In this paper, we investigate the use of variational quantum algorithms for simulating the thermodynamic properties of dinuclear metal complexes. Our study highlights the potential of quantum computing to transform advanced simulations and provide in...
The realization theorem asserts that for a finitely presented group G, the D(2) property and the realization property are equivalent as long as G satisfies a certain finiteness condition. We show that the two properties are in fact equivalent for all...
We investigate the Tits boundary of locally compact CAT(0) 2-complexes. In particular we show that away from the endpoints, a geodesic segment in the Tits boundary is the ideal boundary of an isometrically embedded Euclidean sector. As applications...
The puzzle method was introduced by Choi and Park as an effective method for finding non-singular characteristic maps over wedged simplicial complexes $K(J)$ obtained from a given simplicial complex $K$. We study further the mod 2 case of the puzzle...
The richest and largest structures in the cosmic web are galaxy superclusters, their complexes (associations of several almost connected very rich superclusters), and planes. Superclusters represent a special environment where the evolution of galaxi...
Hu, Kriz and May recently reexamined ideas implicit in Priddy's elegant homotopy theoretic construction of the Brown-Peterson spectrum at a prime p. They discussed May's notions of nuclear complexes and of cores of spaces, spectra, and commutative...
This paper considers three separate matrices associated to graphs and (each dimension of) cell complexes. It relates all the coefficients of their respective characteristic polynomials to the geometric and combinatorial enumeration of three kinds of...
We construct three simplicial presheaves on the site of ringed spaces, and in particular on that of complex manifolds. The descent objects for these simplicial presheaves yield Toledo--Tong's twisting cochains, simplicial twisting cochains, and compl...
Consider 2n points on the unit circle and a reference dissection D of the convex hull of the odd points. The accordion complex of D is the simplicial complex of subsets of pairwise noncrossing diagonals with even endpoints that cross a connected set...
Wiltshire-Gordon has introduced a homotopy model for ordered configuration spaces on a given simplicial complex. That author asserts that, after a suitable subdivision, his model also works for unordered configuration spaces. We supply details justif...
This article introduces proximal Cech nerves and Cech complexes, restricted to finite, bounded regions $K$ of the Euclidean plane. A Cech nerve is a collection of intersecting balls. A Cech complex is a collection of nerves that cover $K$. Cech nerve...
In this work, wild-type and heterozygous \b{eta}-thalassaemic mice were enriched with 57Fe through gastrointestinal absorption to characterize in more details the iron complexes appeared in the measured Mossbauer spectra. The 57Fe enrichment method w...
The activities and interactions of proteins that govern the cellular response to a signal generate a multitude of protein phosphorylation states and heterogeneous protein complexes. Here, using a computational model that accounts for 307 molecular...
In the paper titled "Bockstein basis and resolution theorems in extension theory" (arXiv:0907.0491v2), we stated a theorem that we claimed to be a generalization of the Edwards-Walsh resolution theorem. The goal of this note is to show that the main...
Hodge/Bochner Laplacians of simplicial complexes, their spectra, higher-order diffusion and random walks (⭐ 32)
Triangulated categories arising in algebra can often be described as the homotopy category of a pretriangulated dg-category, a category enriched in chain complexes with a natural notion of shifts and cones that is accessible with all the machinery of...
We introduce in this paper a definition of (non necessarily positive) opetopes where faces are organised in a poset. Then we show that this description is equivalent to that given in terms of constellations by Kock, Joyal, Batanin and Mascari....
We consider the problem of optimality in manifold reconstruction. A random sample $\mathbb{X}_n = \left\{X_1,\ldots,X_n\right\}\subset \mathbb{R}^D$ composed of points close to a $d$-dimensional submanifold $M$, with or without outliers drawn in the...
We associate with any simplicial complex $\K$ and any integer $m$ a system of linear equations and inequalities. If $\K$ has a simplicial embedding in $\R^m$ then the system has an integer solution. This result extends the work of I. Novik (2000)....
We give a new proof of an old identity of Dixon (1865-1936) that uses tools from topological combinatorics. Dixon's identity is re-established by constructing an infinite family of non-pure simplicial complexes $Δ(n)$, indexed by the positive intege...