Update rules and interevent time distributions: Slow ordering vs. no ordering in the Voter Model

We introduce a general methodology of update rules accounting for arbitrary interevent time distributions in simulations of interacting agents. In particular we consider update rules that depend on the state of the agent, so that the update becomes part of the dynamical model. As an illustration we consider the voter model in fully-connected, random and scale free networks with an update probability inversely proportional to the persistence, that is, the time since the last event. We find that in the thermodynamic limit, at variance with standard updates, the system orders slowly. The approach to the absorbing state is characterized by a power law decay of the density of interfaces, observing that the mean time to reach the absorbing state might be not well defined.Comment: 5pages, 4 figure

Joint effect of ageing and multilayer structure prevents ordering in the voter model

The voter model rules are simple, with agents copying the state of a random neighbor, but they lead to non-trivial dynamics. Besides opinion processes, the model has also applications for catalysis and species competition. Inspired by the temporal inhomogeneities found in human interactions, one can introduce ageing in the agents: the probability to update decreases with the time elapsed since the last change. This modified dynamics induces an approach to consensus via coarsening in complex networks. Additionally, multilayer networks produce profound changes in the dynamics of models. In this work, we investigate how a multilayer structure affects the dynamics of an ageing voter model. The system is studied as a function of the fraction of nodes sharing states across layers (multiplexity parameter q ). We find that the dynamics of the system suffers a notable change at an intermediate value q*. Above it, the voter model always orders to an absorbing configuration. While, below, a fraction of the realizations falls into dynamical traps associated to a spontaneous symmetry breaking in which the majority opinion in the different layers takes opposite signs and that due to the ageing indefinitely delay the arrival at the absorbing state.Comment: 10 pages, 8 figure

Lipschitz stability of controlled invariant subspaces

AbstractLet (A,B)∈Cn×n×Cn×m and M be an (A,B)-invariant subspace. In this paper the following results are presented: (i) If M∩ImB={0}, necessary and sufficient conditions for the Lipschitz stability of M are given. (ii) If M contains the controllability subspace of the pair (A,B), sufficient conditions for the Lipschitz stability of the subspace M are given

Nearest southeast submatrix that makes multiple a prescribed eigenvalue. Part 1

AbstractGiven four complex matrices A,B,C and D, where A∈Cn×n and D∈Cm×m, and given a complex number z0: What is the (spectral norm) distance from D to the set of matrices X∈Cm×m such that z0 is a multiple eigenvalue of the matrixABCX?This problem is solved when z0 is not an eigenvalue of A. We also give a conjecture when z0 is an eigenvalue of A

Submatriz sudeste más próxima que hace múltiple un valor propio prescrito

Dadas cuatro matrices complejas A, B, C y D, donde A ∈ C n×n y D ∈ C m×m, estudiamos el problema de Wilkinson generalizado: ¿Cuál es la distancia desde D al conjunto de matrices X ∈ C m×m tales que (A B C X ) tenga algún valor propio múltiple? En esta comunicación resolvemos este problema, salvo en un caso, y damos una conjetura sobre la solución completa.Ministerio de Educación y Cienci

Is the Voter Model a model for voters?

The voter model has been studied extensively as a paradigmatic opinion dynamics' model. However, its ability for modeling real opinion dynamics has not been addressed. We introduce a noisy voter model (accounting for social influence) with agents' recurrent mobility (as a proxy for social context), where the spatial and population diversity are taken as inputs to the model. We show that the dynamics can be described as a noisy diffusive process that contains the proper anysotropic coupling topology given by population and mobility heterogeneity. The model captures statistical features of the US presidential elections as the stationary vote-share fluctuations across counties, and the long-range spatial correlations that decay logarithmically with the distance. Furthermore, it recovers the behavior of these properties when a real-space renormalization is performed by coarse-graining the geographical scale from county level through congressional districts and up to states. Finally, we analyze the role of the mobility range and the randomness in decision making which are consistent with the empirical observations.Comment: 13 pages, 13 figure

Analysis of motor engagement time in physical education: a literature review

El tiempo es un factor importante para un adecuado desarrollo de las clases y del proceso de enseñanza-aprendizaje. La Educación Física se ve más afectada debido a la necesidad de traslados hacia las zonas de práctica deportiva, junto a la colocación y recogida de material para actividades, tiempos de explicación por parte del profesorado, etc., provocando una disminución del tiempo de práctica de actividad física por parte del alumnado. Por tanto, se pretende conocer el tiempo que el alumnado está activo o el Tiempo de Compromiso Motor en las clases de Educación Física, determinando qué tipo de sesiones son más efectivas y qué estrategias metodológicas y organizativas permiten reducir al máximo las pérdidas de tiempo. Para esta revisión, se ha contado con 16 artículos que analizan el Tiempo de Compromiso Motor en sesiones de Educación Física en las etapas de Educación Primaria, Educación Secundaria Obligatoria y Bachillerato. En la mayoría de sesiones no se consigue alcanzar la mitad del tiempo disponible en Tiempo de Compromiso Motor, no cumpliendo con la AF diaria recomendada por la Organización Mundial de la Salud. La madurez del alumnado de las etapas más superiores, permiten agilizar el desarrollo de las clases; resulta necesaria la formación del profesorado de centros bilingües que compatibilicen la enseñanza de un segundo idioma con el movimiento que requiere la Educación Física; las sesiones basadas en estrategias de enseñanza-aprendizaje diferentes a las clases tradicionales con organizaciones subgrupales son las que más efectivas han resultado respecto al Tiempo de Compromiso Motor.Time is an important factor for an adequate development of classes and the teaching-learning process. Physical Education is more affected due to the need to move to the sports practice areas, together with the placement and collection of material for activities, explanation times by teachers, etc. This causes a decrease in the time students spend practicing physical activity. Therefore, the aim is to know the time that the students are active or the Motor Engagement Time in Physical Education classes, determining what type of sessions are more effective and what methodological and organizational strategies allow to reduce as much as possible the loss of time. For this review, 16 articles have been used to analyze the Motor Engagement Time in Physical Education sessions in Primary Education, High School Education and Baccalaureate. In most sessions, half of the time available in Motor Engagement Time is not reached, not complying with the daily PA recommended by the World Health Organization. The maturity of the students in the higher stages makes it possible to speed up the development of the classes; it is necessary to train teachers in bilingual centers to make the teaching of a second language compatible with the movement required by Physical Education; sessions based on teaching-learning strategies different from traditional classes with subgroup organizations are those that have been most effective with respect to Motor Engagement Time

The earliest evidence of true lambdoid craniosynostosis: the case of “Benjamina”, a Homo heidelbergensis child

Background The authors report the morphological and neuroimaging findings of an immature human fossil (Cranium 14) diagnosed with left lambdoid synostosis. Discussion The skull was recovered at the Sima de los Huesos site in Atapuerca (Burgos, Spain). Since the human fossil remains from this site have been dated to a minimum age of 530,000 years, this skull represents the earliest evidence of craniosynostosis occurring in a hominid. A brief historical review of craniosynostosis and cranial deformation is provided

Forma canónica de Kronecker

Este libro trata de explicar con claridad y sencillez la forma canónica de Kronecker de haces de matrices para la relación de equivalencia estricta. El tema es importante para los ingenieros, físicos, químicos, economistas y otros científicos que estudian sistemas lineales con control, por lo que una introducción asequible y rigurosa se echa de menos. También esperamos que el libro sea de utilidad para los matemáticos en un segundo curso de álgebra lineal como complemento natural del estudio de la forma canónica de Jordan. La forma canónica de Kronecker es llamada igualmente de Weierstrass-Kronecker, ya que Weierstrass desarrolla la teoría de los divisores elementales y Kronecker la de los índices minimales. Desde un punto de vista epistemológico e histórico deben relacionarse estas teorías con el estudio geométrico de los haces de cónicas y cuádricas para la formación del estudiante de matemáticas. Este libro no intenta establecer estas conexiones. Al lector que desee proseguir en los precedentes históricos le recomendamos el libro sobre historia de las matemáticas de Bourbaki y también artículos de Robert Thompson, Frank Uhlig y otros en la revista Linear Algebra and Its Applications en los años 1980