1,836 research outputs found

### On Fast and Robust Information Spreading in the Vertex-Congest Model

This paper initiates the study of the impact of failures on the fundamental
problem of \emph{information spreading} in the Vertex-Congest model, in which
in every round, each of the $n$ nodes sends the same $O(\log{n})$-bit message
to all of its neighbors.
Our contribution to coping with failures is twofold. First, we prove that the
randomized algorithm which chooses uniformly at random the next message to
forward is slow, requiring $\Omega(n/\sqrt{k})$ rounds on some graphs, which we
denote by $G_{n,k}$, where $k$ is the vertex-connectivity.
Second, we design a randomized algorithm that makes dynamic message choices,
with probabilities that change over the execution. We prove that for $G_{n,k}$
it requires only a near-optimal number of $O(n\log^3{n}/k)$ rounds, despite a
rate of $q=O(k/n\log^3{n})$ failures per round. Our technique of choosing
probabilities that change according to the execution is of independent
interest.Comment: Appears in SIROCCO 2015 conferenc

### Min-Max Theorems for Packing and Covering Odd $(u,v)$-trails

We investigate the problem of packing and covering odd $(u,v)$-trails in a
graph. A $(u,v)$-trail is a $(u,v)$-walk that is allowed to have repeated
vertices but no repeated edges. We call a trail odd if the number of edges in
the trail is odd. Let $\nu(u,v)$ denote the maximum number of edge-disjoint odd
$(u,v)$-trails, and $\tau(u,v)$ denote the minimum size of an edge-set that
intersects every odd $(u,v)$-trail.
We prove that $\tau(u,v)\leq 2\nu(u,v)+1$. Our result is tight---there are
examples showing that $\tau(u,v)=2\nu(u,v)+1$---and substantially improves upon
the bound of $8$ obtained in [Churchley et al 2016] for $\tau(u,v)/\nu(u,v)$.
Our proof also yields a polynomial-time algorithm for finding a cover and a
collection of trails satisfying the above bounds.
Our proof is simple and has two main ingredients. We show that (loosely
speaking) the problem can be reduced to the problem of packing and covering odd
$(uv,uv)$-trails losing a factor of 2 (either in the number of trails found, or
the size of the cover). Complementing this, we show that the
odd-$(uv,uv)$-trail packing and covering problems can be tackled by exploiting
a powerful min-max result of [Chudnovsky et al 2006] for packing
vertex-disjoint nonzero $A$-paths in group-labeled graphs

### 2-Vertex Connectivity in Directed Graphs

We complement our study of 2-connectivity in directed graphs, by considering
the computation of the following 2-vertex-connectivity relations: We say that
two vertices v and w are 2-vertex-connected if there are two internally
vertex-disjoint paths from v to w and two internally vertex-disjoint paths from
w to v. We also say that v and w are vertex-resilient if the removal of any
vertex different from v and w leaves v and w in the same strongly connected
component. We show how to compute the above relations in linear time so that we
can report in constant time if two vertices are 2-vertex-connected or if they
are vertex-resilient. We also show how to compute in linear time a sparse
certificate for these relations, i.e., a subgraph of the input graph that has
O(n) edges and maintains the same 2-vertex-connectivity and vertex-resilience
relations as the input graph, where n is the number of vertices.Comment: arXiv admin note: substantial text overlap with arXiv:1407.304

### Discrete space-time geometry and skeleton conception of particle dynamics

It is shown that properties of a discrete space-time geometry distinguish
from properties of the Riemannian space-time geometry. The discrete geometry is
a physical geometry, which is described completely by the world function. The
discrete geometry is nonaxiomatizable and multivariant. The equivalence
relation is intransitive in the discrete geometry. The particles are described
by world chains (broken lines with finite length of links), because in the
discrete space-time geometry there are no infinitesimal lengths. Motion of
particles is stochastic, and statistical description of them leads to the
Schr\"{o}dinger equation, if the elementary length of the discrete geometry
depends on the quantum constant in a proper way.Comment: 22 pages, 0 figure

### Analysis of weighted networks

The connections in many networks are not merely binary entities, either
present or not, but have associated weights that record their strengths
relative to one another. Recent studies of networks have, by and large, steered
clear of such weighted networks, which are often perceived as being harder to
analyze than their unweighted counterparts. Here we point out that weighted
networks can in many cases be analyzed using a simple mapping from a weighted
network to an unweighted multigraph, allowing us to apply standard techniques
for unweighted graphs to weighted ones as well. We give a number of examples of
the method, including an algorithm for detecting community structure in
weighted networks and a new and simple proof of the max-flow/min-cut theorem.Comment: 9 pages, 3 figure

### Physics of Fashion Fluctuations

We consider a market where many agents trade many different types of products
with each other. We model development of collective modes in this market, and
quantify these by fluctuations that scale with time with a Hurst exponent of
about 0.7. We demonstrate that individual products in the model occationally
become globally accepted means of exchange, and simultaneously become very
actively traded. Thus collective features similar to money spontaneously
emerge, without any a priori reason.Comment: 9 pages RevTeX, 5 Postscript figure

### Realizability of the Lorentzian (n,1)-Simplex

In a previous article [JHEP 1111 (2011) 072; arXiv:1108.4965] we have
developed a Lorentzian version of the Quantum Regge Calculus in which the
significant differences between simplices in Lorentzian signature and Euclidean
signature are crucial. In this article we extend a central result used in the
previous article, regarding the realizability of Lorentzian triangles, to
arbitrary dimension. This technical step will be crucial for developing the
Lorentzian model in the case of most physical interest: 3+1 dimensions.
We first state (and derive in an appendix) the realizability conditions on
the edge-lengths of a Lorentzian n-simplex in total dimension n=d+1, where d is
the number of space-like dimensions. We then show that in any dimension there
is a certain type of simplex which has all of its time-like edge lengths
completely unconstrained by any sort of triangle inequality. This result is the
d+1 dimensional analogue of the 1+1 dimensional case of the Lorentzian
triangle.Comment: V1: 15 pages, 2 figures. V2: Minor clarifications added to
Introduction and Discussion sections. 1 reference updated. This version
accepted for publication in JHEP. V3: minor updates and clarifications, this
version closely corresponds to the version published in JHE

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### CreaTable Content and Tangible Interaction in Aphasia

Multimedia digital content (combining pictures, text and music) is ubiquitous. The process of creating such content using existing tools typically requires complex, language-laden interactions which pose a challenge for users with aphasia (a language impairment following brain injury). Tangible interactions offer a potential means to address this challenge, however, there has been little work exploring their potential for this purpose. In this paper, we present CreaTable – a platform that enables us to explore tangible interaction as a means of supporting digital content creation for people with aphasia. We report details of the co-design of CreaTable and findings from a digital creativity workshop. Workshop findings indicated that CreaTable enabled people with aphasia to create something they would not otherwise have been able to. We report how users’ aphasia profiles affected their experience, describe tensions in collaborative content creation and provide insight into more accessible content creation using tangibles

### High field cardiac magnetic resonance imaging: a case for ultrahigh field cardiac magnetic resonance

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