Related papers: The devil is in Asymmetries (Rough Version)
This paper depicts algorithms for solving the decision Boolean Satisfiability Problem. An extreme problem is formulated to analyze the complexity of algorithms and the complexity for solving it. A novel and easy reformulation as a lottery…
This is a survey on the use of low-degree polynomials to predict and explain the apparent statistical-computational tradeoffs in a variety of average-case computational problems. In a nutshell, this framework measures the complexity of a…
Given a computable sequence of natural numbers, it is a natural task to find a G\"odel number of a program that generates this sequence. It is easy to see that this problem is neither continuous nor computable. In algorithmic learning…
Asking which sets are fixed-parameter tractable for a given parameterization constitutes much of the current research in parameterized complexity theory. This approach faces some of the core difficulties in complexity theory. By focussing…
We use character polynomials to obtain a positive combinatorial interpretation of the multiplicity of the sign representation in irreducible polynomial representations of $GL_n(\mathbb{C})$ indexed by two-column and hook partitions. Our…
The Lichtenbaum-Quillen conjecture for smooth complex varieties states that algebraic and topological K-theory with finite coefficients become isomorphic in high degrees. We define the "Lichtenbaum-Quillen dimension" of a variety in terms…
We consider a general statistical linear inverse problem, where the solution is represented via a known (possibly overcomplete) dictionary that allows its sparse representation. We propose two different approaches. A model selection…
In this paper, we consider first-order logic over unary functions and study the complexity of the evaluation problem for conjunctive queries described by such kind of formulas. A natural notion of query acyclicity for this language is…
We discuss the computational complexity and feasibility properties of scenario based techniques for uncertain optimization programs. We consider different solution alternatives ranging from the standard scenario approach to recursive…
A way to construct and classify the three dimensional polynomially deformed algebras is given and the irreducible representations is presented. for the quadratic algebras 4 different algebras are obtained and for cubic algebras 12 different…
In the present paper we describe topological obstructions to embedding of a (complex) matrix algebra bundle into a trivial one under some additional arithmetic condition on their dimensions. We explain a relation between this problem and…
Graph polynomials encode fundamental combinatorial invariants of graphs. Their computation is investigated using tree and path decomposition frameworks, with formal definitions of treewidth, k-trees, and pathwidth establishing the…
We study d-variate approximation problems in the average case setting with respect to a zero-mean Gaussian measure. Our interest is focused on measures having a structure of non-homogeneous linear tensor product, where covariance kernel is…
We study quantum algorithms for the hidden shift problem of complex scalar- and vector-valued functions on finite abelian groups. Given oracle access to a shifted function and the Fourier transform of the unshifted function, the goal is to…
Prediction problems often admit competing models that perform almost equally well. This effect challenges key assumptions in machine learning when competing models assign conflicting predictions. In this paper, we define predictive…
This work examines the Conditional Approval Framework for elections involving multiple interdependent issues, specifically focusing on the Conditional Minisum Approval Voting Rule. We first conduct a detailed analysis of the computational…
A theory of numerical path-following in toric varieties was suggested in two previous papers. The motivation is solving systems of polynomials with real or complex coefficients. When those polynomials are not assumed 'dense', solving them…
Machine learning algorithms are powerful tools for data driven tasks such as image classification and feature detection, however their vulnerability to adversarial examples - input samples manipulated to fool the algorithm - remains a…
In this article we study a broad class of integer programming problems in variable dimension. We show that these so-termed {\em n-fold integer programming problems} are polynomial time solvable. Our proof involves two heavy ingredients…
We study the complexity of influencing elections through bribery: How computationally complex is it for an external actor to determine whether by a certain amount of bribing voters a specified candidate can be made the election's winner? We…