Related papers: Eulerian orientations and Hadamard codes: A novel …
We compare and discuss the respective efficiency of three methods (with two variants for each of them), based respectively on Taylor (Maclaurin) series, Pad\'{e} approximants and conformal mappings, for solving quasi-analytically a…
We show that an effective version of Siegel's Theorem on finiteness of integer solutions and an application of elementary Galois theory are key ingredients in a complexity classification of some Holant problems. These Holant problems,…
The orienteering problem is a route optimization problem which consists in finding a simple cycle that maximizes the total collected profit subject to a maximum distance limitation. In the last few decades, the occurrence of this problem in…
In this paper, we consider the equilibrium problems and also their regularized problems under the setting of Hadamard spaces. The solution to the regularized problem is represented in terms of resolvent operators. As an essential machinery…
Diagrammatic techniques to compute perturbatively the spectral properties of Euclidean Random Matrices in the high-density regime are introduced and discussed in detail. Such techniques are developed in two alternative and very different…
Many researchers in artificial intelligence are beginning to explore the use of soft constraints to express a set of (possibly conflicting) problem requirements. A soft constraint is a function defined on a collection of variables which…
Unit derived schemes applied to Hadamard matrices are used to construct and analyse linear block and convolutional codes. Codes are constructed to prescribed types, lengths and rates and multiple series of self-dual, dual-containing, linear…
Unconstrained optimization problems become more common in scientific computing and engineering applications with the rapid development of artificial intelligence, and numerical methods for solving them more quickly and efficiently have been…
This paper begins with a class of convex quadratic programs (QPs) with bounded variables solvable by the parametric principal pivoting algorithm with $\mathcal{O}(n^3)$ strongly polynomial complexity, where $n$ is the number of variables of…
Boolean cardinality constraints state that at most (at least, or exactly) $k$ out of $n$ propositional literals can be true. We propose a new class of selection networks that can be used for an efficient encoding of them. Several comparator…
This paper studies the complexity of problems in PPAD $\cap$ PLS that have unique solutions. Three well-known examples of such problems are the problem of finding a fixpoint of a contraction map, finding the unique sink of a Unique Sink…
Machine learning approaches for solving partial differential equations require learning mappings between function spaces. While convolutional or graph neural networks are constrained to discretized functions, neural operators present a…
A new recursive construction of $N$-ary error-correcting output code (ECOC) matrices for ensemble classification methods is presented, generalizing the classic doubling construction for binary Hadamard matrices. Given any prime integer $N$,…
Partition functions, also known as homomorphism functions, form a rich family of graph invariants that contain combinatorial invariants such as the number of k-colourings or the number of independent sets of a graph and also the partition…
Using appropriate notation systems for proofs, cut-reduction can often be rendered feasible on these notations, and explicit bounds can be given. Developing a suitable notation system for Bounded Arithmetic, and applying these bounds, all…
Undoing operations is an indispensable feature for many collaborative applications, mainly collaborative editors. It provides the ability to restore a correct state of shared data after erroneous operations. In particular, selective undo…
In this work, we propose an optimization approach for constructing various classes of circulant combinatorial designs that can be defined in terms of autocorrelations. The problem is formulated as a so-called feasibility problem having…
This study extends the mathematical framework of Hridaya Kolam patterns by applying modular arithmetic to even-ordered dot arrangements with arm counts co-prime to the number of dots. We analyze the resulting cyclic sequences that…
Nonlinear balanced truncation is a model order reduction technique that reduces the dimension of nonlinear systems in a manner that accounts for either open- or closed-loop observability and controllability aspects of the system. A…
Code concatenation combines two or more component codes to design larger codes with greater noise resilience. Introducing entanglement assistance to concatenated codes provides a further advantage in terms of improved error rates and…