49 resultados para Probability Metrics
em QUB Research Portal - Research Directory and Institutional Repository for Queen's University Belfast
Resumo:
The greatest relaxation time for an assembly of three- dimensional rigid rotators in an axially symmetric bistable potential is obtained exactly in terms of continued fractions as a sum of the zero frequency decay functions (averages of the Legendre polynomials) of the system. This is accomplished by studying the entire time evolution of the Green function (transition probability) by expanding the time dependent distribution as a Fourier series and proceeding to the zero frequency limit of the Laplace transform of that distribution. The procedure is entirely analogous to the calculation of the characteristic time of the probability evolution (the integral of the configuration space probability density function with respect to the position co-ordinate) for a particle undergoing translational diffusion in a potential; a concept originally used by Malakhov and Pankratov (Physica A 229 (1996) 109). This procedure allowed them to obtain exact solutions of the Kramers one-dimensional translational escape rate problem for piecewise parabolic potentials. The solution was accomplished by posing the problem in terms of the appropriate Sturm-Liouville equation which could be solved in terms of the parabolic cylinder functions. The method (as applied to rotational problems and posed in terms of recurrence relations for the decay functions, i.e., the Brinkman approach c.f. Blomberg, Physica A 86 (1977) 49, as opposed to the Sturm-Liouville one) demonstrates clearly that the greatest relaxation time unlike the integral relaxation time which is governed by a single decay function (albeit coupled to all the others in non-linear fashion via the underlying recurrence relation) is governed by a sum of decay functions. The method is easily generalized to multidimensional state spaces by matrix continued fraction methods allowing one to treat non-axially symmetric potentials, where the distribution function is governed by two state variables. (C) 2001 Elsevier Science B.V. All rights reserved.
Resumo:
The chain growth probability (alpha value) is one of the most significant parameters in Fischer-Tropsch (FT) synthesis. To gain insight into the chain growth probability, we systematically studied the hydrogenation and C-C coupling reactions with different chain lengths on the stepped Co(0001) surface using density functional theory calculations. Our findings elucidate the relationship between the barriers of these elementary reactions and the chain length. Moreover, we derived a general expression of the chain growth probability and investigated the behavior of the alpha value observed experimentally. The high methane yield results from the lower chain growth rate for C-1 + C-1 coupling compared with the other coupling reactions. After C-1, the deviation of product distribution in FT synthesis from the Anderson-Schulz-Flory distribution is due to the chain length-dependent paraffin/olefin ratio. (C) 2008 Elsevier Inc. All rights reserved.
Resumo:
The standard linear-quadratic (LQ) survival model for external beam radiotherapy is reviewed with particular emphasis on studying how different schedules of radiation treatment planning may be affected by different tumour repopulation kinetics. The LQ model is further examined in the context of tumour control probability (TCP) models. The application of the Zaider and Minerbo non-Poissonian TCP model incorporating the effect of cellular repopulation is reviewed. In particular the recent development of a cell cycle model within the original Zaider and Minerbo TCP formalism is highlighted. Application of this TCP cell-cycle model in clinical treatment plans is explored and analysed.
Resumo:
The sediment sequence from Hasseldala port in southeastern Sweden provides a unique Lateglacial/early Holocene record that contains five different tephra layers. Three of these have been geochemically identified as the Borrobol Tephra, the Hasseldalen Tephra and the 10-ka Askja Tephra. Twenty-eight high-resolution C-14 measurements have been obtained and three different age models based on Bayesian statistics are employed to provide age estimates for the five different tephra layers. The chrono- and pollen stratigraphic framework supports the stratigraphic position of the Borrobol Tephra as found in Sweden at the very end of the Older Dryas pollen zone and provides the first age estimates for the Askja and Hasseldalen tephras. Our results, however, highlight the limitations that arise in attempting to establish a robust, chronologically independent lacustrine sequence that can be correlated in great detail to ice core or marine records. Radiocarbon samples are prone to error and sedimentation rates in lake basins may vary considerably due to a number of factors. Any type of valid and 'realistic' age model, therefore, has to take these limitations into account and needs to include this information in its prior assumptions. As a result, the age ranges for the specific horizons at Hasseldala port are large and calendar year estimates differ according to the assumptions of the age-model. Not only do these results provide a cautionary note for overdependence on one age-model for the derivation of age estimates for specific horizons, but they also demonstrate that precise correlations to other palaeoarchives to detect leads or lags is problematic. Given the uncertainties associated with establishing age-depth models for sedimentary sequences spanning the Lateglacial period, however, this exercise employing Bayesian probability methods represents the best possible approach and provides the most statistically significant age estimates for the pollen zone boundaries and tephra horizons. Copyright (C) 2006 John Wiley & Sons, Ltd.
Resumo:
In this paper, the performance of the network coded amplify-forward cooperative protocol is studied. The use of network coding can suppress the bandwidth resource consumed by relay transmission, and hence increase the spectral efficiency of cooperative diversity. A distributed strategy of relay selection is applied to the cooperative scheme, which can reduce system overhead and also facilitate the development of the explicit expressions of information metrics, such as outage probability and ergodic capacity. Both analytical and numerical results demonstrate that the proposed protocol can achieve large ergodic capacity and full diversity gain simultaneously.
Resumo:
It is shown that, when expressing arguments in terms of their logarithms, the Laplace transform of a function is related to the antiderivative of this function by a simple convolution. This allows efficient numerical computations of moment generating functions of positive random variables and their inversion. The application of the method is straightforward, apart from the necessity to implement it using high-precision arithmetics. In numerical examples the approach is demonstrated to be particularly useful for distributions with heavy tails, Such as lognormal, Weibull, or Pareto distributions, which are otherwise difficult to handle. The computational efficiency compared to other methods is demonstrated for an M/G/1 queueing problem.
Resumo:
Purpose: The aim of this study is to compare the sensitivity of different metrics to detect differences in complexity of intensity modulated radiation therapy (IMRT) plans following upgrades, changes to planning parameters, and patient geometry. Correlations between complexity metrics are also assessed.
Resumo:
The development of methods providing reliable estimates of demographic parameters (e. g., survival rates, fecundity) for wild populations is essential to better understand the ecology and conservation requirements of individual species. A number of methods exist for estimating the demographics of stage-structured populations, but inherent mathematical complexity often limits their uptake by conservation practitioners. Estimating survival rates for pond-breeding amphibians is further complicated by their complex migratory and reproductive behaviours, often resulting in nonobservable states and successive cohorts of eggs and tadpoles. Here we used comprehensive data on 11 distinct breeding toad populations (Bufo calamita) to clarify and assess the suitability of a relatively simple method [the Kiritani-Nakasuji-Manly (KNM) method] to estimate the survival rates of stage-structured populations with overlapping life stages. The study shows that the KNM method is robust and provides realistic estimates of amphibian egg and larval survival rates for species in which breeding can occur as a single pulse or over a period of several weeks. The study also provides estimates of fecundity for seven distinct toad populations and indicates that it is essential to use reliable estimates of fecundity to limit the risk of under- or overestimating the survival rates when using the KNM method. Survival and fecundity rates for B. calamita populations were then used to define population matrices and make a limited exploration of their growth and viability. The findings of the study recently led to the implementation of practical conservation measures at the sites where populations were most vulnerable to extinction. © 2010 The Society of Population Ecology and Springer.
Resumo:
Multi-threaded processors execute multiple threads concurrently in order to increase overall throughput. It is well documented that multi-threading affects per-thread performance but, more importantly, some threads are affected more than others. This is especially troublesome for multi-programmed workloads. Fairness metrics measure whether all threads are affected equally. However defining equal treatment is not straightforward. Several fairness metrics for multi-threaded processors have been utilized in the literature, although there does not seem to be a consensus on what metric does the best job of measuring fairness. This paper reviews the prevalent fairness metrics and analyzes their main properties. Each metric strikes a different trade-off between fairness in the strict sense and throughput. We categorize the metrics with respect to this property. Based on experimental data for SMT processors, we suggest using the minimum fairness metric in order to balance fairness and throughput.
Resumo:
In three studies we looked at two typical misconceptions of probability: the representativeness heuristic, and the equiprobability bias. The literature on statistics education predicts that some typical errors and biases (e.g., the equiprobability bias) increase with education, whereas others decrease. This is in contrast with reasoning theorists’ prediction who propose that education reduces misconceptions in general. They also predict that students with higher cognitive ability and higher need for cognition are less susceptible to biases. In Experiments 1 and 2 we found that the equiprobability bias increased with statistics education, and it was negatively correlated with students’ cognitive abilities. The representativeness heuristic was mostly unaffected by education, and it was also unrelated to cognitive abilities. In Experiment 3 we demonstrated through an instruction manipulation (by asking participants to think logically vs. rely on their intuitions) that the reason for these differences was that these biases originated in different cognitive processes.
Dual-processes in learning and judgment:Evidence from the multiple cue probability learning paradigm
Resumo:
Multiple cue probability learning (MCPL) involves learning to predict a criterion based on a set of novel cues when feedback is provided in response to each judgment made. But to what extent does MCPL require controlled attention and explicit hypothesis testing? The results of two experiments show that this depends on cue polarity. Learning about cues that predict positively is aided by automatic cognitive processes, whereas learning about cues that predict negatively is especially demanding on controlled attention and hypothesis testing processes. In the studies reported here, negative, but not positive cue learning related to individual differences in working memory capacity both on measures of overall judgment performance and modelling of the implicit learning process. However, the introduction of a novel method to monitor participants' explicit beliefs about a set of cues on a trial-by-trial basis revealed that participants were engaged in explicit hypothesis testing about positive and negative cues, and explicit beliefs about both types of cues were linked to working memory capacity. Taken together, our results indicate that while people are engaged in explicit hypothesis testing during cue learning, explicit beliefs are applied to judgment only when cues are negative. © 2012 Elsevier Inc.