The Monge-Ampere equation: various forms and numerical methods

We present three novel forms of the Monge-Ampere equation, which is used, e.g., in image processing and in reconstruction of mass transportation in the primordial Universe. The central role in this paper is played by our Fourier integral form, for which we establish positivity and sharp bound properties of the kernels. This is the basis for the development of a new method for solving numerically the space-periodic Monge-Ampere problem in an odd-dimensional space. Convergence is illustrated for a test problem of cosmological type, in which a Gaussian distribution of matter is assumed in each localised object, and the right-hand side of the Monge-Ampere equation is a sum of such distributions.Comment: 24 pages, 2 tables, 5 figures, 32 references. Submitted to J. Computational Physics. Times of runs added, multiple improvements of the manuscript implemented

Effects of Spaceflight on Human Induced Pluripotent Stem Cell-Derived Cardiomyocyte Structure and Function.

With extended stays aboard the International Space Station (ISS) becoming commonplace, there is a need to better understand the effects of microgravity on cardiac function. We utilized human induced pluripotent stem cell-derived cardiomyocytes (hiPSC-CMs) to study the effects of microgravity on cell-level cardiac function and gene expression. The hiPSC-CMs were cultured aboard the ISS for 5.5 weeks and their gene expression, structure, and functions were compared with ground control hiPSC-CMs. Exposure to microgravity on the ISS caused alterations in hiPSC-CM calcium handling. RNA-sequencing analysis demonstrated that 2,635 genes were differentially expressed among flight, post-flight, and ground control samples, including genes involved in mitochondrial metabolism. This study represents the first use of hiPSC technology to model the effects of spaceflight on human cardiomyocyte structure and function

methylKit: a comprehensive R package for the analysis of genome-wide DNA methylation profiles

DNA methylation is a chemical modification of cytosine bases that is pivotal for gene regulation, cellular specification and cancer development. Here, we describe an R package, methylKit, that rapidly analyzes genome-wide cytosine epigenetic profiles from high-throughput methylation and hydroxymethylation sequencing experiments. methylKit includes functions for clustering, sample quality visualization, differential methylation analysis and annotation features, thus automating and simplifying many of the steps for discerning statistically significant bases or regions of DNA methylation. Finally, we demonstrate methylKit on breast cancer data, in which we find statistically significant regions of differential methylation and stratify tumor subtypes. methylKit is available at http://code.google.com/p/methylkit

Fast finite difference solvers for singular solutions of the elliptic Monge-Amp\`ere equation

The elliptic Monge-Ampere equation is a fully nonlinear Partial Differential Equation which originated in geometric surface theory, and has been applied in dynamic meteorology, elasticity, geometric optics, image processing and image registration. Solutions can be singular, in which case standard numerical approaches fail. In this article we build a finite difference solver for the Monge-Ampere equation, which converges even for singular solutions. Regularity results are used to select a priori between a stable, provably convergent monotone discretization and an accurate finite difference discretization in different regions of the computational domain. This allows singular solutions to be computed using a stable method, and regular solutions to be computed more accurately. The resulting nonlinear equations are then solved by Newton's method. Computational results in two and three dimensions validate the claims of accuracy and solution speed. A computational example is presented which demonstrates the necessity of the use of the monotone scheme near singularities.Comment: 23 pages, 4 figures, 4 tables; added arxiv links to references, added coment

Developing a keystroke biometric system for continual authentication of computer users,”

Abstract-Data windows of keyboard input are analyzed to continually authenticate computer users and verify that they are the authorized ones. Because the focus is on fast intruder detection, the authentication process operates on short bursts of roughly a minute of keystroke input, while the training process can be extensive and use hours of input. The biometric system consists of components for data capture, feature extraction, authentication classification, and receiveroperating-characteristic curve generation. Using keystroke data from 120 users, system performance was obtained as a function of two independent variables: the user population size and the number of keystrokes per sample. For each population size, the performance increased (and the equal error rate decreased) roughly logarithmically as the number of keystrokes per sample was increased. The best closed-system performance results of 99 percent on 14 participants and 96 percent on 30 participants indicate the potential of this approach

Multi-Biometric System

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Global meta‐analysis of over 50 years of multidisciplinary and international collaborations on transmissible cancers

International audienceAlthough transmissible cancers have, so far, only been documented in three independent animal groups, they not only impact animals that have high economic, environmental and social significance, but they are also one of the most virulent parasitic life forms. Currently known transmissible cancers traverse terrestrial and marine environments, and are predicted to be more widely distributed across animal groups; thus, the implementation of effective collaborative scientific networks is important for combating existing and emerging forms. Here, we quantify how collaborative effort on the three known transmissible cancers has advanced through the formation of collaborative networks among institutions and disciplines. These three cancers occur in bivalves (invertebrates—disseminated neoplasia; DN), Tasmanian devils (vertebrate—marsupial; devil facial tumour disease; DFTD) and dogs (vertebrate—eutherian mammal; canine transmissible venereal tumour; CTVT). Research on CTVT and DN has been conducted since 1876 and 1969, respectively, whereas systematic research on DFTD only started in 2006. Yet, collaborative effort on all three diseases is global, encompassing six major Scopus subject areas. Collaborations steadily increased between 1963 and 2006 for CTVT and DN, with similar acceleration for all three cancers since 2006. Network analyses demonstrated that scientists are organizing themselves into efficient collaborative networks; however, these networks appear to be far stronger for DFTD and DN, possibly due to the recent detection of new strains adding impetus to research and associated publications (enhancing citation trajectories). In particular, global and multidisciplinary collaborations formed almost immediately after DFTD research was initiated, leading to similar research effort and relatively greater research outputs compared to the other two diseases. Therefore, in the event of outbreaks of new lineages of existing transmissible cancers, or the discovery of new transmissible cancers in the future, the rapid formation of international collaborations spanning relevant disciplines is vital for the efficient management of these diseases

An optimized algorithm for detecting and annotating regional differential methylation

Background: DNA methylation profiling reveals important differentially methylated regions (DMRs) of the genome that are altered during development or that are perturbed by disease. To date, few programs exist for regional analysis of enriched or whole-genome bisulfate conversion sequencing data, even though such data are increasingly common. Here, we describe an open-source, optimized method for determining empirically based DMRs (eDMR) from high-throughput sequence data that is applicable to enriched whole-genome methylation profiling datasets, as well as other globally enriched epigenetic modification data. Results: Here we show that our bimodal distribution model and weighted cost function for optimized regional methylation analysis provides accurate boundaries of regions harboring significant epigenetic modifications. Our algorithm takes the spatial distribution of CpGs into account for the enrichment assay, allowing for optimization of the definition of empirical regions for differential methylation. Combined with the dependent adjustment for regional p-value combination and DMR annotation, we provide a method that may be applied to a variety of datasets for rapid DMR analysis. Our method classifies both the directionality of DMRs and their genome-wide distribution, and we have observed that shows clinical relevance through correct stratification of two Acute Myeloid Leukemia (AML) tumor sub-types. Conclusions: Our weighted optimization algorithm eDMR for calling DMRs extends an established DMR R pipeline (methylKit) and provides a needed resource in epigenomics. Our method enables an accurate and scalable way of finding DMRs in high-throughput methylation sequencing experiments. eDMR is available for download at http://code.google.com/p/edmr/.Sheng Li, Francine E Garrett-Bakelman, Altuna Akalin, Paul Zumbo, Ross Levine, Bik L To, Ian D Lewis, Anna L Brown, Richard J D’Andrea, Ari Melnick, Christopher E Maso

An Esrrb and nanog cell fate regulatory module controlled by feed forward loop interactions

Cell fate decisions during development are governed by multi-factorial regulatory mechanisms including chromatin remodeling, DNA methylation, binding of transcription factors to specific loci, RNA transcription and protein synthesis. However, the mechanisms by which such regulatory 'dimensions' coordinate cell fate decisions are currently poorly understood. Here we quantified the multi-dimensional molecular changes that occur in mouse embryonic stem cells (mESCs) upon depletion of Estrogen related receptor beta (Esrrb), a key pluripotency regulator. Comparative analyses of expression changes subsequent to depletion of Esrrb or Nanog, indicated that a system of interlocked feed-forward loops involving both factors, plays a central part in regulating the timing of mESC fate decisions. Taken together, our meta-analyses support a hierarchical model in which pluripotency is maintained by an Oct4-Sox2 regulatory module, while the timing of differentiation is regulated by a Nanog-Esrrb module