Escape times for rigid Brownian rotators in a bistable potential from the time evolution of the Green function and the characteristic time of the probability evolution

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.

Packet classification by multi-level cutting of the classification space: An algorithmic-architectural solution for IP packet classification in next generation networks

Traditionally, the Internet provides only a “best-effort” service, treating all packets going to the same destination equally. However, providing differentiated services for different users based on their quality requirements is increasingly becoming a demanding issue. For this, routers need to have the capability to distinguish and isolate traffic belonging to different flows. This ability to determine the flow each packet belongs to is called packet classification. Technology vendors are reluctant to support algorithmic solutions for classification due to their non-deterministic performance. Although CAMs are favoured by technology vendors due to their deterministic high lookup rates, they suffer from the problems of high power dissipation and high silicon cost. This paper provides a new algorithmic-architectural solution for packet classification that mixes CAMs with algorithms based on multi-level cutting the classification space into smaller spaces. The provided solution utilizes the geometrical distribution of rules in the classification space. It provides the deterministic performance of CAMs, support for dynamic updates, and added flexibility for system designers.

A DFT study of the chain growth probability in Fischer-Tropsch synthesis

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.

Linear quadratic and tumour control probability modelling in external beam radiotherapy

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.

Constraining the age of Lateglacial and early Holocene pollen zones and tephra horizons in southern Sweden with Bayesian probability methods

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.

Laplace transforms of probability distributions and their inversions are easy on logarithmic scales

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.

Algorithmic computation of knot polynomials of secondary structure elements of proteins

The classification of protein structures is an important and still outstanding problem. The purpose of this paper is threefold. First, we utilize a relation between the Tutte and homfly polynomial to show that the Alexander-Conway polynomial can be algorithmically computed for a given planar graph. Second, as special cases of planar graphs, we use polymer graphs of protein structures. More precisely, we use three building blocks of the three-dimensional protein structure-alpha-helix, antiparallel beta-sheet, and parallel beta-sheet-and calculate, for their corresponding polymer graphs, the Tutte polynomials analytically by providing recurrence equations for all three secondary structure elements. Third, we present numerical results comparing the results from our analytical calculations with the numerical results of our algorithm-not only to test consistency, but also to demonstrate that all assigned polynomials are unique labels of the secondary structure elements. This paves the way for an automatic classification of protein structures.

Estimation of survival rate and extinction probability for stage-structured populations with overlapping life stages

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.