A Fast Monte Carlo algorithm for evaluating matrix functions with application in complex networks

We propose a novel stochastic algorithm that randomly samples entire rows and columns of the matrix as a way to approximate an arbitrary matrix function. This contrasts with the "classical" Monte Carlo method which only works with one entry at a time, resulting in a significant better convergence rate than the "classical" approach. To assess the applicability of our method, we compute the subgraph centrality and total communicability of several large networks. In all benchmarks analyzed so far, the performance of our method was significantly superior to the competition, being able to scale up to 64 CPU cores with a remarkable efficiency.Comment: Submitted to the Journal of Scientific Computin

A hybrid probabilistic domain decomposition algorithm suited for very large-scale elliptic PDEs

State of the art domain decomposition algorithms for large-scale boundary value problems (with $M\gg 1$ degrees of freedom) suffer from bounded strong scalability because they involve the synchronisation and communication of workers inherent to iterative linear algebra. Here, we introduce PDDSparse, a different approach to scientific supercomputing which relies on a "Feynman-Kac formula for domain decomposition". Concretely, the interfacial values (only) are determined by a stochastic, highly sparse linear system $G(\omega){\vec u}={\vec b}(\omega)$ of size ${\cal O}(\sqrt{M})$, whose coefficients are constructed with Monte Carlo simulations-hence embarrassingly in parallel. In addition to a wider scope for strong scalability in the deep supercomputing regime, PDDSparse has built-in fault tolerance and is ideally suited for GPUs. A proof of concept example with up to 1536 cores is discussed in detail

The Kuramoto model: A simple paradigm for synchronization phenomena

Synchronization phenomena in large populations of interacting elements are the subject of intense research efforts in physical, biological, chemical, and social systems. A successful approach to the problem of synchronization consists of modeling each member of the population as a phase oscillator. In this review, synchronization is analyzed in one of the most representative models of coupled phase oscillators, the Kuramoto model. A rigorous mathematical treatment, specific numerical methods, and many variations and extensions of the original model that have appeared in the last few years are presented. Relevant applications of the model in different contexts are also included

Ha-ras interference with thyroid cell differentiation is associated with a down-regulation of thyroid transcription factor-1 phosphorylation

7 pages, 6 figures.Mechanisms responsible for the lack of thyroid-specific differentiation markers in Ha-ras transformed FRTL-5 cells have been investigated. In vivo cell labeling and immunoprecipitation demonstrate that phosphorylation of the thyroid transcription factor-1 (TTF-1) is clearly reduced in thyroid cells transformed with the Ha-ras oncogene. Fingerprinting analysis of phosphotryptic peptides from FRTL-5 and Ha-ras-FRTL-5 cells also reveals a heterogeneous pattern of TTF-1 phosphorylation in the transformed cell line. This heterogeneity is localized in the amino terminal cluster of phosphoserines, as determined by transfection of HeLa cells with TTF-1 mutants in which serine residues have been replaced by alanines. Amplification and nucleotide sequence of the 5'-coding region of the TTF-1 gene in Ha-ras-FRTL-5 cells rule out the possibility that differences in phosphorylation were the consequence of any mutational event affecting residues within the N-terminal protein sequence. Hypophosphorylated TTF-1 is still able to bind its DNA consensus sequence within the thyroglobulin promoter, although a reporter construct whose expression is exclusively dependent on TTF-1 is not transactivated. Transfection of Ha-ras-FRTL-5 cells with an expression vector encoding the cAMP dependent protein kinase A (PKA) catalytic subunit partially reestablishes TTF-1 transcriptional activity. Taken together, these results indicate that the lack of specific thyroid gene expression in Ha-ras-FRTL-5 cells could be a direct consequence of the inability of TTF-1 to promote transcription.This work was supported by Grants from Dirección General de Investigación Científica y Técnica (PM97–0065, PM96–0074), Comunidad Autónoma de Madrid (AE00310, AC117), and Fundación Salud 2000 (Spain), and by grants from the Progetto Finalizzato Applicazioni Cliniche della Ricerca Oncologica of Consiglio Nazionale delle Ricerche, the Associazione Italiana per la Ricerca sul Cancro (Italy).Peer reviewe

The allosteric site for the nascent cell wall in penicillin-binding protein 2a: An achilles' heel of methicillin-resistant staphylococcus aureus

© 2015 Bentham Science Publishers. The ability to resist the effect of a wide range of antibiotics makes methicillin-resistant Staphylococcus aureus (MRSA) a leading global human pathogen. A key determinant of resistance to β-lactam antibiotics in this organism is penicillin-binding protein 2a (PBP2a), an enzyme that catalyzes the crosslinking reaction between two adjacent peptide stems during the peptidoglycan biosynthesis. The recently published crystal structure of the complex of PBP2a with ceftaroline, a cephalosporin antibiotic that shows efficacy against MRSA, has revealed the allosteric site at 60-A distance from the transpeptidase domain. Binding of ceftaroline to the allosteric site of PBP2a triggers conformational changes that lead to the opening of the active site from a closed conformation, where a second molecule of ceftaroline binds to give inhibition of the enzyme. The discovery of allostery in MRSA remains the only known example of such regulation of cellwall biosynthesis and represents a new paradigm in fighting MRSA. This review summarizes the present knowledge of the allosteric mechanism, the conformational changes allowing PBP2a catalysis and the means by which some clinical strains have acquired resistance to ceftaroline by disrupting the allosteric mechanism.Peer Reviewe

A highly parallel algorithm for computing the action of a matrix exponential on a vector based on a multilevel Monte Carlo method

A novel algorithm for computing the action of a matrix exponential over a vector is proposed. The algorithm is based on a multilevel Monte Carlo method, and the vector solution is computed probabilistically generating suitable random paths which evolve through the indices of the matrix according to a suitable probability law. The computational complexity is proved in this paper to be significantly better than the classical Monte Carlo method, which allows the computation of much more accurate solutions. Furthermore, the positive features of the algorithm in terms of parallelism were exploited in practice to develop a highly scalable implementation capable of solving some test problems very efficiently using high performance supercomputers equipped with a large number of cores. For the specific case of shared memory architectures the performance of the algorithm was compared with the results obtained using an available Krylov-based algorithm, outperforming the latter in all benchmarks analyzed so far.The work has been performed under the Project HPC-EUROPA3 (INFRAIA-2016-1-730897), with the support of the EC Research Innovation Action under the H2020 Programme; in particular, the authors gratefully acknowledge the support of the Computer Architecture Department at Universitat Politècnica de Catalunya (UPC), Spain and the computer resources and technical support provided by Barcelona Supercomputing Center (BSC), Spain. We acknowledge PRACE, Belgium for awarding us access to Marconi at CINECA, through grant 2010PA4246. This work was also supported by Fundação para a Ciência e a Tecnologia, Portugal under Grant No. UIDB/50021/2020, by the Spanish Ministry of Science and Technology through TIN2015-65316-P project and by the Generalitat de Catalunya, Spain (contract 2017-SGR-1414).Peer ReviewedPostprint (author's final draft

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new domain decomposition approach suite