Related papers: Progress on Polynomial Identity Testing - II
We compute the graded polynomial identities of the infinite dimensional upper triangular matrix algebra over an arbitrary field. If the grading group is finite, we prove that the set of graded polynomial identities admits a finite basis. We…
We study the problems of testing isomorphism of polynomials, algebras, and multilinear forms. Our first main results are average-case algorithms for these problems. For example, we develop an algorithm that takes two cubic forms $f, g\in…
There are three kinds of multiple polylogarithms; complex, finite and symmetric. The dualities for the complex and finite cases are known. In this paper, we present proofs of them via iterated integrals and its symmetric counterpart by a…
We introduce a class of doubly indexed real Hermite polynomials and we deal with their related properties like the associated recurrence formulae, Runge's addition formula, generating function and Nielsen's identity.
Despite interest in communicating ethical problems and social contexts within the undergraduate curriculum to advance Public Interest Technology (PIT) goals, interventions at the graduate level remain largely unexplored. This may be due to…
Prime numbers play a very vital role in modern cryptography and especially the difficulties involved in factoring numbers composed of product of two large prime numbers have been put to use in many modern cryptographic designs. Thus, the…
In this article we present a method to implement orthogonal polynomials and many other special functions in Computer Algebra systems enabling the user to work with those functions appropriately, and in particular to verify different types…
For a broad class of input-output maps, arguments based on the coding theorem from algorithmic information theory (AIT) predict that simple (low Kolmogorov complexity) outputs are exponentially more likely to occur upon uniform random…
This paper follows previous research we have already performed in the area of Bayesian networks models for CAT. We present models using Item Response Theory (IRT - standard CAT method), Bayesian networks, and neural networks. We conducted…
Artificial Intelligence for Theorem Proving has given rise to a plethora of benchmarks and methodologies, particularly in Interactive Theorem Proving (ITP). Research in the area is fragmented, with a diverse set of approaches being spread…
Metamorphic testing has recently been used to check the safety of neural NLP models. Its main advantage is that it does not rely on a ground truth to generate test cases. However, existing studies are mostly concerned with robustness-like…
The aim of this paper is to introduce Bell polynomials and numbers of the second kind and poly-Bell polynomials and numbers of the second kind, and to derive their explicit expressions, recurrence relations and some identities involving…
We perform certain alternating binomial summations with parameters that occur in the analysis of algorithms. A combination of integral and special function and special number representations is used. The results are sufficiently general to…
In this paper we consider the problem of how to computationally test whether a matrix inequality is positive semidefinite on a semialgebraic set. We propose a family of sufficient conditions using the theory of matrix Positivstellensatz…
In this article, we survey the the recent literature surrounding the geometry of complex polynomials. Specific areas surveyed are i) Generalizations of the Gauss--Lucas Theorem, ii) Geometry of Polynomials Level Sets, and iii) Shape…
We study the identity testing problem in the context of spin systems or undirected graphical models, where it takes the following form: given the parameter specification of the model $M$ and a sampling oracle for the distribution…
This thesis settles a number of questions related to computational complexity and algebraic, semidefinite programming based relaxations in optimization and control.
The goal of property testing is to quickly distinguish between objects which satisfy a property and objects that are $\epsilon$-far from satisfying the property. There are now several general results in this area which show that natural…
Person re-identification has received a lot of attention from the research community in recent times. Due to its vital role in security based applications, person re-identification lies at the heart of research relevant to tracking…
This is a survey of some recent developments concerning the p-adic cohomology of algebraic varieties over fields of positive characteristic and local fields of mixed characteristic, plus some related areas like p-adic Hodge theory.