Search PubMed⌕ Search

SEARCH · Search PubMed

Results for “Mathematical Computing”

Search indexed PubMed citations on genomics, clinical trials, systematic reviews and public health. Explore titles, authors and supplied subject terms, then open the PubMed record.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 1,729 records · Page 96Linked to original sources

Search for organising principles: understanding in systems biology.

Due in large measure to the explosive progress in molecular biology, biology has become arguably the most exciting scientific field. The first half of the 21st century is sometimes referred to as the 'era of biology', analogous to the first half of the 20th century, which was considered to be the 'era of physics'. Yet, biology is facing a crisis--or is it an opportunity--reminiscent of the state of biology in pre-double-helix time. The principal challenge facing systems biology is complexity. According to Hood, 'Systems biology defines and analyses the interrelationships of all of the elements in a functioning system in order to understand how the system works.' With 30000+ genes in the human genome the study of all relationships simultaneously becomes a formidably complex problem. Hanahan and Weinberg raised the question as to whether progress will consist of 'adding further layers of complexity to a scientific literature that is already complex almost beyond measure' or whether the progress will lead to a 'science with a conceptual structure and logical coherence that rivals that of chemistry or physics.' At the core of the challenge is the need for a new approach, a shift from reductionism to a holistic perspective. However, more than just a pronouncement of a new approach is needed. We suggest that what is needed is to provide a conceptual framework for systems biology research. We propose that the concept of a complex system, i.e. a system of systems as defined in mathematical general systems theory (MGST), is central to provide such a framework. We further argue that for a deeper understanding in systems biology investigations should go beyond building numerical mathematical or computer models--important as they are. Biological phenomena cannot be predicted with the level of numerical precision as in classical physics. Explanations in terms of how the categories of systems are organised to function in ever changing conditions are more revealing. Non-numerical mathematical tools are appropriate for the task. Such a categorical perspective led us to propose that the core of understanding in systems biology depends on the search for organising principles rather than solely on construction of predictive descriptions (i.e. models) that exactly outline the evolution of systems in space and time. The search for organising principles requires an identification/discovery of new concepts and hypotheses. Some of them, such as coordination motifs for transcriptional regulatory networks and bounded autonomy of levccels in a hierarchy, are outlined in this article. Experimental designs are outlined to help verify the applicability of the interaction balance principle of coordination to transcriptional and posttranscriptional networks.

Cell Physiological Phenomena↗

Studies of reproductive cyclicity: evaluation of computer modeling as a tool.

Assessment of toxic effects on human reproductive function using fetal health or teratogenic criteria presumes the conditions of parental fertility. Toxins that compromise fecundity through derangement of the menstrual cycle may require quite different models and criteria. Nonlinear dynamic interactions of the hormonal and morphological components of the menstrual cycle add to the difficulty of such studies. With appropriate mathematical models, computer simulation can provide a useful guide to the design and conduct of in vivo experiment.

Computer Simulation↗

The effect of overabundant projection directions on 3D reconstruction algorithms.

The experimental process of collecting images from macromolecules in an electron microscope is such that it does not allow for prior specification of the angular distribution of the projection images. As a consequence, an uneven distribution of projection directions may occur. Concerns have been raised recently about the behavior of 3D reconstruction algorithms for the case of unevenly distributed projections. It has been illustrated on experimental data that in the case of a heavily uneven distribution of projection directions some algorithms tend to elongate the reconstructed volumes along the overloaded direction so much as to make a quantitative biological analysis impossible. In answer to these concerns we have developed a strategy for quantitative comparison and optimization of 3D reconstruction algorithms. We apply this strategy to quantitatively analyze algebraic reconstruction techniques (ART) with blobs, simultaneous iterative reconstruction techniques (SIRT) with voxels, and weighted backprojection (WBP). We show that the elongation artifacts that had been previously reported can be strongly reduced. With our specific choices for the free parameters of the three algorithms, WBP reconstructions tend to be inferior to those obtained with either SIRT or ART and the results obtained with ART are comparable to those with SIRT, but at a very small fraction of the computational cost of SIRT.

Algorithms↗

Estimation of average number of nucleotide substitutions when the rate of substitution varies with nucleotide.

A formal mathematical analysis of Kimura's (1981) six-parameter model of nucleotide substitution for the case of unequal substitution rates among different pairs of nucleotides is conducted, a new formulae for estimating the number of nucleotide substitutions and its standard error are obtained. By using computer simulation, the validities and utilities of Jukes and Cantor's (1969) one-parameter formula, Takahata and Kimura's (1981) four-parameter formula, and our six-parameter formula for estimating the number of nucleotide substitutions are examined under three different schemes of nucleotide substitution. It is shown that the one-parameter and four-parameter formulae often give underestimates when the number of nucleotide substitutions is large, whereas the six-parameter formula generally gives a good estimate for all the three substitution schemes examined. However, when the number of nucleotide substitutions is large, the six-parameter and four-parameter formulae are often inapplicable unless the number of nucleotides compared is extremely large. It is also shown that as long as the mean number of nucleotide substitutions is smaller than one per nucleotide site the three formulae give more or less the same estimate regardless of the substitution scheme used.

Base Sequence↗

CANEST: a microcomputer program for estimating cancer in a cohort.

Certain diseases and symptoms carry an overrepresentation of cancer. To be able to measure the strength of such an association it is necessary to be able to predict cancer development in the group being observed. A computer program for computers running under the MS DOS operating system has been developed for this purpose. The program is written in the CLIPPER programming language. The estimates are based on incidence and prevalence data from the Swedish Cancer Registry for the years 1958 to 1986. The program also computes confidence intervals based on the Poisson distribution. The results can be printed out or exported to other programs for further analysis.

Cohort Studies↗

Detecting faking on the Rorschach: computer versus expert clinical judgment.

In a previous study of the ability of expert Rorschach interpreters to detect faking that used true and malingered protocols, the experts faired very poorly. In this study, 50% of these same protocols were scored by the Exner system and analyzed by Exner's Semantic Computer Interpretation program. The program indicated invalidity of protocols only on the basis of low R and designated the faked protocols high on psychotic descriptors, barely indicating psychosis for the true schizophrenic protocols. Unlike the judges, however, the computer gave no psychotic designation to the normal protocols. The scoring-computer analysis method was as susceptible to faking as were the clinical judgments.

Adolescent↗

Age-related reference regions for longitudinal measurements of growth characteristics.

Most studies on age-related reference centiles published up to now have adopted a strictly cross-sectional perspective. Clearly, the results of studies of that type do not provide a tool for the diagnostic assessment of whole series of measurements taken sequentially over time in the same individual. In this paper, the approach of Wellek & Merz (1995) to the construction of age-dependent reference ranges for cross-sectional measurements is generalized in such a way that data sets containing time series of arbitrary length varying between subjects can be accommodated. Since repeated measurements on the same subject are typically correlated, the regression function to be used as the central line for the reference band eventually obtained is determined by fitting a nonlinear mixed model describing the dependence of conditional means on age by growth functions of the same class we proposed in the case of cross-sectional data. Estimation of the parameters of this mixed model is done in a way closely related to the population-averaged GEE approach by Zeger et al. (1988). Given the regression line, the reference band is constructed by means of an iterative procedure guaranteeing that the proportion of observed profiles which nowhere leave the band, has some prespecified value (frequently set equal to 90% in practice). The approach is illustrated with two examples taken from child psychiatry and prenatal sonography.

Adolescent↗

Informatics and public health at CDC.

Since CDC acquired its first mainframe computer in 1964, the use of information technology in public health practice has grown steadily and, during the past 2 decades, dramatically. Public health informatics (PHI) arrived on the scene during the 1990s after medical informatics (intersecting information technology, medicine, and health care) and bioinformatics (intersecting mathematics, statistics, computer science, and molecular biology). Similarly, PHI merged the disciplines of information science and computer science to public health practice, research, and learning. Using strategies and standards, practitioners employ PHI tools and training to maximize health impacts at local, state, and national levels. They develop and deploy information technology solutions that provide accurate, timely, and secure information to guide public health action.

Centers for Disease Control and Prevention, U.S.↗

Polyploidy Arithmetic.

Polyploidy occurs in plants and animals, and is an important force in speciation and genome evolution. The main focus of this paper is the following fundamental question that was recently posed by Huber and Maher: Given the ploidy numbers of a collection of extant species, or their ploidy profile, what is the smallest number of hybridizations needed in any evolutionary history for these species to completely represent these numbers? In this paper, we shall show that this question can be rephrased in terms of addition chains and the closely related addition sequences, which have been studied for over a century in mathematics and computer science. These are sequences of natural numbers that start with 1, so that each number in the sequence larger than 1 is the sum of two other numbers arising earlier in the sequence. In our first main result, we show that finding the smallest number of hybridization events to explain a ploidy profile, or the hybrid number, is equivalent to solving the so-called addition sequence problem. This immediately implies that computing the hybridization number is computationally intractable. Even so, it also leads to new connections to representing polyploid evolution using networks. More specifically, in our second main result we show that ploidy profiles representable by tree-child networks are exactly the addition chains, implying a polynomial-time algorithm for identifying these profiles. We then consider beaded tree-child networks, which permit the representation of autopolyploidy events, and in our third main result we provide a greedy polynomial-time algorithm to decide whether a given profile can be realized by such a network. We expect that our results can be leveraged in future work through, for example, making use of known algorithms for computing short addition sequences to give bounds for the hybrid number, and in guiding network reconstruction for polyploid species.

Polyploidy↗

A three-dimensional kinematic and dynamic model of the lower limb.

A model describing the kinematics and dynamics of the lower limb is presented. The lower limb is modeled as a sequence of four rigid links connected by three universal rotary joints representing the hip, knee and ankle joints. Each joint is modeled as a sequence of three single axis rotational joints thus ascribing to the lower limb a total of 12 degrees of freedom. A method is described to measure the gait variables so that all nine angles can be computed based on the positions of nine markers placed on the subject during a gait study. The gait variables are then used in an iterative Newton-Euler formulation to compute the moments exerted about the axes of each joint during gait.

Adult↗

MULCOX2: a general computer program for the Cox regression analysis of multivariate failure time data.

Multivariate failure time data is commonly encountered in biomedicine, because each study subject may experience multiple events or because there exists clustering of subjects such that failure times within the same cluster are correlated. MULCOX2 implements a general statistical methodology for analyzing such data. This approach formulates the marginal distributions of multivariate failure times by Cox proportional hazards models without specifying the nature of dependence among related failure times. The baseline hazard functions for the marginal models may be identical or different. A variety of statistical inference can be made regarding the effects of (possibly time-dependent) covariates on the failure rates. Although designed primarily for the marginal approach, MULCOX2 is general enough to implement several alternative methods. The program runs on any computer with a FORTRAN compiler. The running time is minimal. Two illustrative examples are provided.

Age Factors↗

DLW: a computer program for the calculation of total energy expenditure in doubly labeled water (2H218O) studies.

The double labeled water technique for determination of the rate of total energy expenditure in human subjects is based on measurement of the differential rates of disappearance of 2H and 18O from body water following oral administration of 2H218O. Two calculation procedures, the "two-point" and "slope-intercept" methods of calculation have previously been validated for use in humans. We describe here a computer program. DLW, that provides options to calculate doubly labeled water data in each of these accepted ways.

Adult↗

Comparing several proportions when the exposure variable is either ordinal or ratio which has been grouped into discrete classes.

The 2-by-C chi 2 test is used for comparing the proportion of "positives" of a binomial response variable among the C levels of an exposure variable. There are actually several versions of the chi 2 test that are fundamentally different, and each is meaningful only for a particular measurement scale of the exposure variable. The ordinary chi-square, which is often used indiscriminately for comparing proportions, is in fact only valid for nominal exposure variable, the chi 2 test for trend is meaningful only for ordinal exposure variable, and the regression-like chi 2 is suitable only for ratio exposure variable which has been grouped into a few discrete classes. Two SAS programs (PC SAS Release 6.04) to carry out the 2-by-C chi 2 test, one for ordinal exposure and the other for discretized-ratio exposure, were described. In addition to the chi 2 test, the programs also compute the exact probability confidence interval of the proportion for each exposure level. Numeric examples were used to illustrate the application of the programs.

Chi-Square Distribution↗

A computer program for regression analysis of ordered categorical repeated measurements.

RMORD is an easy-to-use FORTRAN program for the analysis of clustered ordinal data using the method of Stram, Wei, and Ware. This method constitutes an extension of the proportional-odds model to the situation in which groups of responses are correlated. At each measurement occasion, a proportional-odds regression model is fit to the data by maximizing the occasion-specific likelihood function. The joint asymptotic distribution of the occasion-specific regression parameter estimators is obtained along with a consistent estimator of their asymptotic covariance matrix. RMORD may be used when ordinal measurements are obtained at a common set of observation times for multiple subjects or clusters. Both missing data and covariates which vary within clusters can be accommodated. The program can be run on microcomputers, workstations, and mainframe computers. Two examples illustrating the usage and features of RMORD are provided.

Age Distribution↗

Impossibility of deleting an unknown quantum state

A photon in an arbitrary polarization state cannot be cloned perfectly. But suppose that at our disposal we have several copies of a photon in an unknown state. Is it possible to delete the information content of one or more of these photons by a physical process? Specifically, if two photons are in the same initial polarization state, is there a mechanism that produces one photon in the same initial state and the other in some standard polarization state? If this could be done, then one would create a standard blank state onto which one could copy an unknown state approximately, by deterministic cloning or exactly, by probabilistic cloning. This could in principle be useful in quantum computation, where one could store new information in an already computed state by deleting the old information. Here we show, however, that the linearity of quantum theory does not allow us to delete a copy of an arbitrary quantum state perfectly. Though in a classical computer information can be deleted (reversibly) against a copy, the analogous task cannot be accomplished, even irreversibly, with quantum information.

Journal Article↗

General-purpose computation with neural networks: a survey of complexity theoretic results.

We survey and summarize the literature on the computational aspects of neural network models by presenting a detailed taxonomy of the various models according to their complexity theoretic characteristics. The criteria of classification include the architecture of the network (feedforward versus recurrent), time model (discrete versus continuous), state type (binary versus analog), weight constraints (symmetric versus asymmetric), network size (finite nets versus infinite families), and computation type (deterministic versus probabilistic), among others. The underlying results concerning the computational power and complexity issues of perceptron, radial basis function, winner-take-all, and spiking neural networks are briefly surveyed, with pointers to the relevant literature. In our survey, we focus mainly on the digital computation whose inputs and outputs are binary in nature, although their values are quite often encoded as analog neuron states. We omit the important learning issues.

Algorithms↗

Assessment of apical root resorption using digital reconstruction.

OBJECTIVES: To assess the in vitro and in vivo accuracy of a mathematical computer-based reconstruction of two images that are not taken with the same recording geometry for the measurement of apical root resorption following orthodontic treatment. METHODS: A gold standard for root resorption in vitro was developed from 10 extracted upper central incisors using calipers. Radiographs made with five different projection angles were reconstructed mathematically by two observers. The calculated loss of length was compared with the gold standard. Eighty-two upper central incisors from 61 patients were radiographically evaluated for the prevalence and degree of apical root resorption after orthodontic fixed appliance therapy. The relative amount of reduction was calculated after mathematical reconstruction. RESULTS: The inter-observer error in vitro was 1.8%. The 95% confidence intervals for the difference with the gold standard are small. The duplicate measurement in vivo error was 2.2% and the correlation between duplicate measurements was 0.94. The mean loss of tooth length was 7.8% (s.d. 6.9). CONCLUSIONS: The prevalence of root resorption corresponds well with that in the literature. Digital reconstruction is a reliable method to correct for different projection angles and to monitor the effects of orthodontic movement in serial dental radiographs.

Confidence Intervals↗