Related papers: Nash multiplicities and resolution invariants
A notion of curvature is introduced in multivariable operator theory and an analogue of the Gauss-Bonnet-Chern theorem is established for graded (contractive) Hilbert modules over the complex polynomial algebra in d variables, d=1,2,3,....…
Semantic hashing has become a powerful paradigm for fast similarity search in many information retrieval systems. While fairly successful, previous techniques generally require two-stage training, and the binary constraints are handled…
In this paper we study the sets of integers which are $n$-th terms of Lucas sequences. We establish lower- and upper bounds for the size of these sets. These bounds are sharp for $n$ sufficiently large. We also develop bounds on the growth…
We introduce an extended mathematical programming framework for specifying equilibrium problems and their variational representations, such as generalized Nash equilibrium, multiple optimization problems with equilibrium constraints, and…
We study multiplier algebras for a large class of Banach algebras which contains the group algebra $L_1(G)$, the Beurling algebras $L_1(G, \omega)$, and the Fourier algebra $A(G)$ of a locally compact group $G$. This study yields numerous…
This article shall serve as a quick reference for somebody who needs precise information on concepts and results related to resolution of singularities. As such, it is more a technical manual than a bedtime story. Topics which are covered:…
In this paper, the problem of finding a generalized Nash equilibrium (GNE) of a networked game is studied. Players are only able to choose their decisions from a feasible action set. The feasible set is considered to be a private linear…
Root multiplicities encode information about the structure of Kac-Moody algebras, and appear in applications as far-reaching as string theory and the theory of modular functions. We provide an algorithm based on the Peterson recurrence…
Nash equilibrium is one of the most influential solution concepts in game theory. With the development of computer science and artificial intelligence, there is an increasing demand on Nash equilibrium computation, especially for Internet…
We describe a new complete algorithm for computing Nash equilibrium in multiplayer general-sum games, based on a quadratically-constrained feasibility program formulation. We demonstrate that the algorithm runs significantly faster than the…
NAC-colourings of graphs correspond to flexible quasi-injective realisations in $\mathbb {R} ^2$. A special class of NAC-colourings are those that arise from stable cuts. We give sharp thresholds for the random graph to have no stable cut…
The Sequential Multiple Knapsack Problem is a special case of Multiple knapsack problem in which the items sizes are divisible. A characterization of the optimal solutions of the problem and a description of the convex hull of all the…
We initiate the study of Preference-Based Multi-Agent Reinforcement Learning (PbMARL), exploring both theoretical foundations and empirical validations. We define the task as identifying the Nash equilibrium from a preference-only offline…
The symmetric generalized eigenvalue problem (SGEP) is a fundamental concept in numerical linear algebra. It captures the solution of many classical machine learning problems such as canonical correlation analysis, independent components…
In this paper we investigate realization theory of a class of non-linear systems, called Nash systems. Nash systems are non-linear systems whose vector fields and readout maps are analytic semi-algebraic functions. In this paper we will…
We prove that the numerical invariant $3\mu-4\tau$ of a reduced irreducible plane curve singularity germ is non-negative, non-decreasing under blowups and strictly increasing unless the curve is non-singular. This provides a new perspective…
The Multiplicity conjecture of Herzog, Huneke, and Srinivasan states an upper bound for the multiplicity of any graded $k$-algebra as well as a lower bound for Cohen-Macaulay algebras. In this note we extend this conjecture in several…
We present a hypersurface singularity in positive characteristic which is defined by a purely inseparable power series, and a sequence of point blowups so that, after applying the blowups to the singularity, the same type of singularity…
This thesis describes some of the recent (and some less recent) developments in calculational techniques for scattering amplitudes in quantum field theory. The focus is on on-shell recursion relations in complex momenta and on the use of…
Given a semianalytic set S in a complex space and a point p in S, there is a unique smallest complex-analytic germ at p which contains the germ of S, called the holomorphic closure of S at p. We show that if S is semialgebraic then its…