Numerical Integration of the Master Equation in Some Models of Stochastic Epidemiology

The processes by which disease spreads in a population of individuals are inherently stochastic. The master equation has proven to be a useful tool for modeling such processes. Unfortunately, solving the master equation analytically is possible only in limited cases (e.g., when the model is linear), and thus numerical procedures or approximation methods must be employed. Available approximation methods, such as the system size expansion method of van Kampen, may fail to provide reliable solutions, whereas current numerical approaches can induce appreciable computational cost. In this paper, we propose a new numerical technique for solving the master equation. Our method is based on a more informative stochastic process than the population process commonly used in the literature. By exploiting the structure of the master equation governing this process, we develop a novel technique for calculating the exact solution of the master equation – up to a desired precision – in certain models of stochastic epidemiology. We demonstrate the potential of our method by solving the master equation associated with the stochastic SIR epidemic model. MATLAB software that implements the methods discussed in this paper is freely available as Supporting Information S1

Do Twin Boundaries Always Strengthen Metal Nanowires?

It has been widely reported that twin boundaries strengthen nanowires regardless of their morphology—that is, the strength of nanowires goes up as twin spacing goes down. This article shows that twin boundaries do not always strengthen nanowires. Using classical molecular dynamics simulations, the authors show that whether twin boundaries strengthen nanowires depends on the necessary stress for dislocation nucleation, which in turn depends on surface morphologies. When nanowires are circular cylindrical, the necessary stress of dislocation nucleation is high and the presence of twin boundaries lowers this stress; twin boundaries soften nanowires. In contrast, when nanowires are square cylindrical, the necessary stress of dislocation nucleation is low, and a higher stress is required for dislocations to penetrate twin boundaries; they strengthen nanowires

Quantum Computing

Quantum mechanics---the theory describing the fundamental workings of nature---is famously counterintuitive: it predicts that a particle can be in two places at the same time, and that two remote particles can be inextricably and instantaneously linked. These predictions have been the topic of intense metaphysical debate ever since the theory's inception early last century. However, supreme predictive power combined with direct experimental observation of some of these unusual phenomena leave little doubt as to its fundamental correctness. In fact, without quantum mechanics we could not explain the workings of a laser, nor indeed how a fridge magnet operates. Over the last several decades quantum information science has emerged to seek answers to the question: can we gain some advantage by storing, transmitting and processing information encoded in systems that exhibit these unique quantum properties? Today it is understood that the answer is yes. Many research groups around the world are working towards one of the most ambitious goals humankind has ever embarked upon: a quantum computer that promises to exponentially improve computational power for particular tasks. A number of physical systems, spanning much of modern physics, are being developed for this task---ranging from single particles of light to superconducting circuits---and it is not yet clear which, if any, will ultimately prove successful. Here we describe the latest developments for each of the leading approaches and explain what the major challenges are for the future.Comment: 26 pages, 7 figures, 291 references. Early draft of Nature 464, 45-53 (4 March 2010). Published version is more up-to-date and has several corrections, but is half the length with far fewer reference

Origins of cattle on Chirikof Island, Alaska, elucidated from genome-wide SNP genotypes

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Modelling the Proportion of Influenza Infections within Households during Pandemic and Non-Pandemic Years

Background: The key epidemiological difference between pandemic and seasonal influenza is that the population is largely susceptible during a pandemic, whereas, during non-pandemic seasons a level of immunity exists. The population-level efficacy of household-based mitigation strategies depends on the proportion of infections that occur within households. In general, mitigation measures such as isolation and quarantine are more effective at the population level if the proportion of household transmission is low. Methods/Results: We calculated the proportion of infections within households during pandemic years compared with non-pandemic years using a deterministic model of household transmission in which all combinations of household size and individual infection states were enumerated explicitly. We found that the proportion of infections that occur within households was only partially influenced by the hazard h of infection within household relative to the hazard of infection outside the household, especially for small basic reproductive numbers. During pandemics, the number of within-household infections was lower than one might expect for a given h because many of the susceptible individuals were infected from the community and the number of susceptible individuals within household was thus depleted rapidly. In addition, we found that for the value of h at which 30% of infections occur within households during non-pandemic years, a similar 31% of infections occur within households during pandemic years. Interpretation: We suggest that a trade off between the community force of infection and the number of susceptible individuals in a household explains an apparent invariance in the proportion of infections that occur in households in our model. During a pandemic, although there are more susceptible individuals in a household, the community force of infection is very high. However, during non-pandemic years, the force of infection is much lower but there are fewer susceptible individuals within the household. © 2011 Kwok et al.published_or_final_versio

Specific Gene Expression Responses to Parasite Genotypes Reveal Redundancy of Innate Immunity in Vertebrates

Vertebrate innate immunity is the first line of defense against an invading pathogen and has long been assumed to be largely unspecific with respect to parasite/pathogen species. However, recent phenotypic evidence suggests that immunogenetic variation, i.e. allelic variability in genes associated with the immune system, results in host-parasite genotype-by-genotype interactions and thus specific innate immune responses. Immunogenetic variation is common in all vertebrate taxa and this reflects an effective immunological function in complex environments. However, the underlying variability in host gene expression patterns as response of innate immunity to within-species genetic diversity of macroparasites in vertebrates is unknown. We hypothesized that intra-specific variation among parasite genotypes must be reflected in host gene expression patterns. Here we used high-throughput RNA-sequencing to examine the effect of parasite genotypes on gene expression patterns of a vertebrate host, the three-spined stickleback (Gasterosteus aculeatus). By infecting naïve fish with distinct trematode genotypes of the species Diplostomum pseudospathaceum we show that gene activity of innate immunity in three-spined sticklebacks depended on the identity of an infecting macroparasite genotype. In addition to a suite of genes indicative for a general response against the trematode we also find parasite-strain specific gene expression, in particular in the complement system genes, despite similar infection rates of single clone treatments. The observed discrepancy between infection rates and gene expression indicates the presence of alternative pathways which execute similar functions. This suggests that the innate immune system can induce redundant responses specific to parasite genotypes

Clinical relevance of ErbB-2/HER2 nuclear expression in breast cancer

<p>Abstract</p> <p>Background</p> <p>The biological relevance of nuclear ErbB-2/HER2 (NuclErbB-2) presence in breast tumors remains unexplored. In this study we assessed the clinical significance of ErbB-2 nuclear localization in primary invasive breast cancer. The reporting recommendations for tumor marker prognostic studies (REMARK) guidelines were used as reference.</p> <p>Methods</p> <p>Tissue microarrays from a cohort of 273 primary invasive breast carcinomas from women living in Chile, a Latin American country, were examined for membrane (MembErbB-2) and NuclErbB-2 expression by an immunofluorescence (IF) protocol we developed. ErbB-2 expression was also evaluated by immunohistochemistry (IHC) with a series of antibodies. Correlation between NuclErbB-2 and MembErbB-2, and between NuclErbB-2 and clinicopathological characteristics of tumors was studied. The prognostic value of NuclErbB-2 in overall survival (OS) was evaluated using Kaplan-Meier method, and Cox model was used to explore NuclErbB-2 as independent prognostic factor for OS.</p> <p>Results</p> <p>The IF protocol we developed showed significantly higher sensitivity for detection of NuclErbB-2 than IHC procedures, while its specificity and sensitivity to detect MembErbB-2 were comparable to those of IHC procedures. We found 33.6% NuclErbB-2 positivity, 14.2% MembErbB-2 overexpression by IF, and 13.0% MembErbB-2 prevalence by IHC in our cohort. We identified NuclErbB-2 positivity as a significant independent predictor of worse OS in patients with MembErbB-2 overexpression. NuclErbB-2 was also a biomarker of lower OS in tumors that overexpress MembErbB-2 and lack steroid hormone receptors.</p> <p>Conclusions</p> <p>We revealed a novel role for NuclErbB-2 as an independent prognostic factor of poor clinical outcome in MembErbB-2-positive breast tumors. Our work indicates that patients presenting NuclErbB-2 may need new therapeutic strategies involving specific blockage of ErbB-2 nuclear migration.</p

On computational approaches for size-and-shape distributions from sedimentation velocity analytical ultracentrifugation

Sedimentation velocity analytical ultracentrifugation has become a very popular technique to study size distributions and interactions of macromolecules. Recently, a method termed two-dimensional spectrum analysis (2DSA) for the determination of size-and-shape distributions was described by Demeler and colleagues (Eur Biophys J 2009). It is based on novel ideas conceived for fitting the integral equations of the size-and-shape distribution to experimental data, illustrated with an example but provided without proof of the principle of the algorithm. In the present work, we examine the 2DSA algorithm by comparison with the mathematical reference frame and simple well-known numerical concepts for solving Fredholm integral equations, and test the key assumptions underlying the 2DSA method in an example application. While the 2DSA appears computationally excessively wasteful, key elements also appear to be in conflict with mathematical results. This raises doubts about the correctness of the results from 2DSA analysis

A Self-Organizing Algorithm for Modeling Protein Loops

Protein loops, the flexible short segments connecting two stable secondary structural units in proteins, play a critical role in protein structure and function. Constructing chemically sensible conformations of protein loops that seamlessly bridge the gap between the anchor points without introducing any steric collisions remains an open challenge. A variety of algorithms have been developed to tackle the loop closure problem, ranging from inverse kinematics to knowledge-based approaches that utilize pre-existing fragments extracted from known protein structures. However, many of these approaches focus on the generation of conformations that mainly satisfy the fixed end point condition, leaving the steric constraints to be resolved in subsequent post-processing steps. In the present work, we describe a simple solution that simultaneously satisfies not only the end point and steric conditions, but also chirality and planarity constraints. Starting from random initial atomic coordinates, each individual conformation is generated independently by using a simple alternating scheme of pairwise distance adjustments of randomly chosen atoms, followed by fast geometric matching of the conformationally rigid components of the constituent amino acids. The method is conceptually simple, numerically stable and computationally efficient. Very importantly, additional constraints, such as those derived from NMR experiments, hydrogen bonds or salt bridges, can be incorporated into the algorithm in a straightforward and inexpensive way, making the method ideal for solving more complex multi-loop problems. The remarkable performance and robustness of the algorithm are demonstrated on a set of protein loops of length 4, 8, and 12 that have been used in previous studies