相关论文: Inhomogeneous random 2-SAT

We propose a novel kernel-based nonparametric two-sample test, employing the combined use of kernel mean and kernel covariance embedding. Our test builds on recent results showing how such combined embeddings map distinct probability…

We show that throughout the satisfiable phase the normalised number of satisfying assignments of a random $2$-SAT formula converges in probability to an expression predicted by the cavity method from statistical physics. The proof is based…

The Very Special Relativity Electroweak Standard Model (VSR EW SM) is a theory with $SU(2)_L \times U(1)_R$ symmetry, with the same number of leptons and gauge fields as in the usual Weinberg-Salam (WS) model. No new particles are…

We introduce and solve exactly a family of invariant 2x2 random matrices, depending on one parameter \eta, and we show that rotational invariance and real Dyson index \beta are not incompatible properties. The probability density for the…

We consider "unconstrained" random $k$-XORSAT, which is a uniformly random system of $m$ linear non-homogeneous equations in $\mathbb{F}_2$ over $n$ variables, each equation containing $k \geq 3$ variables, and also consider a "constrained"…

We prove that, with high probability, the contradictory components of a random 2-SAT formula in the subcritical phase of the phase transition have only 3-regular kernels. This follows from the relation between these kernels and the complex…

We study the distribution of Durbin-Wu-Hausman (DWH) and Revankar-Hartley (RH) tests for exogeneity from a finite-sample viewpoint, under the null and alternative hypotheses. We consider linear structural models with possibly non-Gaussian…

We give a nearly linear-time algorithm to approximately sample satisfying assignments in the random $k$-SAT model when the density of the formula scales exponentially with $k$. The best previously known sampling algorithm for the random…

We study two variants of the modified Watts threshold model with a noise (with nonconformity, in the terminology of social psychology) on a complete graph. Within the first version, a noise is introduced via so-called independence, whereas…

Regular signed SAT is a variant of the well-known satisfiability problem in which the variables can take values in a fixed set V \subset [0,1], and the `literals' have the form "x \le a" or "x \ge a". We answer some open question regarding…

We investigate the secure connectivity of wireless sensor networks under a heterogeneous random key predistribution scheme and a heterogeneous channel model. In particular, we study a random graph formed by the intersection of an…

A {\it W$^*$-representation} of a II$_1$ subfactor $N\subset M$ with finite Jones index, $[M:N]<\infty$, is a non-degenerate commuting square embedding of $N\subset M$ into an inclusion of atomic von Neumann algebras $\oplus_{i\in I} \Cal…

Consider a set of $n$ vertices, where each vertex has a location in $\mathbb{R}^d$ that is sampled uniformly from the unit cube in $\mathbb{R}^d$, and a weight associated to it. Construct a random graph by placing edges independently for…

Random $k$-SAT is the single most intensely studied example of a random constraint satisfaction problem. But despite substantial progress over the past decade, the threshold for the existence of satisfying assignments is not known precisely…

The XOR-satisfiability (XORSAT) problem deals with a system of $n$ Boolean variables and $m$ clauses. Each clause is a linear Boolean equation (XOR) of a subset of the variables. A $K$-clause is a clause involving $K$ distinct variables. In…

We develop a hypergraph container method for the Boolean Satisfiability Problem (SAT) via the newly developed container results [Campos and Samotij (2024)]. This provides an explicit connection between the extent of spread of clauses and…

The effect that weighted summands have on each other in approximations of $S=w_1S_1+w_2S_2+\cdots+w_NS_N$ is investigated. Here, $S_i$'s are sums of integer-valued random variables, and $w_i$ denote weights, $i=1,\dots,N$. Two cases are…

We consider a regression framework where the design points are deterministic and the errors possibly non-i.i.d. and heavy-tailed (with a moment of order $p$ in $[1,2]$). Given a class of candidate regression functions, we propose a…

We study the polyhedral structure of the static probabilistic lot-sizing problem and propose valid inequalities that integrate information from the chance constraint and the binary setup variables. We prove that the proposed inequalities…

We introduce a highly structured family of hard satisfiable 3-SAT formulas corresponding to an ordered spin-glass model from statistical physics. This model has provably "glassy" behavior; that is, it has many local optima with large energy…