**Stochastic Processes**: Processes that incorporate some element of randomness, used particularly to refer to a time series of random variables.

**Computer Simulation**: Computer-based representation of physical systems and phenomena such as chemical processes.

**Models, Biological**: Theoretical representations that simulate the behavior or activity of biological processes or diseases. For disease models in living animals, DISEASE MODELS, ANIMAL is available. Biological models include the use of mathematical equations, computers, and other electronic equipment.

**Models, Statistical**: Statistical formulations or analyses which, when applied to data and found to fit the data, are then used to verify the assumptions and parameters used in the analysis. Examples of statistical models are the linear model, binomial model, polynomial model, two-parameter model, etc.

**Markov Chains**: A stochastic process such that the conditional probability distribution for a state at any future instant, given the present state, is unaffected by any additional knowledge of the past history of the system.

**Models, Genetic**: Theoretical representations that simulate the behavior or activity of genetic processes or phenomena. They include the use of mathematical equations, computers, and other electronic equipment.

**Biological Evolution**: The process of cumulative change over successive generations through which organisms acquire their distinguishing morphological and physiological characteristics.

**Population Dynamics**: The pattern of any process, or the interrelationship of phenomena, which affects growth or change within a population.

**Probability**: The study of chance processes or the relative frequency characterizing a chance process.

**Ecosystem**: A functional system which includes the organisms of a natural community together with their environment. (McGraw Hill Dictionary of Scientific and Technical Terms, 4th ed)

**Models, Theoretical**: Theoretical representations that simulate the behavior or activity of systems, processes, or phenomena. They include the use of mathematical equations, computers, and other electronic equipment.

**Monte Carlo Method**: In statistics, a technique for numerically approximating the solution of a mathematical problem by studying the distribution of some random variable, often generated by a computer. The name alludes to the randomness characteristic of the games of chance played at the gambling casinos in Monte Carlo. (From Random House Unabridged Dictionary, 2d ed, 1993)

**Evolution, Molecular**: The process of cumulative change at the level of DNA; RNA; and PROTEINS, over successive generations.

**Algorithms**: A procedure consisting of a sequence of algebraic formulas and/or logical steps to calculate or determine a given task.

**Phylogeny**: The relationships of groups of organisms as reflected by their genetic makeup.

**Selection, Genetic**: Differential and non-random reproduction of different genotypes, operating to alter the gene frequencies within a population.

**Time Factors**: Elements of limited time intervals, contributing to particular results or situations.

**Genetic Variation**: Genotypic differences observed among individuals in a population.

**Mutation**: Any detectable and heritable change in the genetic material that causes a change in the GENOTYPE and which is transmitted to daughter cells and to succeeding generations.

**Kinetics**: The rate dynamics in chemical or physical systems.

**Doob decomposition theorem**: In the theory of stochastic processes in discrete time, a part of the mathematical theory of probability, the Doob decomposition theorem gives a unique decomposition of every adapted and integrable stochastic process as the sum of a martingale and a predictable process (or "drift") starting at zero. The theorem was proved by and is named for Joseph L.

**Interval boundary element method**: Interval boundary element method is classical boundary element method with the interval parameters.

**Matrix model**: == Mathematics and physics ==

**Inverse probability weighting**: Inverse probability weighting is a statistical technique for calculating statistics standardized to a population different from that in which the data was collected. Study designs with a disparate sampling population and population of target inference (target population) are common in application.

**Vladimir Andreevich Markov**: Vladimir Andreevich Markov (; May 8, 1871 – January 18, 1897) was a Russian mathematician, known for proving the Markov brothers' inequality with his older brother Andrey Markov. He died of tuberculosis at the age of 25.

**Matrix population models**: Population models are used in population ecology to model the dynamics of wildlife or human populations. Matrix population models are a specific type of population model that uses matrix algebra.

**Negative probability**: The probability of the outcome of an experiment is never negative, but quasiprobability distributions can be defined that allow a negative probability for some events. These distributions may apply to unobservable events or conditional probabilities.

**Ecosystem**

**Von Neumann regular ring**: In mathematics, a von Neumann regular ring is a ring R such that for every a in R there exists an x in R such that . To avoid the possible confusion with the regular rings and regular local rings of commutative algebra (which are unrelated notions), von Neumann regular rings are also called absolutely flat rings, because these rings are characterized by the fact that every left module is flat.

**Monte Carlo methods for option pricing**: In mathematical finance, a Monte Carlo option model uses Monte Carlo methods Although the term 'Monte Carlo method' was coined by Stanislaw Ulam in the 1940s, some trace such methods to the 18th century French naturalist Buffon, and a question he asked about the results of dropping a needle randomly on a striped floor or table. See Buffon's needle.

**Molecular evolution**: Molecular evolution is a change in the sequence composition of cellular molecules such as DNA, RNA, and proteins across generations. The field of molecular evolution uses principles of evolutionary biology and population genetics to explain patterns in these changes.

**Clonal Selection Algorithm**: In artificial immune systems, Clonal selection algorithms are a class of algorithms inspired by the clonal selection theory of acquired immunity that explains how B and T lymphocytes improve their response to antigens over time called affinity maturation. These algorithms focus on the Darwinian attributes of the theory where selection is inspired by the affinity of antigen-antibody interactions, reproduction is inspired by cell division, and variation is inspired by somatic hypermutation.

**Branching order of bacterial phyla (Gupta, 2001)**: There are several models of the Branching order of bacterial phyla, one of these was proposed in 2001 by Gupta based on conserved indels or protein, termed "protein signatures", an alternative approach to molecular phylogeny. Some problematic exceptions and conflicts are present to these conserved indels, however, they are in agreement with several groupings of classes and phyla.

**Selection (relational algebra)**: In relational algebra, a selection (sometimes called a restriction to avoid confusion with SQL's use of SELECT) is a unary operation written as

**Temporal analysis of products**: Temporal Analysis of Products (TAP), (TAP-2), (TAP-3) is an experimental technique for studying

**Genetic variation**: right|thumb

**Silent mutation**: Silent mutations are mutations in DNA that do not significantly alter the phenotype of the organism in which they occur. Silent mutations can occur in non-coding regions (outside of genes or within introns), or they may occur within exons.

**Burst kinetics**: Burst kinetics is a form of enzyme kinetics that refers to an initial high velocity of enzymatic turnover when adding enzyme to substrate. This initial period of high velocity product formation is referred to as the "Burst Phase".

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**A processive single-headed motor: kinesin superfamily protein KIF1A.**

A single kinesin molecule can move "processively" along a microtubule for more than 1 micrometer before detaching from it. The prevailing explanation for this processive movement is the "walking model," which envisions that each of two motor domains (heads) of the kinesin molecule binds coordinately to the microtubule. This implies that each kinesin molecule must have two heads to "walk" and that a single-headed kinesin could not move processively. Here, a motor-domain construct of KIF1A, a single-headed kinesin superfamily protein, was shown to move processively along the microtubule for more than 1 micrometer. The movement along the microtubules was stochastic and fitted a biased Brownian-movement model. (+info)

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**Influence of sampling on estimates of clustering and recent transmission of Mycobacterium tuberculosis derived from DNA fingerprinting techniques.**

The availability of DNA fingerprinting techniques for Mycobacterium tuberculosis has led to attempts to estimate the extent of recent transmission in populations, using the assumption that groups of tuberculosis patients with identical isolates ("clusters") are likely to reflect recently acquired infections. It is never possible to include all cases of tuberculosis in a given population in a study, and the proportion of isolates found to be clustered will depend on the completeness of the sampling. Using stochastic simulation models based on real and hypothetical populations, the authors demonstrate the influence of incomplete sampling on the estimates of clustering obtained. The results show that as the sampling fraction increases, the proportion of isolates identified as clustered also increases and the variance of the estimated proportion clustered decreases. Cluster size is also important: the underestimation of clustering for any given sampling fraction is greater, and the variability in the results obtained is larger, for populations with small clusters than for those with the same number of individuals arranged in large clusters. A considerable amount of caution should be used in interpreting the results of studies on clustering of M. tuberculosis isolates, particularly when sampling fractions are small. (+info)

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**A fast, stochastic threading algorithm for proteins.**

MOTIVATION: Sequences for new proteins are being determined at a rapid rate, as a result of the Human Genome Project, and related genome research. The ability to predict the three-dimensional structure of proteins from sequence alone would be useful in discovering and understanding their function. Threading, or fold recognition, aims to predict the tertiary structure of a protein by aligning its amino acid sequence with a large number of structures, and finding the best fit. This approach depends on obtaining good performance from both the scoring function, which simulates the free energy for given trial alignments, and the threading algorithm, which searches for the lowest-score alignment. It appears that current scoring functions and threading algorithms need improvement. RESULTS: This paper presents a new threading algorithm. Numerical tests demonstrate that it is more powerful than two popular approximate algorithms, and much faster than exact methods. (+info)

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**Declining survival probability threatens the North Atlantic right whale.**

The North Atlantic northern right whale (Eubalaena glacialis) is considered the most endangered large whale species. Its population has recovered only slowly since the cessation of commercial whaling and numbers about 300 individuals. We applied mark-recapture statistics to a catalog of photographically identified individuals to obtain the first statistically rigorous estimates of survival probability for this population. Crude survival decreased from about 0.99 per year in 1980 to about 0.94 in 1994. We combined this survival trend with a reported decrease in reproductive rate into a branching process model to compute population growth rate and extinction probability. Population growth rate declined from about 1. 053 in 1980 to about 0.976 in 1994. Under current conditions the population is doomed to extinction; an upper bound on the expected time to extinction is 191 years. The most effective way to improve the prospects of the population is to reduce mortality. The right whale is at risk from entanglement in fishing gear and from collisions with ships. Reducing this human-caused mortality is essential to the viability of this population. (+info)

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**FORESST: fold recognition from secondary structure predictions of proteins.**

MOTIVATION: A method for recognizing the three-dimensional fold from the protein amino acid sequence based on a combination of hidden Markov models (HMMs) and secondary structure prediction was recently developed for proteins in the Mainly-Alpha structural class. Here, this methodology is extended to Mainly-Beta and Alpha-Beta class proteins. Compared to other fold recognition methods based on HMMs, this approach is novel in that only secondary structure information is used. Each HMM is trained from known secondary structure sequences of proteins having a similar fold. Secondary structure prediction is performed for the amino acid sequence of a query protein. The predicted fold of a query protein is the fold described by the model fitting the predicted sequence the best. RESULTS: After model cross-validation, the success rate on 44 test proteins covering the three structural classes was found to be 59%. On seven fold predictions performed prior to the publication of experimental structure, the success rate was 71%. In conclusion, this approach manages to capture important information about the fold of a protein embedded in the length and arrangement of the predicted helices, strands and coils along the polypeptide chain. When a more extensive library of HMMs representing the universe of known structural families is available (work in progress), the program will allow rapid screening of genomic databases and sequence annotation when fold similarity is not detectable from the amino acid sequence. AVAILABILITY: FORESST web server at http://absalpha.dcrt.nih.gov:8008/ for the library of HMMs of structural families used in this paper. FORESST web server at http://www.tigr.org/ for a more extensive library of HMMs (work in progress). CONTACT: valedf@tigr.org; munson@helix.nih.gov; garnier@helix.nih.gov (+info)

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**A quantitative method for the detection of edges in noisy time-series.**

A modification of the edge detector of Chung & Kennedy is proposed in which the output provides confidence limits for the presence or absence of sharp edges (steps) in the input waveform. Their switching method with forward and backward averaging windows is retained, but the output approximates an ideal output function equal to the difference in these averages divided by the standard deviation of the noise. Steps are associated with peak output above a pre-set threshold. Formulae for the efficiency and reliability of this ideal detector are derived for input waveforms with Gaussian white noise and sharp edges, and serve as benchmarks for the switching edge detector. Efficiency is kept high if the threshold is a fixed fraction of the step size of interest relative to noise, and reliability is improved by increasing the window width W to reduce false output. For different steps sizes D, the window width for fixed efficiency and reliability scales as 1/D2. Versions with weighted averaging (flat, ramp, triangular) or median averaging but the same window width perform similarly. Binned above-threshold output is used to predict the locations and signs of detected steps, and simulations show that efficiency and reliability are close to ideal. Location times are accurate to order square root of W. Short pulses generate reduced output if the number of data points in the pulse is less than W. They are optimally detected by choosing W as above and collecting data at a rate such that the pulse contains approximately W data points. A Fortran program is supplied. (+info)

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**Strength of a weak bond connecting flexible polymer chains.**

Bond dissociation under steadily rising force occurs most frequently at a time governed by the rate of loading (Evans and Ritchie, 1997 Biophys. J. 72:1541-1555). Multiplied by the loading rate, the breakage time specifies the force for most frequent failure (called bond strength) that obeys the same dependence on loading rate. The spectrum of bond strength versus log(loading rate) provides an image of the energy landscape traversed in the course of unbonding. However, when a weak bond is connected to very compliant elements like long polymers, the load applied to the bond does not rise steadily under constant pulling speed. Because of nonsteady loading, the most frequent breakage force can differ significantly from that of a bond loaded at constant rate through stiff linkages. Using generic models for wormlike and freely jointed chains, we have analyzed the kinetic process of failure for a bond loaded by pulling the polymer linkages at constant speed. We find that when linked by either type of polymer chain, a bond is likely to fail at lower force under steady separation than through stiff linkages. Quite unexpectedly, a discontinuous jump can occur in bond strength at slow separation speed in the case of long polymer linkages. We demonstrate that the predictions of strength versus log(loading rate) can rationalize conflicting results obtained recently for unfolding Ig domains along muscle titin with different force techniques. (+info)

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**Visual form created solely from temporal structure.**

In several experiments, it was found that global perception of spatial form can arise exclusively from unpredictable but synchronized changes among local features. Within an array of nonoverlapping apertures, contours move in one of two directions, with direction reversing randomly over time. When contours within a region of the array reverse directions in synchrony, they stand out conspicuously from the rest of the array where direction reversals are unsynchronized. Clarity of spatial structure from synchronized change depends on the rate of motion reversal and on the proportion of elements reversing direction in synchrony. Evidently, human vision is sensitive to the rich temporal structure in these stochastic events. (+info)

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