Average activity of excitatory and inhibitory neural populations

We develop an extension of the Ott-Antonsen method [E. Ott and T. M. Antonsen, Chaos 18(3), 037113 (2008)] that allows obtaining the mean activity (spiking rate) of a population of excitable units. By means of the Ott-Antonsen method, equations for the dynamics of the order parameters of coupled excitatory and inhibitory populations of excitable units are obtained, and their mean activities are computed. Two different excitable systems are studied: Adler units and theta neurons. The resulting bifurcation diagrams are compared with those obtained from studying the phenomenological Wilson-Cowan model in some regions of the parameter space. Compatible behaviors, as well as higher dimensional chaotic solutions, are observed. We study numerical simulations to further validate the equations.Fil: Roulet, Javier. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; ArgentinaFil: Mindlin, Bernardo Gabriel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; Argentin

Characterization of spatiotemporal chaos in an inhomogeneous active medium

We study a reaction diffusion system of the activator-inhibitor type with inhomogeneous reaction terms showing spatiotemporal chaos. We analyze the topological properties of the unstable periodic orbits in the slow chaotic dynamics appearing, which can be embedded in three dimensions. We perform a bi-orthogonal decomposition analyzing the minimum number of modes necessary to find the same organization of unstable orbits.Comment: 13 pages, 6 figs. Physica D (in press

Characteristics of 5-year-olds who catch-up with MMR: findings from the UK Millennium Cohort Study

Objectives To examine predictors of partial and full measles, mumps and rubella (MMR) vaccination catch-up between 3 and 5 years. Design Secondary data analysis of the nationally representative Millennium Cohort Study (MCS). Setting Children born in the UK, 2000–2002. Participants 751 MCS children who were unimmunised against MMR at age 3, with immunisation information at age 5. Main outcome measures Catch-up status: unimmunised (received no MMR), partial catch-up (received one MMR) or full catch-up (received two MMRs). Results At age 5, 60.3% (n=440) children remained unvaccinated, 16.1% (n=127) had partially and 23.6% (n=184) had fully caught-up. Children from families who did not speak English at home were five times as likely to partially catch-up than children living in homes where only English was spoken (risk ratio 4.68 (95% CI 3.63 to 6.03)). Full catch-up was also significantly more likely in those did not speak English at home (adjusted risk ratio 1.90 (1.08 to 3.32)). In addition, those from Pakistan/Bangladesh (2.40 (1.38 to 4.18)) or ‘other’ ethnicities (such as Chinese) (1.88 (1.08 to 3.29)) were more likely to fully catch-up than White British. Those living in socially rented (1.86 (1.34 to 2.56)) or ‘Other’ (2.52 (1.23 to 5.18)) accommodations were more likely to fully catch-up than home owners, and families were more likely to catch-up if they lived outside London (1.95 (1.32 to 2.89)). Full catch-up was less likely if parents reported medical reasons (0.43 (0.25 to 0.74)), a conscious decision (0.33 (0.23 to 0.48)), or ‘other’ reasons (0.46 (0.29 to 0.73)) for not immunising at age 3 (compared with ‘practical’ reasons). Conclusions Parents who partially or fully catch-up with MMR experience practical barriers and tend to come from disadvantaged or ethnic minority groups. Families who continue to reject MMR tend to have more advantaged backgrounds and make a conscious decision to not immunise early on. Health professionals should consider these findings in light of the characteristics of their local populations

Order in Binary Sequences and the Routes to Chaos

The natural order in the space of binary sequences permits to recover the $U$-sequence. Also the scaling laws of the period-doubling cascade and the intermittency route to chaos defined in that ordered set are explained. These arise as intrinsic properties of this ordered set, and independent from any consideration about dynamical systems.Comment: 13 pages, 2 table

On Dislocations in a Special Class of Generalized Elasticity

In this paper we consider and compare special classes of static theories of gradient elasticity, nonlocal elasticity, gradient micropolar elasticity and nonlocal micropolar elasticity with only one gradient coefficient. Equilibrium equations are discussed. The relationship between the gradient theory and the nonlocal theory is discussed for elasticity as well as for micropolar elasticity. Nonsingular solutions for the elastic fields of screw and edge dislocations are given. Both the elastic deformation (distortion, strain, bend-twist) and the force and couple stress tensors do not possess any singularity unlike `classical' theories.Comment: 28 pages, to appear in: physica status solid