A tandem repeat in DNA is two or more contiguous, approximate copies of a pattern of nucleotides. Tandem repeats have been shown to cause human disease, may play a variety of regulatory and evolutionary roles and are important laboratory and analytic tools. Extensive knowledge about pattern size, copy number, mutational history, etc. for tandem repeats has been limited by the inability to easily detect them in genomic sequence data. In this paper, we present a new algorithm for finding tandem repeats which works without the need to specify either the pattern or pattern size. We model tandem repeats by percent identity and frequency of indels between adjacent pattern copies and use statistically based recognition criteria. We demonstrate the algorithm’s speed and its ability to detect tandem repeats that have undergone extensive mutational change by analyzing four sequences: the human frataxin gene, the human β T cell receptor locus sequence and two yeast chromosomes. These sequences range in size from 3 kb up to 700 kb. A World Wide Web server interface at c3.biomath.mssm.edu/trf.html has been established for automated use of the program.

/pdf/tandem-repeats-finder-a-program-to-analyze-dna-sequences-1oo3g6vnch.pdf

An introduction to probability theory and its applications

Tandem repeats finder: a program to analyze DNA sequences

The notion of a quantum dynamical semigroup is defined using the concept of a completely positive map. An explicit form of a bounded generator of such a semigroup onB(ℋ) is derived. This is a quantum analogue of the Levy-Khinchin formula. As a result the general form of a large class of Markovian quantum-mechanical master equations is obtained.

/pdf/on-the-generators-of-quantum-dynamical-semigroups-45xwlrf1aa.pdf

On the Generators of Quantum Dynamical Semigroups

An intertemporal model for the capital market is deduced from the portfolio selection behavior by an arbitrary number of investors who aot so as to maximize the expected utility of lifetime consumption and who can trade continuously in time. Explicit demand functions for assets are derived, and it is shown that, unlike the one-period model, current demands are affected by the possibility of uncertain changes in future investment opportunities. After aggregating demands and requiring market clearing, the equilibrium relationships among expected returns are derived, and contrary to the classical capital asset pricing model, expected returns on risky assets may differ from the riskless rate even when they have no systematic or market risk. ONE OF THE MORE important developments in modern capital market theory is the Sharpe-Lintner-Mossin mean-variance equilibrium model of exchange, commonly called the capital asset pricing model.2 Although the model has been the basis for more than one hundred academic papers and has had significant impact on the non-academic financial community,' it is still subject to theoretical and empirical criticism. Because the model assumes that investors choose their portfolios according to the Markowitz [21] mean-variance criterion, it is subject to all the theoretical objections to this criterion, of which there are many.4 It has also been criticized for the additional assumptions required,5 especially homogeneous expectations and the single-period nature of the model. The proponents of the model who agree with the theoretical objections, but who argue that the capital market operates "as if" these assumptions were satisfied, are themselves not beyond criticism. While the model predicts that the expected excess return from holding an asset is proportional to the covariance of its return with the market

http://jpkc.fudan.edu.cn/picture/article/296/c7/92/0e8c302443d092d8b77a256079cf/3a6483db-591a-42b5-b904-e2430eb26c6a.pdf

An introduction to probability theory and its applications

Citations

Tandem repeats finder: a program to analyze DNA sequences

On the Generators of Quantum Dynamical Semigroups

An intertemporal capital asset pricing model

Spatial Interaction and the Statistical Analysis of Lattice Systems

Pattern Classification (2nd ed.)

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