Zobrazeno 1 - 10
of 199
pro vyhledávání: '"Macpherson, Robert A."'
We study configuration spaces $C(n; p, q)$ of $n$ ordered unit squares in a $p$ by $q$ rectangle. Our goal is to estimate the Betti numbers for large $n$, $j$, $p$, and $q$. We consider sequences of area-normalized coordinates, where $(\frac{n}{pq},
Externí odkaz:
http://arxiv.org/abs/2207.13139
We discuss ways in which tools from topology can be used to derive lower bounds for the circuit complexity of Boolean functions.
Externí odkaz:
http://arxiv.org/abs/2205.14424
Publikováno v:
Algebr. Geom. Topol. 23 (2023) 2593-2626
We study ordered configuration spaces $C(n;p,q)$ of $n$ hard squares in a $p \times q$ rectangle, a generalization of the well-known "15 Puzzle". Our main interest is in the topology of these spaces. Our first result is to describe a cubical cell com
Externí odkaz:
http://arxiv.org/abs/2010.14480
Autor:
McConnell, Mark, MacPherson, Robert
We present an algorithm to compute the Hecke operators on the equivariant cohomology of an arithmetic subgroup $\Gamma$ of the general linear group $\mathrm{GL}_n$. This includes $\mathrm{GL}_n$ over a number field or a finite-dimensional division al
Externí odkaz:
http://arxiv.org/abs/2010.06036
Publikováno v:
Phys. Rev. Lett. 125, 015501 (2020)
An open question in studying normal grain growth concerns the asymptotic state to which microstructures converge. In particular, the distribution of grain topologies is unknown. We introduce a thermodynamic-like theory to explain these distributions
Externí odkaz:
http://arxiv.org/abs/2007.02167
We study the topology of the configuration spaces $C(n,w)$ of $n$ hard disks of unit diameter in an infinite strip of width $w$. We describe ranges of parameter or "regimes", where homology $H_j [C(n,w)]$ behaves in qualitatively different ways. We s
Externí odkaz:
http://arxiv.org/abs/1908.04241
Akademický článek
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Autor:
MacPherson, Robert, Patel, Amit
Publikováno v:
Advances in Mathematics Volume 386, 6 August 2021, 107795
In this paper, we give lower bounds for the homology of the fibers of a map to a manifold. Using new sheaf theoretic methods, we show that these lower bounds persist over whole open sets of the manifold, and that they are stable under perturbations o
Externí odkaz:
http://arxiv.org/abs/1805.02539
Akademický článek
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Publikováno v:
Phys. Rev. E 96, 023001 (2017)
Many physical systems are composed of polyhedral cells of varying sizes and shapes. These structures are simple in the sense that no more than three faces meet at an edge and no more than four edges meet at a vertex. This means that individual cells
Externí odkaz:
http://arxiv.org/abs/1609.09711