Mathematics

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Viral respiratory tract diseases pose serious public health problems. Our ability to predict and thus, be able to prepare for outbreaks is strained by the complex factors driving the prevalence and severity of these diseases. The abundance of diseases and transmission dynamics of strains are not only affected by external factors, such as weather, but also driven by interactions among viruses mediated by human behavior and immunity. To untangle the complex out-ofphase annual and biennial pattern of three common paramyxoviruses, Respiratory Syncytial Virus (RSV), Human Parainfluenza Virus (HPIV), and Human Metapneumovirus (hMPV), we adopt a theoretical approach that integrates ecological and immunological mechanisms of disease interactions. By estimating parameters from multiyear time series of laboratory-confirmed cases from the intermountain west region of the United States and using statistical inference, we show that models of immune-mediated interactions better explain the data than those based on ecological competition by convalescence. The strength of cross-protective immunity among viruses is correlated with their genetic distance in the phylogenetic tree of the paramyxovirus family. © 2015 PNAS.

(SoNS) School of Natural Sciences

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Proceedings of the National Academy of Sciences of the United States of America

Cross-immunity between strains explains the dynamical pattern of paramyxoviruses

In this paper we characterize for 0 &lt; p ≤ ∞, the closed subspaces of Hp that are invariant under multiplication by all powers of a finite Blaschke factor B, except the first power. Our result clearly generalizes the invariant subspace theorem obtained by Paulsen and Singh [18] which has proved to be the starting point of important work on constrained Nevanlinna- Pick interpolation. Our method of proof can also be readily adapted to the case where the subspace is invariant under all positive powers of B (z) : The two results are in the mould of the classical Lax-Halmos Theorem and can be said to be Lax-Halmos type results in the finite multiplicity case for two commuting shifts and for a single shift respectively. © 2015 University of Houston.

Houston Journal of Mathematics

Lax-Halmos type theorems on Hp spaces

Malaria a global pandemic has engulfed nearly 0.63 million people globally. It is high time that a cure for malaria is required to stop its ever increasing menace. Our commentary discusses the advent and contribution of genetic algorithm (GA) in the drug discovery efforts towards developing cure for malaria. GAs are computational models of Darwinian evolution, ideally capture and mimic the principles of genetic variation and natural selection to evolve good solutions through multiple iterations on the space of all possible candidate solutions, called the search space, to a given optimization problem. Herein we will discuss the applications, advantages, disadvantages and future directions of GA with respect to malaria. © 2015, Springer Science+Business Media Dordrecht.

Chemistry

Systems and Synthetic Biology

Innovative techniques to discover novel antimalarials

We obtain a necessary and sufficient condition for a matrix A to be Birkhoff-James orthogonal to any subspace W of Mn(C). Using this we obtain an expression for the distance of A from any unital C*- subalgebra of Mn(C). © 2013 Elsevier Inc. All rights reserved.

Linear Algebra and Its Applications

Orthogonality to matrix subspaces, and a distance formula

Preclinical Research In this overview, we examine recent developments in network approaches to drug design. A brief overview of networks is followed by a discussion of how chemical similarity networks and their properties address challenges in drug design. Multiple methods used to assess or enhance chemical diversity for early-stage drug discovery are discussed, as well as methods that can be used for drug repositioning and ligand polypharmacology. © 2014 Wiley Periodicals, Inc.

Drug Development Research

Network measures for chemical library design

The traditional frameworks for fuzzy linear optimization problems are inspired by the max-min model proposed by Zimmermann using the Bellman-Zadeh extension principle to aggregate all the fuzzy sets representing flexible (fuzzy) constraints and objective functions together. In this paper, we propose an alternative approach to model fuzzy multi-objective linear programming problems (FMOLPPs) from a perspective of bipolar view in preference modeling. Bipolarity allows us to distinguish between the negative and the positive preferences. Negative preferences denote what is unacceptable while positive preferences are less restrictive and express what is desirable. This framework facilitate a natural fusion of bipolarity in FMOLPPs. The flexible constraints in a fuzzy multi-objective linear programming problem (FMOLPP) are viewed as negative preferences for describing what is somewhat tolerable while the objective functions of the problem are viewed as positive preferences for depicting satisfaction to what is desirable. This approach enables us to handle fuzzy sets representing constraints and objective functions separately and combine them in distinct ways. After aggregating these fuzzy sets separately, coherence (or consistency) condition is used to define the fuzzy decision set. © 2013 Elsevier B.V.

Fuzzy Sets and Systems

A bipolar approach in fuzzy multi-objective linear programming

The application of computational tools can alleviate the challenges (viz. time consumption and cost intensiveness) in drug design. Metaheuristics, a collection of such diverse computational and mathematical tools, whose first application was dated back to the early 1970s, caters to several expectations of rational drug designing. Among the population-based metaheuristics, genetic algorithms most closely mimic natural selection. As a consequence, they are rapidly garnering popularity over other members of evolutionary computation as the most preferred simulation processes for drug trials and designing. This chapter discusses various applications of genetic algorithms in drug design, from designing a combinatorial library, QSAR/QSPR study, and designing lead candidacy in drug discovery to solutions for genetic disease. Genetic algorithms find their place in all. © 2014 Springer International Publishing Switzerland. All rights reserved.

Applications of Metaheuristics in Process Engineering

Genetic algorithms in drug design: A not-so-old story in a newer bottle

Models of biochemical networks are frequently complex and high-dimensional. Reduction methods that preserve important dynamical properties are therefore essential for their study. Interactions in biochemical networks are frequently modeled using Hill functions (xn/Jn+xn). Reduced ODEs and Boolean approximations of such model networks have been studied extensively when the exponent n is large. However, while the case of small constant J EquationSource&gt; appears in practice, it is not well understood. We provide a mathematical analysis of this limit and show that a reduction to a set of piecewise linear ODEs and Boolean networks can be mathematically justified. The piecewise linear systems have closed-form solutions that closely track those of the fully nonlinear model. The simpler, Boolean network can be used to study the qualitative behavior of the original system. We justify the reduction using geometric singular perturbation theory and compact convergence, and illustrate the results in network models of a toggle switch and an oscillator. © 2014, Society for Mathematical Biology.

Bulletin of Mathematical Biology

Piecewise Linear and Boolean Models of Chemical Reaction Networks

Purpose. Large copy number variations (CNV) can contribute to increased burden for neurodegenerative diseases. In this study, we analyzed the genome-wide burden of large CNVs &gt; 100 kb in primary open angle glaucoma (POAG), a neurodegenerative disease of the eye that is the largest cause of irreversible blindness. Methods. Genome-wide analysis of CNVs &gt; 100 kb were analyzed in a total of 1720 individuals, including an Indian cohort (347 POAG cases and 345 controls) and a Caucasian cohort (624 cases and 404 controls). All the CNV data were obtained from experiments performed on Illumina 660W-Quad (infinium) arrays. Results. We observed that for both the populations CNVs &gt; 1 Mb was significantly enriched for gene-rich regions unique to the POAG cases (P &lt; 10-11). In the Indian cohort CNVs &gt; 1 Mb (39 calls) in patients influenced 125 genes while in controls 31 such CNVs influenced only 5 genes with no overlap. In both cohorts we observed 1.9-fold gene enrichment in patients for deletions compared to duplications, while such a bias was not observed in controls (0.3-fold). Overall duplications &gt; 1 Mb were more than deletions (Del/Dup = 0.82) confirming that the enrichment of gene-rich deletions in patients was associated with the disease. Of the 39 CNVs &gt; 1 Mb from Indian patients, 28 (72\%) also were implicated in other neurodegenerative disorders, like autism, schizophrenia, sensorineural hearing loss, and so forth. We found one large duplication encompassing CNTN4 gene in Indian and Caucasian POAG patients that was absent in the controls. Conclusions. To our knowledge, our study is the first report on large CNV bias for gene-rich regions in glaucomatous neurodegeneration, implicating its impact across populations of contrasting ethnicities. We identified CNTN4 as a novel candidate gene for POAG. © 2014 The Association for Research in Vision and Ophthalmology, Inc.

Investigative Ophthalmology and Visual Science

Gene-rich large deletions are overrepresented in POAG patients of Indian and Caucasian origins

In the recent and important context of Nevanlinna-Pick interpolation theory for classes of holomorphic functions with constraints, see [4],[5], and [14], the starting point has been to describe the common invariant subspaces of the operators of multiplication by S2 and S3 on the Hardy classes. In the same spirit this paper offers as a new result the charcterization of the common invariant subspaces of S2 and S3 on the space BMOA. In addition we present a new, elementary and short proof of the invariant subspace characterization of the operator S on BMOA and use this to give a new proof of the invariant subspace characterization of the backward shift on the Hardy space H1 that is also short and elementary. © 2014 University of Houston.