Related papers: Exact enumeration of satisfiable 2-SAT formulae
For the sl_2 Gaudin model (degenerated quantum integrable XXX spin chain) an exponential generating function of correlators is calculated explicitely. The calculation relies on the Gauss decomposition for the SL_2 loop group. From the…
Inferring road graphs from satellite imagery is a challenging computer vision task. Prior solutions fall into two categories: (1) pixel-wise segmentation-based approaches, which predict whether each pixel is on a road, and (2) graph-based…
Adversarial SAT (AdSAT) is a generalization of the satisfiability (SAT) problem in which two players try to make a boolean formula true (resp. false) by controlling their respective sets of variables. AdSAT belongs to a higher complexity…
The exact 2-point function of certain physically motivated operators in SYK-like spin glass models is computed, bypassing the Schwinger-Dyson equations. The models possess an IR low energy conformal window, but our results are exact at all…
This paper derives the analytic form of the $h$-step ahead prediction density of a GARCH(1,1) process under Gaussian innovations, with a possibly asymmetric news impact curve. The contributions of the paper consists both in the derivation…
While static symmetry breaking has been explored in the SAT community for decades, only as of 2010 research has focused on exploiting the same discovered symmetry dynamically, during the run of the SAT solver, by learning extra clauses. The…
We present the generating function approach to the perturbative exponentiation of correlators of a product of Wilson lines and loops. The exponentiated expression is presented in closed form as an algebraic function of correlators of known…
We enumerate the independent sets of several classes of regular and almost regular graphs and compute the corresponding generating functions. We also note the relations between these graphs and other combinatorial objects and, in some…
Boolean Satisfiability (SAT) problems are critical in fields such as artificial intelligence and cryptography, where efficient solutions are essential. Conventional probabilistic solvers often encounter scalability issues due to complex…
Polygons are described as almost-convex if their perimeter differs from the perimeter of their minimum bounding rectangle by twice their `concavity index', $m$. Such polygons are called \emph{$m$-convex} polygons and are characterised by…
One of the main problems of importance sampling in Bayesian networks is representation of the importance function, which should ideally be as close as possible to the posterior joint distribution. Typically, we represent an importance…
Data assimilation plays a crucial role in numerical modeling, enabling the integration of real-world observations into mathematical models to enhance the accuracy and predictive capabilities of simulations. This approach is widely applied…
In this paper we introduced an arithmetic graph function which associates with every group G the directed graph whose vertices corresponds to the divisors of |G|. With the help of such functions we introduced arithmetic graphs of classes of…
Using the theoretical basis developed by Yao and Zeilberger, we consider certain graph families whose structure results in a rational generating function for sequences related to spanning tree enumeration. Said families are Powers of Cycles…
Gaussian graphical regressions have emerged as a powerful approach for regressing the precision matrix of a Gaussian graphical model on covariates, which, unlike traditional Gaussian graphical models, can help determine how graphs are…
Data generation is a fundamental research problem in data management due to its diverse use cases, ranging from testing database engines to data-specific applications. However, real-world entities often involve complex interactions that…
In this work a method is presented to derive the generating functional in path integral form for a system with an arbitrary number of degrees of freedom and constrained by general conditions. The method is applied to the case of the…
In this revised version we correct some mistakes, realizing the supersymmetry algebra on the exact S matrix, taking into account several phase factros. We study the constraint imposed by supersymmetry on the exact $S$-matrix of $\Complex…
Graph Neural Networks (GNNs) have become a building block in graph data processing, with wide applications in critical domains. The growing needs to deploy GNNs in high-stakes applications necessitate explainability for users in the…
A product formula for the parity generating function of the number of 1's in invertible matrices over Z_2 is given. The computation is based on algebraic tools such as the Bruhat decomposition. The same technique is used to obtain a parity…