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PubMed2005

Complex networks and simple models in biology.

The analysis of molecular networks, such as transcriptional, metabolic and protein interaction networks, has progressed substantially because of the power of models from statistical physics. Increasingly, the data are becoming so detailed--though not always complete or correct--that the simple models are reaching the limits of their usefulness. Here, we will discuss how network information can be described and to some extent quantified. In particular statistics offers a range of tools, such as model selection, which have not yet been widely applied in the analysis of biological networks. We will also outline a number of present challenges posed by biological network data in systems biology, and the extent to which these can be addressed by new developments in statistics, physics and applied mathematics.

Animals↗
PubMed1989

Physics and statistics of medical imaging.

Extraordinary progress has been made over the last two decades in the development and dissemination of new medical imaging technologies. The development of computed tomography, positron emission tomography, and magnetic resonance imaging, as well as major innovations to the conventional imaging modalities, have revolutionized medical diagnostic imaging. Despite their many differences, all of these modalities can be viewed from a common perspective: being described in terms of the underlying physical properties imaged, the type of radiation/detection system used to produce the images, and the imaging performance that the modality achieves, both in absolute terms and relative to that of a conceptual ideal observer. This is a US government work. There are no restrictions on its use.

Diagnostic Imaging↗
PubMed2005

The estimation of distributions and the minimum relative entropy principle.

Estimation of Distribution Algorithms (EDA) have been proposed as an extension of genetic algorithms. In this paper we explain the relationship of EDA to algorithms developed in statistics, artificial intelligence, and statistical physics. The major design issues are discussed within a general interdisciplinary framework. It is shown that maximum entropy approximations play a crucial role. All proposed algorithms try to minimize the Kullback-Leibler divergence KLD between the unknown distribution p(x) and a class q(x) of approximations. However, the Kullback-Leibler divergence is not symmetric. Approximations which suppose that the function to be optimized is additively decomposed (ADF) minimize KLD(q||p), the methods which learn the approximate model from data minimize KLD(p||q). This minimization is identical to maximizing the log-likelihood. In the paper three classes of algorithms are discussed. FDA uses the ADF to compute an approximate factorization of the unknown distribution. The factors are marginal distributions, whose values are computed from samples. The second class is represented by the Bethe-Kikuchi approach which has recently been rediscovered in statistical physics. Here the values of the marginals are computed from a difficult constrained minimization problem. The third class learns the factorization from the data. We analyze our learning algorithm LFDA in detail. It is shown that learning is faced with two problems: first, to detect the important dependencies between the variables, and second, to create an acyclic Bayesian network of bounded clique size.

Algorithms↗
PubMed2001

A joint physics-based statistical deformable model for multimodal brain image analysis.

A probabilistic deformable model for the representation of multiple brain structures is described. The statistically learned deformable model represents the relative location of different anatomical surfaces in brain magnetic resonance images (MRIs) and accommodates their significant variability across different individuals. The surfaces of each anatomical structure are parameterized by the amplitudes of the vibration modes of a deformable spherical mesh. For a given MRI in the training set, a vector containing the largest vibration modes describing the different deformable surfaces is created. This random vector is statistically constrained by retaining the most significant variation modes of its Karhunen-Loève expansion on the training population. By these means, the conjunction of surfaces are deformed according to the anatomical variability observed in the training set. Two applications of the joint probabilistic deformable model are presented: isolation of the brain from MRI using the probabilistic constraints embedded in the model and deformable model-based registration of three-dimensional multimodal (magnetic resonance/single photon emission computed tomography) brain images without removing nonbrain structures. The multi-object deformable model may be considered as a first step toward the development of a general purpose probabilistic anatomical atlas of the brain.

Anatomy, Cross-Sectional↗
PubMed2002

Analysis of symbolic sequences using the Jensen-Shannon divergence.

We study statistical properties of the Jensen-Shannon divergence D, which quantifies the difference between probability distributions, and which has been widely applied to analyses of symbolic sequences. We present three interpretations of D in the framework of statistical physics, information theory, and mathematical statistics, and obtain approximations of the mean, the variance, and the probability distribution of D in random, uncorrelated sequences. We present a segmentation method based on D that is able to segment a nonstationary symbolic sequence into stationary subsequences, and apply this method to DNA sequences, which are known to be nonstationary on a wide range of different length scales.

Computational Biology↗
PubMed1978

Statistical power in physical anthropology: a technical report.

A statistical power analysis of The American Journal of Physical Anthropology (Volume 44, 1976) was conducted. Twenty-five articles, which included 3,304 major significance tests, constituted the final sample. Resultant power estimates of 0.38, 0.62, and 0.81, corresponding to small, medium, and large population effects respectively, were obtained. Although the medium effect size estimate falls short of the recommended 0.80 level, the statistical power of physical anthropological research fares well relative to several of the social scientific fields of inquiry.

Anthropology, Physical↗
PubMed2006

Spacing distributions for point processes on a regular fractal.

The homogeneous Poisson point process in Rd (denoted by Pd) is a basic model of stochastic geometry and modern statistical physics. Using ideas from fractal geometry, geometrical statistics, and random matrix theory, we introduce the model of random points on a self-similar fractal as a model of intermediate statistics, in the sense that the interpoint spacing statistics of the model are intermediate between those of P1 and P2 when the fractal dimension is in between 1 and 2, and intermediate between those of P2 and P3 when the fractal dimension is in between 2 and 3, and so on. We also introduce the idea of using a continuous family of such models to interpolate between P1 and P2 and thereby effectuate crossover transitions between P1 statistics and P2 statistics. We first derive the kth-nearest-neighbor spacing distribution for the general model, and then study the interpoint spacing statistics of several realizations of the model involving Sierpinski fractals in R2 and R3. We also study a realization of a continuous interpolation between P1 and P2, in particular a continuous interpolation between a point process on a line and a point process on a plane-filling curve, using the continuous family of self-similar Koch curves in R2. In the latter study, we specifically analyze the second-nearest-neighbor interpoint spacing statistics, which undergo a crossover transition between semi-Poisson and Ginibre statistics.

Journal Article↗
PubMed2002

Scaling laws for geometry and macromolecules in solution: an interdisciplinary approach to statistical and thermal physics.

An interdisciplinary program, dealing with statistics within basic geometry, is presented and discussed across some modern physics. Its fundamentals are of general interest in physical chemistry, but specially suit investigating conformational statistics and universal scaling of polymer chains in solution. We pointed out an equivalence principle for shape and statistics that can straightforwardly link probability distributions to geometrical quantities at smaller length scales. The average polymer size is thus expected following analytically from the energy surface of its dimeric unit. This would finally suggest extending molecular mechanics to a geometrical setting that reaches the limit of vanishing scales.

Journal Article↗
PubMed2004

An allometric model for trees.

This paper presents a general mathematical model for the morphometric description of trees. This model is based on the introduction of fractal theory, and more particularly of the concept of self-similarity, into a statistical physics rationale. Fractal theory provides the necessary tools to describe the complexity of tree structure. Statistics, when applied to physics, makes it possible to explain the properties of complex objects starting from their components. The combination of both tools allowed us to develop a theoretical model that is the probability density function of the morphometric lengths of trees. An example of validation of this law is given here: the theoretical model of morphometric lengths is compared with experimental data of Cupressocyparis.

Cupressus↗
PubMed2025

Repeats mimic pathogen-associated patterns across a vast evolutionary landscape.

An emerging hallmark of many human diseases is transcription of typically silenced repetitive DNA containing pathogen-associated molecular patterns (PAMPs). These PAMPs engage the innate immune system via pattern recognition receptors (PRRs)-a phenomenon known as viral mimicry. We propose a statistical physics framework to quantify viral mimicry by measuring "selective forces" that enrich PAMPs compared to a genome-wide reference distribution. We validate our predictions by identifying repeats that bind different PRRs and show potential viral mimics in different repeat families across eukaryotic genomes, suggesting shared mechanisms drive emergence and retention. We propose two non-exclusive evolutionary hypotheses. The first "repeat-centric" hypothesis posits PAMPs are integral to the repeat life cycle and are therefore enriched as they mediate repeat expansion. The second "organism-centric" hypothesis proposes viral mimicry functions as a cell-intrinsic feedback mechanism for sensing and reacting to transcriptional dysregulation, which provides a selective pressure to maintain PAMPs in genomes.

Humans↗
PubMed1994

ODS_BOOTSTRAP: assessing the statistical reliability of physical maps by bootstrap resampling.

In the program ODS_BOOTSTRAP we provide a methodology for quickly ordering clones in a genomic library into a physical map and for applying a statistical tool known as the bootstrap to assess the statistical reliability of a clonal ordering. Each clone is assigned a binary fingerprint by one of a variety of experimental approaches to physical mapping. For example, the binary fingerprints might be generated by hybridizing a panel of m probes to a library of n clones. The resulting n x m binary data matrix, X, is input to ODS_BOOTSTRAP, which utilizes the similarity in binary fingerprints of clones to construct a physical map. Under this particular implementation of bootstrap resampling, the m probes (or columns of the data matrix) are sampled randomly with replacement in the computer to generate a new n x m data matrix, X*, from which a second physical map is constructed. The resampling process is repeated 100 or more times to generate 100 or more X* matrices. The resulting 100 or more physical maps are compared with the original physical map based on the original data matrix X by counting how often links in the original physical map reappear. Three confidence statistics are introduced for each link in a physical map. The statistic C1 is defined as the percentage of time two neighboring clones on the original map reappear as neighbors under resampling. The statistic C2 is defined as the percentage of time that two neighboring clones i and j on the original map reappear as neighbors or that a clone with an identical binary fingerprint to clone i reappears as a neighbor to clone j. The statistic C3 is defined as the percentage of time that two neighboring clones on the original map reappear in the same contig under resampling.

Algorithms↗