8,356 research outputs found

    Stochastic Generalized Porous Media and Fast Diffusion Equations

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    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 σ\sigma-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 NN-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

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    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

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    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

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    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 55. 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 (1−o(1))n(1-o(1))^n-fraction of patterns of length nn satisfy a nontrivial c-forest-Wilf equivalence and that there are c-forest-Wilf equivalence classes of patterns of length nn 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

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    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

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    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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