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PubMed2002

On Wiener filtering and the physics behind statistical modeling.

The closed-form solution of the so-called statistical multivariate calibration model is given in terms of the pure component spectral signal, the spectral noise, and the signal and noise of the reference method. The "statistical" calibration model is shown to be as much grounded on the physics of the pure component spectra as any of the "physical" models. There are no fundamental differences between the two approaches since both are merely different attempts to realize the same basic idea, viz., the spectrometric Wiener filter. The concept of the application-specific signal-to-noise ratio (SNR) is introduced, which is a combination of the two SNRs from the reference and the spectral data. Both are defined and the central importance of the latter for the assessment and development of spectroscopic instruments and methods is explained. Other statistics like the correlation coefficient, prediction error, slope deficiency, etc., are functions of the SNR. Spurious correlations and other practically important issues are discussed in quantitative terms. Most important, it is shown how to use a priori information about the pure component spectra and the spectral noise in an optimal way, thereby making the distinction between statistical and physical calibrations obsolete and combining the best of both worlds. Companies and research groups can use this article to realize significant savings in cost and time for development efforts.

Algorithms↗
PubMed1989

A critical review of the physics and statistics of condoms and their role in individual versus societal survival of the AIDS epidemic.

Condom failure rates for HIV are substantially greater than for pregnancy, even for highly motivated people who may reach the limit set by allowed manufacturing imperfections. This makes condoms ineffective for lifelong protection from HIV-infected sexual partners; therefore, in general, condoms provide inadequate risk reduction for the individual. Nevertheless, they are sufficiently effective that if everyone used condoms, the AIDS epidemic would stop. Quantitative public health goals to reduce the "reproductive rate" of HIV from an estimated 4-12 people infected per infected person to below 1 are needed. Government and scientific testing of condoms could be improved statistically and by utilizing relevant physics.

Acquired Immunodeficiency Syndrome↗
PubMed2000

Information geometry of mean-field approximation.

I present a general theory of mean-field approximation based on information geometry and applicable not only to Boltzmann machines but also to wider classes of statistical models. Using perturbation expansion of the Kullback divergence (or Plefka expansion in statistical physics), a formulation of mean-field approximation of general orders is derived. It includes in a natural way the "naive" mean-field approximation and is consistent with the Thouless-Anderson-Palmer (TAP) approach and the linear response theorem in statistical physics.

Artificial Intelligence↗
PubMed2002

[Assessment of image reconstruction parameters in PET using physical and statistical figures of merit].

The aim of this study was to analyze the recommended OSEM image reconstruction parameters in positron emission tomography (PET). Spatial resolution, signal-to-noise ratio, and contrast were used as physical figures of merit (FOM). For statistical FOMs, the t-value and the area under the receiver operating characteristic (ROC) were employed. The spatial resolution was measured with 21 point sources. The signal-to-noise ratio, the contrast, and the t-value were investigated with a whole-body phantom with hollow spheres inserted. A phantom containing line sources was used for ROC analysis. As result, the reconstruction parameters recommended for visual evaluation lead to images with an adequate lesion detectability. The quantitative reconstruction, however, needs improvement.

Artifacts↗
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↗
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↗
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↗
PubMedDate not supplied

[Mathematical model of microorganism biomass growth in the absence of a limiting substrate and inhibiting agents].

A mathematical model for the growth of microbial cells upon submerged cultivation was constructed. The model describes the growth phases of the biomass of microorganisms in the absence of inhibiting agents and limitation by substrate in the medium. At the basis of model is the requirement that cells should not be in physical contact during some time in order that they can divide. The model involves the known concepts of statistical physics. The consequences of the model are discussed.

Biomass↗
PubMed1998

A molar entropy model of age differences in spatial memory.

Two very-short-term-memory, spatial scanning aging experiments were conducted involving a graphics character as a target stimulus. On the probe portion of a trial, the stimulus was presented in the same position as it was on the target portion of the trial (i.e., a same trial) 50% of the time. However, on the remaining 50% of the trials, the probe stimulus was shifted (or transposed) 1, 2, or 3 positions to the right or left of the original presentation (target) position. In Experiment 1, exposure duration was manipulated. In Experiment 2, the number of potential target display positions was manipulated. For both experiments, older adults showed larger transposition distance effects than younger adults for errors. In the past (e.g., P.A. Allen, 1990, 1991), this effect has been attributed to higher levels of internal noise (entropy) in older than younger adults. This research provides converging operations to this contention by using statistical physics methods to rigorously compute the entropy in a molar neural network across age groups. After successfully fitting the statistical mechanics model to the data, the model is proved to have external validity by fitting a simplified version of it to an earlier spatial memory aging experiment reported by P. R. Bruce and J. F. Herman (1986). The results of both traditional reaction time and error rate analyses, as well as the entropy modeling analyses, indicated that older adults exhibited higher levels of entropy than did the younger adults and that this effect appeared to be generalized across processing stage.

Adolescent↗