Iterated birth and death process as a model of radiation cell survival

The iterated birth and death process is defined as an n-fold iteration of a stochastic process consisting of the combination of instantaneous random killing of individuals in a certain population with a given survival probability s with a Markov birth and death process describing subsequent population dynamics. A long standing problem of computing the distribution of the number of clonogenic tumor cells surviving a fractionated radiation schedule consisting of n equal doses separated by equal time intervals tau is solved within the framework of iterated birth and death processes. For any initial tumor size i, an explicit formula for the distribution of the number M of surviving clonogens at moment tau after the end of treatment is found. It is shown that if i-->infinity and s-->0 so that is(n) tends to a finite positive limit, the distribution of random variable M converges to a probability distribution, and a formula for the latter is obtained. This result generalizes the classical theorem about the Poisson limit of a sequence of binomial distributions. The exact and limiting distributions are also found for the number of surviving clonogens immediately after the nth exposure. In this case, the limiting distribution turns out to be a Poisson distribution.     

Collapsing a Perfect Superposition to a Chosen Quantum State without Measurement

Given a perfect superposition of states on a quantum system of qubits. We propose a fast quantum algorithm for collapsing the perfect superposition to a chosen quantum state without applying any measurements. The basic idea is to use a phase destruction mechanism. Two operators are used, the first operator applies a phase shift and a temporary entanglement to mark in the superposition, and the second operator applies selective phase shifts on the states in the superposition according to their Hamming distance with . The generated state can be used as an excellent input state for testing quantum memories and linear optics quantum computers. We make no assumptions about the used operators and applied quantum gates, but our result implies that for this purpose the number of qubits in the quantum register offers no advantage, in principle, over the obvious measurement-based feedback protocol.     

An exact sampling formula for the Wright-Fisher model and a solution to a conjecture about the finite-island model

An exact sampling formula for a Wright-Fisher population of fixed size N under the infinitely many neutral alleles model is deduced. This extends the Ewens formula for the configuration of a random sample to the case where the sample is drawn from a population of small size, that is, without the usual large-N and small-mutation-rate assumption. The formula is used to prove a conjecture ascertaining the validity of a diffusion approximation for the frequency of a mutant-type allele under weak selection in segregation with a wild-type allele in the limit finite-island model, namely, a population that is subdivided into a finite number of demes of size N and that receives an expected fraction m of migrants from a common migrant pool each generation, as the number of demes goes to infinity. This is done by applying the formula to the migrant ancestors of a single deme and sampling their types at random. The proof of the conjecture confirms an analogy between the island model and a random-mating population, but with a different timescale that has implications for estimation procedures.     

Magnetic susceptibility and Landau diamagnetism of quantum collisional plasma

Quantum collisional plasma with an arbitrary degree of degeneracy of the electron gas is considered. Using the exact expression for the transverse electric conductivity of quantum collisional plasma, the magnetic susceptibility is described using the kinetic approach and a formula for calculating Landau diamagnetism is derived. Quantum Maxwellian plasma is considered as a special case. To this end, in the formulas derived, the limit is taken for the chemical potential tending to minus infinity. The properties of the magnetic susceptibility of quantum plasma are compared to those of degenerate and Maxwellian plasmas.     

Nanofabrication of Gate-defined GaAs/AlGaAs Lateral Quantum Dots

A quantum computer is a computer composed of quantum bits (qubits) that takes advantage of quantum effects, such as superposition of states and entanglement, to solve certain problems exponentially faster than with the best known algorithms on a classical computer. Gate-defined lateral quantum dots on GaAs/AlGaAs are one of many avenues explored for the implementation of a qubit. When properly fabricated, such a device is able to trap a small number of electrons in a certain region of space. The spin states of these electrons can then be used to implement the logical 0 and 1 of the quantum bit. Given the nanometer scale of these quantum dots, cleanroom facilities offering specialized equipment- such as scanning electron microscopes and e-beam evaporators- are required for their fabrication. Great care must be taken throughout the fabrication process to maintain cleanliness of the sample surface and to avoid damaging the fragile gates of the structure. This paper presents the detailed fabrication protocol of gate-defined lateral quantum dots from the wafer to a working device. Characterization methods and representative results are also briefly discussed. Although this paper concentrates on double quantum dots, the fabrication process remains the same for single or triple dots or even arrays of quantum dots. Moreover, the protocol can be adapted to fabricate lateral quantum dots on other substrates, such as Si/SiGe.     

A stochastic model of tumor response to fractionated radiation: limit theorems and rate of convergence

The iterated birth and death Markov process is defined as an n-fold iteration of a birth and death Markov process describing kinetics of certain population combined with random killing of individuals in the population at moments tau 1,...,tau n with given survival probabilities s1,...,sn. A long-standing problem of computing the distribution of the number of clonogenic tumor cells surviving an arbitrary fractionated radiation schedule is solved within the framework of iterated birth and death Markov process. It is shown that, for any initial population size iota, the distribution of the size N of the population at moment t > or = tau n is generalized negative binomial, and an explicit computationally feasible formula for the latter is found. It is shown that if i --> infinity and sn --> 0 so that the product iota s1...sn tends to a finite positive limit, the distribution of random variable N converges to a probability distribution, which for t = tau n turns out to be Poisson. In the latter case, an estimate of the rate of convergence in the total variation metric similar to the classical Law of Rare Events is obtained.     

Computer program for calculating recombination values from electrophoretic data

A FORTRAN computer program was developed to calculate recombination values from F2 data. The input to the program is data on codominant alleles in any number of F2 families segregating for any number of loci, the limit being applied by the computer's memory capacity. For each pair of loci, regardless of the number of segregating progenies used, one recombination value is estimated by the method of maximum likelihood and reported with its standard error. In cases in which more than one family is used for the estimation, the chi-square for the homogeneity of the data also is reported.     

Maximum Likelihood Estimation of the Number of Nucleotide Substitutions from Restriction Sites Data

A simple method of the maximum likelihood estimation of the number of nucleotide substitutions is presented for the case where restriction sites data from many different restriction enzymes are available. An iteration method, based on nucleotide counting, is also developed. This method is simpler than the maximum likelihood method but gives the same estimate. A formula for computing the variance of a maximum likelihood estimate is also presented.     

Finding confidence limits on population growth rates: Bootstrap and analytic methods

When predicting population dynamics, the value of the prediction is not enough and should be accompanied by a confidence interval that integrates the whole chain of errors, from observations to predictions via the estimates of the parameters of the model. Matrix models are often used to predict the dynamics of age- or size-structured populations. Their parameters are vital rates. This study aims (1) at assessing the impact of the variability of observations on vital rates, and then on model’s predictions, and (2) at comparing three methods for computing confidence intervals for values predicted from the models. The first method is the bootstrap. The second method is analytic and approximates the standard error of predictions by their asymptotic variance as the sample size tends to infinity. The third method combines use of the bootstrap to estimate the standard errors of vital rates with the analytical method to then estimate the errors of predictions from the model. Computations are done for an Usher matrix models that predicts the asymptotic (as time goes to infinity) stock recovery rate for three timber species in French Guiana. Little difference is found between the hybrid and the analytic method. Their estimates of bias and standard error converge towards the bootstrap estimates when the error on vital rates becomes small enough, which corresponds in the present case to a number of observations greater than 5000 trees.     

DNA计算机的分子生物学研究进展

DNA(脱氧核糖核酸)计算机研究是一个新领域。从字面上看,它既包含DNA研究也包含计算机的研究,因而也包含DNA技术与计算机技术如何交融的研究。1994年,Adleman在Science上报道了首例DNA计算的研究结果;2001年,Benenson等在Nature报道了一种由DNA分子和相应的酶分子构成的、有图灵机功能的可程序试管型DNA计算机,标志着DNA计算机研究的重大进展。DNA计算机最大的特点是超大规模的并行运算能力和潜在的巨大的数据储存能力。目前DNA计算机研究已涉及许多领域,包括生物学、数学、物理、化学、计算机科学和自动化工程等具体应用,是计算概念上的一次革命。DNA计算机的研究大大促进了DNA分子操作技术尤其是在纳米尺度下操作DNA分子的研究速度。从DNA计算机的基本原理、应用形式、与基因组学研究的重要关系等方面总结和评述了相关研究进展。     

LOGIT: a program for dose-response analysis.

We describe a FORTRAN computer program for fitting the logistic distribution function: (formula: see text) Where x represents dose or time, to dose-response data. The program determines both weighted least squares and maximum likelihood estimates for the parameters alpha and beta. It also calculates the standard errors of alpha and beta under both estimation methods, as well as the median lethal dose (LD50) and its standard error. Dose--response curves found by both fitting methods can be plotted as well as the 95% confidence bands for these lines.     

Parameter Estimation of Fractional-Order Chaotic Systems by Using Quantum Parallel Particle Swarm Optimization Algorithm

Parameter estimation for fractional-order chaotic systems is an important issue in fractional-order chaotic control and synchronization and could be essentially formulated as a multidimensional optimization problem. A novel algorithm called quantum parallel particle swarm optimization (QPPSO) is proposed to solve the parameter estimation for fractional-order chaotic systems. The parallel characteristic of quantum computing is used in QPPSO. This characteristic increases the calculation of each generation exponentially. The behavior of particles in quantum space is restrained by the quantum evolution equation, which consists of the current rotation angle, individual optimal quantum rotation angle, and global optimal quantum rotation angle. Numerical simulation based on several typical fractional-order systems and comparisons with some typical existing algorithms show the effectiveness and efficiency of the proposed algorithm.     

Free energy changes associated with amino acid substitution in proteins

The estimation of free energy differences from computer simulation of macromolecular systems is important for rational strategies for drug design and for protein engineering. As an example of one mutation, we have studied the free energy change resulting from the conversion of a polar group (OH) to an apolar group (CH3) in aqueous solution. We have estimated the effect of various local environments on the magnitude of the free energy difference and find that significant environmental effects are found. We have also studied the reliability of the results in detail.     

The conditional ancestral selection graph with strong balancing selection

Using a heuristic separation-of-time-scales argument, we describe the behavior of the conditional ancestral selection graph with very strong balancing selection between a pair of alleles. In the limit as the strength of selection tends to infinity, we find that the ancestral process converges to a neutral structured coalescent, with two subpopulations representing the two alleles and mutation playing the role of migration. This agrees with a previous result of Kaplan et al., obtained using a different approach. We present the results of computer simulations to support our heuristic mathematical results. We also present a more rigorous demonstration that the neutral conditional ancestral process converges to the Kingman coalescent in the limit as the mutation rate tends to infinity.     

Ligation errors in DNA computing

DNA computing is a novel method of computing proposed by Adleman (1994), in which the data is encoded in the sequences of oligonucleotides. Massively parallel reactions between oligonucleotides are expected to make it possible to solve huge problems. In this study, reliability of the ligation process employed in the DNA computing is tested by estimating the error rate at which wrong oligonucleotides are ligated. Ligation of wrong oligonucleotides would result in a wrong answer in the DNA computing. The dependence of the error rate on the number of mismatches between oligonucleotides and on the combination of bases is investigated.     

Overfitting,generalization, and MSE in class probability estimation with high‐dimensional data

Accurate class probability estimation is important for medical decision making but is challenging, particularly when the number of candidate features exceeds the number of cases. Special methods have been developed for nonprobabilistic classification, but relatively little attention has been given to class probability estimation with numerous candidate variables. In this paper, we investigate overfitting in the development of regularized class probability estimators. We investigate the relation between overfitting and accurate class probability estimation in terms of mean square error. Using simulation studies based on real datasets, we found that some degree of overfitting can be desirable for reducing mean square error. We also introduce a mean square error decomposition for class probability estimation that helps clarify the relationship between overfitting and prediction accuracy.     

Accuracy of haplotype frequency estimation for biallelic loci, via the expectation-maximization algorithm for unphased diploid genotype data

Haplotype analyses have become increasingly common in genetic studies of human disease because of their ability to identify unique chromosomal segments likely to harbor disease-predisposing genes. The study of haplotypes is also used to investigate many population processes, such as migration and immigration rates, linkage-disequilibrium strength, and the relatedness of populations. Unfortunately, many haplotype-analysis methods require phase information that can be difficult to obtain from samples of nonhaploid species. There are, however, strategies for estimating haplotype frequencies from unphased diploid genotype data collected on a sample of individuals that make use of the expectation-maximization (EM) algorithm to overcome the missing phase information. The accuracy of such strategies, compared with other phase-determination methods, must be assessed before their use can be advocated. In this study, we consider and explore sources of error between EM-derived haplotype frequency estimates and their population parameters, noting that much of this error is due to sampling error, which is inherent in all studies, even when phase can be determined. In light of this, we focus on the additional error between haplotype frequencies within a sample data set and EM-derived haplotype frequency estimates incurred by the estimation procedure. We assess the accuracy of haplotype frequency estimation as a function of a number of factors, including sample size, number of loci studied, allele frequencies, and locus-specific allelic departures from Hardy-Weinberg and linkage equilibrium. We point out the relative impacts of sampling error and estimation error, calling attention to the pronounced accuracy of EM estimates once sampling error has been accounted for. We also suggest that many factors that may influence accuracy can be assessed empirically within a data set-a fact that can be used to create "diagnostics" that a user can turn to for assessing potential inaccuracies in estimation.     

Analytic computation of the expectation of the linkage disequilibrium coefficient r2

The squared correlation coefficient r(2) (sometimes denoted Delta(2)) is a measure of linkage disequilibrium that is widely used, but computing its expectation E[r(2)] in the population has remained an intriguing open problem. The expectation E[r(2)] is often approximated by the standard linkage deviation sigma(d)(2), which is a ratio of two expectations amenable to analytic computation. In this paper, a method of computing the population-wide E[r(2)] is introduced for a model with recurrent mutation, genetic drift and recombination. The approach is algebraic and is based on the diffusion process approximation. In the limit as the population-scaled recombination rate rho approaches infinity, it is shown rigorously that the asymptotic behavior of E[r(2)] is given by 1/rho+O(rho(-2)), which, incidentally, is the same as that of sigma(d)(2). A computer software that computes E[r(2)] numerically is available upon request.     

Wind Power Error Estimation in Resource Assessments

Estimating the power output is one of the elements that determine the techno-economic feasibility of a renewable project. At present, there is a need to develop reliable methods that achieve this goal, thereby contributing to wind power penetration. In this study, we propose a method for wind power error estimation based on the wind speed measurement error, probability density function, and wind turbine power curves. This method uses the actual wind speed data without prior statistical treatment based on 28 wind turbine power curves, which were fitted by Lagrange''s method, to calculate the estimate wind power output and the corresponding error propagation. We found that wind speed percentage errors of 10% were propagated into the power output estimates, thereby yielding an error of 5%. The proposed error propagation complements the traditional power resource assessments. The wind power estimation error also allows us to estimate intervals for the power production leveled cost or the investment time return. The implementation of this method increases the reliability of techno-economic resource assessment studies.     

Computer control of fermentation processes

A review of computer control of fermentation processes is presented. Hardware and software technologies that have been used to implement computer control are discussed. This includes instrumentation, interfacing techniques, computer hardware configurations, data logging and documentation, displays and man-machine interaction, low-level control, back-up and error detection and programming techniques. Advanced control of fermentation processes with the utilization of modern control techniques is also presented. This topic is divided into steady state optimization and dynamic optimization. Finally, on-line estimation of bioreactor parameters for feedback control is presented.