Distribution Of Fixation Times Research Articles

General spin-up time distribution for energy-aware IaaS cloud service models

Cloud computing services provided over the Internet are realized by servers in physically distributed data centers that consume tremendous power for operational and maintenance purposes. To minimize energy consumption, modern cloud systems adopt intelligent sever power switching with thresholds based on the current system load and are bounded by the number of idle servers. The time taken to power on physical or virtual servers, known as the spin-up time, can significantly impact the delay incurred in service delivery and elasticity of real cloud platforms. In this paper, we model and assess the asymptotic performance of an energy-aware cloud data center assuming general distribution for server spin-up time. The waiting time of a newly arriving request is defined in the service-level agreement (SLA) and for each busy server, the fixation time distribution derived from an absorbing birth-and-death process characterizes the impact of thresholds. Simulation results show that the proposed model calculates the probability of SLA violation for different threshold values with less than 0.5% error.

Fitness dependence of the fixation-time distribution for evolutionary dynamics on graphs.

Evolutionary graph theory models the effects of natural selection and random drift on structured populations of competing mutant and nonmutant individuals. Recent studies have found that fixation times in such systems often have right-skewed distributions. Little is known, however, about how these distributions and their skew depend on mutant fitness. Here we calculate the fitness dependence of the fixation-time distribution for the Moran Birth-death process in populations modeled by two extreme networks: the complete graph and the one-dimensional ring lattice, obtaining exact solutions in the limit of large network size. We find that with non-neutral fitness, the Moran process on the ring has normally distributed fixation times, independent of the relative fitness of mutants and nonmutants. In contrast, on the complete graph, the fixation-time distribution is a fitness-weighted convolution of two Gumbel distributions. When fitness is neutral, the fixation-time distribution jumps discontinuously and becomes highly skewed on both the complete graph and the ring. Even on these simple networks, the fixation-time distribution exhibits a rich fitness dependence, with discontinuities and regions of universality. Extensions of our results to two-fitness Moran models, times to partial fixation, and evolution on random networks are discussed.

Effects of aging and text-stimulus quality on the word-frequency effect during Chinese reading.

Age-related reading difficulty is well established for alphabetic languages. Compared to young adults (18-30 years), older adults (65+ years) read more slowly, make more and longer fixations, make more regressions, and produce larger word-frequency effects. However, whether similar effects are observed for nonalphabetic languages like Chinese remains to be determined. In particular, recent research has suggested Chinese readers experience age-related reading difficulty but do not produce age differences in the word-frequency effect. This might represent an important qualitative difference in aging effects, so we investigated this further by presenting young and older adult Chinese readers with sentences that included high- or low-frequency target words. Additionally, to test theories that suggest reductions in text-stimulus quality differentially affect lexical processing by adult age groups, we presented either the target words (Experiment 1) or all characters in sentences (Experiment 2) normally or with stimulus quality reduced. Analyses based on mean eye-movement parameters and distributional analyses of fixation times for target words showed typical age-related reading difficulty. We also observed age differences in the word-frequency effect, predominantly in the tails of fixation-time distributions, consistent with an aging effect on the processing of high- and low-frequency words. Reducing stimulus quality disrupted eye movements more for the older readers, but the influence of stimulus quality on the word-frequency effect did not differ across age groups. This suggests Chinese older readers' lexical processing is resilient to reductions in stimulus quality, perhaps due to greater experience recognizing words from impoverished visual input. (PsycINFO Database Record

Mean-field approximations of fixation time distributions of evolutionary game dynamics on graphs

The mean fixation time is often not accurate for describing the timescales of fixation probabilities of evolutionary games taking place on complex networks. We simulate the game dynamics on top of complex network topologies and approximate the fixation time distributions using a mean-field approach. We assume that there are two absorbing states. Numerically, we show that the mean fixation time is sufficient in characterizing the evolutionary timescales when network structures are close to the well-mixing condition. In contrast, the mean fixation time shows large inaccuracies when networks become sparse. The approximation accuracy is determined by the network structure, and hence by the suitability of the mean-field approach. The numerical results show good agreement with the theoretical predictions.

Moran-type bounds for the fixation probability in a frequency-dependent Wright-Fisher model.

We study stochastic evolutionary game dynamics in a population of finite size. Individuals in the population are divided into two dynamically evolving groups. The structure of the population is formally described by a Wright-Fisher type Markov chain with a frequency dependent fitness. In a strong selection regime that favors one of the two groups, we obtain qualitatively matching lower and upper bounds for the fixation probability of the advantageous population. In the infinite population limit we obtain an exact result showing that a single advantageous mutant can invade an infinite population with a positive probability. We also give asymptotically sharp bounds for the fixation time distribution.

Contrasting eye-movements in reading aloud and reading silently to localise a speech deficit.

Contrasting eye-movements in reading aloud and reading silently to localise a speech deficit.

When the mean is not enough: Calculating fixation time distributions in birth-death processes.

Studies of fixation dynamics in Markov processes predominantly focus on the mean time to absorption. This may be inadequate if the distribution is broad and skewed. We compute the distribution of fixation times in one-step birth-death processes with two absorbing states. These are expressed in terms of the spectrum of the process, and we provide different representations as forward-only processes in eigenspace. These allow efficient sampling of fixation time distributions. As an application we study evolutionary game dynamics, where invading mutants can reach fixation or go extinct. We also highlight the median fixation time as a possible analog of mixing times in systems with small mutation rates and no absorbing states, whereas the mean fixation time has no such interpretation.

A Study on Eye Fixation Time Distribution in Subjective Selection with Paired Food Pictures

Eye fixation time distributions in subjective selection of paired food pictures by opinions ‘Like’ and ‘Dislike’ were measured, respectively. Results show frequency of eye fixation in diffusive search is larger than that in specific search. And the frequency of eye fixation for ‘selected’ pictures is larger than that for ‘not selected’ pictures in the specific search.

Population Genetics in Compressible Flows

We study competition between two biological species advected by a compressible velocity field. Individuals are treated as discrete Lagrangian particles that reproduce or die in a density-dependent fashion. In the absence of a velocity field and fitness advantage, number fluctuations lead to a coarsening dynamics typical of the stochastic Fisher equation. We investigate three examples of compressible advecting fields: a shell model of turbulence, a sinusoidal velocity field and a linear velocity sink. In all cases, advection leads to a striking drop in the fixation time, as well as a large reduction in the global carrying capacity. We find localization on convergence zones, and very rapid extinction compared to well-mixed populations. For a linear velocity sink, one finds a bimodal distribution of fixation times. The long-lived states in this case are demixed configurations with a single interface, whose location depends on the fitness advantage.

Pairwise comparison and selection temperature in evolutionary game dynamics

Recently, the frequency-dependent Moran process has been introduced in order to describe evolutionary game dynamics in finite populations. Here, an alternative to this process is investigated that is based on pairwise comparison between two individuals. We follow a long tradition in the physics community and introduce a temperature (of selection) to account for stochastic effects. We calculate the fixation probabilities and fixation times for any symmetric 2 × 2 game, for any intensity of selection and any initial number of mutants. The temperature can be used to gauge continuously from neutral drift to the extreme selection intensity known as imitation dynamics. For some payoff matrices the distribution of fixation times can become so broad that the average value is no longer very meaningful.

Does the Distribution of Fixation Times Refer to the Underlying Process of Information Input?

Two experiments were conducted to assess whether the distribution of fixation times might be related to the prevailing cognitive activity involved with two different tasks, i.e., driving and observing colored fields. The results suggest that the distribution of fixation times can be associated with the prevailing cognitive activity while viewing.

On the weak convergence of Wright-Fisher model

We prove that the sequence of stochastic processes obtained from Wright-Fisher models by transforming the time scales and state spaces in the usual way converges weakly to a diffusion process on the time interval [0,∞). Convergence of fixation probabilities and fixation time distributions are obtained as corollaries. These results extend a theorem of Watterson, who proved convergence in distribution to a diffusion at any given single time point for these processes.

Habituation Rate and the Infant's Response to Visual Discrepancies

MCCALL, ROBERT B.; HOGARTY, PAMELA S.; HAMILTON, JAYNE S.; and VINCENT, JOHN H. Habituation Rate and the Infant's Response to Visual Discrepancies. CHILD DEVELOPMENT, 1973, 44, 280-287. A simple visual stimulus was repeatedly presented to 120 infants 12 and 18 weeks of age until visual fixation reached a habituation criterion. A discrepant stimulus followed that varied in its magnitude of discrepancy from the familiar standard. In contrast to the age effects observed for the rate of habituation (though they interacted with specific stimuli), there were no age differences in the distribution of fixation times to the several magnitudes of discrepancy. Infants who habituated rapidly displayed an inverted-U curve of fixation as a function of discrepancy in accord with the discrepancy hypothesis, whereas slow habituators gave their maximum response to the largest discrepancy.