Related papers: Two Algorithms for Computing Rational Univariate R…

In this thesis, I explore the possibilities of conducting Bayesian optimization techniques in high dimensional domains. Although high dimensional domains can be defined to be between hundreds and thousands of dimensions, we will primarily…

Elimination of unknowns in a system of differential equations is often required when analysing (possibly nonlinear) dynamical systems models, where only a subset of variables are observable. One such analysis, identifiability, often relies…

The numerical methods for differential equation solution allow obtaining a discrete field that converges towards the solution if the method is applied to the correct problem. Nevertheless, the numerical methods have the restricted class of…

We use recurrence equations (alias difference equations) to enumerate the number of formula-representations of positive integers using only addition and multiplication, and using addition, multiplication, and exponentiation, where all the…

Abramov's algorithm enables us to decide whether a univariate rational function can be written as a difference of another rational function, which has been a fundamental algorithm for rational summation. In 2014, Chen and Singer generalized…

We develop an algorithm for sampling from the unitary invariant random matrix ensembles. The algorithm is based on the representation of their eigenvalues as a determinantal point process whose kernel is given in terms of orthogonal…

Symbolic recovery of differential equations is the ambitious attempt at automating the derivation of governing equations with the use of machine learning techniques. In contrast to classical methods which assume the structure of the…

Modern convolutional neural networks (CNNs) have massive identical convolution blocks, and, hence, recursive sharing of parameters across these blocks has been proposed to reduce the amount of parameters. However, naive sharing of…

We describe an algorithm for computing Macaulay dual spaces for multi-graded ideals. For homogeneous ideals, the natural grading is inherited by the Macaulay dual space which has been leveraged to develop algorithms to compute the Macaulay…

We present a new algorithm for computing the real radical of an ideal and, more generally, the-radical of, which is based on convex moment optimization. A truncated positive generic linear functional vanishing on the generators of is…

A parameterized surface can be represented as a projection from a certain toric surface. This generalizes the classical homogeneous and bihomogeneous parameterizations. We extend to the toric case two methods for computing the implicit…

We consider a new class of Parareal algorithms, which use ideas from localized reduced basis methods to construct the coarse solver from spectral approximations of the transfer operators mapping initial values for a given time interval to…

Several quantities important in condensed matter physics, quantum information, and quantum chemistry, as well as quantities required in meta-optimization of machine learning algorithms, can be expressed as gradients of implicitly defined…

This paper describes serial and parallel compositional models of multiple objects with part sharing. Objects are built by part-subpart compositions and expressed in terms of a hierarchical dictionary of object parts. These parts are…

A parameter estimation problem is considered for a stochastic parabolic equation with multiplicative noise under the assumption that the equation can be reduced to an infinite system of uncoupled diffusion processes. From the point of view…

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,…

In classical and real algebraic geometry there are several notions of the radical of an ideal I. There is the vanishing radical defined as the set of all real polynomials vanishing on the real zero set of I, and the real radical defined as…

We first propose a concise singular value decomposition of dual matrices. Then, the randomized version of the decomposition is presented. It can significantly reduce the computational cost while maintaining the similar accuracy. We analyze…

Given a symbolic power of a homogeneous ideal in a polynomial ring, we study the problem of determining which powers of the ideal contain it. For ideals defining 0-dimensional subschemes of projective space, as an immediate corollary of our…

The reduction algorithm is used to compute reduced ideals of a number field. However, there are reduced ideals that can never be obtained from this algorithm. In this paper, we will show that these ideals have inverses of larger norms among…