8,687 research outputs found
Cues for shelter use in a phytophagous insect
Many insects spend a large proportion of their life inactive, often hiding in shelters. The presence of shelters may, therefore, influence where insects feed. This study examines stimuli affecting the use of shelters by adults of the pine weevil, Hylobius abietis (L.) (Coleoptera, Curculionidae). This species is an economically important forest pest in Europe since the adults feed on the stem bark of newly planted conifer seedlings. When there are hiding or burrowing places present in close proximity to a seedling, pine weevils may hide there and repeatedly return to feed on the same seedling. Experiments were conducted in a laboratory arena with above-ground or below-ground shelters and in the presence or absence of wind. Pine weevils were highly attracted to shelters both above and below ground. Weevils in shelters were often observed assuming a characteristic "resting" posture. Experiments with opaque and transparent shelters showed that visual stimuli are used for orientation towards shelters and also increase the probability of an individual remaining in a shelter. The presence of wind increased the weevils' propensity to use shelters both above and below ground. The present study indicates that shelters have a major influence on the behavior of the pine weevil and possible implications of the results are discussed
Random Walks on countable groups
We begin by giving a new proof of the equivalence between the Liouville
property and vanishing of the drift for symmetric random walks with finite
first moments on finitely generated groups; a result which was first
established by Kaimanovich-Vershik and Karlsson-Ledrappier. We then proceed to
prove that the product of the Poisson boundary of any countable measured group
with any ergodic -space is still ergodic, which in
particular yields a new proof of weak mixing for the double Poisson boundary of
when is symmetric. Finally, we characterize the failure of
weak-mixing for an ergodic -space as the existence of a non-trivial
measure-preserving isometric factor.Comment: 8 pages, no figures. Substantial overlap with the (longer) paper
"Five remarks about random walks on groups", http://arxiv.org/abs/1406.076
Determinant Sums for Undirected Hamiltonicity
We present a Monte Carlo algorithm for Hamiltonicity detection in an
-vertex undirected graph running in time. To the best of
our knowledge, this is the first superpolynomial improvement on the worst case
runtime for the problem since the bound established for TSP almost
fifty years ago (Bellman 1962, Held and Karp 1962). It answers in part the
first open problem in Woeginger's 2003 survey on exact algorithms for NP-hard
problems.
For bipartite graphs, we improve the bound to time. Both the
bipartite and the general algorithm can be implemented to use space polynomial
in .
We combine several recently resurrected ideas to get the results. Our main
technical contribution is a new reduction inspired by the algebraic sieving
method for -Path (Koutis ICALP 2008, Williams IPL 2009). We introduce the
Labeled Cycle Cover Sum in which we are set to count weighted arc labeled cycle
covers over a finite field of characteristic two. We reduce Hamiltonicity to
Labeled Cycle Cover Sum and apply the determinant summation technique for Exact
Set Covers (Bj\"orklund STACS 2010) to evaluate it.Comment: To appear at IEEE FOCS 201
Coloring Graphs having Few Colorings over Path Decompositions
Lokshtanov, Marx, and Saurabh SODA 2011 proved that there is no
time algorithm for
deciding if an -vertex graph with pathwidth
admits a proper vertex coloring with colors unless the Strong Exponential
Time Hypothesis (SETH) is false. We show here that nevertheless, when
, where is the maximum degree in the
graph , there is a better algorithm, at least when there are few colorings.
We present a Monte Carlo algorithm that given a graph along with a path
decomposition of with pathwidth runs in time, that
distinguishes between -colorable graphs having at most proper
-colorings and non--colorable graphs. We also show how to obtain a
-coloring in the same asymptotic running time. Our algorithm avoids
violating SETH for one since high degree vertices still cost too much and the
mentioned hardness construction uses a lot of them.
We exploit a new variation of the famous Alon--Tarsi theorem that has an
algorithmic advantage over the original form. The original theorem shows a
graph has an orientation with outdegree less than at every vertex, with a
different number of odd and even Eulerian subgraphs only if the graph is
-colorable, but there is no known way of efficiently finding such an
orientation. Our new form shows that if we instead count another difference of
even and odd subgraphs meeting modular degree constraints at every vertex
picked uniformly at random, we have a fair chance of getting a non-zero value
if the graph has few -colorings. Yet every non--colorable graph gives a
zero difference, so a random set of constraints stands a good chance of being
useful for separating the two cases.Comment: Strengthened result from uniquely -colorable graphs to graphs with
few -colorings. Also improved running tim
Exact Covers via Determinants
Given a k-uniform hypergraph on n vertices, partitioned in k equal parts such
that every hyperedge includes one vertex from each part, the k-dimensional
matching problem asks whether there is a disjoint collection of the hyperedges
which covers all vertices. We show it can be solved by a randomized polynomial
space algorithm in time O*(2^(n(k-2)/k)). The O*() notation hides factors
polynomial in n and k.
When we drop the partition constraint and permit arbitrary hyperedges of
cardinality k, we obtain the exact cover by k-sets problem. We show it can be
solved by a randomized polynomial space algorithm in time O*(c_k^n), where
c_3=1.496, c_4=1.642, c_5=1.721, and provide a general bound for larger k.
Both results substantially improve on the previous best algorithms for these
problems, especially for small k, and follow from the new observation that
Lovasz' perfect matching detection via determinants (1979) admits an embedding
in the recently proposed inclusion-exclusion counting scheme for set covers,
despite its inability to count the perfect matchings
The asymptotic shape theorem for generalized first passage percolation
We generalize the asymptotic shape theorem in first passage percolation on
to cover the case of general semimetrics. We prove a structure
theorem for equivariant semimetrics on topological groups and an extended
version of the maximal inequality for -cocycles of Boivin and
Derriennic in the vector-valued case. This inequality will imply a very general
form of Kingman's subadditive ergodic theorem. For certain classes of
generalized first passage percolation, we prove further structure theorems and
provide rates of convergence for the asymptotic shape theorem. We also
establish a general form of the multiplicative ergodic theorem of Karlsson and
Ledrappier for cocycles with values in separable Banach spaces with the
Radon--Nikodym property.Comment: Published in at http://dx.doi.org/10.1214/09-AOP491 the Annals of
Probability (http://www.imstat.org/aop/) by the Institute of Mathematical
Statistics (http://www.imstat.org
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