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PubMed2001

MUNIN: a new approach to multi-dimensional NMR spectra interpretation.

A new method, MUNIN (Multi-dimensional NMR spectra interpretation), is introduced for the automated interpretation of three-dimensional NMR spectra. It is based on a mathematical concept referred to as three-way decomposition. An NMR spectrum is decomposed into a sum of components, with each component corresponding to one or a group of peaks. Each component is defined as the direct product of three one-dimensional shapes. A consequence is reduction in dimensionality of the spectral data used in further analysis. The decomposition may be applied to frequency-domain or time-domain data, or to a mixture of these. Features of MUNIN include good resolution in crowded regions and the absence of assumptions about line shapes. Uniform sampling of time-domain data, a prerequisite for discrete Fourier transform, is not required. This opens an avenue for the processing of NMR data that do not follow oscillating behaviour, e.g. from relaxation measurements. The application of MUNIN is illustrated for a 1H-15N-NOESY-HSQC, where each component is defined as the set of all NOE peaks formed by a given amide group. As a result, the extraction of structural information simply consists of one-dimensional peak picking of the shape along the NOE-axis obtained for each amide group.

Algorithms↗
PubMed2001

MUNIN: application of three-way decomposition to the analysis of heteronuclear NMR relaxation data.

MUNIN (Multidimensional NMR Spectra Interpretation), a recently introduced approach exploiting the mathematical concept of three-way decomposition, is proposed for separation and quantitative relaxation measurements of strongly overlapped resonances in sets of heteronuclear two-dimensional spectra that result from typical relaxation experiments. The approach is general and may also be applied to sets of two-dimensional spectra with arbitrary modulation along the third dimension (e.g., J-coupling, diffusion). Here, the method is applied for the analysis of 15N rotating frame relaxation data.

Azurin↗
PubMed2003

Heterochromatin and complexity: a theoretical approach.

Heterochromatin represents 30% of eukaryotic genome in Drosophila and 15% in humans. Despite extensive research spanning many decades, its evolutionary significance, as well as the forces that guarantee its maintenance, are still elusive. Many theoretical and experimental approaches have led researchers to propose several conceptual frameworks to elucidate the nature of this huge mysterious genetic material and its spreading in all eukaryotic genomes. "Junk DNA" as well as "selfish genetic material" are two examples of such attempts, but several lines of evidence suggest that such explanations are incomplete. In fact, if the selfish DNA hypothesis does not explain the mapping of genetic functions in heterochromatin, then the junk DNA hypothesis is incomplete in describing both emergence of genetic functions and their maintenance in the eukaryotic heterochromatin. Recent developments in the physics of complex systems and mathematical concepts such as fractals provide new conceptual clues to answer several basic questions concerning the emergence of heterochromatin in eukaryotic genomes, its evolutionary significance, the forces that guarantee its maintenance, and its peculiar behavior in the eukaryotic cell. The aim of this paper is to provide a new theoretical framework for the heterochromatin, considering such genetic material in physical terms as a complex adaptive system. We apply some computer calculations to demonstrate the nonlinearity of the flux of genetic information along the phylogenic tree. Fractal dimensions of representative heterochromatic sequences are provided. A theory is proposed in which heterochromatin is considered a system that evolves in a self-organized manner at the edge of cellular and environmental chaos.

Animals↗
PubMed1999

Micromachines in endoscopy.

Conventional endoscopy has reached a plateau in technical development, necessitating the exploration of bold new ideas in order to make further advances. One such idea is a self-navigating, independent, intelligent colonoscopic micro-robot. The design of a vehicle that can negotiate the difficult and hostile terrain of the colon is a complex task. Options include wheeled or tracked vehicles and pneumatically driven devices. The development of navigation and lesion recognition software to drive such a vehicle is also challenging. The various mathematical concepts involved in the development of such software are explored in this article.

Animals↗
PubMed2000

An historical review of application of optical solitons for high speed communications.

The history of application of optical solitons for high speed communications presents an interesting example of how an abstract mathematical concept has been put into practical use. The historical development introduced in this manuscript is divided into five stages: (1) historical background and the discovery of the optical soliton, (2) the idea and demonstration of all optical soliton transmission systems, (3) identification of possible problems, (4) demonstration of soliton control and (5) discovery of dispersion managed optical solitons (DMS). Although there are many interesting related subjects such as modulational instability, dark solitons, and spatial solitons, the manuscript focuses only on the subject of primarily theoretical developments of soliton based communications in fibers. (c) 2000 American Institute of Physics.

Journal Article↗
PubMed1976

Linking numbers and nucleosomes.

In considering supercoils formed by closed double-stranded molecules of DNA certain mathematical concepts, such as the linking number and the twist, are needed. The meaning of these for a closed ribbon is explained and also that of the writhing number of a closed curve. Some simple examples are given, some of which may be relevant to the structure of chromatin.

Chromatin↗
PubMed1984

A mathematical overview of a computer simulation model of maternity histories with illustrative examples.

A mathematical overview of a stochastic computer simulation model of maternity histories is provided. Various components of human reproduction are accommodated in the model through distributions of waiting times among live births. Included in these components are distributions of age at first marriage in a cohort of women, waiting times to pregnancy for fecundable women, and the lengths of infecundable periods following live births. Probabilities that pregnancies end in either a live birth, induced abortion, or some other type of outcome are also included. Elements of renewal theory and semi-Markov processes in discrete time were the basic mathematical concepts used in the construction of the model. A brief description of an interactive software package called MATHIST, which may be used to implement the model on a computer, is also included. Four illustrative computer runs with MATHIST, pertinent to the operation of family planning programmes in Africa, are also described and discussed.

Adult↗
PubMed1988

The "stress analogy" in the context of psychoneuroimmunology.

The "stress analogy" is examined from the perspective of psychoneuroimmunology. Arguments are presented that do not support a linear and mathematical conception of psychosocial stress, as defended by the "stress analogy" concept. Implications for the study of schizophrenia are discussed.

Adaptation, Psychological↗
PubMed1989

The molecular basis of stochastic and nonstochastic effects.

Stochastic effects have been defined as those for which the probability increases with dose, without a threshold. Nonstochastic effects are those for which incidence and severity depends on dose, but for which there is a threshold dose. These definitions suggest that the two types of effects are not related. In this paper it will be shown that at least some of the nonstochastic effects are the consequence of accumulated stochastic effects and that both types of effect can be related to a common cellular damage. It is proposed that, at the cellular level, effects such as mutation induction and cell reproductive death are related to DNA double-strand breaks caused by radiation. Further, we propose that stochastic effects depend on a mutational event induced in a critical cell of a target organ. Nonstochastic effects are considered to arise because the function of a substantial proportion of critical cells is impaired. In some cases the predominant effect is comparable to cell reproductive death. Animal mortality, for instance, may occur because a substantial proportion of bone marrow cells is killed. Using this concept, mathematical formulas can be derived for the various effects. Modification of the irradiation conditions (e.g., low dose rate or density ionizing radiation) leads to changes in the initial molecular lesions and, consequently, to changes in the dose effect relationships of stochastic and nonstochastic effects. Experimental support will be discussed, using animal mortality as an endpoint. The implications of this approach will be discussed with emphasis on its application to radiological protection.

Animals↗
PubMed1992

Fractal mechanisms in the electrophysiology of the heart.

The mathematical concept of fractals provides insights into complex anatomic branching structures that lack a characteristic (single) length scale, and certain complex physiologic processes, such as heart rate regulation, that lack a single time scale. Heart rate control is perturbed by alterations in neuro-autonomic function in a number of important clinical syndromes, including sudden cardiac death, congestive failure, cocaine intoxication, fetal distress, space sickness and physiologic aging. These conditions are associated with a loss of the normal fractal complexity of interbeat interval dynamics. Such changes, which may not be detectable using conventional statistics, can be quantified using new methods derived from "chaos theory."

Computer Simulation↗
PubMed2006

LPC cepstral distortion measure for protein sequence comparison.

Protein sequence comparison is the most powerful tool for the inference of novel protein structure and function. This type of inference is commonly based on the similar sequence-similar structure-similar function paradigm, and derived by sequence similarity searching on databases of protein sequences. As entire genomes have been being determined at a rapid rate, computational methods for comparing protein sequences will be more essential for probing the complexity of molecular machines. In this paper we introduce a pattern-comparison algorithm, which is based on the mathematical concepts of linear predictive coding (LPC) and LPC cepstral distortion measure, for computing similarities/dissimilarities between protein sequences. Experimental results on a real data set of functionally related and functionally nonrelated protein sequences have shown the effectiveness of the proposed approach on both accuracy and computational efficiency.

Algorithms↗
PubMed2005

Numeracy for adults with Down syndrome: it's a matter of quality of life.

BACKGROUND: Numeracy development is widely accepted as critical for adults in the general community which is equally the case for adults with Down syndrome. This paper reports some of the findings of a study including the research question: What is the justification for numeracy development for adults with Down syndrome? Investigating this question led to the search for a framework to support the ongoing development of numeracy. METHOD: The research used a case study methodology. Five adults were observed and interviewed in two contexts each. The data were analyzed to identify links to the quality of life model. RESULTS: The research illustrates how a quality of life approach can be used to justify and guide the lifelong development of numeracy. Data from the case studies linked numeracy to quality of life under the principles of personal contexts, variability, life-span perspective, values, choices and personal control, perceptions and self-image. CONCLUSIONS: The principles of quality of life can provide a framework for the development of numeracy in the context of adulthood and Down syndrome. Preparation for the numeracy needs of a long and satisfying adulthood should begin in early childhood, continue in schools with the teaching of underlying mathematics concepts and skills, and be modified and refined throughout adulthood by the use of a numeracy development plan. Carers and professionals interacting in the contexts need to adopt a teaching role for numeracy.

Adult↗
PubMed2004

Computerized calculation scheme for toric intraocular lenses.

BACKGROUND AND PURPOSE: While a number of intraocular lens (IOL) power prediction formulae are well established for determination of spherical lenses, no common strategy has been published for the computation of toric IOLs. The purpose of this study is to describe a paraxial computing scheme for tracing an axial pencil of rays through the 'optical system eye' containing astigmatic refractive surfaces with their axes at random. The capabilities of this computing scheme are demonstrated with clinical examples. METHODS: Based on a schematic model eye with spherocylindric surfaces, we use two alternative notations for description of vergences or prescriptions: (1) standard notation (refraction in both cardinal meridians and axis), and (2) component notation (spherical equivalent and cylindric component in 0 degrees and 45 degrees. Refractive surfaces are added to the vergence in component notation, whereas the transformation of the vergence through media is performed in the standard notation for both cardinal meridians. For calculation of the toric lens implant, a pencil of rays is traced through the spectacle and the cornea to the estimated lens position as well as backwards from the retina to the estimated lens position. For calculation of residual spectacle refraction, a pencil of rays is traced backwards from the retina through the toric lens implant and the cornea to the spectacle plane. RESULTS: In example 1 we calculate a 'thin toric lens' for compensation of a corneal astigmatism to achieve a spherical target refraction. In example 2 we compute a 'thick toric lens', which has to compensate for an oblique corneal astigmatism and rotate the spectacle cylinder to the against the rule position to enhance near vision. In example 3 we estimate the residual refraction at the corneal plane after implantation of a thick toric lens, when the cylinder of the lens implant is compensating the corneal cylinder in part and the axis of implantation is not fully aligned with the axis of the corneal astigmatism. CONCLUSION: This novel mathematical concept for computation of toric IOLs or prediction of the refractive outcome with a toric implant in place is a straightforward, computer-based approach, which may substitute for more or less empirical methods of determining toric IOL implants.

Aged↗
PubMed1988

Dynamic pattern generation in behavioral and neural systems.

In the search for principles of pattern generation in complex biological systems, an operational approach is presented that embraces both theory and experiment. The central mathematical concepts of self-organization in nonequilibrium systems (including order parameter dynamics, stability, fluctuations, and time scales) are used to show how a large number of empirically observed features of temporal patterns can be mapped onto simple low-dimensional (stochastic, nonlinear) dynamical laws that are derivable from lower levels of description. The theoretical framework provides a language and a strategy, accompanied by new observables, that may afford an understanding of dynamic patterns at several scales of analysis (including behavioral patterns, neural networks, and individual neurons) and the linkage among them.

Animals↗
PubMed1962

Viability and estimation of shelf-life of bacterial populations.

Mathematical concepts associated with the exponential and probit models are developed, and the similarity of the two methods is discussed. Because of its greater flexibility in design, the probit method was used to estimate the shelf-life for four bacterial populations, wet and dry spores of Bacillus anthracis and wet and dry cells of Pasteurella tularensis. On the basis of data gained by storing these organisms at high temperature, the probit method was used to predict the time at which 50% viability would occur for cells stored at 3 C. A plane passing through a three-space showing change in percentage viability of bacteria was formulated by a multiple regression method. With this functional technique, the percentage viability, expressed as a probit, was linearily related to a logarithm of storage time and storage temperature. The use of this method to study the effect of controlled variables on the viability of cells is demonstrated by comparing the effect of viability associated with three additives used prior to drying. The results of the test gave shelf-life estimates which were too low for all additives; however, the order of stability was ranked properly as confirmed by long-term tests.

Bacillus anthracis↗
PubMed2003

Fundamental measures of diagnostic examination performance: usefulness for clinical decision making and research.

Measures of diagnostic accuracy, such as sensitivity, specificity, predictive values, and receiver operating characteristic curves, can often seem like abstract mathematic concepts that have a minimal relationship with clinical decision making or clinical research. The purpose of this article is to provide definitions and examples of these concepts that illustrate their usefulness in specific clinical decision-making tasks. In particular, nine principles are provided to guide the use of these concepts in daily radiology practice, in interpreting clinical literature, and in designing clinical research studies. An understanding of these principles and of the measures of diagnostic accuracy to which they apply is vital to the appropriate evaluation and use of diagnostic imaging examinations.

Decision Making↗
PubMed2006

Small-world brain networks.

Many complex networks have a small-world topology characterized by dense local clustering or cliquishness of connections between neighboring nodes yet a short path length between any (distant) pair of nodes due to the existence of relatively few long-range connections. This is an attractive model for the organization of brain anatomical and functional networks because a small-world topology can support both segregated/specialized and distributed/integrated information processing. Moreover, small-world networks are economical, tending to minimize wiring costs while supporting high dynamical complexity. The authors introduce some of the key mathematical concepts in graph theory required for small-world analysis and review how these methods have been applied to quantification of cortical connectivity matrices derived from anatomical tract-tracing studies in the macaque monkey and the cat. The evolution of small-world networks is discussed in terms of a selection pressure to deliver cost-effective information-processing systems. The authors illustrate how these techniques and concepts are increasingly being applied to the analysis of human brain functional networks derived from electroencephalography/magnetoencephalography and fMRI experiments. Finally, the authors consider the relevance of small-world models for understanding the emergence of complex behaviors and the resilience of brain systems to pathological attack by disease or aberrant development. They conclude that small-world models provide a powerful and versatile approach to understanding the structure and function of human brain systems.

Animals↗