Related papers: Modeling amortization systems with vector spaces
We investigate the applications of ovals in projective planes to distributed storage, with a focus on the Service Rate Region problem. Leveraging the incidence relations between lines and ovals, we describe a class of non-systematic MDS…
We present assume-guarantee contracts for continuous-time linear dynamical systems with inputs and outputs. These contracts are used to express specifications on the dynamic behaviour of a system. Contrary to existing approaches, we use…
Stabiliser states play a central role in the theory of quantum computation. For example, they are used to encode computational basis states in the most common quantum error correction schemes. Arbitrary quantum states admit many stabiliser…
A matrix approach to continuous iteration is proposed for general formal series. It leads, in particular, to an order{to{order iteration of the exponential function, and consequently to an algorithmic approach to tetration. Lower{order…
The relation between entanglement entropy and the computational difficulty of classically simulating Quantum Mechanics is briefly reviewed. Matrix product states are proven to provide an efficient representation of one-dimensional quantum…
Inflation is often described through the dynamics of a scalar field, slow-rolling in a suitable potential. Ultimately, this inflaton must be identified as the expectation value of a quantum field, evolving in a quantum effective potential.…
The vector transform operators are investigated; these operators are used at the solution of boundary value problems in piecewise homogeneous spherically symmetric areas. In particular, examples of transformation operators for vector…
Neural posterior estimation has emerged as a powerful tool for amortized inference, with growing adoption across scientific and applied domains. In many of these applications, the conditioning variable is a set of observations whose…
A recent suggestion that vector potentials in electrodynamics (ED) are nontensorial objects under 4D frame rotations is found to be both unnecessary and confusing. As traditionally used in ED, a vector potential $A$ always transforms…
Recently, purpose-built analog hardware that can efficiently minimize the Ising energy and thereby solve a variety of combinatorial optimization problems has been receiving widespread attention. In this work, we show how multidimensional,…
We consider the time and space required for quantum computers to solve a wide variety of problems involving matrices, many of which have only been analyzed classically in prior work. Our main results show that for a range of linear algebra…
Classical continuum mechanical theories operate on three-dimensional Eu-clidian space using scalar, vector, and tensor-valued quantities usually up to the order of four. For their numerical treatment, it is common practice to transform the…
Motivated by a model in quantum computation we study orthogonal sets of integral vectors of the same norm that can be extended with new vectors keeping the norm and the orthogonality. Our approach involves some arithmetic properties of the…
The aim of this work is to design implicit and semi-implicit high-order well-balanced finite-volume numerical methods for 1D systems of balance laws. The strategy introduced by two of the authors in a previous paper for explicit schemes…
We discuss the quantization of mechanical systems for which the Hamiltonian vector fields of observables form the deformation of $n$-dimensional oscilator algebra. Because of this fact these systems can be considered as "deformations" of…
This work provides an efficient virtual element scheme for the modeling of nonlinear elastodynamics undergoing large deformations. The virtual element method (VEM) has been applied to various engineering problems such as elasto-plasticity,…
We consider the problem of automatically proving resource bounds. That is, we study how to prove that an integer-valued resource variable is bounded by a given program expression. Automatic resource-bound analysis has recently received…
Iteration method is commonly used in solving linear systems of equations. We present quantum algorithms for the relaxed row and column iteration methods by constructing unitary matrices in the iterative processes, which generalize row and…
It is well-known that the theories of semi-vector spaces and semi-algebras -- which were not much studied over time -- are utilized/applied in Fuzzy Set Theory in order to obtain extensions of the concept of fuzzy numbers as well as to…
We discuss four different constructions of vector space bases associated to vanishing ideals of points. We show how to compute normal forms with respect to these bases and give new complexity bounds. As an application, we improve the…