Transitions in active rotator systems: invariant hyperbolic manifold approach

Our main focus is on a general class of active rotators with mean field interactions, that is globally coupled large families of dynamical systems on the unit circle with non-trivial stochastic dynamics. Each isolated system is a diffusion process on a circle, with drift -delta V', where V' is a periodic function and delta is an intensity parameter. It is well known that the interacting dynamics is accurately described, in the limit of infinitely many interacting components, by a Fokker-Planck PDE and the model reduces for delta=0 to a particular case of the Kuramoto synchronization model, for which one can show the existence of a stable normally hyperbolic manifold of stationary solutions for the corresponding Fokker-Planck equation (we are interested in the case in which this manifold is non-trivial, that happens when the interaction is sufficiently strong, that is in the synchronized regime of the Kuramoto model). We use the robustness of normally hyperbolic structures to infer qualitative and quantitative results on the |delta|< delta0 cases, with delta0 a suitable threshold: as a matter of fact, we obtain an accurate description of the dynamics on the invariant manifold for delta=0 and we link it explicitly to the potential V . This approach allows to have a complete description of the phase diagram of the active rotators model, at least for |delta|< delta0, thus identifying for which values of the parameters (notably, noise intensity and/or coupling strength) the system exhibits periodic pulse waves or stabilizes at a quiescent resting state. Moreover, some of our results are very explicit and this brings a new insight into the combined effect of active rotator dynamics, noise and interaction. The links with the literature on specific systems, notably neuronal models, are discussed in detail.Comment: 29 pages, 4 figures. Version 2: some changes in introduction, added reference

Reducing the cost of group communication with semantic view synchrony

View Synchrony (VS) is a powerful abstraction in the design and implementation of de- pendable distributed systems. By ensuring that processes deliver the same set of messages in each view, it allows them to maintain consistency across membership changes. However, experience indicates that it is hard to combine strong reliability guarantees as offered by VS with stable high performance. In this paper we propose a novel abstraction, Semantic View Synchrony (SVS), that exploits the application's semantics to cope with high throughput applications. This is achieved by allowing some messages to be dropped while still preserving consistency when new views are installed. Thus, SVS inherits the elegance of view synchronous communi- cation. The paper describes how SVS can be implemented and illustrates its usefulness in the context of distributed multi-player games

VIOLA - A multi-purpose and web-based visualization tool for neuronal-network simulation output

Neuronal network models and corresponding computer simulations are invaluable tools to aid the interpretation of the relationship between neuron properties, connectivity and measured activity in cortical tissue. Spatiotemporal patterns of activity propagating across the cortical surface as observed experimentally can for example be described by neuronal network models with layered geometry and distance-dependent connectivity. The interpretation of the resulting stream of multi-modal and multi-dimensional simulation data calls for integrating interactive visualization steps into existing simulation-analysis workflows. Here, we present a set of interactive visualization concepts called views for the visual analysis of activity data in topological network models, and a corresponding reference implementation VIOLA (VIsualization Of Layer Activity). The software is a lightweight, open-source, web-based and platform-independent application combining and adapting modern interactive visualization paradigms, such as coordinated multiple views, for massively parallel neurophysiological data. For a use-case demonstration we consider spiking activity data of a two-population, layered point-neuron network model subject to a spatially confined excitation originating from an external population. With the multiple coordinated views, an explorative and qualitative assessment of the spatiotemporal features of neuronal activity can be performed upfront of a detailed quantitative data analysis of specific aspects of the data. Furthermore, ongoing efforts including the European Human Brain Project aim at providing online user portals for integrated model development, simulation, analysis and provenance tracking, wherein interactive visual analysis tools are one component. Browser-compatible, web-technology based solutions are therefore required. Within this scope, with VIOLA we provide a first prototype.Comment: 38 pages, 10 figures, 3 table

Towards a cyber physical system for personalised and automatic OSA treatment

Obstructive sleep apnea (OSA) is a breathing disorder that takes place in the course of the sleep and is produced by a complete or a partial obstruction of the upper airway that manifests itself as frequent breathing stops and starts during the sleep. The real-time evaluation of whether or not a patient is undergoing OSA episode is a very important task in medicine in many scenarios, as for example for making instantaneous pressure adjustments that should take place when Automatic Positive Airway Pressure (APAP) devices are used during the treatment of OSA. In this paper the design of a possible Cyber Physical System (CPS) suited to real-time monitoring of OSA is described, and its software architecture and possible hardware sensing components are detailed. It should be emphasized here that this paper does not deal with a full CPS, rather with a software part of it under a set of assumptions on the environment. The paper also reports some preliminary experiments about the cognitive and learning capabilities of the designed CPS involving its use on a publicly available sleep apnea database

Mean-Field Theory of Meta-Learning

We discuss here the mean-field theory for a cellular automata model of meta-learning. The meta-learning is the process of combining outcomes of individual learning procedures in order to determine the final decision with higher accuracy than any single learning method. Our method is constructed from an ensemble of interacting, learning agents, that acquire and process incoming information using various types, or different versions of machine learning algorithms. The abstract learning space, where all agents are located, is constructed here using a fully connected model that couples all agents with random strength values. The cellular automata network simulates the higher level integration of information acquired from the independent learning trials. The final classification of incoming input data is therefore defined as the stationary state of the meta-learning system using simple majority rule, yet the minority clusters that share opposite classification outcome can be observed in the system. Therefore, the probability of selecting proper class for a given input data, can be estimated even without the prior knowledge of its affiliation. The fuzzy logic can be easily introduced into the system, even if learning agents are build from simple binary classification machine learning algorithms by calculating the percentage of agreeing agents.Comment: 23 page

Spontaneous Resonances and the Coherent States of the Queuing Networks

We present an example of a highly connected closed network of servers, where the time correlations do not go to zero in the infinite volume limit. This phenomenon is similar to the continuous symmetry breaking at low temperatures in statistical mechanics. The role of the inverse temperature is played by the average load.Comment: 3 figures added, small correction

Comparing Fully General Relativistic and Newtonian Calculations of Structure Formation

In the standard approach to studying cosmological structure formation, the overall expansion of the Universe is assumed to be homogeneous, with the gravitational effect of inhomogeneities encoded entirely in a Newtonian potential. A topic of ongoing debate is to what degree this fully captures the dynamics dictated by general relativity, especially in the era of precision cosmology. To quantitatively assess this, we directly compare standard N-body Newtonian calculations to full numerical solutions of the Einstein equations, for cold matter with various magnitude initial inhomogeneities on scales comparable to the Hubble horizon. We analyze the differences in the evolution of density, luminosity distance, and other quantities defined with respect to fiducial observers. This is carried out by reconstructing the effective spacetime and matter fields dictated by the Newtonian quantities, and by taking care to distinguish effects of numerical resolution. We find that the fully general relativistic and Newtonian calculations show excellent agreement, even well into the nonlinear regime. They only notably differ in regions where the weak gravity assumption breaks down, which arise when considering extreme cases with perturbations exceeding standard values.Comment: 17 pages, 14 figures; revised to match PRD versio

Perturbatively constructed cosmological model with periodically distributed dust inhomogeneities

We constructed a simple cosmological model which approximates the Einstein-de Sitter background with periodically distributed dust inhomogeneities. By taking the metric as a power series up to the third order in some perturbative parameter $\lambda$, we are able to achieve large values of the density contrast. With a metric explicitly given, many model properties can be calculated in a straightforward way which is interesting in the context of the current discussion concerning the averaging of the inhomogeneities and their backreaction in cosmology. Although the Einstein-de Sitter model can be thought as the model \emph{average}, the light propagation differs from that of the Einstein-de Sitter. The angular diameter distance-redshift relation is affected by the presence of inhomogeneities and depends on the observer's position. The model construction scheme enables some generalizations in the future, so the present work is a step towards more realistic cosmological model described by a relatively simple analytical metric