8,356 research outputs found
Stochastic Generalized Porous Media and Fast Diffusion Equations
We present a generalization of Krylov-Rozovskii's result on the existence and
uniqueness of solutions to monotone stochastic differential equations. As an
application, the stochastic generalized porous media and fast diffusion
equations are studied for -finite reference measures, where the drift
term is given by a negative definite operator acting on a time-dependent
function, which belongs to a large class of functions comparable with the
so-called -functions in the theory of Orlicz spaces.Comment: 36 pages, BiBoS-Preprint No. 06-02-20
The State of the Art in Fuel Cell Condition Monitoring and Maintenance
Fuel cell vehicles are considered to be a viable solution to problems such as carbon emissions and fuel shortages for road transport. Proton Exchange Membrane (PEM) Fuel Cells are mainly used in this purpose because they can run at low temperatures and have a simple structure. Yet to make this technology commercially viable, there are still many hurdles to overcome. Apart from the high cost of fuel cell systems, high maintenance costs and short lifecycle are two main issues need to be addressed. The main purpose of this paper is to review the issues affecting the reliability and lifespan of fuel cells and present the state of the art in fuel cell condition monitoring and maintenance. The Structure of PEM fuel cell is introduced and examples of its application in a variety of applications are presented. The fault modes including membrane flooding/drying, fuel/gas starvation, physical defects of membrane, and catalyst poisoning are listed and assessed for their impact. Then the relationship between causes, faults, symptoms and long term implications of fault conditions are summarized. Finally the state of the art in PEM fuel cell condition monitoring and maintenance is reviewed and conclusions are drawn regarding suggested maintenance strategies and the optimal structure for an integrated, cost effective condition monitoring and maintenance management system
Quasispecies Theory for Evolution of Modularity
Biological systems are modular, and this modularity evolves over time and in
different environments. A number of observations have been made of increased
modularity in biological systems under increased environmental pressure. We
here develop a quasispecies theory for the dynamics of modularity in
populations of these systems. We show how the steady-state fitness in a
randomly changing environment can be computed. We derive a fluctuation
dissipation relation for the rate of change of modularity and use it to derive
a relationship between rate of environmental changes and rate of growth of
modularity. We also find a principle of least action for the evolved modularity
at steady state. Finally, we compare our predictions to simulations of protein
evolution and find them to be consistent.Comment: 21 pages, 4 figures; presentation reordered; to appear in Phys. Rev.
Wilf Equivalences and Stanley-Wilf Limits for Patterns in Rooted Labeled Forests
Building off recent work of Garg and Peng, we continue the investigation into
classical and consecutive pattern avoidance in rooted forests, resolving some
of their conjectures and questions and proving generalizations whenever
possible. Through extensions of the forest Simion-Schmidt bijection introduced
by Anders and Archer, we demonstrate a new family of forest-Wilf equivalences,
completing the classification of forest-Wilf equivalence classes for sets
consisting of a pattern of length 3 and a pattern of length at most . We
also find a new family of nontrivial c-forest-Wilf equivalences between single
patterns using the forest analogue of the Goulden-Jackson cluster method,
showing that a -fraction of patterns of length satisfy a
nontrivial c-forest-Wilf equivalence and that there are c-forest-Wilf
equivalence classes of patterns of length of exponential size.
Additionally, we consider a forest analogue of super-strong-c-Wilf equivalence,
introduced for permutations by Dwyer and Elizalde, showing that
super-strong-c-forest-Wilf equivalences are trivial by enumerating linear
extensions of forest cluster posets. Finally, we prove a forest analogue of the
Stanley-Wilf conjecture for avoiding a single pattern as well as certain other
sets of patterns. Our techniques are analytic, easily generalizing to different
types of pattern avoidance and allowing for computations of convergent lower
bounds of the forest Stanley-Wilf limit in the cases covered by our result. We
end with several open questions and directions for future research, including
some on the limit distributions of certain statistics of pattern-avoiding
forests.Comment: 53 pages, 19 figure
Physical Model of the Immune Response of Bacteria Against Bacteriophage Through the Adaptive CRISPR-Cas Immune System
Bacteria and archaea have evolved an adaptive, heritable immune system that
recognizes and protects against viruses or plasmids. This system, known as the
CRISPR-Cas system, allows the host to recognize and incorporate short foreign
DNA or RNA sequences, called `spacers' into its CRISPR system. Spacers in the
CRISPR system provide a record of the history of bacteria and phage
coevolution. We use a physical model to study the dynamics of this coevolution
as it evolves stochastically over time. We focus on the impact of mutation and
recombination on bacteria and phage evolution and evasion. We discuss the
effect of different spacer deletion mechanisms on the coevolutionary dynamics.
We make predictions about bacteria and phage population growth, spacer
diversity within the CRISPR locus, and spacer protection against the phage
population.Comment: 37 pages, 13 figure
A Framework for Bioacoustic Vocalization Analysis Using Hidden Markov Models
Using Hidden Markov Models (HMMs) as a recognition framework for automatic classification of animal vocalizations has a number of benefits, including the ability to handle duration variability through nonlinear time alignment, the ability to incorporate complex language or recognition constraints, and easy extendibility to continuous recognition and detection domains. In this work, we apply HMMs to several different species and bioacoustic tasks using generalized spectral features that can be easily adjusted across species and HMM network topologies suited to each task. This experimental work includes a simple call type classification task using one HMM per vocalization for repertoire analysis of Asian elephants, a language-constrained song recognition task using syllable models as base units for ortolan bunting vocalizations, and a stress stimulus differentiation task in poultry vocalizations using a non-sequential model via a one-state HMM with Gaussian mixtures. Results show strong performance across all tasks and illustrate the flexibility of the HMM framework for a variety of species, vocalization types, and analysis tasks
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