Related papers: Grothendieck-type inequalities in combinatorial op…
It is well known that general variational inequalities provide us with a unified, natural, novel and simple framework to study a wide class of unrelated problems, which arise in pure and applied sciences. In this paper, we present a number…
We prove concentration inequalities for functions of independent random variables {under} sub-gaussian and sub-exponential conditions. The utility of the inequalities is demonstrated by an extension of the now classical method of Rademacher…
In this article, by combining appropriate refined Bohr's inequalities with some techniques concerning bounded analytic functions defined in the unit disk, we generalize and improve several Bohr type inequalities for such functions.
In this thesis I discuss combinatorial optimization problems, from the statistical physics perspective. The starting point are the motivations which brought physicists together with computer scientists and mathematicians to work on this…
We define a notion on preadditive categories which plays a role similar to the notion of a Grothendieck pretopology on an unenriched category. Each such additive pretopology defines an additive Grothendieck topology and suffices to define…
Some new Gruss type inequalities in inner product spaces and applications for integrals are given.
We consider cohomology of small categories with coefficients in a natural system in the sense of Baues and Wirsching. For any funtor L: K -> CAT, we construct a spectral sequence abutting to the cohomology of the Grothendieck construction…
In this note we study the eigenvalue problem for a quadratic form associated with Strichartz estimates for the Schr\"{o}dinger equation, proving in particular a sharp Strichartz inequality for the case of odd initial data. We also describe…
We formally investigate some computational obstacles to tractability of computing the variety determined by K complex polynomials in N boolean variables. We show that using algebraic methods for solving combinatorial problems, the obstacles…
In this paper we prove the pluricomplex counterpart of the Moser-Trudinger and Sobolev inequalities in complex space. We consider these inequalities for plurisubharmonic functions with finite pluricomplex energy, and we estimate the…
Translating notions and results from category theory to the theory of computability models of Longley and Normann, we introduce the Grothendieck computability model and the first-projection-simulation. We prove some basic properties of the…
One of the most common problem-solving heuristics is by analogy. For a given problem, a solver can be viewed as a strategic walk on its fitness landscape. Thus if a solver works for one problem instance, we expect it will also be effective…
We show how to treat families of $\infty$-categories fibered in categorical patterns (e.g., $\infty$-operads and monoidal $\infty$-categories) in terms of fibrations by relativizing the Grothendieck construction. As applications, we…
In this work we prove a Brunn-Minkowski-type inequality in the context of symplectic geometry and discuss some of its applications.
A new calculus of planar diagrams involving diagrammatics for biadjoint functors and degenerate affine Hecke algebras is introduced. The calculus leads to an additive monoidal category whose Grothendieck ring contains an integral form of…
In practice, optimization tasks have some structure that allows developing new algorithms for every problem with faster convergence rates. Using the structure of optimization tasks, we can propose algorithms with more optimistic convergence…
A procedure for constructing bivariant theories by means of Grothendieck duality is developed. This produces, in particular, a bivariant theory of Hochschild (co)homology on the category of schemes that are flat, separated and essentially…
Genetic Programming (GP) has found various applications. Understanding this type of algorithm from a theoretical point of view is a challenging task. The first results on the computational complexity of GP have been obtained for problems…
In this note we present a refinement of the AM-GM inequality, and then we estimate in a special case the typical size of the improvement.
We consider optimization problems with polynomial inequality constraints in non-commuting variables. These non-commuting variables are viewed as bounded operators on a Hilbert space whose dimension is not fixed and the associated polynomial…