317,035 research outputs found
Z-Vortex Percolation in the Electroweak Crossover Region
We study the statistical properties of Z-vortices and Nambu monopoles in the
3D SU(2) Higgs model for a Higgs mass M_H \approx 100 GeV near and above the
crossover temperature, where these defects are thermally excited. Although
there is no phase transition at that strong selfcoupling, we observe that the
Z-vortices exhibit the percolation transition that has been found recently to
accompany the first order thermal transition that exists at smaller Higgs mass.
Above the crossover temperature percolating networks of Z-vortex lines are
ubiquitous, whereas vortices form a dilute gas of closed vortex loops and
(Nambu) monopolium states on the low-temperature side of the crossover. The
percolation temperature turns out to be roughly independent of the lattice
spacing. We find that the Higgs modulus is smaller (the gauge action is larger)
inside the vortices, compared to the bulk average. This correlation becomes
very strong on the low-temperature side. The percolation transition is a
prerequisite of some string mediated baryon number generation scenarios.Comment: 16 pages, LaTeX, 12 figures, epsf.sty needed; final version to appear
in Phys. Lett.
Finding Non-overlapping Clusters for Generalized Inference Over Graphical Models
Graphical models use graphs to compactly capture stochastic dependencies
amongst a collection of random variables. Inference over graphical models
corresponds to finding marginal probability distributions given joint
probability distributions. In general, this is computationally intractable,
which has led to a quest for finding efficient approximate inference
algorithms. We propose a framework for generalized inference over graphical
models that can be used as a wrapper for improving the estimates of approximate
inference algorithms. Instead of applying an inference algorithm to the
original graph, we apply the inference algorithm to a block-graph, defined as a
graph in which the nodes are non-overlapping clusters of nodes from the
original graph. This results in marginal estimates of a cluster of nodes, which
we further marginalize to get the marginal estimates of each node. Our proposed
block-graph construction algorithm is simple, efficient, and motivated by the
observation that approximate inference is more accurate on graphs with longer
cycles. We present extensive numerical simulations that illustrate our
block-graph framework with a variety of inference algorithms (e.g., those in
the libDAI software package). These simulations show the improvements provided
by our framework.Comment: Extended the previous version to include extensive numerical
simulations. See http://www.ima.umn.edu/~dvats/GeneralizedInference.html for
code and dat
Rings and rigidity transitions in network glasses
Three elastic phases of covalent networks, (I) floppy, (II) isostatically
rigid and (III) stressed-rigid have now been identified in glasses at specific
degrees of cross-linking (or chemical composition) both in theory and
experiments. Here we use size-increasing cluster combinatorics and constraint
counting algorithms to study analytically possible consequences of
self-organization. In the presence of small rings that can be locally I, II or
III, we obtain two transitions instead of the previously reported single
percolative transition at the mean coordination number , one from a
floppy to an isostatic rigid phase, and a second one from an isostatic to a
stressed rigid phase. The width of the intermediate phase and the
order of the phase transitions depend on the nature of medium range order
(relative ring fractions). We compare the results to the Group IV
chalcogenides, such as Ge-Se and Si-Se, for which evidence of an intermediate
phase has been obtained, and for which estimates of ring fractions can be made
from structures of high T crystalline phases.Comment: 29 pages, revtex, 7 eps figure
Constructing Light Spanners Deterministically in Near-Linear Time
Graph spanners are well-studied and widely used both in theory and practice. In a recent breakthrough, Chechik and Wulff-Nilsen [Shiri Chechik and Christian Wulff-Nilsen, 2018] improved the state-of-the-art for light spanners by constructing a (2k-1)(1+epsilon)-spanner with O(n^(1+1/k)) edges and O_epsilon(n^(1/k)) lightness. Soon after, Filtser and Solomon [Arnold Filtser and Shay Solomon, 2016] showed that the classic greedy spanner construction achieves the same bounds. The major drawback of the greedy spanner is its running time of O(mn^(1+1/k)) (which is faster than [Shiri Chechik and Christian Wulff-Nilsen, 2018]). This makes the construction impractical even for graphs of moderate size. Much faster spanner constructions do exist but they only achieve lightness Omega_epsilon(kn^(1/k)), even when randomization is used.
The contribution of this paper is deterministic spanner constructions that are fast, and achieve similar bounds as the state-of-the-art slower constructions. Our first result is an O_epsilon(n^(2+1/k+epsilon\u27)) time spanner construction which achieves the state-of-the-art bounds. Our second result is an O_epsilon(m + n log n) time construction of a spanner with (2k-1)(1+epsilon) stretch, O(log k * n^(1+1/k) edges and O_epsilon(log k * n^(1/k)) lightness. This is an exponential improvement in the dependence on k compared to the previous result with such running time. Finally, for the important special case where k=log n, for every constant epsilon>0, we provide an O(m+n^(1+epsilon)) time construction that produces an O(log n)-spanner with O(n) edges and O(1) lightness which is asymptotically optimal. This is the first known sub-quadratic construction of such a spanner for any k = omega(1).
To achieve our constructions, we show a novel deterministic incremental approximate distance oracle. Our new oracle is crucial in our construction, as known randomized dynamic oracles require the assumption of a non-adaptive adversary. This is a strong assumption, which has seen recent attention in prolific venues. Our new oracle allows the order of the edge insertions to not be fixed in advance, which is critical as our spanner algorithm chooses which edges to insert based on the answers to distance queries. We believe our new oracle is of independent interest
Fission of Halving Edges Graphs
In this paper we discuss an operation on halving edges graph that we call
fission. Fission replaces each point in a given configuration with a small
cluster of k points. The operation interacts nicely with halving edges, so we
examine its properties in detail.Comment: 17 pages, 10 figure
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