Design of delay-dependent state estimator for discrete-time recurrent neural networks with interval discrete and infinite-distributed time-varying delays

The state estimation problem for discrete-time recurrent neural networks with both interval discrete and infinite-distributed time-varying delays is studied in this paper, where interval discrete time-varying delay is in a given range. The activation functions are assumed to be globally Lipschitz continuous. A delay-dependent condition for the existence of state estimators is proposed based on new bounding techniques. Via solutions to certain linear matrix inequalities, general full-order state estimators are designed that ensure globally asymptotic stability. The significant feature is that no inequality is needed for seeking upper bounds for the inner product between two vectors, which can reduce the conservatism of the criterion by employing the new bounding techniques. Two illustrative examples are given to demonstrate the effectiveness and applicability of the proposed approach.     

Computational experience with a parallel algorithm for tetrangle inequality bound smoothing

Determining molecular structure from interatomic distances is an important and challenging problem. Given a molecule with n atoms, lower and upper bounds on interatomic distances can usually be obtained only for a small subset of the atom pairs, using NMR. Given the bounds so obtained on the distances between some of the atom pairs, it is often useful to compute tighter bounds on all the pairwise distances. This process is referred to as bound smoothing. The initial lower and upper bounds for the pairwise distances not measured are usually assumed to be 0 and ∞. One method for bound smoothing is to use the limits imposed by the triangle inequality. The distance bounds so obtained can often be tightened further by applying the tetrangle inequality—the limits imposed on the six pairwise distances among a set of four atoms (instead of three for the triangle inequalities). The tetrangle inequality is expressed by the Cayley—Menger determinants. For every quadruple of atoms, each pass of the tetrangle inequality bound smoothing procedure finds upper and lower limits on each of the six distances in the quadruple. Applying the tetrangle inequalities to each of the ( ₄ ⁿ ) quadruples requires O(n ⁴) time. Here, we propose a parallel algorithm for bound smoothing employing the tetrangle inequality. Each pass of our algorithm requires O(n ³ log n) time on a CREW PRAM (Concurrent Read Exclusive Write Parallel Random Access Machine) with processors. An implementation of this parallel algorithm on the Intel Paragon XP/S and its performance are also discussed.     

Proof of the Feldman–Karlin conjecture on the maximum number of equilibria in an evolutionary system

Feldman and Karlin conjectured that the number of isolated fixed points for deterministic models of viability selection and recombination among n possible haplotypes has an upper bound of 2ⁿ−1. Here a proof is provided. The upper bound of 3ⁿ⁻¹ obtained by Lyubich et al. (2001) using Bézout’s Theorem (1779) is reduced here to 2ⁿ through a change of representation that reduces the third-order polynomials to second order. A further reduction to 2ⁿ−1 is obtained using the homogeneous representation of the system, which yields always one solution ‘at infinity’. While the original conjecture was made for systems of selection and recombination, the results here generalize to viability selection with any arbitrary system of bi-parental transmission, which includes recombination and mutation as special cases. An example is constructed of a mutation-selection system that has 2ⁿ−1 fixed points given any n, which shows that 2ⁿ−1 is the sharpest possible upper bound that can be found for the general space of selection and transmission coefficients.     

Protective Vaccine Efficacy when Vaccine Response is Random

Vaccine induced protection against infection is often random because of primary vaccine failures and variation in the immune systems of hosts. We introduce a concept of protective vaccine efficacy in terms of mean relative susceptibility of vaccinated individuals and derive both a lower and an upper bound for it. These bounds apply for all distributions of the vaccine response and can be estimated from data on the size of a major epidemic. Standard errors are given for estimates of the bounds. Bounds are also given for the vaccination coverage required to prevent epidemics and these are also estimable from data on the size of a major epidemic. The results are applied to data on an outbreak of mumps.     

A model for the minimum cost configuration problem in flexible manufacturing systems

This paper presents a mathematical programming model to help select equipment for a flexible manufacturing system, i.e., the selection of the types and numbers of CNC machines, washing stations, load/unload stations, transportation vehicles, and pallets. The objective is to minimize equipment costs and work-in-process inventory cost, while fulfilling production requirements for an average period. Queueing aspects and part flow interactions are considered with the help of a Jacksonian-type closed queueing network model in order to evaluate the system's performance. Since the related decision problem of our model can be shown to be NP-complete, the proposed solution procedure is based on implicit enumeration. Four bounds are provided, two lower and two upper bounds. A tight lower bound is obtained by linearizing the model through the application of asymptotic bound analysis. Furthermore, asymptotic bound analysis allows the calculation of a lower bound for the number of pallets in the system. The first upper bound is given by the best feasible solution and the second is based on the anti-starshaped form of the throughput function.     

Minimizing total flow time on a single flexible machine

In this study, we address a job sequencing and tool switching problem arising in flexible manufacturing systems. We consider the single machine problem of minimizing total flow time. We prove that the problem is NP-hard in the strong sense and show that the tool switching problem is polynomially solvable for a given sequence. We propose a branch-and-bound algorithm whose efficiency is improved by precedence relations and several lower and upper bounding techniques. Our computational results reveal that the branch and bound approach produces optimal solutions in reasonable times for moderate sized problems. Our upper bounds produce very satisfactory solutions; therefore they can be an attractive alternative to solve larger sized problems.     

The strike rate index: a new index for journal quality based on journal size and the h-index of citations

Quantifying the impact of scientific research is almost always controversial, and there is a need for a uniform method that can be applied across all fields. Increasingly, however, the quantification has been summed up in the impact factor of the journal in which the work is published, which is known to show differences between fields. Here the h-index, a way to summarize an individual's highly cited work, was calculated for journals over a twenty year time span and compared to the size of the journal in four fields, Agriculture, Condensed Matter Physics, Genetics and Heredity and Mathematical Physics. There is a linear log-log relationship between the h-index and the size of the journal: the larger the journal, the more likely it is to have a high h-index. The four fields cannot be separated from each other suggesting that this relationship applies to all fields. A strike rate index (SRI) based on the log relationship of the h-index and the size of the journal shows a similar distribution in the four fields, with similar thresholds for quality, allowing journals across diverse fields to be compared to each other. The SRI explains more than four times the variation in citation counts compared to the impact factor.     

Nearest Neighbor Classification Rule for Mixtures of Discrete and Continuous Random Variables

In this paper very simple nonparametric classification rule for mixtures of discrete and continuous random variables is described. It is based on the method of nearest neighbor proposed by Cover and Hart (1967). The bounds on the limit of the nearest neighbor rule risks are given. Both lower and upper bound depend on the Bayes risk and the loss function. Finally the method is compared with other existing methods on some practical data set.     

Mining Pure,Strict Epistatic Interactions from High-Dimensional Datasets: Ameliorating the Curse of Dimensionality

Background

The interaction between loci to affect phenotype is called epistasis. It is strict epistasis if no proper subset of the interacting loci exhibits a marginal effect. For many diseases, it is likely that unknown epistatic interactions affect disease susceptibility. A difficulty when mining epistatic interactions from high-dimensional datasets concerns the curse of dimensionality. There are too many combinations of SNPs to perform an exhaustive search. A method that could locate strict epistasis without an exhaustive search can be considered the brass ring of methods for analyzing high-dimensional datasets.

Methodology/Findings

A SNP pattern is a Bayesian network representing SNP-disease relationships. The Bayesian score for a SNP pattern is the probability of the data given the pattern, and has been used to learn SNP patterns. We identified a bound for the score of a SNP pattern. The bound provides an upper limit on the Bayesian score of any pattern that could be obtained by expanding a given pattern. We felt that the bound might enable the data to say something about the promise of expanding a 1-SNP pattern even when there are no marginal effects. We tested the bound using simulated datasets and semi-synthetic high-dimensional datasets obtained from GWAS datasets. We found that the bound was able to dramatically reduce the search time for strict epistasis. Using an Alzheimer''s dataset, we showed that it is possible to discover an interaction involving the APOE gene based on its score because of its large marginal effect, but that the bound is most effective at discovering interactions without marginal effects.

Conclusions/Significance

We conclude that the bound appears to ameliorate the curse of dimensionality in high-dimensional datasets. This is a very consequential result and could be pivotal in our efforts to reveal the dark matter of genetic disease risk from high-dimensional datasets.     

PubFocus: semantic MEDLINE/PubMed citations analytics through integration of controlled biomedical dictionaries and ranking algorithm

Background  

Understanding research activity within any given biomedical field is important. Search outputs generated by MEDLINE/PubMed are not well classified and require lengthy manual citation analysis. Automation of citation analytics can be very useful and timesaving for both novices and experts.     

The Pagerank-Index: Going beyond Citation Counts in Quantifying Scientific Impact of Researchers

Quantifying and comparing the scientific output of researchers has become critical for governments, funding agencies and universities. Comparison by reputation and direct assessment of contributions to the field is no longer possible, as the number of scientists increases and traditional definitions about scientific fields become blurred. The h-index is often used for comparing scientists, but has several well-documented shortcomings. In this paper, we introduce a new index for measuring and comparing the publication records of scientists: the pagerank-index (symbolised as π). The index uses a version of pagerank algorithm and the citation networks of papers in its computation, and is fundamentally different from the existing variants of h-index because it considers not only the number of citations but also the actual impact of each citation. We adapt two approaches to demonstrate the utility of the new index. Firstly, we use a simulation model of a community of authors, whereby we create various ‘groups’ of authors which are different from each other in inherent publication habits, to show that the pagerank-index is fairer than the existing indices in three distinct scenarios: (i) when authors try to ‘massage’ their index by publishing papers in low-quality outlets primarily to self-cite other papers (ii) when authors collaborate in large groups in order to obtain more authorships (iii) when authors spend most of their time in producing genuine but low quality publications that would massage their index. Secondly, we undertake two real world case studies: (i) the evolving author community of quantum game theory, as defined by Google Scholar (ii) a snapshot of the high energy physics (HEP) theory research community in arXiv. In both case studies, we find that the list of top authors vary very significantly when h-index and pagerank-index are used for comparison. We show that in both cases, authors who have collaborated in large groups and/or published less impactful papers tend to be comparatively favoured by the h-index, whereas the pagerank-index highlights authors who have made a relatively small number of definitive contributions, or written papers which served to highlight the link between diverse disciplines, or typically worked in smaller groups. Thus, we argue that the pagerank-index is an inherently fairer and more nuanced metric to quantify the publication records of scientists compared to existing measures.     

Sensitivity of vertebral compressive strength to endplate loading distribution

The sensitivity of vertebral body strength to the distribution of axial forces along the endplate has not been comprehensively evaluated. Using quantitative computed tomography-based finite element models of 13 vertebral bodies, an optimization analysis was performed to determine the endplate force distributions that minimized (lower bound) and maximized (upper bound) vertebral strength for a given set of externally applied axial compressive loads. Vertebral strength was also evaluated for three generic boundary conditions: uniform displacement, uniform force, and a nonuniform force distribution in which the interior of the endplate was loaded with a force that was 1.5 times greater than the periphery. Our results showed that the relative difference between the upper and lower bounds on vertebral strength was 14.2 +/- 7.0% (mean +/- SD). While there was a weak trend for the magnitude of the strength bounds to be inversely proportional to bone mineral density (R2 = 0.32, p = 0.02), both upper and lower bound vertebral strength measures were well predicted by the strength response under uniform displacement loading conditions (R2 = 0.91 and R2 = 0.99, respectively). All three generic boundary conditions resulted in vertebral strength values that were statistically indistinguishable from the loading condition that resulted in an upper bound on strength. The results of this study indicate that the uncertainty in strength arising from the unknown condition of the disc is dependent on the condition of the bone (whether it is osteoporotic or normal). Although bone mineral density is not a good predictor of strength sensitivity, vertebral strength under generic boundary conditions, i.e., uniform displacement or force, was strongly correlated with the relative magnitude of the strength bounds. Thus, explicit disc modeling may not be necessary.     

Expected waiting time for the visual response

Let the light-quanta be absorbed in the retina according to a Poisson process. The present paper derives bounds for the expected waiting time for an occurence of a visual response. These bounds can serve as control limits for a proposed coincidence threshold. An upper bound for the probability that a visual response has not occured in (O,t) is derived and is used to obtain an upper bound for the mean visual threshold.     

Algorithms to distinguish the role of gene-conversion from single-crossover recombination in the derivation of SNP sequences in populations.

Meiotic recombination is a fundamental biological event and one of the principal evolutionary forces responsible for shaping genetic variation within species. In addition to its fundamental role, recombination is central to several critical applied problems. The most important example is "association mapping" in populations, which is widely hoped to help find genes that influence genetic diseases (Carlson et al., 2004; Clark, 2003). Hence, a great deal of recent attention has focused on problems of inferring the historical derivation of sequences in populations when both mutations and recombinations have occurred. In the algorithms literature, most of that recent work has been directed to single-crossover recombination. However, gene-conversion is an important, and more common, form of (two-crossover) recombination which has been much less investigated in the algorithms literature. In this paper, we explicitly incorporate gene-conversion into discrete methods to study historical recombination. We are concerned with algorithms for identifying and locating the extent of historical crossing-over and gene-conversion (along with single-nucleotide mutation), and problems of constructing full putative histories of those events. The novel technical issues concern the incorporation of gene-conversion into recently developed discrete methods (Myers and Griffiths, 2003; Song et al., 2005) that compute lower and upper-bound information on the amount of needed recombination without gene-conversion. We first examine the most natural extension of the lower bound methods from Myers and Griffiths (2003), showing that the extension can be computed efficiently, but that this extension can only yield weak lower bounds. We then develop additional ideas that lead to higher lower bounds, and show how to solve, via integer-linear programming, a more biologically realistic version of the lower bound problem. We also show how to compute effective upper bounds on the number of needed single-crossovers and gene-conversions, along with explicit networks showing a putative history of mutations, single-crossovers and gene-conversions. Both lower and upper bound methods can handle data with missing entries, and the upper bound method can be used to infer missing entries with high accuracy. We validate the significance of these methods by showing that they can be effectively used to distinguish simulation-derived sequences generated without gene-conversion from sequences that were generated with gene-conversion. We apply the methods to recently studied sequences of Arabidopsis thaliana, identifying many more regions in the sequences than were previously identified (Plagnol et al., 2006), where gene-conversion may have played a significant role. Demonstration software is available at www.csif.cs.ucdavis.edu/~gusfield.     

Body size and abundance of benthic animals in Mirror Lake, New Hampshire

1. There is a strong negative correlation between body mass and population density for 192 species from the zoobenthos of Mirror Lake, a small, oligotrophic lake. This correlation spans seven—nine orders of magnitude in body mass. 2. The slopes of both the regression and the upper bound on the distribution of data points are significantly shallower than -0.75, the slope that has been suggested to imply that metabolic constraints limit animal abundance. 3. The regressions for individual taxonomic groups (i.e. classes, phyla) do not conform closely to the overall regression line. 4. It is suggested that metabolic constraints on community structure need not be expressed by a slope of -0.75 for regressions (or upper bounds) on body mass—abundance functions.     

Measures and limits of models of fixation selection

Models of fixation selection are a central tool in the quest to understand how the human mind selects relevant information. Using this tool in the evaluation of competing claims often requires comparing different models' relative performance in predicting eye movements. However, studies use a wide variety of performance measures with markedly different properties, which makes a comparison difficult. We make three main contributions to this line of research: First we argue for a set of desirable properties, review commonly used measures, and conclude that no single measure unites all desirable properties. However the area under the ROC curve (a classification measure) and the KL-divergence (a distance measure of probability distributions) combine many desirable properties and allow a meaningful comparison of critical model performance. We give an analytical proof of the linearity of the ROC measure with respect to averaging over subjects and demonstrate an appropriate correction of entropy-based measures like KL-divergence for small sample sizes in the context of eye-tracking data. Second, we provide a lower bound and an upper bound of these measures, based on image-independent properties of fixation data and between subject consistency respectively. Based on these bounds it is possible to give a reference frame to judge the predictive power of a model of fixation selection. We provide open-source python code to compute the reference frame. Third, we show that the upper, between subject consistency bound holds only for models that predict averages of subject populations. Departing from this we show that incorporating subject-specific viewing behavior can generate predictions which surpass that upper bound. Taken together, these findings lay out the required information that allow a well-founded judgment of the quality of any model of fixation selection and should therefore be reported when a new model is introduced.     

Designs for restricted exploration in mixture experiments

Extreme Vertices designs were developed by MCLEAN and ANDERSON (1966) for situations where components of a mixture are restricted by lower and upper bounds, SNEE and MARQUARDT (1974) and SNEE (1975) gave algorithms to construct optimum designs in these situations. SAXENA and NIGAM (1975) evolved a transformation which provides designs for restricted exploration using Symmetric Simplex designs. In this paper a procedure has been given which provides alternative designs with uniform exploration in constrained mixture experiments. The procedure is illustrated by an example.     

Upper and lower bounds from the maximum principle. Intracellular diffusion with Michaelis-Menten kinetics

Analytical bounding functions for diffusion problems with Michaelis-Menten kinetics were recently presented by Anderson and Arthurs, 1985 (Bull. math. Biol. 47, 145–153). Their methods, successful to some extent for a small range of parameters, has the disadvantage of providing a weak upper bound. The optimal approach for the use of one-line bounding kinetics is presented. The use of two-line bounding kinetics is also shown, in order to give, sufficient accuracy in those cases where the one-line approach does not provide satisfactory results. The bounding functions provide excellent upper and lower bounds on the true solution for the entire range of kinetic and transport parameters.     

A composite micromechanical model for connective tissues: Part II--Application to rat tail tendon and joint capsule.

A micromechanical model of fibrous soft tissue has been developed which predicts upper and lower bounds on mechanical properties based on the structure and properties of tissue components by Ault and Hoffman [3, 4]. In this paper, two types of biological tissue are modeled and the results compared to experimental test data. The highly organized structure of rat tail tendon is modeled using the upper bound aggregation rule which predicts uniform strain behavior in the composite material. This model fits the experimental data and results in a correlation coefficient of 0.98. Applied to cat knee joint capsule, the lower bound aggregation rule of the model correlates with the data and predicts uniform stress within this more loosely organized tissue structure. These studies show that the nature of the interactions between the components in tissue differs depending upon its structure and that the biomechanical model is capable of analyzing such differences in structure.