Sparse approaches for the exact distribution of patterns in long state sequences generated by a Markov source

We present two novel approaches for the computation of the exact distribution of a pattern in a long sequence. Both approaches take into account the sparse structure of the problem and are two-part algorithms. The first approach relies on a partial recursion after a fast computation of the second largest eigenvalue of the transition matrix of a Markov chain embedding. The second approach uses fast Taylor expansions of an exact bivariate rational reconstruction of the distribution. We illustrate the interest of both approaches on a simple toy-example and two biological applications: the transcription factors of the Human Chromosome 5 and the PROSITE signatures of functional motifs in proteins. On these example our methods demonstrate their complementarity and their hability to extend the domain of feasibility for exact computations in pattern problems to a new level

Status of the differential transformation method

Further to a recent controversy on whether the differential transformation method (DTM) for solving a differential equation is purely and solely the traditional Taylor series method, it is emphasized that the DTM is currently used, often only, as a technique for (analytically) calculating the power series of the solution (in terms of the initial value parameters). Sometimes, a piecewise analytic continuation process is implemented either in a numerical routine (e.g., within a shooting method) or in a semi-analytical procedure (e.g., to solve a boundary value problem). Emphasized also is the fact that, at the time of its invention, the currently-used basic ingredients of the DTM (that transform a differential equation into a difference equation of same order that is iteratively solvable) were already known for a long time by the "traditional"-Taylor-method users (notably in the elaboration of software packages --numerical routines-- for automatically solving ordinary differential equations). At now, the defenders of the DTM still ignore the, though much better developed, studies of the "traditional"-Taylor-method users who, in turn, seem to ignore similarly the existence of the DTM. The DTM has been given an apparent strong formalization (set on the same footing as the Fourier, Laplace or Mellin transformations). Though often used trivially, it is easily attainable and easily adaptable to different kinds of differentiation procedures. That has made it very attractive. Hence applications to various problems of the Taylor method, and more generally of the power series method (including noninteger powers) has been sketched. It seems that its potential has not been exploited as it could be. After a discussion on the reasons of the "misunderstandings" which have caused the controversy, the preceding topics are concretely illustrated.Comment: To appear in Applied Mathematics and Computation, 29 pages, references and further considerations adde

Subduction and volcanism in the Iberia-North Africa collision zone from tomographic images of the upper mantle

New tomographic images of the upper mantle beneath the westernmost Mediterranean suggest that the evolution of the region experienced two subduction-related episodes. First subduction of oceanic and/or extended continental lithosphere, now located mainly beneath the Betics at depths greater than 400 km, took place on a NW-SE oriented subduction zone. This was followed by a slab-tear process that initiated in the east and propagated to the west, leading to westward slab rollback and possibly lower crustal delamination. The current position of the slab tear is located approximately at 4°W, and to the west of this location the subducted lithosphere is still attached to the surface along the Gibraltar Arc. Our new P-wave velocity model is able to image the attached subducted lithosphere as a narrow high-velocity body extending to shallow depths, coinciding with the region of maximum curvature of the Gibraltar Arc, the occurrence of intermediate-depth earthquakes, and anomalously thick crust. This thick crust has a large influence in the measured teleseismic travel time residuals and therefore in the obtained P-wave tomographic model. We show that removing the effects of the thick crust significantly improves the shallow images of the slab and therefore the interpretations based on the seismic structureThis is a contribution of the Team Consolider-Ingenio 2010 TOPO-IBERIA (CSD2006-00041). Additional fundingwas provided by the SIBERIA (CGL2006-01171), RIFSIS (CGL2009-09727) and ALERTES-RIM (CGL2013-45724-C3-3-R) projects.Peer reviewe

Distribution of Random Streams for Simulation Practitioners

International audienceThere is an increasing interest in the distribution of parallel random number streamsin the high-performance computing community particularly, with the manycore shift. Even ifwe have at our disposal statistically sound random number generators according to the latestand thorough testing libraries, their parallelization can still be a delicate problem. Indeed, aset of recent publications shows it still has to be mastered by the scientific community. Withthe arrival of multi-core and manycore processor architectures on the scientist desktop, modelerswho are non-specialists in parallelizing stochastic simulations need help and advice in distributingrigorously their experimental plans and replications according to the state of the art in pseudo-random numbers parallelization techniques. In this paper, we discuss the different partitioningtechniques currently in use to provide independent streams with their corresponding software. Inaddition to the classical approaches in use to parallelize stochastic simulations on regular processors,this paper also presents recent advances in pseudo-random number generation for general-purposegraphical processing units. The state of the art given in this paper is written for simulationpractitioners

Task swapping networks in distributed systems

In this paper we propose task swapping networks for task reassignments by using task swappings in distributed systems. Some classes of task reassignments are achieved by using iterative local task swappings between software agents in distributed systems. We use group-theoretic methods to find a minimum-length sequence of adjacent task swappings needed from a source task assignment to a target task assignment in a task swapping network of several well-known topologies.Comment: This is a preprint of a paper whose final and definite form is published in: Int. J. Comput. Math. 90 (2013), 2221-2243 (DOI: 10.1080/00207160.2013.772985

The Newcomb-Benford Law in Its Relation to Some Common Distributions

An often reported, but nevertheless persistently striking observation, formalized as the Newcomb-Benford law (NBL), is that the frequencies with which the leading digits of numbers occur in a large variety of data are far away from being uniform. Most spectacular seems to be the fact that in many data the leading digit 1 occurs in nearly one third of all cases. Explanations for this uneven distribution of the leading digits were, among others, scale- and base-invariance. Little attention, however, found the interrelation between the distribution of the significant digits and the distribution of the observed variable. It is shown here by simulation that long right-tailed distributions of a random variable are compatible with the NBL, and that for distributions of the ratio of two random variables the fit generally improves. Distributions not putting most mass on small values of the random variable (e.g. symmetric distributions) fail to fit. Hence, the validity of the NBL needs the predominance of small values and, when thinking of real-world data, a majority of small entities. Analyses of data on stock prices, the areas and numbers of inhabitants of countries, and the starting page numbers of papers from a bibliography sustain this conclusion. In all, these findings may help to understand the mechanisms behind the NBL and the conditions needed for its validity. That this law is not only of scientific interest per se, but that, in addition, it has also substantial implications can be seen from those fields where it was suggested to be put into practice. These fields reach from the detection of irregularities in data (e.g. economic fraud) to optimizing the architecture of computers regarding number representation, storage, and round-off errors

Vaccination with nanoparticles combined with micro-adjuvants protects against cancer.

Induction of strong T cell responses, in particular cytotoxic T cells, is a key for the generation of efficacious therapeutic cancer vaccines which yet, remains a major challenge for the vaccine developing world. Here we demonstrate that it is possible to harness the physiological properties of the lymphatic system to optimize the induction of a protective T cell response. Indeed, the lymphatic system sharply distinguishes between nanoscale and microscale particles. The former reaches the fenestrated lymphatic system via diffusion, while the latter either need to be transported by dendritic cells or form a local depot. Our previously developed cucumber-mosaic virus-derived nanoparticles termed (CuMV <sub>TT</sub> -VLPs) incorporating a universal Tetanus toxoid epitope TT830-843 were assessed for their draining kinetics using stereomicroscopic imaging. A nano-vaccine has been generated by coupling p33 epitope as a model antigen to CuMV <sub>TT</sub> -VLPs using bio-orthogonal Cu-free click chemistry. The CuMV <sub>TT</sub> -p33 nano-sized vaccine has been next formulated with the micron-sized microcrystalline tyrosine (MCT) adjuvant and the formed depot effect was studied using confocal microscopy and trafficking experiments. The immunogenicity of the nanoparticles combined with the micron-sized adjuvant was next assessed in an aggressive transplanted murine melanoma model. The obtained results were compared to other commonly used adjuvants such as B type CpGs and Alum. Our results showed that CuMV <sub>TT</sub> -VLPs can efficiently and rapidly drain into the lymphatic system due to their nano-size of ~ 30 nm. However, formulating the nanoparticles with the micron-sized MCT adjuvant of ~ 5 μM resulted in a local depot for the nanoparticles and a longer exposure time for the immune system. The preclinical nano-vaccine CuMV <sub>TT</sub> -p33 formulated with the micron-sized MCT adjuvant has enhanced the specific T cell response in the stringent B16F10p33 murine melanoma model. Furthermore, the micron-sized MCT adjuvant was as potent as B type CpGs and clearly superior to the commonly used Alum adjuvant when total CD8 <sup>+</sup> , specific p33 T cell response or tumour protection were assessed. The combination of nano- and micro-particles may optimally harness the physiological properties of the lymphatic system. Since the nanoparticles are well defined virus-like particles and the micron-sized adjuvant MCT has been used for decades in allergen-specific desensitization, this approach may readily be translated to the clinic

Modeling Structure-Function Relationships in Synthetic DNA Sequences using Attribute Grammars

Recognizing that certain biological functions can be associated with specific DNA sequences has led various fields of biology to adopt the notion of the genetic part. This concept provides a finer level of granularity than the traditional notion of the gene. However, a method of formally relating how a set of parts relates to a function has not yet emerged. Synthetic biology both demands such a formalism and provides an ideal setting for testing hypotheses about relationships between DNA sequences and phenotypes beyond the gene-centric methods used in genetics. Attribute grammars are used in computer science to translate the text of a program source code into the computational operations it represents. By associating attributes with parts, modifying the value of these attributes using rules that describe the structure of DNA sequences, and using a multi-pass compilation process, it is possible to translate DNA sequences into molecular interaction network models. These capabilities are illustrated by simple example grammars expressing how gene expression rates are dependent upon single or multiple parts. The translation process is validated by systematically generating, translating, and simulating the phenotype of all the sequences in the design space generated by a small library of genetic parts. Attribute grammars represent a flexible framework connecting parts with models of biological function. They will be instrumental for building mathematical models of libraries of genetic constructs synthesized to characterize the function of genetic parts. This formalism is also expected to provide a solid foundation for the development of computer assisted design applications for synthetic biology

The distribution of inverted repeat sequences in the Saccharomyces cerevisiae genome

Although a variety of possible functions have been proposed for inverted repeat sequences (IRs), it is not known which of them might occur in vivo. We investigate this question by assessing the distributions and properties of IRs in the Saccharomyces cerevisiae (SC) genome. Using the IRFinder algorithm we detect 100,514 IRs having copy length greater than 6 bp and spacer length less than 77 bp. To assess statistical significance we also determine the IR distributions in two types of randomization of the S. cerevisiae genome. We find that the S. cerevisiae genome is significantly enriched in IRs relative to random. The S. cerevisiae IRs are significantly longer and contain fewer imperfections than those from the randomized genomes, suggesting that processes to lengthen and/or correct errors in IRs may be operative in vivo. The S. cerevisiae IRs are highly clustered in intergenic regions, while their occurrence in coding sequences is consistent with random. Clustering is stronger in the 3′ flanks of genes than in their 5′ flanks. However, the S. cerevisiae genome is not enriched in those IRs that would extrude cruciforms, suggesting that this is not a common event. Various explanations for these results are considered