Chimera states: Coexistence of coherence and incoherence in networks of coupled oscillators

A chimera state is a spatio-temporal pattern in a network of identical coupled oscillators in which synchronous and asynchronous oscillation coexist. This state of broken symmetry, which usually coexists with a stable spatially symmetric state, has intrigued the nonlinear dynamics community since its discovery in the early 2000s. Recent experiments have led to increasing interest in the origin and dynamics of these states. Here we review the history of research on chimera states and highlight major advances in understanding their behaviour.Comment: 26 pages, 3 figure

Basins of Attraction for Chimera States

Chimera states---curious symmetry-broken states in systems of identical coupled oscillators---typically occur only for certain initial conditions. Here we analyze their basins of attraction in a simple system comprised of two populations. Using perturbative analysis and numerical simulation we evaluate asymptotic states and associated destination maps, and demonstrate that basins form a complex twisting structure in phase space. Understanding the basins' precise nature may help in the development of control methods to switch between chimera patterns, with possible technological and neural system applications.Comment: Please see Ancillary files for the 4 supplementary videos including description (PDF

A model balancing cooperation and competition explains our right-handed world and the dominance of left-handed athletes

An overwhelming majority of humans are right-handed. Numerous explanations for individual handedness have been proposed, but this population-level handedness remains puzzling. Here we use a minimal mathematical model to explain this population-level hand preference as an evolved balance between cooperative and competitive pressures in human evolutionary history. We use selection of elite athletes as a test-bed for our evolutionary model and account for the surprising distribution of handedness in many professional sports. Our model predicts strong lateralization in social species with limited combative interaction, and elucidates the rarity of compelling evidence for "pawedness" in the animal world.Comment: 5 pages of text and 3 figures in manuscript, 8 pages of text and two figures in supplementary materia

Epilepsy Pipeline Conference Summary

Each year the Epilepsy Therapy Project in conjunction with the Epilepsy Foundation puts on a conference for new development in diagnostics, device and medication therapies emerging in the field of epilepsy. We summarize below a few of the presentations that we thought would be of interest to the JHN readership. For a full listing of the presentations please see http://www.epilepsy.com/ accelerating-new-therapies/2016-epilepsy-pipeline-conference. In the new mechanism of action therapies there were three new products that were presented. Scotts Edwards updated the conference on progress of the compound SF0034 which a potent and selective KCNQ2/3 activator designed to suppress neuronal hyperexcitability in patients with partial-onset epilepsy. SF0034 was found to have significantly greater potency and selectivity in preclinical models of epilepsy compared with the known product ritagabine. Tansna President Mark Robbins, presented progress fir a new novel non-sedating agent derived from propofol which in early work had a favorable efficacy and side effect profile. Michael Ragowski presented on a new Inhaled treatment for refractory epilepsy, which is a prodrug of propofol, as a potential rescue for patients having seizures and want to try and avoid the oncoming seizure. Lastly and for a similar target, Jackie French presented data on Phase 2a for a status epileptic rescue medication that being developed by Alexza Pharmaceuticals for patients who have repetitive seizures and want to stop after the first seizure. Page: 3

Chimera states in networks of phase oscillators: the case of two small populations

Chimera states are dynamical patterns in networks of coupled oscillators in which regions of synchronous and asynchronous oscillation coexist. Although these states are typically observed in large ensembles of oscillators and analyzed in the continuum limit, chimeras may also occur in systems with finite (and small) numbers of oscillators. Focusing on networks of $2N$ phase oscillators that are organized in two groups, we find that chimera states, corresponding to attracting periodic orbits, appear with as few as two oscillators per group and demonstrate that for $N>2$ the bifurcations that create them are analogous to those observed in the continuum limit. These findings suggest that chimeras, which bear striking similarities to dynamical patterns in nature, are observable and robust in small networks that are relevant to a variety of real-world systems.Comment: 13 pages, 16 figure

Is schizoaffective disorder a distinct categorical diagnosis? A critical review of the literature

Considerable debate surrounds the inclusion of schizoaffective disorder in psychiatric nosology. Schizoaffective disorder may be a variant of schizophrenia in which mood symptoms are unusually prominent but not unusual in type. This condition may instead reflect a severe form of either major depressive or bipolar disorder in which episode-related psychotic symptoms fail to remit completely between mood episodes. Alternatively, schizoaffective disorder may reflect the co-occurrence of two relatively common psychiatric illnesses, schizophrenia and a mood disorder (major depressive or bipolar disorder). Each of these formulations of schizoaffective disorder presents nosological challenges because the signs and symptoms of this condition cross conventional categorical diagnostic boundaries between psychotic disorders and mood disorders. The study, evaluation, and treatment of persons presently diagnosed with schizoaffective may be more usefully informed by a dimensional approach. It is in this context that this article reviews and contrasts the categorical and dimensional approaches to its description, neurobiology, and treatment. Based on this review, an argument for the study and treatment of this condition using a dimensional approach is offered

Eigenvalue Estimation of Differential Operators

We demonstrate how linear differential operators could be emulated by a quantum processor, should one ever be built, using the Abrams-Lloyd algorithm. Given a linear differential operator of order 2S, acting on functions psi(x_1,x_2,...,x_D) with D arguments, the computational cost required to estimate a low order eigenvalue to accuracy Theta(1/N^2) is Theta((2(S+1)(1+1/nu)+D)log N) qubits and O(N^{2(S+1)(1+1/nu)} (D log N)^c) gate operations, where N is the number of points to which each argument is discretized, nu and c are implementation dependent constants of O(1). Optimal classical methods require Theta(N^D) bits and Omega(N^D) gate operations to perform the same eigenvalue estimation. The Abrams-Lloyd algorithm thereby leads to exponential reduction in memory and polynomial reduction in gate operations, provided the domain has sufficiently large dimension D > 2(S+1)(1+1/nu). In the case of Schrodinger's equation, ground state energy estimation of two or more particles can in principle be performed with fewer quantum mechanical gates than classical gates.Comment: significant content revisions: more algorithm details and brief analysis of convergenc

Chimera States for Coupled Oscillators

Arrays of identical oscillators can display a remarkable spatiotemporal pattern in which phase-locked oscillators coexist with drifting ones. Discovered two years ago, such "chimera states" are believed to be impossible for locally or globally coupled systems; they are peculiar to the intermediate case of nonlocal coupling. Here we present an exact solution for this state, for a ring of phase oscillators coupled by a cosine kernel. We show that the stable chimera state bifurcates from a spatially modulated drift state, and dies in a saddle-node bifurcation with an unstable chimera.Comment: 4 pages, 4 figure