Related papers: Lower Bounds for Symmetric Circuits for the Determ…
With perfectly balanced gain and loss, dynamical systems with indefinite damping can obey the exact PT-symmetry being marginally stable with a pure imaginary spectrum. At an exceptional point where the symmetry is spontaneously broken, the…
Discrete translational symmetry plays a fundamental role in condensed matter physics and lattice gauge theories, enabling the analysis of systems that would otherwise be intractable. Despite this, many open problems remain. Quantum…
Parametric quantum circuits play a crucial role in the performance of many variational quantum algorithms. To successfully implement such algorithms, one must design efficient quantum circuits that sufficiently approximate the solution…
An important yet challenging problem in numerical linear algebra is finding a principal submatrix with maximum determinant from a given symmetric positive semidefinite matrix. This problem arises in experimental design, statistics, and…
Recently much attention has been paid to quantum circuit design to prepare for the future "quantum computation era." Like the conventional logic synthesis, it should be important to verify and analyze the functionalities of generated…
The problem of expressing a specific polynomial as the determinant of a square matrix of affine-linear forms arises from algebraic geometry, optimisation, complexity theory, and scientific computing. Motivated by recent developments in this…
In recent years, a very exciting and promising method for proving lower bounds for arithmetic circuits has been proposed. This method combines the method of {\it depth reduction} developed in the works of Agrawal-Vinay [AV08], Koiran…
We introduce a renormalized 1PI vertex part scalar field theory setting in momentum space to computing the critical exponents $\nu$ and $\eta$, at least at two-loop order, for a layered parallel plate geometry separated by a distance L,…
The development of machine learning in particular and artificial intelligent in general has been strongly conditioned by the lack of an appropriated framework to specify and integrate learning processes, data transformation processes and…
Minimizing divergence measures under a constraint is an important problem. We derive a sufficient condition that binary divergence measures provide lower bounds for symmetric divergence measures under a given triangular discrimination or…
Algebraic Branching Programs(ABPs) are standard models for computing polynomials. Syntactic multilinear ABPs (smABPs) are restrictions of ABPs where every variable is allowed to occur at most once in every path from the start to the…
Symmetries play an critical role in finding analytic solutions to nonlinear differential equations. A symmetry is a mapping of the solutions of the differential equation into the solutions and have been studied extensively for over a…
Totally symmetric sets are a recently introduced tool for studying homomorphisms between groups. In this paper, we give full classifications of totally symmetric sets in certain families of groups and bound their sizes in others. As a…
We prove that every randomized Boolean function admits a supersimulator: a randomized polynomial-size circuit whose output on random inputs cannot be efficiently distinguished from reality with constant advantage, even by polynomially…
Discrete Laplacian operators arise ubiquitously in scientific computing and frequently appear in quantum algorithms for tasks such as linear algebra, Hamiltonian simulation, and partial differential equations. Block encoding provides the…
This paper focuses on controlling the absorbing set spectrum for a class of regular LDPC codes known as separable, circulant-based (SCB) codes. For a specified circulant matrix, SCB codes all share a common mother matrix, examples of which…
Generalized symmetry extends the usual notion of symmetry to ones that are of higher-form, acting on subsystems, non-invertible, etc. The concept was originally defined in the field theory context using the idea of topological defects. On…
This paper presents a Cramer-Rao bound (CRB) for the estimation of parameters confined to an arbitrary set. Unlike existing results that rely on equality or inequality constraints, manifold structures, or the nonsingularity of the Fisher…
We identify a common scheme in several existing algorithms addressing computational problems on linear differential equations with polynomial coefficients. These algorithms reduce to computing a linear relation between vectors obtained as…
Consider an algorithm computing in a differential field with several commuting derivations such that the only operations it performs with the elements of the field are arithmetic operations, differentiation, and zero testing. We show that,…