3,998 research outputs found
Dynamic message-passing approach for kinetic spin models with reversible dynamics
A method to approximately close the dynamic cavity equations for synchronous
reversible dynamics on a locally tree-like topology is presented. The method
builds on a graph expansion to eliminate loops from the normalizations of
each step in the dynamics, and an assumption that a set of auxilary
probability distributions on histories of pairs of spins mainly have
dependencies that are local in time. The closure is then effectuated by
projecting these probability distributions on -step Markov processes. The
method is shown in detail on the level of ordinary Markov processes (),
and outlined for higher-order approximations (). Numerical validations of
the technique are provided for the reconstruction of the transient and
equilibrium dynamics of the kinetic Ising model on a random graph with
arbitrary connectivity symmetry.Comment: 6 pages, 4 figure
Doeblin Trees
This paper is centered on the random graph generated by a Doeblin-type
coupling of discrete time processes on a countable state space whereby when two
paths meet, they merge. This random graph is studied through a novel subgraph,
called a bridge graph, generated by paths started in a fixed state at any time.
The bridge graph is made into a unimodular network by marking it and selecting
a root in a specified fashion. The unimodularity of this network is leveraged
to discern global properties of the larger Doeblin graph. Bi-recurrence, i.e.,
recurrence both forwards and backwards in time, is introduced and shown to be a
key property in uniquely distinguishing paths in the Doeblin graph, and also a
decisive property for Markov chains indexed by . Properties related
to simulating the bridge graph are also studied.Comment: 44 pages, 4 figure
Broadcasting on Random Directed Acyclic Graphs
We study a generalization of the well-known model of broadcasting on trees.
Consider a directed acyclic graph (DAG) with a unique source vertex , and
suppose all other vertices have indegree . Let the vertices at
distance from be called layer . At layer , is given a random
bit. At layer , each vertex receives bits from its parents in
layer , which are transmitted along independent binary symmetric channel
edges, and combines them using a -ary Boolean processing function. The goal
is to reconstruct with probability of error bounded away from using
the values of all vertices at an arbitrarily deep layer. This question is
closely related to models of reliable computation and storage, and information
flow in biological networks.
In this paper, we analyze randomly constructed DAGs, for which we show that
broadcasting is only possible if the noise level is below a certain degree and
function dependent critical threshold. For , and random DAGs with
layer sizes and majority processing functions, we identify the
critical threshold. For , we establish a similar result for NAND
processing functions. We also prove a partial converse for odd
illustrating that the identified thresholds are impossible to improve by
selecting different processing functions if the decoder is restricted to using
a single vertex.
Finally, for any noise level, we construct explicit DAGs (using expander
graphs) with bounded degree and layer sizes admitting
reconstruction. In particular, we show that such DAGs can be generated in
deterministic quasi-polynomial time or randomized polylogarithmic time in the
depth. These results portray a doubly-exponential advantage for storing a bit
in DAGs compared to trees, where but layer sizes must grow exponentially
with depth in order to enable broadcasting.Comment: 33 pages, double column format. arXiv admin note: text overlap with
arXiv:1803.0752
Modeling the mobility of living organisms in heterogeneous landscapes: Does memory improve foraging success?
Thanks to recent technological advances, it is now possible to track with an
unprecedented precision and for long periods of time the movement patterns of
many living organisms in their habitat. The increasing amount of data available
on single trajectories offers the possibility of understanding how animals move
and of testing basic movement models. Random walks have long represented the
main description for micro-organisms and have also been useful to understand
the foraging behaviour of large animals. Nevertheless, most vertebrates, in
particular humans and other primates, rely on sophisticated cognitive tools
such as spatial maps, episodic memory and travel cost discounting. These
properties call for other modeling approaches of mobility patterns. We propose
a foraging framework where a learning mobile agent uses a combination of
memory-based and random steps. We investigate how advantageous it is to use
memory for exploiting resources in heterogeneous and changing environments. An
adequate balance of determinism and random exploration is found to maximize the
foraging efficiency and to generate trajectories with an intricate
spatio-temporal order. Based on this approach, we propose some tools for
analysing the non-random nature of mobility patterns in general.Comment: 14 pages, 4 figures, improved discussio
GenEvA (I): A new framework for event generation
We show how many contemporary issues in event generation can be recast in
terms of partonic calculations with a matching scale. This framework is called
GenEvA, and a key ingredient is a new notion of phase space which avoids the
problem of phase space double-counting by construction and includes a built-in
definition of a matching scale. This matching scale can be used to smoothly
merge any partonic calculation with a parton shower. The best partonic
calculation for a given region of phase space can be determined through physics
considerations alone, independent of the algorithmic details of the merging. As
an explicit example, we construct a positive-weight partonic calculation for
e+e- -> n jets at next-to-leading order (NLO) with leading-logarithmic (LL)
resummation. We improve on the NLO/LL result by adding additional
higher-multiplicity tree-level (LO) calculations to obtain a merged NLO/LO/LL
result. These results are implemented using a new phase space generator
introduced in a companion paper [arXiv:0801.4028].Comment: 60 pages, 22 figures, v2: corrected typos, added reference
A compact statistical model of the song syntax in Bengalese finch
Songs of many songbird species consist of variable sequences of a finite
number of syllables. A common approach for characterizing the syntax of these
complex syllable sequences is to use transition probabilities between the
syllables. This is equivalent to the Markov model, in which each syllable is
associated with one state, and the transition probabilities between the states
do not depend on the state transition history. Here we analyze the song syntax
in a Bengalese finch. We show that the Markov model fails to capture the
statistical properties of the syllable sequences. Instead, a state transition
model that accurately describes the statistics of the syllable sequences
includes adaptation of the self-transition probabilities when states are
repeatedly revisited, and allows associations of more than one state to the
same syllable. Such a model does not increase the model complexity
significantly. Mathematically, the model is a partially observable Markov model
with adaptation (POMMA). The success of the POMMA supports the branching chain
network hypothesis of how syntax is controlled within the premotor song nucleus
HVC, and suggests that adaptation and many-to-one mapping from neural
substrates to syllables are important features of the neural control of complex
song syntax
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