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This paper studies the Craig variant of the Golub-Kahan bidiagonalization algorithm as an iterative solver for linear systems with saddle point structure. Such symmetric indefinite systems in 2x2 block form arise in many applications, but…
We investigate the algebraic structure underlying the stochastic Taylor solution expansion for stochastic differential systems.Our motivation is to construct efficient integrators. These are approximations that generate strong numerical…
Laplacian matrices of graphs arise in large-scale computational applications such as semi-supervised machine learning; spectral clustering of images, genetic data and web pages; transportation network flows; electrical resistor circuits;…
The standard goal for an effective algebraic multigrid (AMG) algorithm is to develop relaxation and coarse-grid correction schemes that attenuate complementary error modes. In the nonsymmetric setting, coarse-grid correction $\Pi$ will…
We present a detailed study of a parametric Lie algebra encompassing the symmetry algebras of various models, both continuous and discrete. This algebraic structure characterizes the isotropic oscillator (with positive, purely imaginary,…
Von Neumann architecture based computers isolate/physically separate computation and storage units i.e. data is shuttled between computation unit (processor) and memory unit to realize logic/ arithmetic and storage functions. This…
This paper proposes a general framework of Riemannian adaptive optimization methods. The framework encapsulates several stochastic optimization algorithms on Riemannian manifolds and incorporates the mini-batch strategy that is often used…
A great deal of effort has recently been invested in developing methods of calculating scattering amplitudes that bypass the traditional construction based on Lagrangians and Feynman rules. Motivated by this progress, we investigate the…
In this communication the advantages and drawbacks of the isogeometric analysis (IGA) are reviewed in the context of electromagnetic simulations. IGA extends the set of polynomial basis functions, commonly employed by the classical Finite…
The proliferation of agentic systems has thrust the reasoning capabilities of AI into the forefront of contemporary machine learning. While it is known that there \emph{exist} neural networks which can reason through any Boolean task…
Bayesian Neural Networks (BNNs) provide superior estimates of uncertainty by generating an ensemble of predictive distributions. However, inference via ensembling is resource-intensive, requiring additional entropy sources to generate…
Concept Bottleneck Models (CBMs) provide a basis for semantic abstractions within a neural network architecture. Such models have primarily been seen through the lens of interpretability so far, wherein they offer transparency by inferring…
Algebraic multigrid (AMG) methods are among the most efficient solvers for linear systems of equations and they are widely used for the solution of problems stemming from the discretization of Partial Differential Equations (PDEs). The most…
Practical memristor came into picture just few years back and instantly became the topic of interest for researchers and scientists. Memristor is the fourth basic two-terminal passive circuit element apart from well known resistor,…
We present principles of algebraic diversity (AD), a group-theoretic approach to signal processing exploiting signal symmetry to extract more information per observation, complementing classical methods that use temporal and spatial…
Beilinson Completion Algebras (BCAs) are generalizations of complete local rings, and have a rich algebraic-analytic structure. These algebras were introduced in my paper "Traces and Differential Operators over Beilinson Completion…
We propose a graph-based extension of Boolean logic called Boolean Graph Logic (BGL). Construing formula trees as the cotrees of cographs, we may state semantic notions such as evaluation and entailment in purely graph-theoretic terms,…
Our main result is that any topological algebra based on a Boolean space is the extended Stone dual space of a certain associated Boolean algebra with additional operations. A particular case of this result is that the profinite completion…
Slater basis functions have desirable properties that can improve electronic structure simulations, but improved numerical integration methods are needed. This work builds upon the SlaterGPU library for evaluation of Hamiltonian matrix…
We study the lattice of extensions of four-valued Belnap--Dunn logic, called super-Belnap logics by analogy with superintuitionistic logics. We describe the global structure of this lattice by splitting it into several subintervals, and…