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The classical way of extending an $[n, k, d]$ linear code $\C$ is to add an overall parity-check coordinate to each codeword of the linear code $\C$. This extended code, denoted by $\overline{\C}(-\bone)$ and called the standardly extended…
A new approach to finite basis sets for the Dirac equation is developed. It solves the problem of spurious states and, as a result, improves the convergence properties of basis set calculations. The efficiency of the method is demonstrated…
In recent years, the expander decomposition method was used to develop many graph algorithms, resulting in major improvements to longstanding complexity barriers. This powerful hammer has led the community to (1) believe that most problems…
In this work, following the discrete de Rham (DDR) approach, we develop a discrete counterpart of a two-dimensional de Rham complex with enhanced regularity. The proposed construction supports general polygonal meshes and arbitrary…
This article deals with two different problems in commutative algebra. In the first part, we give a proof of generalized forms of the Direct Summand Theorem (DST (or DCS)) for module-finite extension rings of mixed characteristic $R\subset…
The accuracy of the reduced-order model (ROM) mainly depends on the selected basis. Therefore, it is essential to compute an appropriate basis with an efficient numerical procedure when applying ROM to nonlinear problems. In this paper, we…
This paper is about minimum cost constrained selection of inputs and outputs for generic arbitrary pole placement. The input-output set is constrained in the sense that the set of states that each input can influence and the set of states…
Binary embedding is a nonlinear dimension reduction methodology where high dimensional data are embedded into the Hamming cube while preserving the structure of the original space. Specifically, for an arbitrary $N$ distinct points in…
This work proposes a basis for improved throughput of matrix-free evaluation of discontinuous Galerkin symmetric interior penalty discretizations on hexahedral elements. The basis relies on ideas of Hermite polynomials. It is used in a…
Current state-of-the-art methods for solving discrete optimization problems are usually restricted to convex settings. In this paper, we propose a general approach based on cutting planes for solving nonlinear, possibly nonconvex, binary…
We develop a discontinuous Galerkin (DG) framework for automatically constructing adaptive basis sets for electronic structure calculations. By allowing basis functions to be discontinuous across element interfaces, our approach supports…
Meeting real-time constraints for high-performance Approximate Nearest Neighbor (ANN) search remains a critical challenge in remote sensing edge devices, which are essentially fusion systems like micro-satellites and UAVs, largely due to…
A number of regularization methods for discrete inverse problems consist in considering weighted versions of the usual least square solution. However, these so-called filter methods are generally restricted to monotonic transformations,…
Simplicial complexes are extensively studied in the field of algebraic topology. They have gained attention in recent time due to their applications in fields like theoretical distributed computing and simplicial neural networks. Graphs are…
We study permissionless spot--perpetual basis trading in decentralized finance as a collateral control problem. The strategy holds spot inventory, hedges directional exposure with a short perpetual, and allocates capital between spot…
Efficient implementations of sets and maps (dictionaries) are important in computer science, and balanced binary search trees are the basis of the best practical implementations. Pedagogically, however, they are often quite complicated,…
Exact solutions for symmetric discrete breathers (DBs) are obtained in forced-damped linear chain with on-site vibro-impact constraints. The damping is related to inelastic impacts; the forcing may be chosen from broad class of periodic…
We present a new one parameter family of second derivative discontinuous solutions to the simplest scale invariant linear ordinary differential equation. We also point out how the construction could be extended to generate families of…
First-principles density functional theory (DFT) codes which employ a localized basis offer advantages over those which use plane-wave bases, such as better scaling with system size and better suitability to low-dimensional systems. The…
We consider the elastic scattering problem by multiple disjoint arcs or \emph{cracks} in two spatial dimensions. A key aspect of our approach lies in the parametric description of each arc's shape, which is controlled by a potentially…