i_{1}} possesses the category a {\displaystyle a} of q 1 {\displaystyle q_{1}} , d {\displaystyle d} of q 2 {\displaystyle q_{2}} and f {\displaystyle f} of q 3 {\displaystyle q_{3}} . Applied to these data, the MCA function included in the R Package FactoMineR provides to the classical graph in Figure 1. The relationship square (Figure 2) makes easier the reading of the classic factorial plane. It indicates that: The first factor is related to the three variables but especially q 3 {\displaystyle q_{3}} (which have a very high coordinate along the first axis) and then q 2 {\displaystyle q_{2}} . The second factor is related only to q 1 {\displaystyle q_{1}} and q 3 {\displaystyle q_{3}} (and not to q 2 {\displaystyle q_{2}} which has a coordinate along axis 2 equal to 0) and that in a strong and equal manner. All this is visible on the classic graphic but not so clearly. The role of the relationship square is first to assist in reading a conventional graphic. This is precious when the variables are numerous and possess numerous coordinates. == Extensions == This representation may be supplemented with those of quantitative variables, the coordinates of the latter being the square of correlation coefficients (and not of correlation ratios). Thus, the second advantage of the relationship square lies in the ability to represent simultaneously quantitative and qualitative variables. The relationship square can be constructed from any factorial analysis of a table individuals x variables. In particular, it is (or should be) used systematically: in multiple correspondences analysis (MCA); in principal components analysis (PCA) when there are many supplementary variables; in factor analysis of mixed data (FAMD). An extension of this graphic to groups of variables (how to represent a group of variables by a single point ?) is used in Multiple Factor Analysis (MFA) == History == The idea of representing the qualitative variables themselves by a point (and not the categories) is due to Brigitte Escofier. The graphic as it is used now has been introduced by Brigitte Escofier and Jérôme Pagès in the framework of multiple factor analysis == Conclusion == In MCA, the relationship square provides a synthetic view of the connections between mixed variables, all the more valuable as there are many variables having many categories. This representation iscan be useful in any factorial analysis when there are numerous mixed variables, active and/or supplementary.

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  Softplus

  In mathematics and machine learning, the softplus function is f ( x ) = ln ⁡ ( 1 + e x ) . {\displaystyle f(x)=\ln(1+e^{x}).} It is a smooth approximation (in fact, an analytic function) to the ramp function, which is known as the rectifier or ReLU (rectified linear unit) in machine learning. For large negative x {\displaystyle x} it is ln ⁡ ( 1 + e x ) = ln ⁡ ( 1 + ϵ ) ⪆ ln ⁡ 1 = 0 {\displaystyle \ln(1+e^{x})=\ln(1+\epsilon )\gtrapprox \ln 1=0} , so just above 0, while for large positive x {\displaystyle x} it is ln ⁡ ( 1 + e x ) ⪆ ln ⁡ ( e x ) = x {\displaystyle \ln(1+e^{x})\gtrapprox \ln(e^{x})=x} , so just above x {\displaystyle x} . The names softplus and SmoothReLU are used in machine learning. The name "softplus" (2000), by analogy with the earlier softmax (1989) is presumably because it is a smooth (soft) approximation of the positive part of x, which is sometimes denoted with a superscript plus, x + := max ( 0 , x ) {\displaystyle x^{+}:=\max(0,x)} . == Alternative forms == This function can be approximated as: ln ⁡ ( 1 + e x ) ≈ { ln ⁡ 2 , x = 0 , x 1 − e − x / ln ⁡ 2 , x ≠ 0 {\displaystyle \ln \left(1+e^{x}\right)\approx {\begin{cases}\ln 2,&x=0,\\[6pt]{\frac {x}{1-e^{-x/\ln 2}}},&x\neq 0\end{cases}}} By making the change of variables x = y ln ⁡ ( 2 ) {\displaystyle x=y\ln(2)} , this is equivalent to log 2 ⁡ ( 1 + 2 y ) ≈ { 1 , y = 0 , y 1 − e − y , y ≠ 0. {\displaystyle \log _{2}(1+2^{y})\approx {\begin{cases}1,&y=0,\\[6pt]{\frac {y}{1-e^{-y}}},&y\neq 0.\end{cases}}} A sharpness parameter k {\displaystyle k} may be included: f ( x ) = ln ⁡ ( 1 + e k x ) k , f ′ ( x ) = e k x 1 + e k x = 1 1 + e − k x . {\displaystyle f(x)={\frac {\ln(1+e^{kx})}{k}},\qquad \qquad f'(x)={\frac {e^{kx}}{1+e^{kx}}}={\frac {1}{1+e^{-kx}}}.} Additionally, the softplus function is equivalent to the log of the sigmoid function in the following way: − ln ⁡ ( sigmoid ( − x ) ) = − ln ⁡ ( 1 1 + e x ) = ln ⁡ ( 1 + e x ) = softplus ( x ) {\displaystyle -\ln({\text{sigmoid}}(-x))=-\ln \left({\frac {1}{1+e^{x}}}\right)=\ln \left(1+e^{x}\right)={\text{softplus}}(x)} == Related functions == The derivative of softplus is the standard logistic function: f ′ ( x ) = e x 1 + e x = 1 1 + e − x {\displaystyle f'(x)={\frac {e^{x}}{1+e^{x}}}={\frac {1}{1+e^{-x}}}} The logistic function or the sigmoid function is a smooth approximation of the rectifier, the Heaviside step function. === LogSumExp === The multivariable generalization of single-variable softplus is the LogSumExp with the first argument set to zero: L S E 0 + ⁡ ( x 1 , … , x n ) := LSE ⁡ ( 0 , x 1 , … , x n ) = ln ⁡ ( 1 + e x 1 + ⋯ + e x n ) . {\displaystyle \operatorname {LSE_{0}} ^{+}(x_{1},\dots ,x_{n}):=\operatorname {LSE} (0,x_{1},\dots ,x_{n})=\ln(1+e^{x_{1}}+\cdots +e^{x_{n}}).} The LogSumExp function is LSE ⁡ ( x 1 , … , x n ) = ln ⁡ ( e x 1 + ⋯ + e x n ) , {\displaystyle \operatorname {LSE} (x_{1},\dots ,x_{n})=\ln(e^{x_{1}}+\cdots +e^{x_{n}}),} and its gradient is the softmax; the softmax with the first argument set to zero is the multivariable generalization of the logistic function. Both LogSumExp and softmax are used in machine learning. === Convex conjugate === The convex conjugate (specifically, the Legendre transformation) of the softplus function is the negative binary entropy function (with base e). This is because (following the definition of the Legendre transformation: the derivatives are inverse functions) the derivative of softplus is the logistic function, whose inverse function is the logit, which is the derivative of negative binary entropy. Softplus can be interpreted as logistic loss (as a positive number), so, by duality, minimizing logistic loss corresponds to maximizing entropy. This justifies the principle of maximum entropy as loss minimization.

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  Charge based boundary element fast multipole method

  The charge-based formulation of the boundary element method (BEM) is a dimensionality reduction numerical technique that is used to model quasistatic electromagnetic phenomena in highly complex conducting media (targeting, e.g., the human brain) with a very large (up to approximately 1 billion) number of unknowns. The charge-based BEM solves an integral equation of the potential theory written in terms of the induced surface charge density. This formulation is naturally combined with fast multipole method (FMM) acceleration, and the entire method is known as charge-based BEM-FMM. The combination of BEM and FMM is a common technique in different areas of computational electromagnetics and, in the context of bioelectromagnetism, it provides improvements over the finite element method. == Historical development == Along with more common electric potential-based BEM, the quasistatic charge-based BEM, derived in terms of the single-layer (charge) density, for a single-compartment medium has been known in the potential theory since the beginning of the 20th century. For multi-compartment conducting media, the surface charge density formulation first appeared in discretized form (for faceted interfaces) in the 1964 paper by Gelernter and Swihart. A subsequent continuous form, including time-dependent and dielectric effects, appeared in the 1967 paper by Barnard, Duck, and Lynn. The charge-based BEM has also been formulated for conducting, dielectric, and magnetic media, and used in different applications. In 2009, Greengard et al. successfully applied the charge-based BEM with fast multipole acceleration to molecular electrostatics of dielectrics. A similar approach to realistic modeling of the human brain with multiple conducting compartments was first described by Makarov et al. in 2018. Along with this, the BEM-based multilevel fast multipole method has been widely used in radar and antenna studies at microwave frequencies as well as in acoustics. == Physical background - surface charges in biological media == The charge-based BEM is based on the concept of an impressed (or primary) electric field E i {\displaystyle \mathbf {E} ^{i}} and a secondary electric field E s {\displaystyle \mathbf {E} ^{s}} . The impressed field is usually known a priori or is trivial to find. For the human brain, the impressed electric field can be classified as one of the following: A conservative field E i {\displaystyle \mathbf {E} ^{i}} derived from an impressed density of EEG or MEG current sources in a homogeneous infinite medium with the conductivity σ {\displaystyle \sigma } at the source location; An instantaneous solenoidal field E i {\displaystyle \mathbf {E} ^{i}} of an induction coil obtained from Faraday's law of induction in a homogeneous infinite medium (air), when transcranial magnetic stimulation (TMS) problems are concerned; A surface field E i {\displaystyle \mathbf {E} ^{i}} derived from an impressed surface current density J i = σ E i {\displaystyle \mathbf {J} ^{i}=\sigma \mathbf {E} ^{i}} of current electrodes injecting electric current at a boundary of a compartment with conductivity σ {\displaystyle \sigma } when transcranial direct-current stimulation (tDCS) or deep brain stimulation (DBS) are concerned; A conservative field E i {\displaystyle \mathbf {E} ^{i}} of charges deposited on voltage electrodes for tDCS or DBS. This specific problem requires a coupled treatment since these charges will depend on the environment; In application to multiscale modeling, a field E i {\displaystyle \mathbf {E} ^{i}} obtained from any other macroscopic numerical solution in a small (mesoscale or microscale) spatial domain within the brain. For example, a constant field can be used. When the impressed field is "turned on", free charges located within a conducting volume D immediately begin to redistribute and accumulate at the boundaries (interfaces) of regions of different conductivity in D. A surface charge density ρ ( r ) {\displaystyle \rho (\mathbf {r} )} appears on the conductivity interfaces. This charge density induces a secondary conservative electric field E s {\displaystyle \mathbf {E} ^{s}} following Coulomb's law. One example is a human under a direct current powerline with the known field E i {\displaystyle \mathbf {E} ^{i}} directed down. The superior surface of the human's conducting body will be charged negatively while its inferior portion is charged positively. These surface charges create a secondary electric field that effectively cancels or blocks the primary field everywhere in the body so that no current will flow within the body under DC steady state conditions. Another example is a human head with electrodes attached. At any conductivity interface with a normal vector n {\displaystyle \mathbf {n} } pointing from an "inside" (-) compartment of conductivity σ − {\displaystyle \sigma ^{-}} to an "outside" (+) compartment of conductivity σ + {\displaystyle \sigma ^{+}} , Kirchhoff's current law requires continuity of the normal component of the electric current density. This leads to the interfacial boundary condition in the form for every facet at a triangulated interface. As long as σ ± {\displaystyle \sigma ^{\pm }} are different from each other, the two normal components of the electric field, E ± ⋅ n {\displaystyle \mathbf {E} ^{\pm }\cdot \mathbf {n} } , must also be different. Such a jump across the interface is only possible when a sheet of surface charge exists at that interface. Thus, if an electric current or voltage is applied, the surface charge density follows. The goal of the numerical analysis is to find the unknown surface charge distribution and thus the total electric field E = E i + E s {\displaystyle \mathbf {E} =\mathbf {E} ^{i}+\mathbf {E} ^{s}} (and the total electric potential if required) anywhere in space. == System of equations for surface charges == Below, a derivation is given based on Gauss's law and Coulomb's law. All conductivity interfaces, denoted by S, are discretized into planar triangular facets t m {\displaystyle t_{m}} with centers r m {\displaystyle \mathbf {r} _{m}} . Assume that an m-th facet with the normal vector n m {\displaystyle \mathbf {n} _{m}} and area A m {\displaystyle A_{m}} carries a uniform surface charge density ρ m {\displaystyle \rho _{m}} . If a volumetric tetrahedral mesh were present, the charged facets would belong to tetrahedra with different conductivity values. We first compute the electric field E m + {\displaystyle \mathbf {E} _{m}^{+}} at the point r m + δ n m {\displaystyle \mathbf {r} _{m}+\delta \mathbf {n} _{m}} , for δ → 0 + {\displaystyle \delta \rightarrow 0^{+}} i.e., just outside facet 𝑚 at its center. This field contains three contributions: The continuous impressed electric field E i {\displaystyle \mathbf {E} ^{i}} itself; An electric field of the m-th charged facet itself. Very close to the facet, it can be approximated as the electric field of an infinite sheet of uniform surface charge ρ m {\displaystyle \rho _{m}} . By Gauss's law, it is given by + ρ m / 2 ε 0 ⋅ n m {\displaystyle +\rho _{m}/2\varepsilon _{0}\cdot \mathbf {n} _{m}} where ε 0 {\displaystyle \varepsilon _{0}} is a background electrical permittivity; An electric field generated by all other facets t n {\displaystyle t_{n}} , which we approximate as point charges of charge A n ρ n {\displaystyle A_{n}\rho _{n}} at each center r n {\displaystyle \mathbf {r} _{n}} . A similar treatment holds for the electric field E m − {\displaystyle \mathbf {E} _{m}^{-}} just inside facet 𝑚, but the electric field of the flat sheet of charge changes its sign. Using Coulomb's law to calculate the contribution of facets different from t m {\displaystyle t_{m}} , we find From this equation, we see that the normal component of the electric field indeed undergoes a jump through the charged interface. This is equivalent to a jump relation of the potential theory. As a second step, the two expressions for E m ± {\displaystyle \mathbf {E} _{m}^{\pm }} are substituted into the interfacial boundary condition σ − E m − ⋅ n m = σ + E m + ⋅ n m {\displaystyle \sigma ^{-}\mathbf {E} _{m}^{-}\cdot \mathbf {n} _{m}=\sigma ^{+}\mathbf {E} _{m}^{+}\cdot \mathbf {n} _{m}} , applied to every facet 𝑚. This operation leads to a system of linear equations for unknown charge densities ρ m {\displaystyle \rho _{m}} which solves the problem: where K m = σ − − σ + σ − + σ + {\displaystyle K_{m}={\frac {\sigma ^{-}-\sigma ^{+}}{\sigma ^{-}+\sigma ^{+}}}} is the electric conductivity contrast at the m-th facet. The normalization constant ε 0 {\displaystyle \varepsilon _{0}} will cancel out after the solution is substituted in the expression for E s {\displaystyle \mathbf {E} ^{s}} and becomes redundant. == Application of fast multipole method == For modern characterizations of brain topologies with ever-increasing levels of complexity, the above system of equations for ρ m {\displaystyle \rho _{m}} is very large; it is t

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  Multi-task learning

  Multi-task learning (MTL) is a subfield of machine learning in which multiple learning tasks are solved at the same time, while exploiting commonalities and differences across tasks. This can result in improved learning efficiency and prediction accuracy for the task-specific models, when compared to training the models separately. Inherently, Multi-task learning is a multi-objective optimization problem having trade-offs between different tasks. Early versions of MTL were called "hints". In a widely cited 1997 paper, Rich Caruana gave the following characterization:Multitask Learning is an approach to inductive transfer that improves generalization by using the domain information contained in the training signals of related tasks as an inductive bias. It does this by learning tasks in parallel while using a shared representation; what is learned for each task can help other tasks be learned better. In the classification context, MTL aims to improve the performance of multiple classification tasks by learning them jointly. One example is a spam-filter, which can be treated as distinct but related classification tasks across different users. To make this more concrete, consider that different people have different distributions of features which distinguish spam emails from legitimate ones, for example an English speaker may find that all emails in Russian are spam, not so for Russian speakers. Yet there is a definite commonality in this classification task across users, for example one common feature might be text related to money transfer. Solving each user's spam classification problem jointly via MTL can let the solutions inform each other and improve performance. Further examples of settings for MTL include multiclass classification and multi-label classification. Multi-task learning works because regularization induced by requiring an algorithm to perform well on a related task can be superior to regularization that prevents overfitting by penalizing all complexity uniformly. One situation where MTL may be particularly helpful is if the tasks share significant commonalities and are generally slightly under sampled. However, as discussed below, MTL has also been shown to be beneficial for learning unrelated tasks. == Methods == The key challenge in multi-task learning, is how to combine learning signals from multiple tasks into a single model. This may strongly depend on how well different task agree with each other, or contradict each other. There are several ways to address this challenge: === Task grouping and overlap === Within the MTL paradigm, information can be shared across some or all of the tasks. Depending on the structure of task relatedness, one may want to share information selectively across the tasks. For example, tasks may be grouped or exist in a hierarchy, or be related according to some general metric. Suppose, as developed more formally below, that the parameter vector modeling each task is a linear combination of some underlying basis. Similarity in terms of this basis can indicate the relatedness of the tasks. For example, with sparsity, overlap of nonzero coefficients across tasks indicates commonality. A task grouping then corresponds to those tasks lying in a subspace generated by some subset of basis elements, where tasks in different groups may be disjoint or overlap arbitrarily in terms of their bases. Task relatedness can be imposed a priori or learned from the data. Hierarchical task relatedness can also be exploited implicitly without assuming a priori knowledge or learning relations explicitly. For example, the explicit learning of sample relevance across tasks can be done to guarantee the effectiveness of joint learning across multiple domains. === Exploiting unrelated tasks: Auxiliary learning === In auxiliary learning, one attempts learning a group of principal tasks using a group of auxiliary tasks, unrelated to the principal ones. With the right unrelated tasks, joint learning of unrelated tasks which use the same input data have been shown to be beneficial, and provide significant improvement over standard MTL. The reason is that prior knowledge about task relatedness can lead to sparser and more informative representations for each task grouping, essentially by screening out idiosyncrasies of the data distribution. It has been proposed to build on a prior multitask methodology by favoring a shared low-dimensional representation within each task grouping, and imposing a penalty on tasks from different groups which encourages the two representations to be orthogonal. Learning with auxiliary unrelated tasks poses two major challenges: Finding useful auxiliary tasks and combining losses of all tasks in a useful way. Some methods can learn these from data together with the training process, and combine tasks efficiently. === Transfer of knowledge === Related to multi-task learning is the concept of knowledge transfer. Whereas traditional multi-task learning implies that a shared representation is developed concurrently across tasks, transfer of knowledge implies a sequentially shared representation. Large scale machine learning projects such as the deep convolutional neural network GoogLeNet, an image-based object classifier, can develop robust representations which may be useful to further algorithms learning related tasks. For example, the pre-trained model can be used as a feature extractor to perform pre-processing for another learning algorithm. Or the pre-trained model can be used to initialize a model with similar architecture which is then fine-tuned to learn a different classification task. === Multiple non-stationary tasks === Traditionally Multi-task learning and transfer of knowledge are applied to stationary learning settings. Their extension to non-stationary environments is termed Group online adaptive learning (GOAL). Sharing information could be particularly useful if learners operate in continuously changing environments, because a learner could benefit from previous experience of another learner to quickly adapt to their new environment. Such group-adaptive learning has numerous applications, from predicting financial time-series, through content recommendation systems, to visual understanding for adaptive autonomous agents. === Multi-task optimization === Multi-task optimization focuses on solving optimizing the whole process. The paradigm has been inspired by the well-established concepts of transfer learning and multi-task learning in predictive analytics. The key motivation behind multi-task optimization is that if optimization tasks are related to each other in terms of their optimal solutions or the general characteristics of their function landscapes, the search progress can be transferred to substantially accelerate the search on the other. The success of the paradigm is not necessarily limited to one-way knowledge transfers from simpler to more complex tasks. In practice an attempt is to intentionally solve a more difficult task that may unintentionally solve several smaller problems. There is a direct relationship between multitask optimization and multi-objective optimization. In some cases, the simultaneous training of seemingly related tasks may hinder performance compared to single-task models. Commonly, MTL models employ task-specific modules on top of a joint feature representation obtained using a shared module. Since this joint representation must capture useful features across all tasks, MTL may hinder individual task performance if the different tasks seek conflicting representation, i.e., the gradients of different tasks point to opposing directions or differ significantly in magnitude. This phenomenon is commonly referred to as negative transfer. To mitigate this issue, various MTL optimization methods have been proposed. It has been reported that meta-knowledge transfer could help avoid negative transfer.Besides, the per-task gradients are combined into a joint update direction through various aggregation algorithms or heuristics. There are several common approaches for multi-task optimization: Bayesian optimization, evolutionary computation, and approaches based on Game theory. ==== Multi-task Bayesian optimization ==== Multi-task Bayesian optimization is a modern model-based approach that leverages the concept of knowledge transfer to speed up the automatic hyperparameter optimization process of machine learning algorithms. The method builds a multi-task Gaussian process model on the data originating from different searches progressing in tandem. The captured inter-task dependencies are thereafter utilized to better inform the subsequent sampling of candidate solutions in respective search spaces. ==== Evolutionary multi-tasking ==== Evolutionary multi-tasking has been explored as a means of exploiting the implicit parallelism of population-based search algorithms to simultaneously progress multiple distinct optimization tasks. By mapping all task

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  Kubeflow

  Kubeflow is an open-source platform for machine learning and MLOps on Kubernetes introduced by Google. The different stages in a typical machine learning lifecycle are represented with different software components in Kubeflow, including model development (Kubeflow Notebooks), model training (Kubeflow Pipelines, Kubeflow Training Operator), model serving (KServe), and automated machine learning (Katib). Each component of Kubeflow can be deployed separately, and it is not a requirement to deploy every component. == History == The Kubeflow project was first announced at KubeCon + CloudNativeCon North America 2017 by Google engineers David Aronchick, Jeremy Lewi, and Vishnu Kannan to address a perceived lack of flexible options for building production-ready machine learning systems. The project has also stated it began as a way for Google to open-source how they ran TensorFlow internally. The first release of Kubeflow (Kubeflow 0.1) was announced at KubeCon + CloudNativeCon Europe 2018. Kubeflow 1.0 was released in March 2020 via a public blog post announcing that many Kubeflow components were graduating to a "stable status", indicating they were now ready for production usage. In October 2022, Google announced that the Kubeflow project had applied to join the Cloud Native Computing Foundation. In July 2023, the foundation voted to accept Kubeflow as an incubating stage project. == Components == === Kubeflow Notebooks for model development === Machine learning models are developed in the notebooks component called Kubeflow Notebooks. The component runs web-based development environments inside a Kubernetes cluster, with native support for Jupyter Notebook, Visual Studio Code, and RStudio. === Kubeflow Pipelines for model training === Once developed, models are trained in the Kubeflow Pipelines component. The component acts as a platform for building and deploying portable, scalable machine learning workflows based on Docker containers. Google Cloud Platform has adopted the Kubeflow Pipelines DSL within its Vertex AI Pipelines product. === Kubeflow Training Operator for model training === For certain machine learning models and libraries, the Kubeflow Training Operator component provides Kubernetes custom resources support. The component runs distributed or non-distributed TensorFlow, PyTorch, Apache MXNet, XGBoost, and MPI training jobs on Kubernetes. === KServe for model serving === The KServe component (previously named KFServing) provides Kubernetes custom resources for serving machine learning models on arbitrary frameworks including TensorFlow, XGBoost, scikit-learn, PyTorch, and ONNX. KServe was developed collaboratively by Google, IBM, Bloomberg, NVIDIA, and Seldon. Publicly disclosed adopters of KServe include Bloomberg, Gojek, the Wikimedia Foundation, and others. === Katib for automated machine learning === Lastly, Kubeflow includes a component for automated training and development of machine learning models, the Katib component. It is described as a Kubernetes-native project and features hyperparameter tuning, early stopping, and neural architecture search. == Release timeline ==

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  Linear discriminant analysis

  Linear discriminant analysis (LDA), normal discriminant analysis (NDA), canonical variates analysis (CVA), or discriminant function analysis is a generalization of Fisher's linear discriminant, a method used in statistics and other fields, to find a linear combination of features that characterizes or separates two or more classes of objects or events. The resulting combination may be used as a linear classifier, or, more commonly, for dimensionality reduction before later classification. LDA is closely related to analysis of variance (ANOVA) and regression analysis, which also attempt to express one dependent variable as a linear combination of other features or measurements. However, ANOVA uses categorical independent variables and a continuous dependent variable, whereas discriminant analysis has continuous independent variables and a categorical dependent variable (i.e. the class label). Logistic regression and probit regression are more similar to LDA than ANOVA is, as they also explain a categorical variable by the values of continuous independent variables. These other methods are preferable in applications where it is not reasonable to assume that the independent variables have a normal distribution, which is a fundamental assumption of the LDA method. LDA is also closely related to principal component analysis (PCA) and factor analysis in that they both look for linear combinations of variables which best explain the data. LDA explicitly attempts to model the difference between the classes of data. PCA, in contrast, does not take into account any difference in class, and factor analysis builds the feature combinations based on similarities rather than differences. Discriminant analysis is also different from factor analysis in that it is not an interdependence technique: a distinction between independent variables and dependent variables (also called criterion variables) must be made. LDA works when the measurements made on independent variables for each observation are continuous quantities. When dealing with categorical independent variables, the equivalent technique is discriminant correspondence analysis. Discriminant analysis is used when groups are known a priori (unlike in cluster analysis). Each case must have a score on one or more quantitative predictor measures, and a score on a group measure. In simple terms, discriminant function analysis is classification - the act of distributing things into groups, classes or categories of the same type. == History == The original dichotomous discriminant analysis was developed by Sir Ronald Fisher in 1936. It is different from an ANOVA or MANOVA, which is used to predict one (ANOVA) or multiple (MANOVA) continuous dependent variables by one or more independent categorical variables. Discriminant function analysis is useful in determining whether a set of variables is effective in predicting category membership. == LDA for two classes == Consider a set of observations x → {\displaystyle {\vec {x}}} (also called features, attributes, variables or measurements) for each sample of an object or event with known class y {\displaystyle y} . This set of samples is called the training set in a supervised learning context. The classification problem is then to find a good predictor for the class y {\displaystyle y} of any sample of the same distribution (not necessarily from the training set) given only an observation x → {\displaystyle {\vec {x}}} . LDA approaches the problem by assuming that the conditional probability density functions p ( x → | y = 0 ) {\displaystyle p({\vec {x}}|y=0)} and p ( x → | y = 1 ) {\displaystyle p({\vec {x}}|y=1)} are both the normal distribution with mean and covariance parameters ( μ → 0 , Σ 0 ) {\displaystyle \left({\vec {\mu }}_{0},\Sigma _{0}\right)} and ( μ → 1 , Σ 1 ) {\displaystyle \left({\vec {\mu }}_{1},\Sigma _{1}\right)} , respectively. Under this assumption, the Bayes-optimal solution is to predict points as being from the second class if the log of the likelihood ratios is bigger than some threshold T, so that: 1 2 ( x → − μ → 0 ) T Σ 0 − 1 ( x → − μ → 0 ) + 1 2 ln ⁡ | Σ 0 | − 1 2 ( x → − μ → 1 ) T Σ 1 − 1 ( x → − μ → 1 ) − 1 2 ln ⁡ | Σ 1 | > T {\displaystyle {\frac {1}{2}}({\vec {x}}-{\vec {\mu }}_{0})^{\mathrm {T} }\Sigma _{0}^{-1}({\vec {x}}-{\vec {\mu }}_{0})+{\frac {1}{2}}\ln |\Sigma _{0}|-{\frac {1}{2}}({\vec {x}}-{\vec {\mu }}_{1})^{\mathrm {T} }\Sigma _{1}^{-1}({\vec {x}}-{\vec {\mu }}_{1})-{\frac {1}{2}}\ln |\Sigma _{1}|\ >\ T} Without any further assumptions, the resulting classifier is referred to as quadratic discriminant analysis (QDA). LDA instead makes the additional simplifying homoscedasticity assumption (i.e. that the class covariances are identical, so Σ 0 = Σ 1 = Σ {\displaystyle \Sigma _{0}=\Sigma _{1}=\Sigma } ) and that the covariances have full rank. In this case, several terms cancel: x → T Σ 0 − 1 x → = x → T Σ 1 − 1 x → {\displaystyle {\vec {x}}^{\mathrm {T} }\Sigma _{0}^{-1}{\vec {x}}={\vec {x}}^{\mathrm {T} }\Sigma _{1}^{-1}{\vec {x}}} x → T Σ i − 1 μ → i = μ → i T Σ i − 1 x → {\displaystyle {\vec {x}}^{\mathrm {T} }{\Sigma _{i}}^{-1}{\vec {\mu }}_{i}={{\vec {\mu }}_{i}}^{\mathrm {T} }{\Sigma _{i}}^{-1}{\vec {x}}} because both sides are scalar and transpose to each other ( Σ i {\displaystyle \Sigma _{i}} is Hermitian) and the above decision criterion becomes a threshold on the dot product w → T x → > c {\displaystyle {\vec {w}}^{\mathrm {T} }{\vec {x}}>c} for some threshold constant c, where w → = Σ − 1 ( μ → 1 − μ → 0 ) {\displaystyle {\vec {w}}=\Sigma ^{-1}({\vec {\mu }}_{1}-{\vec {\mu }}_{0})} c = 1 2 w → T ( μ → 1 + μ → 0 ) {\displaystyle c={\frac {1}{2}}\,{\vec {w}}^{\mathrm {T} }({\vec {\mu }}_{1}+{\vec {\mu }}_{0})} This means that the criterion of an input x → {\displaystyle {\vec {x}}} being in a class y {\displaystyle y} is purely a function of this linear combination of the known observations. It is often useful to see this conclusion in geometrical terms: the criterion of an input x → {\displaystyle {\vec {x}}} being in a class y {\displaystyle y} is purely a function of projection of multidimensional-space point x → {\displaystyle {\vec {x}}} onto vector w → {\displaystyle {\vec {w}}} (thus, we only consider its direction). In other words, the observation belongs to y {\displaystyle y} if corresponding x → {\displaystyle {\vec {x}}} is located on a certain side of a hyperplane perpendicular to w → {\displaystyle {\vec {w}}} . The location of the plane is defined by the threshold c {\displaystyle c} . == Assumptions == The assumptions of discriminant analysis are the same as those for MANOVA. The analysis is quite sensitive to outliers and the size of the smallest group must be larger than the number of predictor variables. Multivariate normality: Independent variables are normal for each level of the grouping variable. Homogeneity of variance/covariance (homoscedasticity): Variances among group variables are the same across levels of predictors. Can be tested with Box's M statistic. It has been suggested, however, that linear discriminant analysis be used when covariances are equal, and that quadratic discriminant analysis may be used when covariances are not equal. Independence: Participants are assumed to be randomly sampled, and a participant's score on one variable is assumed to be independent of scores on that variable for all other participants. It has been suggested that discriminant analysis is relatively robust to slight violations of these assumptions, and it has also been shown that discriminant analysis may still be reliable when using dichotomous variables (where multivariate normality is often violated). == Discriminant functions == Discriminant analysis works by creating one or more linear combinations of predictors, creating a new latent variable for each function. These functions are called discriminant functions. The number of functions possible is either N g − 1 {\displaystyle N_{g}-1} where N g {\displaystyle N_{g}} = number of groups, or p {\displaystyle p} (the number of predictors), whichever is smaller. The first function created maximizes the differences between groups on that function. The second function maximizes differences on that function, but also must not be correlated with the previous function. This continues with subsequent functions with the requirement that the new function not be correlated with any of the previous functions. Given group j {\displaystyle j} , with R j {\displaystyle \mathbb {R} _{j}} sets of sample space, there is a discriminant rule such that if x ∈ R j {\displaystyle x\in \mathbb {R} _{j}} , then x ∈ j {\displaystyle x\in j} . Discriminant analysis then, finds “good” regions of R j {\displaystyle \mathbb {R} _{j}} to minimize classification error, therefore leading to a high percent correct classified in the classification table. Each function is given a discriminant score to determine how well it predicts group placement. Structure Corr

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  U-matrix

  The U-matrix (unified distance matrix) is a representation of a self-organizing map (SOM) where the Euclidean distance between the codebook vectors of neighboring neurons is depicted in a grayscale image. This image is used to visualize the data in a high-dimensional space using a 2D image. == Construction procedure == Once the SOM is trained using the input data, the final map is not expected to have any twists. If the map is twist-free, the distance between the codebook vectors of neighboring neurons gives an approximation of the distance between different parts of the underlying data. When such distances are depicted in a grayscale image, light colors depict closely spaced node codebook vectors and darker colors indicate more widely separated node codebook vectors. Thus, groups of light colors can be considered as clusters, and the dark parts as the boundaries between the clusters. This representation can help to visualize the clusters in the high-dimensional spaces, or to automatically recognize them using relatively simple image processing techniques.

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  ChatGPT

  ChatGPT is a generative artificial intelligence chatbot developed by OpenAI. Originally released in November 2022, the product uses large language models—specifically generative pre-trained transformers (GPTs)—to generate text, speech, and images in response to user prompts. ChatGPT accelerated the AI boom, an ongoing period marked by rapid investment and public attention toward the field of artificial intelligence (AI). OpenAI operates the service on a freemium model. Users can interact with ChatGPT through text, audio, and image prompts. ChatGPT was quickly adopted, reaching 100 million monthly active users two months after its release and 900 million weekly active users in February 2026. It has been lauded for its potential to transform numerous professional fields, and has instigated public debate about the nature of creativity and the future of knowledge work. The chatbot has also been criticized for its limitations and potential for unethical use. It can generate plausible-sounding but incorrect or nonsensical answers, known as hallucinations. Biases in its training data have been reflected in its responses. The chatbot can facilitate academic dishonesty, generate misinformation, and create malicious code. The ethics of its development, particularly the use of copyrighted content as training data, have also drawn controversy. == Features == ChatGPT is a chatbot and AI assistant built on large language model (LLM) technology. It is designed to generate human-like text and can carry out a wide variety of tasks. These include, among many others, writing and debugging computer programs, composing music, scripts, fairy tales, and essays, answering questions (sometimes at a level exceeding that of an average human test-taker), and generating business concepts. ChatGPT is frequently used for translation and summarization tasks, and can simulate interactive environments such as a Linux terminal, a multi-user chat room, or simple text-based games such as tic-tac-toe. Users interact with ChatGPT through conversations which consist of text, audio, and image inputs and outputs. The user's inputs to these conversations are referred to as prompts. An optional "Memory" feature allows users to tell ChatGPT to memorize specific information. Another option allows ChatGPT to recall old conversations. GPT-based moderation classifiers are used to reduce the risk of harmful outputs being presented to users. In March 2023, OpenAI added support for plugins for ChatGPT. This includes both plugins made by OpenAI, such as web browsing and code interpretation, and external plugins from developers such as Expedia, OpenTable, and Zapier. From October to December 2024, ChatGPT Search was deployed. It allows ChatGPT to search the web in an attempt to make more accurate and up-to-date responses. It increased OpenAI's direct competition with major search engines. OpenAI allows businesses to tailor how their content appears in the ChatGPT Search results and influence what sources are used. In December 2024, OpenAI launched a new feature allowing users to call ChatGPT with a telephone for up to 15 minutes per month for free. In September 2025, OpenAI added a feature called Pulse, which generates a daily analysis of a user's chats and connected apps such as Gmail and Google Calendar. In October 2025, OpenAI launched ChatGPT Atlas, a browser integrating the ChatGPT assistant directly into web navigation, to compete with existing browsers such as Google Chrome. It has an additional feature called "agentic mode" that allows it to take online actions for the user. === Paid tier === ChatGPT was initially free to the public and remains free in a limited capacity. In February 2023, OpenAI launched a premium service, ChatGPT Plus, that costs US$20 per month. What was offered on the paid plan versus the free tier changed as OpenAI has continued to update ChatGPT, and a Pro tier at $200/mo was introduced in December 2024. The Pro launch coincided with the release of the o1 model. In August 2025, ChatGPT Go was offered in India for ₹399 per month. The plan has higher limits than the free version. === Mobile apps === In May-July 2023, OpenAI began offering ChatGPT iOS and Android apps. ChatGPT can also power Android's assistant. An app for Windows launched on the Microsoft Store on October 15, 2024. === Languages === OpenAI met Icelandic President Guðni Th. Jóhannesson in 2022. In 2023, OpenAI worked with a team of 40 Icelandic volunteers to fine-tune ChatGPT's Icelandic conversation skills as a part of Iceland's attempts to preserve the Icelandic language. ChatGPT (based on GPT-4) was better able to translate Japanese to English when compared to Bing, Bard, and DeepL Translator in 2023. In December 2023, the Albanian government decided to use ChatGPT for the rapid translation of European Union documents and the analysis of required changes needed for Albania's accession to the EU. Several studies have shown that ChatGPT can outperform Google Translate in some mainstream translation tasks. However, as of 2024, no machine translation services match human expert performance. In August 2024, a representative of the Asia Pacific wing of OpenAI made a visit to Taiwan, during which a demonstration of ChatGPT's Chinese abilities was made. ChatGPT's Mandarin Chinese abilities were lauded, but the ability of the AI to produce content in Mandarin Chinese in a Taiwanese accent was found to be "less than ideal" due to differences between mainland Mandarin Chinese and Taiwanese Mandarin. === GPT Store === In November 2023, OpenAI released GPT Builder, a tool allowing users to customize ChatGPT's behavior for a specific use case. The customized systems are referred to as GPTs. In January 2024, OpenAI launched the GPT Store, a marketplace for GPTs. At launch, OpenAI included more than 3 million GPTs created by GPT Builder users in the GPT Store. === ChatGPT Apps === In September 2025, OpenAI added support for Model Context Protocol (MCP) to ChatGPT apps. When enabled in developer mode, this allows for improved third-party access to ChatGPT tools and servers. === Deep Research === In February 2025, OpenAI released Deep Research, a feature that generates reports based on extensive web searches. It was initially based on the reasoning model o3 and took 5 to 30 minutes per report. === Images === In October 2023, OpenAI's image generation model DALL-E 3 was integrated into ChatGPT. The integration used ChatGPT to write prompts for DALL-E guided by conversations with users. In March 2025, OpenAI updated ChatGPT to generate images using GPT Image instead of DALL-E. One of the most significant improvements was in the generation of text within images, which is especially useful for branded content. However, this ability is noticeably worse in non-Latin alphabets. The model can also generate new images based on existing ones provided in the prompt. These images are generated with C2PA metadata, which can be used to verify that they are AI-generated. OpenAI has emplaced additional safeguards to prevent what the company deems to be harmful image generation. === Agents === In 2025, OpenAI added several features to make ChatGPT more agentic (capable of autonomously performing longer tasks). In January, Operator was released. It was capable of autonomously performing tasks through web browser interactions, including filling forms, placing online orders, scheduling appointments, and other browser-based tasks. It was controlling a software environment inside a virtual machine with limited internet connectivity and with safety restrictions. It struggled with complex user interfaces. In May 2025, OpenAI introduced an agent for coding named Codex. It is capable of writing software, answering codebase questions, running tests, and proposing pull requests. It is based on a fine-tuned version of OpenAI o3. It has two versions, one running in a virtual machine in the cloud, and one where the agent runs in the cloud, but performs actions on a local machine connected via API. In July 2025, OpenAI released ChatGPT agent, an AI agent that can perform multi-step tasks. Like Operator, it controls a virtual computer. It also inherits from Deep Research's ability to gather and summarize significant volumes of information. The user can interrupt tasks or provide additional instructions as needed. In September 2025, OpenAI partnered with Stripe, Inc. to release Agentic Commerce Protocol, enabling purchases through ChatGPT. At launch, the feature was limited to purchases on Etsy from US users with a payment method linked to their OpenAI account. OpenAI takes an undisclosed cut from the merchant's payment. === ChatGPT Health === On January 7, 2026, OpenAI introduced a feature called "ChatGPT Health", whereby ChatGPT can discuss the user's health in a way that is separate from other chats. The feature is not available for users in the United Kingdom, Switzerland, or the European Economic Area, and is available on a waitli

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  Cartesian genetic programming

  Cartesian genetic programming is a form of genetic programming that uses a graph representation to encode computer programs. It grew from a method of evolving digital circuits developed by Julian F. Miller and Peter Thomson in 1997. The term ‘Cartesian genetic programming’ first appeared in 1999 and was proposed as a general form of genetic programming in 2000. It is called ‘Cartesian’ because it represents a program using a two-dimensional grid of nodes. Miller's keynote explains how CGP works. He edited a book entitled Cartesian Genetic Programming, published in 2011 by Springer. The open source project dCGP implements a differentiable version of CGP developed at the European Space Agency by Dario Izzo, Francesco Biscani and Alessio Mereta able to approach symbolic regression tasks, to find solution to differential equations, find prime integrals of dynamical systems, represent variable topology artificial neural networks and more.

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  Sample exclusion dimension

  In computational learning theory, sample exclusion dimensions arise in the study of exact concept learning with queries. In algorithmic learning theory, a concept over a domain X is a Boolean function over X. Here we only consider finite domains. A partial approximation S of a concept c is a Boolean function over Y ⊆ X {\displaystyle Y\subseteq X} such that c is an extension to S. Let C be a class of concepts and c be a concept (not necessarily in C). Then a specifying set for c w.r.t. C, denoted by S is a partial approximation S of c such that C contains at most one extension to S. If we have observed a specifying set for some concept w.r.t. C, then we have enough information to verify a concept in C with at most one more mind change. The exclusion dimension, denoted by XD(C), of a concept class is the maximum of the size of the minimum specifying set of c' with respect to C, where c' is a concept not in C.

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  Multilinear principal component analysis

  Multilinear principal component analysis (MPCA) is a multilinear extension of principal component analysis (PCA) that is used to analyze M-way arrays, also informally referred to as "data tensors". M-way arrays may be modeled by linear tensor models, such as CANDECOMP/Parafac, or by multilinear tensor models, such as multilinear principal component analysis (MPCA) or multilinear (tensor) independent component analysis (MICA). In 2005, Vasilescu and Terzopoulos introduced the Multilinear PCA terminology as a way to better differentiate between multilinear data models that employed 2nd order statistics versus higher order statistics to compute a set of independent components for each mode, such as Multilinear ICA Multilinear PCA may be applied to compute the causal factors of data formation, or as signal processing tool on data tensors whose individual observation have either been vectorized, or whose observations are treated as a collection of column/row observations, an "observation as a matrix", and concatenated into a data tensor. The latter approach is suitable for compression and reducing redundancy in the rows, columns and fibers that are unrelated to the causal factors of data formation. Vasilescu and Terzopoulos in their paper "TensorFaces" introduced the M-mode SVD algorithm which are algorithms misidentified in the literature as the HOSVD or the Tucker which employ the power method or gradient descent, respectively. Vasilescu and Terzopoulos framed the data analysis, recognition and synthesis problems as multilinear tensor problems. Data is viewed as the compositional consequence of several causal factors, that are well suited for multi-modal tensor factor analysis. The power of the tensor framework was showcased by analyzing human motion joint angles, facial images or textures in the following papers: Human Motion Signatures (CVPR 2001, ICPR 2002), face recognition – TensorFaces, (ECCV 2002, CVPR 2003, etc.) and computer graphics – TensorTextures (Siggraph 2004). == The algorithm == The MPCA solution follows the alternating least square (ALS) approach. It is iterative in nature. As in PCA, MPCA works on centered data. Centering is a little more complicated for tensors, and it is problem dependent. == Feature selection == MPCA features: Supervised MPCA is employed in causal factor analysis that facilitates object recognition while a semi-supervised MPCA feature selection is employed in visualization tasks. == Extensions == Various extension of MPCA: Robust MPCA (RMPCA) Multi-Tensor Factorization, that also finds the number of components automatically (MTF)

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  Alexander Y. Tetelbaum

  Alexander Y. Tetelbaum (born August 16, 1948) is a Ukrainian American computer scientist, inventor, and academic who has contributed to electronic design automation (EDA) and artificial intelligence (AI) since the late 1960s; and holds 46 U.S. patents in EDA and related fields. Tetelbaum is the founding president of International Solomon University, the first Jewish university in Ukraine, established during a period of renewed efforts to address antisemitism in Ukraine. == Early life and education == He graduated from a Kyiv mathematical high school with a silver medal in 1966. Tetelbaum enrolled at the Kyiv Polytechnic Institute (KPI), now National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute" in 1966, graduating in 1972 with an MS in Electronics with honors. He earned his PhD in Electrical and Computer Engineering from KPI in 1975, with a dissertation on electronic design automation, and his Doctor of Engineering Science in 1986. == Academic career == Tetelbaum began his academic career at KPI in 1973 as a junior scientist, becoming a professor in the Computer and Electrical Engineering Department in 1980. Later, he founded and served as president of International Solomon University in Kyiv from 1991 to 1996, the first Jewish university in Ukraine. The university became a major academic center for computer science and Jewish studies in the post-Soviet era. He was a visiting and adjunct professor at Michigan State University from 1993 to 1996. == Professional career == Tetelbaum worked as an engineer at the Kiev Institute of Cybernetics from 1972 to 1973, and later, he led the Design Automation Lab at Kyiv Polytechnic Institute from 1975 to 1987. In the United States, he served as EDA manager at Silicon Graphics Corporation from 1996 to 1998 and principal engineer at LSI Corporation from 1998 to 2012. He founded and served as CEO of Abelite Design Automation, Inc., from 2012 to 2022. == Contributions in computer science == Tetelbaum has contributed to electronic design automation (EDA) and artificial intelligence (AI) since the 1960s. His early work included methods for EDA, particularly physical design automation and mathematical optimization; and he developed force-directed placement and topological routing methods. Tetelbaum generalized Rent's rule for hierarchical systems and large blocks, proposing a graph-based framework that extends applicability to arbitrary partition sizes with improved accuracy. Additional IEEE and related conference contributions from the mid-1990s include: "Path Search for Complicated Function", 1995 IEEE International Symposium on Circuits and Systems "A Performance-driven Placement Approach of Standard Cells" (International Conference on Intelligent Systems, 1995) "Framework of a New Methodology for Behavioral to Physical Design Linkage" (38th Midwest Symposium on Circuits and Systems, 1996) Statistical timing design and variations Test Methodologies These and other works and patents contributed to timing-driven placement, crosstalk reduction, clock tree synthesis, and interconnect optimization in VLSI design. == Patents == Tetelbaum holds 46 U.S. patents in EDA and related fields. Notable examples include: For the full list of patents, see Justia Patents or Google Patents. == Publications == === Early publications in the Soviet Union === Before the appearance of American books on electronic design automation (EDA), Tetelbaum published several scientific books and monographs on the subject in Russian/Ukrainian. Electronic Design Automation, Kiev: Znanie Publisher, 1975. Planar Design of Electronic Circuits, Kiev: Znanie Publisher, 1977. Formal Design of Computer Systems, Moscow: Sovetskoe Radio, 1979. CAD of Electronic Equipment: Topological Approach, Kiev: Vyssha Shkola, 1980; 2nd ed. 1981. Automated Design of Electronic Circuits (1981) CAD of VLSI Circuits, Kiev: Vyssha Shkola, 1983. Topological Algorithms of Multilayer Printed Circuit Boards Routing, Moscow: Radio i Svyaz, 1983. CAD of VLSI Circuits on Master Slice Chips, Moscow: Radio i Svyaz, 1988. Increasing the Effectiveness of CAD Systems, Kiev: UMKVO, 1991. === Scientific Monographs (English) === Minimum Number of Timing Signoff Corners (2022) Interviewing AI (2026) The AI Debate (2026) New Nostradamus Predictions: 2026: The Next Decade & Beyond (2035–2050+) (2026) For a consolidated record of Tetelbaum's publications, see Alexander Y. Tetelbaum, Wikidata Q4720205. === Other publications === Tetelbaum also published educational books on problem-solving methods: Yes-No Puzzles-Games Puzzle Games for Kids Solving Non-Standard Problems Solving Non-Standard Very Hard Problems Additionally, Tetelbaum published three thrillers: Omerta Operations Executive Director Eruption Yacht Finally, he published his memoir and an entertaining book: Unfinished Equations Artificially Intelligent Humor

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  Harrison White

  Harrison Colyar White (March 21, 1930 – May 18, 2024) was an American sociologist who was the Giddings Professor of Sociology at Columbia University. White played an influential role in the “Harvard Revolution” in social networks and the New York School of relational sociology. He is credited with the development of a number of mathematical models of social structure including vacancy chains and blockmodels. He has been a leader of a revolution in sociology that is still in process, using models of social structure that are based on patterns of relations instead of the attributes and attitudes of individuals. Among social network researchers, White is widely respected. For instance, at the 1997 International Network of Social Network Analysis conference, the organizer held a special “White Tie” event, dedicated to White. Social network researcher Emmanuel Lazega refers to him as both “Copernicus and Galileo” because he invented both the vision and the tools. The most comprehensive documentation of his theories can be found in the book Identity and Control, first published in 1992. A major rewrite of the book appeared in June 2008. In 2011, White received the W.E.B. DuBois Career of Distinguished Scholarship Award from the American Sociological Association, which honors "scholars who have shown outstanding commitment to the profession of sociology and whose cumulative work has contributed in important ways to the advancement of the discipline." Before his retirement to live in Tucson, Arizona, White was interested in sociolinguistics and business strategy as well as sociology. == Life and career == === Early years === White was born on March 21, 1930, in Washington, D.C. He had three siblings and his father was a doctor in the US Navy. Although moving around to different Naval bases throughout his adolescence, he considered himself Southern, and Nashville, TN to be his home. At the age of 15, he entered the Massachusetts Institute of Technology (MIT), receiving his undergraduate degree at 20 years of age; five years later, in 1955, he received a doctorate in theoretical physics, also from MIT with John C. Slater as his advisor. His dissertation was titled A quantum-mechanical calculation of inter-atomic force constants in copper. This was published in the Physical Review as "Atomic Force Constants of Copper from Feynman's Theorem" (1958). While at MIT he also took a course with the political scientist Karl Deutsch, who White credits with encouraging him to move toward the social sciences. === Princeton University === After receiving his PhD in theoretical physics, he received a Fellowship from the Ford Foundation to begin his second doctorate in sociology at Princeton University. His dissertation advisor was Marion J. Levy. White also worked with Wilbert Moore, Fred Stephan, and Frank W. Notestein while at Princeton. His cohort was very small, with only four or five other graduate students including David Matza, and Stanley Udy. At the same time, he took up a position as an operations analyst at the Operations Research Office, Johns Hopkins University from 1955 to 1956. During this period, he worked with Lee S. Christie on Queuing with Preemptive Priorities or with Breakdown, which was published in 1958. Christie previously worked alongside mathematical psychologist R. Duncan Luce in the Small Group Laboratory at MIT while White was completing his first PhD in physics also at MIT. While continuing his studies at Princeton, White also spent a year as a fellow at the Center for Advanced Study in the Behavioral Sciences, Stanford University, California where he met Harold Guetzkow. Guetzkow was a faculty member at the Carnegie Institute of Technology, known for his application of simulations to social behavior and long-time collaborator with many other pioneers in organization studies, including Herbert A. Simon, James March, and Richard Cyert. Upon meeting Simon through his mutual acquaintance with Guetzkow, White received an invitation to move from California to Pittsburgh to work as an assistant professor of Industrial Administration and Sociology at the Graduate School of Industrial Administration, Carnegie Institute of Technology (later Carnegie-Mellon University), where he stayed for a couple of years, between 1957 and 1959. In an interview, he claimed to have fought with the dean, Leyland Bock, to have the word "sociology" included in his title. It was also during his time at the Stanford Center for Advanced Study that White met his first wife, Cynthia A. Johnson, who was a graduate of Radcliffe College, where she had majored in art history. The couple's joint work on the French Impressionists, Canvases and Careers (1965) and “Institutional Changes in the French Painting World” (1964), originally grew out of a seminar on art in 1957 at the Center for Advanced Study led by Robert Wilson. White originally hoped to use sociometry to map the social structure of French art to predict shifts, but he had an epiphany that it was not social structure but institutional structure which explained the shift. It was also during these years that White, still a graduate student in sociology, wrote and published his first social scientific work, "Sleep: A Sociological Interpretation" in Acta Sociologica in 1960, together with Vilhelm Aubert, a Norwegian sociologist. This work was a phenomenological examination of sleep which attempted to "demonstrate that sleep was more than a straightforward biological activity... [but rather also] a social event". For his dissertation, White carried out empirical research on a research and development department in a manufacturing firm, consisting of interviews and a 110-item questionnaire with managers. He specifically used sociometric questions, which he used to model the "social structure" of relationships between various departments and teams in the organization. In May 1960 he submitted as his doctoral dissertation, titled Research and Development as a Pattern in Industrial Management: A Case Study in Institutionalisation and Uncertainty, earning a PhD in sociology from Princeton University. His first publication based on his dissertation was ''Management conflict and sociometric structure'' in the American Journal of Sociology. === University of Chicago === In 1959 James Coleman left the University of Chicago to found a new department of social relations at Johns Hopkins University, this left a vacancy open for a mathematical sociologist like White. He moved to Chicago to start working as an associate professor at the Department of Sociology. At that time, highly influential sociologists, such as Peter Blau, Mayer Zald, Elihu Katz, Everett Hughes, Erving Goffman were there. As Princeton only required one year in residence, and White took the opportunity to take positions at Johns Hopkins, Stanford, and Carnegie while still working on his dissertation, it was at Chicago that White credits as being his "real socialization in a way, into sociology." It was here that White advised his first two graduate students Joel H. Levine and Morris Friedell, both who went on to make contributions to social network analysis in sociology. While at the Center for Advanced Study, White began learning anthropology and became fascinated with kinship. During his stay at the University of Chicago White was able to finish An Anatomy of Kinship, published in 1963 within the Prentice-Hall series in Mathematical Analysis of Social Behavior, with James Coleman and James March as chief editors. The book received significant attention from many mathematical sociologists of the time, and contributed greatly to establish White as a model builder. === The Harvard Revolution === In 1963, White left Chicago to be an associate professor of sociology at the Harvard Department of Social Relations—the same department founded by Talcott Parsons and still heavily influenced by the structural-functionalist paradigm of Parsons. As White previously only taught graduate courses at Carnegie and Chicago, his first undergraduate course was An Introduction to Social Relations (see Influence) at Harvard, which became infamous among network analysts. As he "thought existing textbooks were grotesquely unscientific," the syllabus of the class was noted for including few readings by sociologists, and comparatively more readings by anthropologists, social psychologists, and historians. White was also a vocal critic of what he called the "attributes and attitudes" approach of Parsonsian sociology, and came to be the leader of what has been variously known as the “Harvard Revolution," the "Harvard breakthrough," or the "Harvard renaissance" in social networks. He worked closely with small group researchers George C. Homans and Robert F. Bales, which was largely compatible with his prior work in organizational research and his efforts to formalize network analysis. Overlapping White's early years, Charles Tilly, a graduate of the Harvard Department of Social

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  Frequent pattern discovery

  Frequent pattern discovery (or FP discovery, FP mining, or Frequent itemset mining) is part of knowledge discovery in databases, Massive Online Analysis, and data mining; it describes the task of finding the most frequent and relevant patterns in large datasets. The concept was first introduced for mining transaction databases. Frequent patterns are defined as subsets (itemsets, subsequences, or substructures) that appear in a data set with frequency no less than a user-specified or auto-determined threshold. == Techniques == Techniques for FP mining include: market basket analysis cross-marketing catalog design clustering classification recommendation systems For the most part, FP discovery can be done using association rule learning with particular algorithms Eclat, FP-growth and the Apriori algorithm. Other strategies include: Frequent subtree mining Structure mining Sequential pattern mining and respective specific techniques. Implementations exist for various machine learning systems or modules like MLlib for Apache Spark.

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