Generalized beta generated distributions

This article introduces generalized beta-generated (GBG) distributions. Sub-models include all classical beta-generated, Kumaraswamy-generated and exponentiated distributions. They are maximum entropy distributions under three intuitive conditions, which show that the classical beta generator skewness parameters only control tail entropy and an additional shape parameter is needed to add entropy to the centre of the parent distribution. This parameter controls skewness without necessarily differentiating tail weights. The GBG class also has tractable properties: we present various expansions for moments, generating function and quantiles. The model parameters are estimated by maximum likelihood and the usefulness of the new class is illustrated by means of some real data sets.

Synchronization of digital data decoders

Burst timing synchronisation is maintained in a digital data decoder during multiple burst reception in a TDMA system. The data within a multiple burst are streamed into memory storage and data corresponding to a first burst in the series of bursts are selected on the basis of a current timing estimate derived from a synchronisation burst. Selections of data corresponding to other bursts in the series of bursts are modified in accordance with updated timing estimates derived from previously processed bursts.

Response theory for equilibrium and non-equilibrium statistical mechanics: causality and generalized Kramers-Kronig relations

We consider the general response theory recently proposed by Ruelle for describing the impact of small perturbations to the non-equilibrium steady states resulting from Axiom A dynamical systems. We show that the causality of the response functions entails the possibility of writing a set of Kramers-Kronig (K-K) relations for the corresponding susceptibilities at all orders of nonlinearity. Nonetheless, only a special class of directly observable susceptibilities obey K-K relations. Specific results are provided for the case of arbitrary order harmonic response, which allows for a very comprehensive K-K analysis and the establishment of sum rules connecting the asymptotic behavior of the harmonic generation susceptibility to the short-time response of the perturbed system. These results set in a more general theoretical framework previous findings obtained for optical systems and simple mechanical models, and shed light on the very general impact of considering the principle of causality for testing self-consistency: the described dispersion relations constitute unavoidable benchmarks that any experimental and model generated dataset must obey. The theory exposed in the present paper is dual to the time-dependent theory of perturbations to equilibrium states and to non-equilibrium steady states, and has in principle similar range of applicability and limitations. In order to connect the equilibrium and the non equilibrium steady state case, we show how to rewrite the classical response theory by Kubo so that response functions formally identical to those proposed by Ruelle, apart from the measure involved in the phase space integration, are obtained. These results, taking into account the chaotic hypothesis by Gallavotti and Cohen, might be relevant in several fields, including climate research. In particular, whereas the fluctuation-dissipation theorem does not work for non-equilibrium systems, because of the non-equivalence between internal and external fluctuations, K-K relations might be robust tools for the definition of a self-consistent theory of climate change.

Numerical convergence of the Block-Maxima approach to the generalized extreme value distribution

In this paper we perform an analytical and numerical study of Extreme Value distributions in discrete dynamical systems. In this setting, recent works have shown how to get a statistics of extremes in agreement with the classical Extreme Value Theory. We pursue these investigations by giving analytical expressions of Extreme Value distribution parameters for maps that have an absolutely continuous invariant measure. We compare these analytical results with numerical experiments in which we study the convergence to limiting distributions using the so called block-maxima approach, pointing out in which cases we obtain robust estimation of parameters. In regular maps for which mixing properties do not hold, we show that the fitting procedure to the classical Extreme Value Distribution fails, as expected. However, we obtain an empirical distribution that can be explained starting from a different observable function for which Nicolis et al. (Phys. Rev. Lett. 97(21): 210602, 2006) have found analytical results.

On the stability radius of a generalized state-space system

The concept of “distance to instability” of a system matrix is generalized to system pencils which arise in descriptor (semistate) systems. Difficulties arise in the case of singular systems, because the pencil can be made unstable by an infinitesimal perturbation. It is necessary to measure the distance subject to restricted, or structured, perturbations. In this paper a suitable measure for the stability radius of a generalized state-space system is defined, and a computable expression for the distance to instability is derived for regular pencils of index less than or equal to one. For systems which are strongly controllable it is shown that this measure is related to the sensitivity of the poles of the system over all feedback matrices assigning the poles.

Robust control system design for generalized state-space systems

Robustness in multi-variable control system design requires that the solution to the design problem be insensitive to perturbations in the system data. In this paper we discuss measures of robustness for generalized state-space, or descriptor, systems and describe algorithmic techniques for optimizing robustness for various applications.

Transition from an anti-phase error-correction-mode to a synchronization mode in the mutual hand tracking

Proactive motion in hand tracking and in finger bending, in which the body motion occurs prior to the reference signal, was reported by the preceding researchers when the target signals were shown to the subjects at relatively high speed or high frequencies. These phenomena indicate that the human sensory-motor system tends to choose an anticipatory mode rather than a reactive mode, when the target motion is relatively fast. The present research was undertaken to study what kind of mode appears in the sensory-motor system when two persons were asked to track the hand position of the partner with each other at various mean tracking frequency. The experimental results showed a transition from a mutual error-correction mode to a synchronization mode occurred in the same region of the tracking frequency with that of the transition from a reactive error-correction mode to a proactive anticipatory mode in the mechanical target tracking experiments. Present research indicated that synchronization of body motion occurred only when both of the pair subjects operated in a proactive anticipatory mode. We also presented mathematical models to explain the behavior of the error-correction mode and the synchronization mode.

Symmetric stability of compressible zonal flows on a generalized equatorial β plane

Sufficient conditions are derived for the linear stability with respect to zonally symmetric perturbations of a steady zonal solution to the nonhydrostatic compressible Euler equations on an equatorial � plane, including a leading order representation of the Coriolis force terms due to the poleward component of the planetary rotation vector. A version of the energy–Casimir method of stability proof is applied: an invariant functional of the Euler equations linearized about the equilibrium zonal flow is found, and positive definiteness of the functional is shown to imply linear stability of the equilibrium. It is shown that an equilibrium is stable if the potential vorticity has the same sign as latitude and the Rayleigh centrifugal stability condition that absolute angular momentum increase toward the equator on surfaces of constant pressure is satisfied. The result generalizes earlier results for hydrostatic and incompressible systems and for systems that do not account for the nontraditional Coriolis force terms. The stability of particular equilibrium zonal velocity, entropy, and density fields is assessed. A notable case in which the effect of the nontraditional Coriolis force is decisive is the instability of an angular momentum profile that decreases away from the equator but is flatter than quadratic in latitude, despite its satisfying both the centrifugal and convective stability conditions.

When long-range zero-lag synchronization is feasible in cortical networks

Many studies have reported long-range synchronization of neuronal activity between brain areas, in particular in the beta and gamma bands with frequencies in the range of 14–30 and 40–80 Hz, respectively. Several studies have reported synchrony with zero phase lag, which is remarkable considering the synaptic and conduction delays inherent in the connections between distant brain areas. This result has led to many speculations about the possible functional role of zero-lag synchrony, such as for neuronal communication, attention, memory, and feature binding. However, recent studies using recordings of single-unit activity and local field potentials report that neuronal synchronization may occur with non-zero phase lags. This raises the questions whether zero-lag synchrony can occur in the brain and, if so, under which conditions. We used analytical methods and computer simulations to investigate which connectivity between neuronal populations allows or prohibits zero-lag synchrony. We did so for a model where two oscillators interact via a relay oscillator. Analytical results and computer simulations were obtained for both type I Mirollo–Strogatz neurons and type II Hodgkin–Huxley neurons. We have investigated the dynamics of the model for various types of synaptic coupling and importantly considered the potential impact of Spike-Timing Dependent Plasticity (STDP) and its learning window. We confirm previous results that zero-lag synchrony can be achieved in this configuration. This is much easier to achieve with Hodgkin–Huxley neurons, which have a biphasic phase response curve, than for type I neurons. STDP facilitates zero-lag synchrony as it adjusts the synaptic strengths such that zero-lag synchrony is feasible for a much larger range of parameters than without STDP.

Self-organized 40Hz synchronization in a physiological theory of EEG

We present evidence that large-scale spatial coherence of 40 Hz oscillations can emerge dynamically in a cortical mean field theory. The simulated synchronization time scale is about 150 ms, which compares well with experimental data on large-scale integration during cognitive tasks. The same model has previously provided consistent descriptions of the human EEG at rest, with tranquilizers, under anesthesia, and during anesthetic-induced epileptic seizures. The emergence of coherent gamma band activity is brought about by changing just one physiological parameter until cortex becomes marginally unstable for a small range of wavelengths. This suggests for future study a model of dynamic computation at the edge of cortical stability.

A generalized collectively compact operator theory with an application to integral equations on unbounded domains

In this paper a generalization of collectively compact operator theory in Banach spaces is developed. A feature of the new theory is that the operators involved are no longer required to be compact in the norm topology. Instead it is required that the image of a bounded set under the operator family is sequentially compact in a weaker topology. As an application, the theory developed is used to establish solvability results for a class of systems of second kind integral equations on unbounded domains, this class including in particular systems of Wiener-Hopf integral equations with L1 convolutions kernels

Mechanism for synchronized motion between two humans in mutual tapping experiments: Transition from alternative mode to synchronization mode

We performed mutual tapping experiments between two humans to investigate the conditions required for synchronized motion. A transition from an alternative mode to a synchronization mode was discovered under the same conditions when a subject changed from a reactive mode to an anticipation mode in single tapping experiments. Experimental results suggest that the cycle time for each tapping motion is tuned by a proportional control that is based on synchronization errors and cycle time errors. As the tapping frequency increases, the mathematical model based on the feedback control in the sensory-motor closed loop predicts a discrete mode transition as the gain factors of the proportional control decease. The conditions of the synchronization were shown as a consequence of the coupled dynamics based on the subsequent feedback loop in the sensory-motor system.

Generalized Bayesian cloud detection for satellite imagery. part 1: technique and validation for night-time imagery over land and sea

Numerical Weather Prediction (NWP) fields are used to assist the detection of cloud in satellite imagery. Simulated observations based on NWP are used within a framework based on Bayes' theorem to calculate a physically-based probability of each pixel with an imaged scene being clear or cloudy. Different thresholds can be set on the probabilities to create application-specific cloud-masks. Here, this is done over both land and ocean using night-time (infrared) imagery. We use a validation dataset of difficult cloud detection targets for the Spinning Enhanced Visible and Infrared Imager (SEVIRI) achieving true skill scores of 87% and 48% for ocean and land, respectively using the Bayesian technique, compared to 74% and 39%, respectively for the threshold-based techniques associated with the validation dataset.