相关论文: On the survey-propagation equations for the random…

Spectral morphisms between Banach algebras are useful for comparing their K-theory and their "noncommutative dimensions" as expressed by various notions of stable ranks. In practice, one often encounters situations where the spectral…

We show that the Survey Propagation-guided decimation algorithm fails to find satisfying assignments on random instances of the "Not-All-Equal-$K$-SAT" problem if the number of message passing iterations is bounded by a constant independent…

LECTURE GIVEN AT TH2002. Given a set of Boolean variables, and some constraints between them, is it possible to find a configuration of the variables which satisfies all constraints? This problem, which is at the heart of combinatorial…

We revisit the \textsc{$k$-Secluded Tree} problem. Given a vertex-weighted undirected graph $G$, its objective is to find a maximum-weight induced subtree $T$ whose open neighborhood has size at most $k$. We present a fixed-parameter…

Here we study the NP-complete $K$-SAT problem. Although the worst-case complexity of NP-complete problems is conjectured to be exponential, there exist parametrized random ensembles of problems where solutions can typically be found in…

A Direct Sum Theorem holds in a model of computation, when solving some k input instances together is k times as expensive as solving one. We show that Direct Sum Theorems hold in the models of deterministic and randomized decision trees…

We show that for many models of random trees, the independence number divided by the size converges almost surely to a constant as the size grows to infinity; the trees that we consider include random recursive trees, binary and $m$-ary…

The random k-SAT model is the most important and well-studied distribution over k-SAT instances. It is closely connected to statistical physics; it is used as a testbench for satisfiability algorithms, and average-case hardness over this…

Using methods and ideas from statistical mechanics, we propose a simple method for obtaining rigorous upper bounds for satisfiability transition in random boolean expressions composed of N variables and M clauses with K variables per…

In this paper, we study the $k$-forest problem in the model of resource augmentation. In the $k$-forest problem, given an edge-weighted graph $G(V,E)$, a parameter $k$, and a set of $m$ demand pairs $\subseteq V \times V$, the objective is…

Random forests are a very effective and commonly used statistical method, but their full theoretical analysis is still an open problem. As a first step, simplified models such as purely random forests have been introduced, in order to shed…

This work considers the allocation problem for multivariate stratified random sampling as a problem of integer non-linear stochastic multiobjective mathematical programming. With this goal in mind the asymptotic distribution of the vector…

In this paper we study a variation of the random $k$-SAT problem, called polarized random $k$-SAT. In this model there is a polarization parameter $p$, and in half of the clauses each variable occurs negated with probability $p$ and pure…

Finding a good compromise between the exploitation of known resources and the exploration of unknown, but potentially more profitable choices, is a general problem, which arises in many different scientific disciplines. We propose a…

Motivated by online recommendation systems, we study a family of random forests. The vertices of the forest are labeled by integers. Each non-positive integer $i\le 0$ is the root of a tree. Vertices labeled by positive integers $n \ge 1$…

Exact rational solutions of the generalized Hunter-Saxton equation are obtained using Pad\'e approximant approach for the traveling-wave and self-similarity reduction. A larger class of algebraic solutions are also obtained by extending a…

We introduce a new model for the generation of random satisfiability problems. It is an extension of the hyper-SAT model of Ricci-Tersenghi, Weigt and Zecchina, which is a variant of the famous K-SAT model: it is extended to q-state…

We study parameterized Constraint Satisfaction Problem for infinite constraint languages. The parameters that we study are weight of the satisfying assignment, number of constraints, maximum number of occurrences of a variable in the…

We demonstrate an iterative scheme to approximate the optimal transportation problem with a discrete target measure under certain standard conditions on the cost function. Additionally, we give a finite upper bound on the number of…

Variable projection solves structured optimization problems by completely minimizing over a subset of the variables while iterating over the remaining variables. Over the last 30 years, the technique has been widely used, with empirical and…