A new heuristic approach for minimizing possibly nonlinear and non-differentiable continuous space functions is presented. By means of an extensive testbed it is demonstrated that the new method converges faster and with more certainty than many other acclaimed global optimization methods. The new method requires few control variables, is robust, easy to use, and lends itself very well to parallel computation.

/pdf/differential-evolution-a-simple-and-efficient-heuristic-for-4vrb5o5ldc.pdf

Differential Evolution – A Simple and Efficient Heuristic for Global Optimization over Continuous Spaces

We propose a new global optimization method (Simulated Tempering) for simulating effectively a system with a rough free-energy landscape (i.e., many coexisting states) at finite nonzero temperature. This method is related to simulated annealing, but here the temperature becomes a dynamic variable, and the system is always kept at equilibrium. We analyse the method on the Random Field Ising Model, and we find a dramatic improvement over conventional Metropolis and cluster methods. We analyse and discuss the conditions under which the method has optimal performances.

/pdf/simulated-tempering-a-new-monte-carlo-scheme-1l77zz4ypv.pdf

Simulated tempering: a new Monte Carlo scheme

http://www.decom.ufop.br/marcone/Disciplinas/InteligenciaComputacional/OptimGlobal.pdf

Global Optimization of Statistical Functions with Simulated Annealing

Microsatellites, or tandem simple sequence repeats (SSR), are abundant across genomes and show high levels of polymorphism. SSR genetic and evolutionary mechanisms remain controversial. Here we attempt to summarize the available data related to SSR distribution in coding and noncoding regions of genomes and SSR functional importance. Numerous lines of evidence demonstrate that SSR genomic distribution is nonrandom. Random expansions or contractions appear to be selected against for at least part of SSR loci, presumably because of their effect on chromatin organization, regulation of gene activity, recombination, DNA replication, cell cycle, mismatch repair system, etc. This review also discusses the role of two putative mutational mechanisms, replication slippage and recombination, and their interaction in SSR variation.

https://onlinelibrary.wiley.com/doi/pdf/10.1046/j.1365-294X.2002.01643.x

Microsatellites: genomic distribution, putative functions and mutational mechanisms: a review.

Electrostatic Basis for Enzyme Catalysis

Let ℝ
 n
 be then-dimensional real Euclidean space,x=(x
1,x
2, ,x
n)T ∈ ℝ
 n
 , and letf:ℝ
 n
 → R be a real-valued function We consider the problem of finding the global minimizers off A new method to compute numerically the global minimizers by following the paths of a system of stochastic differential equations is proposed This method is motivated by quantum mechanics Some numerical experience on a set of test problems is presented The method compares favorably with other existing methods for global optimization

Global optimization and stochastic differential equations

Hidden Markov Models (HMMs) became recently important and popular among bioinformatics researchers, and many software tools are based on them. In this survey, we first consider in some detail the mathematical foundations of HMMs, we describe the most important algorithms, and provide useful comparisons, pointing out advantages and drawbacks. We then consider the major bioinformatics applications, such as alignment, labeling, and profiling of sequences, protein structure prediction, and pattern recognition. We finally provide a critical appraisal of the use and perspectives of HMMs in bioinformatics.

/pdf/hidden-markov-models-in-bioinformatics-4q2eueou3o.pdf

Hidden Markov Models in Bioinformatics

Motivation and results: The importance of Tandem Repeats in some genomes is now well established. We have reported elsewhere some interesting new results obtained by means of a preliminary program for finding Tandem Repeats in DNA sequences, together with a brief description of the basic ideas of the algorithm. We describe here a completely new program based only in part on those ideas, we briefly discuss the interpretation of the results, and, by way of example, we provide a few novel results relative to the parasites responsible of two re-emerging diseases, Plasmodium falciparum and Mycobacterium tuberculosis. Our program is portable, effective, powerful and fast: it can run on current desktop computers, and it finds all significant Tandem Repeats also in the longest segments of sequences in databases (up to millions of bases), in short times (minutes). Availability: An academic version of the algorithm (full source listing in standard C language) can be freely downloaded (http://www.caspur.it/∼castri/STRING/). Contact: valerio.parisi@roma2.infn.it Supplementary information: Some illustrative figures and some sample results are provided as supplementary material at: http://www.caspur.it/∼castri/STRING/.

/pdf/string-finding-tandem-repeats-in-dna-sequences-2ck5t2ccvg.pdf

STRING: finding tandem repeats in DNA sequences

An iterative method for solving nonlinear simultaneous equations is proposed. The method associates a system of differential equations with the equations, whose roots we are interested in, and integrates the former numerically. The system of differential equations is inspired by classical mechanics and is of second order. The method can easily handle nonlinear least squares problems.

A New Method for Solving Nonlinear Simultaneous Equations

The uniform sampling of convex polytopes is an interesting computational problem with many applications in inference from linear constraints, but the performances of sampling algorithms can be affected by ill-conditioning. This is the case of inferring the feasible steady states in models of metabolic networks, since they can show heterogeneous time scales. In this work we focus on rounding procedures based on building an ellipsoid that closely matches the sampling space, that can be used to define an efficient hit-and-run (HR) Markov Chain Monte Carlo. In this way the uniformity of the sampling of the convex space of interest is rigorously guaranteed, at odds with non markovian methods. We analyze and compare three rounding methods in order to sample the feasible steady states of metabolic networks of three models of growing size up to genomic scale. The first is based on principal component analysis (PCA), the second on linear programming (LP) and finally we employ the Lovazs ellipsoid method (LEM). Our results show that a rounding procedure dramatically improves the performances of the HR in these inference problems and suggest that a combination of LEM or LP with a subsequent PCA perform the best. We finally compare the distributions of the HR with that of two heuristics based on the Artificially Centered hit-and-run (ACHR), gpSampler and optGpSampler. They show a good agreement with the results of the HR for the small network, while on genome scale models present inconsistencies.

/pdf/uniform-sampling-of-steady-states-in-metabolic-networks-4a87f0i97t.pdf

Valerio Parisi

Papers

Global optimization and stochastic differential equations

Hidden Markov Models in Bioinformatics

STRING: finding tandem repeats in DNA sequences

A New Method for Solving Nonlinear Simultaneous Equations

Uniform Sampling of Steady States in Metabolic Networks: Heterogeneous Scales and Rounding