The extinction of a single species due to demographic stochasticity is analyzed. The discrete nature of the individual agents
and the Poissonian noise related to the birth-death processes result in local extinction of a metastable population, as the
system hits the absorbing state. The Fokker-Planck formulation of that problem fails to capture the statistics of large deviations
from the metastable state, while approximations appropriate close to the absorbing state become, in general, invalid as the
population becomes large. To connect these two regimes, a real space WKB method based on the master equation is presented,
and is shown to yield an excellent approximation for the decay rate and the extreme events statistics all the way down to
the absorbing state. The details of the underlying microscopic process, smeared out in a mean field treatment, are shown to
be crucial for an exact determination of the extinction exponent. This general scheme is shown to reproduce the known results
in the field, to yield new corollaries and to fit quite precisely the numerical solutions. Moreover it allows for systematic
improvement via a series expansion where the small parameter is the inverse of the number of individuals in the metastable
state. 相似文献
The inference of past demographic parameters from current genetic polymorphism is a fundamental problem in population genetics.
The standard techniques utilize a reconstruction of the gene-genealogy, a cumbersome process that may be applied only to small
numbers of sequences. We present a method that compares the total number of haplotypes (distinct sequences) with the model
prediction. By chopping the DNA sequence into pieces we condense the immense information hidden in sequence space into a function
for the number of haplotypes versus subsequence size. The details of this curve are robust to statistical fluctuations and
are seen to reflect the process parameters. This procedure allows for a clear visualization of the quality of the fit and,
crucially, the numerical complexity grows only linearly with the number of sequences. Our procedure is tested against both
simulated data as well as empirical mtDNA data from China and provides excellent fits in both cases. 相似文献
Degenerate band edges (DBEs) of a photonic bandgap have the form (ω-ω(D)) ∝k(2m) for integers m>1, with ω(D) the frequency at the band edge. We show theoretically that DBEs lead to efficient coupling into slow-light modes without a transition region, and that the field strength in the slow mode can far exceed that in the incoming medium. A method is proposed to create a DBE of arbitrary order m by coupling m optical modes with multiple superimposed gratings. The enhanced coupling near a DBE occurs because of the presence of one or more evanescent modes, which are absent at conventional quadratic band edges. We furthermore show that the coupling can be increased or suppressed by varying the number of excited evanescent waves. 相似文献
Circular dichroism (CD) is frequently used to assess the secondary structure of peptides and proteins, whereas less attention has been given to their building blocks, that is, single amino acids, as they do not possess a secondary structure. Here, we follow the CD signal of amino acids and reveal that several acids exhibit a unique CD pattern as a function of their concentration. Accordingly, we propose an eight‐level classification of the CD signal of the various amino acids. Special focus is given to the CD pattern of phenylalanine (Phe), for which we observe the formation of an ultra‐narrow CD peak (full width at high maximum of only 5 nm). This CD peak can be attributed to the formation of Phe‐based chiral structural features. Further support for the formation of an ordered structure is given by using NMR, and the additional self‐assembly process of Phe to tubular structures. 相似文献
A structure in a first‐order language is indivisible if for every colouring of its universe M in two colours, there is a monochromatic such that . Additionally, we say that is symmetrically indivisible if can be chosen to be symmetrically embedded in (that is, every automorphism of can be extended to an automorphism of ). In the following paper we give a general method for constructing new symmetrically indivisible structures out of existing ones. Using this method, we construct many non‐isomorphic symmetrically indivisible countable structures in given (elementary) classes and answer negatively the following question from 6 : Let be a symmetrically indivisible structure in a language . Let . Is symmetrically indivisible? 相似文献
Cloud computing task management has a critical role in the efficient operation of the cloud resources, i.e., the servers. The task management handles critical and complicated decisions, overcoming the inherent dynamic nature of cloud computing systems and the additional complexity due to the large magnitude of resources in such systems (tens of thousands of servers). Due to the fact that servers may fail, task management is required to conduct both task admissions and task preservation decisions. Moreover, both these decisions require considering future system trajectories and the interplay between preservation and admission. In this paper we study the combined problem of task admission and preservation in a dynamic environment of cloud computing systems through analysis of a queueing system based on a Markov decision process (MDP). We show that the optimal operational policy is of a double switching curve type. On face value, the extraction of the optimal policy is rather complicated, yet our analysis reveals that the optimal policy can be reduced to a single rule, since the rules can effectively be decoupled. Based on this result, we propose two heuristic approaches that approximate the optimal rule for the most relevant system settings in cloud computing systems. Our results provide a simple policy scheme for the combined admission and preservation problem that can be applied in a complex cloud computing environments, and eliminate the need for sophisticated real-time control mechanisms.
Proteins are the main proton mediators in various biological proton circuits. Using proteins for the formation of long-range proton conductors is offering a bioinspired approach for proton conductive polymers. One of the main challenges in the field of proton conductors is to explore the local environment within the polymers, along with deciphering the conduction mechanism. Here, we show that the protonic conductivity across a protein-based biopolymer can be hindered using straightforward chemical modifications, targeting carboxylate- or amine-terminated residues of the protein, as well as exploring the effect of surface hydrophobicity on proton conduction. We further use the natural tryptophan residue as a local fluorescent probe for the inner local hydration state of the protein surface and its tendency to form hydrogen bonds with nearby water molecules, along with the dynamicity of the process. Our electrical and spectroscopic measurements of the different chemically-modified protein materials as well as the material at different water–aprotic solvent mixtures result in our fundamental understanding of the proton mediators within the material and gaining important insights on the proton conduction mechanism. Our biopolymer can be used as an attractive platform for the study of bio-related protonic circuits as well as a proton conducting biopolymer for various applications, such as protonic transistors, ionic transducers and fuel cells.Post formation modification of protein-based materials can attenuate the proton conduction efficiency resulting from change in conduction mechanism, charge carrier mobility, carrier concentrations and inner hydration layer.相似文献
Supramolecular gels often become destabilized by the transition of the gelator into a more stable crystalline phase, but often the long timescale and sporadic localization of the crystalline phase preclude a persistent observation of this process. We present a pentapeptide gel–crystal phase transition amenable for continuous visualization and quantification by common microscopic methods, allowing the extraction of kinetics and visualization of the dynamics of the transition. Using optical microscopy and microrheology, we show that the transition is a sporadic event in which gel dissolution is associated with microcrystalline growth that follows a sigmoidal rate profile. The two phases are based on β‐sheets of similar yet distinct configuration. We also demonstrate that the transition kinetics and crystal morphology can be modulated by extrinsic factors, including temperature, solvent composition, and mechanical perturbation. This work introduces an accessible model system and methodology for studying phase transitions in supramolecular gels. 相似文献