Related papers: Second Moment Method on k-SAT: a General Framework
We let $f$ be a half-integral weight modular form of weight $\kappa>4$ on $\Gamma_0(4)$ that is an eigenfunction of all Hecke operators $T_n$, so that $T_nf = \Lambda_f(n)n^{\frac{\kappa-1}{2}}f$. Let $\|f\|$ denote the Petersson norm of…
We present a novel theoretical formulation for performing quantum dynamics in terms of moments within the single-particle description. By expressing the quantum dynamics in terms of increasing orders of moments, instead of single-particle…
This work proposes a universal and adaptive second-order method for minimizing second-order smooth, convex functions. Our algorithm achieves $O(\sigma / \sqrt{T})$ convergence when the oracle feedback is stochastic with variance $\sigma^2$,…
This paper proposes a data-driven learning framework for identifying governing laws of generalized diffusions with non-gradient components. By combining energy dissipation laws with a physically consistent penalty and first-moment…
The main ideas in the CDSAT (Conflict-Driven Satisfiability) framework for SMT are summarized, leading to approaches to proof generation in CDSAT.
In this paper, we generalise the formula for the fourth moment of a random determinant to account for entries with asymmetric distribution. We also derive the second moment of a random Gram determinant.
We present a novel framework for user representation in large-scale recommender systems, aiming at effectively representing diverse user taste in a generalized manner. Our approach employs a two-stage methodology combining representation…
While symmetries are well understood for Boolean formulas and successfully exploited in practical SAT solving, less is known about symmetries in quantified Boolean formulas (QBF). There are some works introducing adaptions of propositional…
In this paper, novel closed-form point estimators of the beta distribution are proposed and investigated. The first estimators are a modified version of Pearson's method of moments. The underlying idea is to involve the sufficient…
The generalized problem of moments is a conic linear optimization problem over the convex cone of positive Borel measures with given support. It has a large variety of applications, including global optimization of polynomials and rational…
We show that with a few modifications the Adomian's method for solving second order differential equations can be used to obtain the known results of the special functions of mathematical physics. The modifications are necessary in order to…
Adaptive moment methods have been remarkably successful in deep learning optimization, particularly in the presence of noisy and/or sparse gradients. We further the advantages of adaptive moment techniques by proposing a family of double…
Suppose $K$ is a number field and $a_K(m)$ is the number of integral ideals of norm equal to $m$ in $K$, then for any integer $l$, we asymptotically evaluate the sum \[ \sum_{m\leqslant T} a_K^l(m) \] as $T\to\infty$. We also consider the…
We study the distribution of work induced by the two-point measurement protocol for a driven open quantum system. We first derive a general form for the generating function of work for the total system, bearing in mind that the Hamiltonian…
A conversion matrix approach to solving network problems involving time-varying circuit components is applied to the method of moments for electromagnetic scattering analysis. Detailed formulations of this technique's application to the…
In this paper we consider generalized moment functions of higher order. These functions are closely related to the well-known functions of binomial type which have been investigated on various abstract structures. In our former paper we…
In this short paper we present a survey of some results concerning the random SAT problems. To elaborate, the Boolean Satisfiability (SAT) Problem refers to the problem of determining whether a given set of $m$ Boolean constraints over $n$…
We obtain exact expressions counting the satisfiable 2-SAT formulae and describe the structure of associated implication digraphs. Our approach is based on generating function manipulations. To reflect the combinatorial specificities of the…
Stochastic Gradient Descent (SGD) methods see many uses in optimization problems. Modifications to the algorithm, such as momentum-based SGD methods have been known to produce better results in certain cases. Much of this, however, is due…
We introduce completion moment detection for actions - the problem of locating the moment of completion, when the action's goal is confidently considered achieved. The paper proposes a joint classification-regression recurrent model that…