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Model reduction plays a critical role in system control, with established methods such as balanced truncation widely used for linear systems. However, extending these methods to nonlinear settings, particularly polynomial dynamical systems…
Hyperdimensional computing (HDC) is an emerging computing paradigm that imitates the brain's structure to offer a powerful and efficient processing and learning model. In HDC, the data are encoded with long vectors, called hypervectors,…
An infinite-dimensional family of exact solutions of a three-dimensional biharmonic equation was constructed by the hypercomplex method.
Computational models are quantitative representations of systems. By analyzing and comparing the outputs of such models, it is possible to gain a better understanding of the system itself. Though as the complexity of model outputs…
This invention addresses fixed-point representations of convolutional neural networks (CNN) in integrated circuits. When quantizing a CNN for a practical implementation there is a trade-off between the precision used for operations between…
Tensor network methods provide a scalable solution to represent high-dimensional data. However, their efficacy is often limited by static, expert-defined structures that fail to adapt to evolving data correlations. We address this…
The widespread use of multisensor technology and the emergence of big datasets have created the need to develop tools to reduce, approximate, and classify large and multimodal data such as higher-order tensors. While early approaches…
Methods for solving Maxwell's equations are integral part of optical metrology and computational lithography setups. Applications require accurate geometrical resolution, high numerical accuracy and/or low computation times. We present a…
Hyperdimensional computing (HDC) is a novel computational paradigm that operates on long-dimensional vectors known as hypervectors. The hypervectors are constructed as long bit-streams and form the basic building blocks of HDC systems. In…
A method of representation of a solution as segments of the series in powers of the step of the independent variable is expanded for solving complex systems of ordinary differential equations (ODE): the Lorenz system and other systems. A…
The purpose of this paper is to present a recursive algorithm and its implementation in Maple and Mathematica for the computation of joint moments and cumulants of Hawkes processes with exponential kernels. Numerical results and computation…
A finite sum of exponential functions may be expressed by a linear combination of powers of the independent variable and by successive integrals of the sum. This is proved for the general case and the connection between the parameters in…
Various data visualization applications such as reverse engineering and interactive authoring require a vocabulary that describes the structure of visualization scenes and the procedure to manipulate them. A few scene abstractions have been…
We present algorithms to solve coupled systems of linear differential equations, arising in the calculation of massive Feynman diagrams with local operator insertions at 3-loop order, which do {\it not} request special choices of bases.…
Prediction and explanation are key objects in supervised machine learning, where predictive models are known as black boxes and explanatory models are known as glass boxes. Explanation provides the necessary and sufficient information to…
We use fast-growing finite and infinite sequences of natural numbers and more complicated constructs to define models of hypercomputation and interpret non-arithmetic predicates, with the strongest extensions reaching full second order…
The main object of this work is to show how some rather elementary techniques based upon certain inverse pairs of symbolic operators would lead us easily to several decomposition formulas associated with confluent hypergeometric functions…
We make progress towards a 3D finite-element model for the magnetization of a high temperature superconductor (HTS): We suggest a method that takes into account demagnetisation effects and flux creep, while it neglects the effects…
We consider a set of probabilistic functions of some input variables as a representation of the inputs. We present bounds on how informative a representation is about input data. We extend these bounds to hierarchical representations so…
Scientific computations or measurements may result in huge volumes of data. Often these can be thought of representing a real-valued function on a high-dimensional domain, and can be conceptually arranged in the format of a tensor of high…