Related papers: ZZPolyCalc: An open-source code with fragment cach…
We report a closed-form formula for the Zhang-Zhang polynomial (aka ZZ polynomial or Clar covering polynomial) of an important class of elementary pericondensed benzenoids $Rb\left(n_{1},n_{2},m_{1},m_{2}\right)$ usually referred to as…
We exhibit an algorithm to compute the strongest polynomial (or algebraic) invariants that hold at each location of a given affine program (i.e., a program having only non-deterministic (as opposed to conditional) branching and all of whose…
The Clar covering polynomial (also called Zhang-Zhang polynomial in some chemical literature) of a hexagonal system is a counting polynomial for some types of resonant structures called Clar covers, which can be used to determine Kekul\'e…
We develop the first algorithms for computing the Skyscraper Invariant [FJNT24]. This is a filtration of the classical rank invariant for multiparameter persistence modules defined by the Harder-Narasimhan filtrations along every central…
The barcode of a persistence module serves as a complete combinatorial invariant of its isomorphism class. Barcodes are typically extracted by performing changes of basis on a persistence module until the constituent matrices have a special…
Graph polynomials encode fundamental combinatorial invariants of graphs. Their computation is investigated using tree and path decomposition frameworks, with formal definitions of treewidth, k-trees, and pathwidth establishing the…
This article makes the key observation that when using cylindrical algebraic decomposition (CAD) to solve a problem with respect to a set of polynomials, it is not always the signs of those polynomials that are of paramount importance but…
We demonstrate theoretically that hydrogenation and annealing applied to nanoscale carbon structures play a crucial role in determining the final shape of the system. In particular, graphene flakes characterized by the linear and…
In this paper, we first prove that when the associated graph of a polynomial set is chordal, a particular triangular set computed by a general algorithm in top-down style for computing the triangular decomposition of this polynomial set has…
We demonstrate theoretically that an array of carbon nanoscrolls acts as a hyperbolic magnetic metamaterial in the THz regime with genuine subwavelength operation corresponding to wavelength-to-structure ratio of about 200. Due to the low…
We study the problem of finding elements in the intersection of an arbitrary conic variety in $\mathbb{F}^n$ with a given linear subspace (where $\mathbb{F}$ can be the real or complex field). This problem captures a rich family of…
Efficient handling of sparse data is a key challenge in Computer Science. Binary convolutions, such as polynomial multiplication or the Walsh Transform are a useful tool in many applications and are efficiently solved. In the last decade,…
Since proposed in [X. Zhang and C.-W. Shu, J. Comput. Phys., 229: 3091--3120, 2010], the Zhang--Shu framework has attracted extensive attention and motivated many bound-preserving (BP) high-order discontinuous Galerkin and finite volume…
In this paper we show a new way of constructing deterministic polynomial-time approximation algorithms for computing complex-valued evaluations of a large class of graph polynomials on bounded degree graphs. In particular, our approach…
An algorithm is developed for structure identification of amorphous carbonaceous nanomaterials with a joint x-ray and neutron diffraction data analysis, using the data on the chemical composition of the sample from other diagnostics. The…
Nanoparticles have become increasingly interesting for a wide range of applications, because in principle it is possible to tailor their properties by controlling size, shape and composition. One of these applications is heterogeneous…
Spatial self-attention layers, in the form of Non-Local blocks, introduce long-range dependencies in Convolutional Neural Networks by computing pairwise similarities among all possible positions. Such pairwise functions underpin the…
Motivated by a connection with the factorization of multivariate polynomials, we study integral convex polytopes and their integral decompositions in the sense of the Minkowski sum. We first show that deciding decomposability of integral…
We propose new algorithms for computing triangular decompositions of polynomial systems incrementally. With respect to previous works, our improvements are based on a {\em weakened} notion of a polynomial GCD modulo a regular chain, which…
Colored knot polynomials possess a peculiar Z-expansion in certain combinations of differentials, which depends on the representation. The coefficients of this expansion are functions of the three variables (A,q,t) and can be considered as…