Collective behavior of animals: swarming and complex patterns

En esta nota repasamos algunos modelos basados en individuos para describir el movimiento colectivo de agentes, a lo que nos referimos usando la voz inglesa swarming. Estos modelos se basan en EDOs (ecuaciones diferenciales ordinarias) y muestran un comportamiento asintótico complejo y rico en patrones, que mostramos numéricamente. Además, comentamos cómo se conectan estos modelos de partículas con las ecuaciones en derivadas parciales para describir la evolución de densidades de individuos de forma continua. Las cuestiones matemáticas relacionadas con la estabilidad de de estos modelos de EDP's (ecuaciones en derivadas parciales) despiertan gran interés en la investigación en biología matemáticaIn this short note we review some of the individual based models of the collective motion of agents, called swarming. These models based on ODEs (ordinary differential equations) exhibit a complex rich asymptotic behavior in terms of patterns, that we show numerically. Moreover, we comment on how these particle models are connected to partial differential equations to describe the evolution of densities of individuals in a continuum manner. The mathematical questions behind the stability issues of these PDE (partial differential equations) models are questions of actual interest in mathematical biology researc

Alternative Technique for "Complex" Spectra Analysis

. The choice of a suitable random matrix model of a complex system is very sensitive to the nature of its complexity. The statistical spectral analysis of various complex systems requires, therefore, a thorough probing of a wide range of random matrix ensembles which is not an easy task. It is highly desirable, if possible, to identify a common mathematcal structure among all the ensembles and analyze it to gain information about the ensemble- properties. Our successful search in this direction leads to Calogero Hamiltonian, a one-dimensional quantum hamiltonian with inverse-square interaction, as the common base. This is because both, the eigenvalues of the ensembles, and, a general state of Calogero Hamiltonian, evolve in an analogous way for arbitrary initial conditions. The varying nature of the complexity is reflected in the different form of the evolution parameter in each case. A complete investigation of Calogero Hamiltonian can then help us in the spectral analysis of complex systems.Comment: 20 pages, No figures, Revised Version (Minor Changes

Application of the Jacobi Davidson method for spectral low-rank preconditioning in computational electromagnetics problems

[EN] We consider the numerical solution of linear systems arising from computational electromagnetics applications. For large scale problems the solution is usually obtained iteratively with a Krylov subspace method. It is well known that for ill conditioned problems the convergence of these methods can be very slow or even it may be impossible to obtain a satisfactory solution. To improve the convergence a preconditioner can be used, but in some cases additional strategies are needed. In this work we study the application of spectral lowrank updates (SLRU) to a previously computed sparse approximate inverse preconditioner.The updates are based on the computation of a small subset of the eigenpairs closest to the origin. Thus, the performance of the SLRU technique depends on the method available to compute the eigenpairs of interest. The SLRU method was first used using the IRA s method implemented in ARPACK. In this work we investigate the use of a Jacobi Davidson method, in particular its JDQR variant. The results of the numerical experiments show that the application of the JDQR method to obtain the spectral low-rank updates can be quite competitive compared with the IRA s method.Mas Marí, J.; Cerdán Soriano, JM.; Malla Martínez, N.; Marín Mateos-Aparicio, J. (2015). Application of the Jacobi Davidson method for spectral low-rank preconditioning in computational electromagnetics problems. Journal of the Spanish Society of Applied Mathematics. 67:39-50. doi:10.1007/s40324-014-0025-6S395067Bergamaschi, L., Pini, G., Sartoretto, F.: Computational experience with sequential, and parallel, preconditioned Jacobi–Davidson for large sparse symmetric matrices. J. Comput. Phys. 188(1), 318–331 (2003)Carpentieri, B.: Sparse preconditioners for dense linear systems from electromagnetics applications. PhD thesis, Institut National Polytechnique de Toulouse, CERFACS (2002)Carpentieri, B., Duff, I.S., Giraud, L.: Sparse pattern selection strategies for robust Frobenius-norm minimization preconditioners in electromagnetism. Numer. Linear Algebr. Appl. 7(7–8), 667–685 (2000)Carpentieri, B., Duff, I.S., Giraud, L.: A class of spectral two-level preconditioners. SIAM J. Sci. Comput. 25(2), 749–765 (2003)Carpentieri, B., Duff, I.S., Giraud, L., Magolu monga Made, M.: Sparse symmetric preconditioners for dense linear systems in electromagnetism. Numer. Linear Algebr. Appl. 11(8–9), 753–771 (2004)Carpentieri, B., Duff, I.S., Giraud, L., Sylvand, G.: Combining fast multipole techniques and an approximate inverse preconditioner for large electromagnetism calculations. SIAM J. Sci. Comput. 27(3), 774–792 (2005)Darve, E.: The fast multipole method I: error analysis and asymptotic complexity. SIAM J. Numer. Anal. 38(1), 98–128 (2000)Fokkema, D.R., Sleijpen, G.L., Van der Vorst, H.A.: Jacobi–Davidson style QR and QZ algorithms for the reduction of matrix pencils. SIAM J. Sci. Comput. 20(1), 94–125 (1998)Greengard, L., Rokhlin, V.: A fast algorithm for particle simulations. J. Comput. Phys. 73(3), 325–348 (1987)Grote, M., Huckle, T.: Parallel preconditioning with sparse approximate inverses. SIAM J. Sci. Comput. 18(3), 838–853 (1997)Harrington, R.: Origin and development of the method of moments for field computation. IEEE Antenna Propag. Mag. (1990)Kunz, K.S., Luebbers, R.J.: The finite difference time domain method for electromagnetics. SIAM J. Sci. Comput. 18(3), 838–853 (1997)Maxwell, J.C.: A dynamical theory of the electromagnetic field. Roy. S. Trans. CLV, (1864). Reprinted in Tricker, R. A. R. The Contributions of Faraday and Maxwell to Electrial Science, Pergamon Press (1966)Marín, J., Malla M.: Some experiments preconditioning via spectral low rank updates for electromagnetism applications. In: Proceedings of the international conference on preconditioning techniques for large sparse matrix problems in scientific and industrial applications (Preconditioning 2007), Toulouse (2007)Meijerink, J.A., van der Vorst, H.A.: An iterative solution method for linear systems of which the coefficient matrix is a symmetric M-matrix. Math. Comput. 31, 148–162 (1977)Sorensen, D.C., Lehoucq, R.B., Yang, C.: ARPACK users’ guide: solution of large-scale eigenvalue problems with implicitly restarted Arnoldi methods. SIAM, Philadelphia (1998)Rao, S.M., Wilton, D.R., Glisson, A.W.: Electromagnetic scattering by surfaces of arbitrary shape. IEEE Trans. Antenna Propag. 30, 409–418 (1982)Saad, Y.: Iterative methods for sparse linear systems. PWS Publishing Company, Boston (1996)Silvester, P.P., Ferrari, R.L.: Finite elements for electrical engineers. Cambridge University Press, Cambridge (1990)Sleijpen, S.L., van der Vorst, H.A.: A Jacobi–Davidson iteration method for linear eigenvalue problems. SIAM J. Matrix Anal. Appl. 17, 401–425 (1996)van der Vorst, H.A.: Bi-CGSTAB: a fast and smoothly converging variant of Bi-CG for the solution of non-symmetric linear systems. SIAM J. Sci. Stat. Comput. 12(6), 631–644 (1992

FIRE (facilitating implementation of research evidence) : a study protocol

Research evidence underpins best practice, but is not always used in healthcare. The Promoting Action on Research Implementation in Health Services (PARIHS) framework suggests that the nature of evidence, the context in which it is used, and whether those trying to use evidence are helped (or facilitated) affect the use of evidence. Urinary incontinence has a major effect on quality of life of older people, has a high prevalence, and is a key priority within European health and social care policy. Improving continence care has the potential to improve the quality of life for older people and reduce the costs associated with providing incontinence aids

Natural Variation in Small Molecule–Induced TIR-NB-LRR Signaling Induces Root Growth Arrest via EDS1- and PAD4-Complexed R Protein VICTR in Arabidopsis

In a chemical genetics screen we identified the small-molecule [5-(3,4-dichlorophenyl)furan-2-yl]-piperidine-1-ylmethanethione (DFPM) that triggers rapid inhibition of early abscisic acid signal transduction via PHYTOALEXIN DEFICIENT4 (PAD4)- and ENHANCED DISEASE SUSCEPTIBILITY1 (EDS1)-dependent immune signaling mechanisms. However, mechanisms upstream of EDS1 and PAD4 in DFPM-mediated signaling remain unknown. Here, we report that DFPM generates an Arabidopsis thaliana accession-specific root growth arrest in Columbia-0 (Col-0) plants. The genetic locus responsible for this natural variant, VICTR (VARIATION IN COMPOUND TRIGGERED ROOT growth response), encodes a TIR-NB-LRR (for Toll-Interleukin1 Receptor–nucleotide binding–Leucine-rich repeat) protein. Analyses of T-DNA insertion victr alleles showed that VICTR is necessary for DFPM-induced root growth arrest and inhibition of abscisic acid–induced stomatal closing. Transgenic expression of the Col-0 VICTR allele in DFPM-insensitive Arabidopsis accessions recapitulated the DFPM-induced root growth arrest. EDS1 and PAD4, both central regulators of basal resistance and effector-triggered immunity, as well as HSP90 chaperones and their cochaperones RAR1 and SGT1B, are required for the DFPM-induced root growth arrest. Salicylic acid and jasmonic acid signaling pathway components are dispensable. We further demonstrate that VICTR associates with EDS1 and PAD4 in a nuclear protein complex. These findings show a previously unexplored association between a TIR-NB-LRR protein and PAD4 and identify functions of plant immune signaling components in the regulation of root meristematic zone-targeted growth arrest

Brane-World Gravity

The observable universe could be a 1+3-surface (the "brane") embedded in a 1+3+\textit{d}-dimensional spacetime (the "bulk"), with Standard Model particles and fields trapped on the brane while gravity is free to access the bulk. At least one of the \textit{d} extra spatial dimensions could be very large relative to the Planck scale, which lowers the fundamental gravity scale, possibly even down to the electroweak ($\sim$ TeV) level. This revolutionary picture arises in the framework of recent developments in M theory. The 1+10-dimensional M theory encompasses the known 1+9-dimensional superstring theories, and is widely considered to be a promising potential route to quantum gravity. At low energies, gravity is localized at the brane and general relativity is recovered, but at high energies gravity "leaks" into the bulk, behaving in a truly higher-dimensional way. This introduces significant changes to gravitational dynamics and perturbations, with interesting and potentially testable implications for high-energy astrophysics, black holes, and cosmology. Brane-world models offer a phenomenological way to test some of the novel predictions and corrections to general relativity that are implied by M theory. This review analyzes the geometry, dynamics and perturbations of simple brane-world models for cosmology and astrophysics, mainly focusing on warped 5-dimensional brane-worlds based on the Randall--Sundrum models. We also cover the simplest brane-world models in which 4-dimensional gravity on the brane is modified at \emph{low} energies -- the 5-dimensional Dvali--Gabadadze--Porrati models. Then we discuss co-dimension two branes in 6-dimensional models.Comment: A major update of Living Reviews in Relativity 7:7 (2004) "Brane-World Gravity", 119 pages, 28 figures, the update contains new material on RS perturbations, including full numerical solutions of gravitational waves and scalar perturbations, on DGP models, and also on 6D models. A published version in Living Reviews in Relativit

Intratumoral Genetic and Functional Heterogeneity in Pediatric Glioblastoma.

Pediatric glioblastoma (pGBM) is a lethal cancer with no effective therapies. To understand the mechanisms of tumor evolution in this cancer, we performed whole-genome sequencing with linked reads on longitudinally resected pGBM samples. Our analyses showed that all diagnostic and recurrent samples were collections of genetically diverse subclones. Clonal composition rapidly evolved at recurrence, with less than 8% of nonsynonymous single-nucleotide variants being shared in diagnostic-recurrent pairs. To track the origins of the mutational events observed in pGBM, we generated whole-genome datasets for two patients and their parents. These trios showed that genetic variants could be (i) somatic, (ii) inherited from a healthy parent, or (iii) de novo in the germlines of pGBM patients. Analysis of variant allele frequencies supported a model of tumor growth involving slow-cycling cancer stem cells that give rise to fast-proliferating progenitor-like cells and to nondividing cells. Interestingly, radiation and antimitotic chemotherapeutics did not increase overall tumor burden upon recurrence. These findings support an important role for slow-cycling stem cell populations in contributing to recurrences, because slow-cycling cell populations are expected to be less prone to genotoxic stress induced by these treatments and therefore would accumulate few mutations. Our results highlight the need for new targeted treatments that account for the complex functional hierarchies and genomic heterogeneity of pGBM. SIGNIFICANCE: This work challenges several assumptions regarding the genetic organization of pediatric GBM and highlights mutagenic programs that start during early prenatal development.Graphical Abstract: http://cancerres.aacrjournals.org/content/canres/79/9/2111/F1.large.jpg.Wellcome Trust Royal Societ

f(R) theories

Over the past decade, f(R) theories have been extensively studied as one of the simplest modifications to General Relativity. In this article we review various applications of f(R) theories to cosmology and gravity - such as inflation, dark energy, local gravity constraints, cosmological perturbations, and spherically symmetric solutions in weak and strong gravitational backgrounds. We present a number of ways to distinguish those theories from General Relativity observationally and experimentally. We also discuss the extension to other modified gravity theories such as Brans-Dicke theory and Gauss-Bonnet gravity, and address models that can satisfy both cosmological and local gravity constraints.Comment: 156 pages, 14 figures, Invited review article in Living Reviews in Relativity, Published version, Comments are welcom

Determinants of social media adoption by B2B organizations

This study contributes to the current dearth of knowledge on the potential of social media as a marketing tool in industrial settings, by focusing on factors that determine social media adoption by B2B organizations. A conceptual model, which draws on the technology acceptance model and resource-based theory, is developed and tested using quantitative data from B2B organizations in the UK. Findings suggest that perceived usefulness of social media within B2B organizational contexts is determined by image, perceived ease of use and perceived barriers. Additionally, the results show that adoption of social media is significantly affected by organizational innovativeness and perceived usefulness. The moderating role of organizational innovativeness is also tested but no support is found. The findings of the study are further validated via nine qualitative interviews with B2B senior managers, yielding additional interesting and in-depth insights into the drivers of social media adoption by B2B organizations