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Local Problems on Trees from the Perspectives of Distributed Algorithms, Finitary Factors, and Descriptive Combinatorics

Information Technology Convergence and Services, 2021
We study connections between distributed local algorithms, finitary factors of iid processes, and descriptive combinatorics in the context of regular trees.
Sebastian Brandt   +5 more
semanticscholar   +1 more source

CP-PSIS: CRT and polynomial-based progressive secret image sharing

Signal Processing, 2021
In (k, n) Progressive Secret Image Sharing (PSIS) schemes, n shares are obtained by sharing a secret image. With k to n shares, the secret image can be recovered progressively. No information of the secret image can be constructed by k-1 or fewer shares.
Lizhi Xiong, Xiao Han, Ching-Nung Yang
semanticscholar   +1 more source

A Hamiltonian ∐n BO(n)-action, stratified Morse theory and the J-homomorphism

Compositio Mathematica, 2019
We use sheaves of spectra to quantize a Hamiltonian $\coprod _n BO(n)$-action on $\varinjlim _{N}T^*\mathbf {R}^N$ that naturally arises from Bott periodicity.
Xin Jin
semanticscholar   +1 more source

Lower Bounds for the Graph Homomorphism Problem

International Colloquium on Automata, Languages and Programming, 2015
The graph homomorphism problem (HOM) asks whether the vertices of a given n-vertex graph G can be mapped to the vertices of a given h-vertex graph H such that each edge of G is mapped to an edge of H.
F. Fomin   +3 more
semanticscholar   +1 more source

Monotone Bounded-Depth Complexity of Homomorphism Polynomials

International Symposium on Mathematical Foundations of Computer Science
For every fixed graph $H$, it is known that homomorphism counts from $H$ and colorful $H$-subgraph counts can be determined in $O(n^{t+1})$ time on $n$-vertex input graphs $G$, where $t$ is the treewidth of $H$. On the other hand, a running time of $n^{o(
C. Bhargav   +3 more
semanticscholar   +1 more source

Zimmer's conjecture: Subexponential growth, measure rigidity, and strong property (T)

Annals of Mathematics, 2016
We prove several cases of Zimmer's conjecture for actions of higher-rank cocompact lattices on low dimensional manifolds. For example, if $\Gamma$ is a cocompact lattice in $\mathrm{Sl}(n, \mathbb R)$, $M$ is a compact manifold, and $\omega$ a volume ...
Aaron W. Brown   +2 more
semanticscholar   +1 more source

Multiple solutions to a magnetic nonlinear Choquard equation

, 2011
We consider the stationary nonlinear magnetic Choquard equation $$(- {\rm i}\nabla+ A(x))^{2}u + V (x)u = \left(\frac{1}{|x|^{\alpha}}\ast |u|^{p}\right) |u|^{p-2}u,\quad x\in\mathbb{R}^{N}$$where A is a real-valued vector potential, V is a real-valued ...
S. Cingolani, M. Clapp, S. Secchi
semanticscholar   +1 more source

The algebraic structure of non-commutative analytic Toeplitz algebras

, 1998
The non-commutative analytic Toeplitz algebra is the wot– closed algebra generated by the left regular representation of the free semigroup on n generators. We develop a detailed picture of the algebraic structure of this algebra.
K. Davidson, D. Pitts
semanticscholar   +1 more source

Monotone Arithmetic Complexity of Graph Homomorphism Polynomials

Algorithmica, 2023
Balagopal Komarath   +2 more
semanticscholar   +1 more source

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