Stability regions for synchronized τ-periodic orbits of coupled maps with coupling delay τ

Motivated by the chaos suppression methods based on stabilizing an unstable periodic orbit, westudy the stability of synchronized periodic orbits of coupled map systems when the period of theorbit is the same as the delay in the information transmission between coupled units. We show thatthe stability region of a synchronized periodic orbit is determined by the Floquet multiplier of theperiodic orbit for the uncoupled map, the coupling constant, the smallest and the largest Laplacianeigenvalue of the adjacency matrix. We prove that the stabilization of an unstable τ-periodic orbitvia coupling with delay τ is possible only when the Floquet multiplier of the orbit is negative andthe connection structure is not bipartite. For a given coupling structure, it is possible to find thevalues of the coupling strength that stabilizes unstable periodic orbits. The most suitableconnection topology for stabilization is found to be the all-to-all coupling. On the other hand, anegative coupling constant may lead to destabilization of τ-periodic orbits that are stable for theuncoupled map. We provide examples of coupled logistic maps demonstrating the stabilization anddestabilization of synchronized τ-periodic orbits as well as chaos suppression via stabilization of asynchronized τ-periodic orbit

Mapping dynamical systems onto complex networks

A procedure to characterize chaotic dynamical systems with concepts of complex networks is pursued, in which a dynamical system is mapped onto a network. The nodes represent the regions of space visited by the system, while edges represent the transitions between these regions. Parameters used to quantify the properties of complex networks, including those related to higher order neighborhoods, are used in the analysis. The methodology is tested for the logistic map, focusing the onset of chaos and chaotic regimes. It is found that the corresponding networks show distinct features, which are associated to the particular type of dynamics that have generated them.Comment: 13 pages, 8 eps files in 5 figure

Multifocal peliosis hepatis: MR and diffusion-weighted MR-imaging findings of an atypical case

Peliosis is a rare benign disorder that is characterized by the presence of diffuse blood-filled cystic spaces and can occur in the liver, spleen, bone-marrow, and lungs. We present a 10-year-old boy with Fanconi anemia who presented with peliosis hepatis due to androgen treatment. Magnetic resonance (MR) imaging revealed multiple non-enhancing masses. Some of the lesions revealed fluid-fluid levels and extrahepatic extension on MR images. Diffusion-weighted (DW) imaging showed restricted diffusion. Fluid-fluid levels and extrahepatic extensions are unusual findings for hepatic peliotic lesions. In addition, DW imaging findings of peliosis hepatis have not been reported previously

Discovering universal statistical laws of complex networks

Different network models have been suggested for the topology underlying complex interactions in natural systems. These models are aimed at replicating specific statistical features encountered in real-world networks. However, it is rarely considered to which degree the results obtained for one particular network class can be extrapolated to real-world networks. We address this issue by comparing different classical and more recently developed network models with respect to their generalisation power, which we identify with large structural variability and absence of constraints imposed by the construction scheme. After having identified the most variable networks, we address the issue of which constraints are common to all network classes and are thus suitable candidates for being generic statistical laws of complex networks. In fact, we find that generic, not model-related dependencies between different network characteristics do exist. This allows, for instance, to infer global features from local ones using regression models trained on networks with high generalisation power. Our results confirm and extend previous findings regarding the synchronisation properties of neural networks. Our method seems especially relevant for large networks, which are difficult to map completely, like the neural networks in the brain. The structure of such large networks cannot be fully sampled with the present technology. Our approach provides a method to estimate global properties of under-sampled networks with good approximation. Finally, we demonstrate on three different data sets (C. elegans' neuronal network, R. prowazekii's metabolic network, and a network of synonyms extracted from Roget's Thesaurus) that real-world networks have statistical relations compatible with those obtained using regression models

Identification of plastic constitutive parameters at large deformations from three dimensional displacement fields

The aim of this paper is to provide a general procedure to extract the constitutive parameters of a plasticity model starting from displacement measurements and using the Virtual Fields Method. This is a classical inverse problem which has been already investigated in the literature, however several new features are developed here. First of all the procedure applies to a general three-dimensional displacement field which leads to large plastic deformations, no assumptions are made such as plane stress or plane strain although only pressure-independent plasticity is considered. Moreover the equilibrium equation is written in terms of the deviatoric stress tensor that can be directly computed from the strain field without iterations. Thanks to this, the identification routine is much faster compared to other inverse methods such as finite element updating. The proposed method can be a valid tool to study complex phenomena which involve severe plastic deformation and where the state of stress is completely triaxial, e.g. strain localization or necking occurrence. The procedure has been validated using a three dimensional displacement field obtained from a simulated experiment. The main potentialities as well as a first sensitivity study on the influence of measurement errors are illustrated

Kernel reconstruction for delayed neural field equations

Understanding the neural field activity for realistic living systems is a challenging task in contemporary neuroscience. Neural fields have been studied and developed theoretically and numerically with considerable success over the past four decades. However, to make effective use of such models, we need to identify their constituents in practical systems. This includes the determination of model parameters and in particular the reconstruction of the underlying effective connectivity in biological tissues. In this work, we provide an integral equation approach to the reconstruction of the neural connectivity in the case where the neural activity is governed by a delay neural field equation. As preparation, we study the solution of the direct problem based on the Banach fixed point theorem. Then we reformulate the inverse problem into a family of integral equations of the first kind. This equation will be vector valued when several neural activity trajectories are taken as input for the inverse problem. We employ spectral regularization techniques for its stable solution. A sensitivity analysis of the regularized kernel reconstruction with respect to the input signal u is carried out, investigating the Frechet differentiability of the kernel with respect to the signal. Finally, we use numerical examples to show the feasibility of the approach for kernel reconstruction, including numerical sensitivity tests, which show that the integral equation approach is a very stable and promising approach for practical computational neuroscience

Modeling Brain Resonance Phenomena Using a Neural Mass Model

Stimulation with rhythmic light flicker (photic driving) plays an important role in the diagnosis of schizophrenia, mood disorder, migraine, and epilepsy. In particular, the adjustment of spontaneous brain rhythms to the stimulus frequency (entrainment) is used to assess the functional flexibility of the brain. We aim to gain deeper understanding of the mechanisms underlying this technique and to predict the effects of stimulus frequency and intensity. For this purpose, a modified Jansen and Rit neural mass model (NMM) of a cortical circuit is used. This mean field model has been designed to strike a balance between mathematical simplicity and biological plausibility. We reproduced the entrainment phenomenon observed in EEG during a photic driving experiment. More generally, we demonstrate that such a single area model can already yield very complex dynamics, including chaos, for biologically plausible parameter ranges. We chart the entire parameter space by means of characteristic Lyapunov spectra and Kaplan-Yorke dimension as well as time series and power spectra. Rhythmic and chaotic brain states were found virtually next to each other, such that small parameter changes can give rise to switching from one to another. Strikingly, this characteristic pattern of unpredictability generated by the model was matched to the experimental data with reasonable accuracy. These findings confirm that the NMM is a useful model of brain dynamics during photic driving. In this context, it can be used to study the mechanisms of, for example, perception and epileptic seizure generation. In particular, it enabled us to make predictions regarding the stimulus amplitude in further experiments for improving the entrainment effect

Anisotropy effects on the plasmonic response of nanoparticle dimers

We present an ab initio study of the anisotropy and atomic relaxation effects on the optical properties of nanoparticle dimers. Special emphasis is placed on the hybridization process of localized surface plasmons, plasmon-mediated photoinduced currents, and electric-field enhancement in the dimer junction. We show that there is a critical range of separations between the clusters (0.1–0.5 nm) in which the detailed atomic structure in the junction and the relative orientation of the nanoparticles have to be considered to obtain quantitative predictions for realistic nanoplasmonic devices. It is worth noting that this regime is characterized by the emergence of electron tunneling as a response to the driven electromagnetic field. The orientation of the particles not only modifies the attainable electric field enhancement but can lead to qualitative changes in the optical absorption spectrum of the system.We thankfully acknowledge financial support by the European Research Council (ERC-2010-AdG Proposal No. 267374 and ERC-2011-AdG Proposal No. 290891), the Spanish Government (Grants MAT2011-28581-C02-01, FIS2013-46159-C3-1-P, and MAT2014-53432-C5-5-R), and the Basque Country Government (Grupos Consolidados IT-578-13).Peer Reviewe

Centering inclusivity in the design of online conferences: An OHBM-Open Science perspective

As the global health crisis unfolded, many academic conferences moved online in 2020. This move has been hailed as a positive step towards inclusivity in its attenuation of economic, physical, and legal barriers and effectively enabled many individuals from groups that have traditionally been underrepresented to join and participate. A number of studies have outlined how moving online made it possible to gather a more global community and has increased opportunities for individuals with various constraints, e.g., caregiving responsibilities. Yet, the mere existence of online conferences is no guarantee that everyone can attend and participate meaningfully. In fact, many elements of an online conference are still significant barriers to truly diverse participation: the tools used can be inaccessible for some individuals; the scheduling choices can favour some geographical locations; the set-up of the conference can provide more visibility to well-established researchers and reduce opportunities for early-career researchers. While acknowledging the benefits of an online setting, especially for individuals who have traditionally been underrepresented or excluded, we recognize that fostering social justice requires inclusivity to actively be centered in every aspect of online conference design. Here, we draw from the literature and from our own experiences to identify practices that purposefully encourage a diverse community to attend, participate in, and lead online conferences. Reflecting on how to design more inclusive online events is especially important as multiple scientific organizations have announced that they will continue offering an online version of their event when in-person conferences can resume