Noise and periodic modulations in neural excitable medium

We have analyzed the interplay between noise and periodic modulations in a mean field model of a neural excitable medium. For this purpose, we have considered two types of modulations, namely, variations of the resistance and oscillations of the threshold. In both cases, stochastic resonance is present, irrespective of whether the system is monostable or bistable.

Mean first-passage times for systems driven by equilibrium persistent-periodic dichotomous noise

In a recent paper, [J. M. Porrà, J. Masoliver, and K. Lindenberg, Phys. Rev. E 48, 951 (1993)], we derived the equations for the mean first-passage time for systems driven by the coin-toss square wave, a particular type of dichotomous noisy signal, to reach either one of two boundaries. The coin-toss square wave, which we here call periodic-persistent dichotomous noise, is a random signal that can only change its value at specified time points, where it changes its value with probability q or retains its previous value with probability p=1-q. These time points occur periodically at time intervals t. Here we consider the stationary version of this signal, that is, equilibrium periodic-persistent noise. We show that the mean first-passage time for systems driven by this stationary noise does not show either the discontinuities or the oscillations found in the case of nonstationary noise. We also discuss the existence of discontinuities in the mean first-passage time for random one-dimensional stochastic maps.

Difussion in a titled periodic potential: Enhancement, universality, and scaling

An exact analytical expression for the effective diffusion coefficient of an overdamped Brownian particle in a tilted periodic potential is derived for arbitrary potentials and arbitrary strengths of the thermal noise. Near the critical tilt (threshold of deterministic running solutions) a scaling behavior for weak thermal noise is revealed and various universality classes are identified. In comparison with the bare (potential-free) thermal diffusion, the effective diffusion coefficient in a critically tilted periodic potential may be, in principle, arbitrarily enhanced. For a realistic experimental setup, an enhancement by 14 orders of magnitude is predicted so that thermal diffusion should be observable on a macroscopic scale at room temperature.

Seizure detection with automated EEG analysis: a validation study focusing on periodic patterns.

OBJECTIVE: To evaluate an automated seizure detection (ASD) algorithm in EEGs with periodic and other challenging patterns. METHODS: Selected EEGs recorded in patients over 1year old were classified into four groups: A. Periodic lateralized epileptiform discharges (PLEDs) with intermixed electrical seizures. B. PLEDs without seizures. C. Electrical seizures and no PLEDs. D. No PLEDs or seizures. Recordings were analyzed by the Persyst P12 software, and compared to the raw EEG, interpreted by two experienced neurophysiologists; Positive percent agreement (PPA) and false-positive rates/hour (FPR) were calculated. RESULTS: We assessed 98 recordings (Group A=21 patients; B=29, C=17, D=31). Total duration was 82.7h (median: 1h); containing 268 seizures. The software detected 204 (=76.1%) seizures; all ictal events were captured in 29/38 (76.3%) patients; in only in 3 (7.7%) no seizures were detected. Median PPA was 100% (range 0-100; interquartile range 50-100), and the median FPR 0/h (range 0-75.8; interquartile range 0-4.5); however, lower performances were seen in the groups containing periodic discharges. CONCLUSION: This analysis provides data regarding the yield of the ASD in a particularly difficult subset of EEG recordings, showing that periodic discharges may bias the results. SIGNIFICANCE: Ongoing refinements in this technique might enhance its utility and lead to a more extensive application.

Periodic points of holomorphic maps via Lefschetz numbers

In this paper we study the set of periods of holomorphic maps on compact manifolds, using the periodic Lefschetz numbers introduced by Dold and Llibre, which can be computed from the homology class of the map. We show that these numbers contain information about the existence of periodic points of a given period; and, if we assume the map to be transversal, then they give us the exact number of such periodic orbits. We apply this result to the complex projective space of dimension n and to some special type of Hopf surfaces, partially characterizing their set of periods. In the first case we also show that any holomorphic map of CP(n) of degree greater than one has infinitely many distinct periodic orbits, hence generalizing a theorem of Fornaess and Sibony. We then characterize the set of periods of a holomorphic map on the Riemann sphere, hence giving an alternative proof of Baker's theorem.

International periodic fever, aphthous stomatitis, pharyngitis, cervical adenitis syndrome cohort: description of distinct phenotypes in 301 patients.

OBJECTIVES: The aims of this study were to describe the clinical features of periodic fever, aphthous stomatitis, pharyngitis and cervical adenitis (PFAPA) and identify distinct phenotypes in a large cohort of patients from different countries. METHODS: We established a web-based multicentre cohort through an international collaboration within the periodic fevers working party of the Pediatric Rheumatology European Society (PReS). The inclusion criterion was a diagnosis of PFAPA given by an experienced paediatric rheumatologist participating in an international working group on periodic fever syndromes. RESULTS: Of the 301 patients included from the 15 centres, 271 had pharyngitis, 236 cervical adenitis, 171 oral aphthosis and 132 with all three clinical features. A total of 228 patients presented with additional symptoms (131 gastrointestinal symptoms, 86 arthralgias and/or myalgias, 36 skin rashes, 8 neurological symptoms). Thirty-one patients had disease onset after 5 years and they reported more additional symptoms. A positive family history for recurrent fever or recurrent tonsillitis was found in 81 patients (26.9%). Genetic testing for monogenic periodic fever syndromes was performed on 111 patients, who reported fewer occurrences of oral aphthosis or additional symptoms. Twenty-four patients reported symptoms (oral aphthosis and malaise) outside the flares. The CRP was >50 mg/l in the majority (131/190) of the patients tested during the fever. CONCLUSION: We describe the largest cohort of PFAPA patients presented so far. We confirm that PFAPA may present with varied clinical manifestations and we show the limitations of the commonly used diagnostic criteria. Based on detailed analysis of this cohort, a consensus definition of PFAPA with better-defined criteria should be proposed.

First-principles periodic calculation of four-body spin terms in high-Tc cuprate superconductors

A general mapping between the energy of pertinent magnetic solutions and the diagonal terms of the spin Hamiltonian in a local representation provides the first general framework to extract accurate values for the many body terms of extended spin Hamiltonians from periodic first-principle calculations. Estimates of these terms for La2CuO4, the paradigm of high-Tc superconductor parent compounds, and for the SrCu2O3 ladder compound are reported. For La2CuO4, present results support experimental evidence by Toader et al. [Phys. Rev. Lett. 94, 197202 (2005)]. For SrCu2O3 even larger four-body spin amplitudes are found together with Jl/Jr=1 and non-negligible ferromagnetic interladder exchange.

First-principles periodic calculation of four-body spin terms in high-Tc Cuprate superconductors

A general mapping between the energy of pertinent magnetic solutions and the diagonal terms of the spin Hamiltonian in a local representation provides the first general framework to extract accurate values for the many body terms of extended spin Hamiltonians from periodic first-principle calculations. Estimates of these terms for La2CuO4, the paradigm of high-Tc superconductor parent compounds, and for the SrCu2O3 ladder compound are reported. For La2CuO4, present results support experimental evidence by Toader et al. [Phys. Rev. Lett. 94, 197202 (2005)]. For SrCu2O3 even larger four-body spin amplitudes are found together with Jl/Jr=1 and non-negligible ferromagnetic interladder exchange.

Enhanced pulse propagation in non-linear arrays of oscillators

The propagation of a pulse in a nonlinear array of oscillators is influenced by the nature of the array and by its coupling to a thermal environment. For example, in some arrays a pulse can be speeded up while in others a pulse can be slowed down by raising the temperature. We begin by showing that an energy pulse (one dimension) or energy front (two dimensions) travels more rapidly and remains more localized over greater distances in an isolated array (microcanonical) of hard springs than in a harmonic array or in a soft-springed array. Increasing the pulse amplitude causes it to speed up in a hard chain, leaves the pulse speed unchanged in a harmonic system, and slows down the pulse in a soft chain. Connection of each site to a thermal environment (canonical) affects these results very differently in each type of array. In a hard chain the dissipative forces slow down the pulse while raising the temperature speeds it up. In a soft chain the opposite occurs: the dissipative forces actually speed up the pulse, while raising the temperature slows it down. In a harmonic chain neither dissipation nor temperature changes affect the pulse speed. These and other results are explained on the basis of the frequency vs energy relations in the various arrays

Periodic forcing of scroll rings and control of Winfree turbulence in excitable media

By simulations of the Barkley model, action of uniform periodic nonresonant forcing on scroll rings and wave turbulence in three-dimensional excitable media is investigated. Sufficiently strong rapid forcing converts expanding scroll rings into the collapsing ones and suppresses the Winfree turbulence caused by the negative tension of wave filaments. Slow strong forcing has an opposite effect, leading to expansion of scroll rings and induction of the turbulence. These effects are explained in the framework of the phenomenological kinematic theory of scroll waves.

Breathers and thermal relaxation in Fermi-Pasta-Ulam arrays

Breather stability and longevity in thermally relaxing nonlinear arrays depend sensitively on their interactions with other excitations. We review numerical results for the relaxation of breathers in Fermi¿Pasta¿Ulam arrays, with a specific focus on the different relaxation channels and their dependence on the interparticle interactions, dimensionality, initial condition, and system parameters

Mixed mating in androdioecious Mercurialis annua inferred using progeny arrays and diploid-acting microsatellite loci in a hexaploid background.

Background and Aims The frequency at which males can be maintained with hermaphrodites in androdioecious populations is predicted to depend on the selfing rate, because self-fertilization by hermaphrodites reduces prospective siring opportunities for males. In particular, high selfing rates by hermaphrodites are expected to exclude males from a population. Here, the first estimates are provided of the mating system from two wild hexaploid populations of the androdioecious European wind-pollinated plant M. annua with contrasting male frequencies.Methods Four diploid microsatellite loci were used to genotype 19-20 progeny arrays from two populations of M. annua, one with males and one without. Mating-system parameters were estimated using the program MLTR.Key Results Both populations had similar, intermediate outcrossing rates (t(m) = 0.64 and 0.52 for the population with and without males, respectively). The population without males showed a lower level of correlated paternity and biparental inbreeding and higher allelic richness and gene diversity than the population with males.Conclusions The results demonstrate the utility of new diploid microsatellite loci for mating system analysis in a hexaploid plant. It would appear that androdioecious M. annua has a mixed-mating system in the wild, an uncommon finding for wind-pollinated species. This study sets a foundation for future research to assess the relative importance of the sexual system, plant-density variation and stochastic processes for the regulation of male frequencies in M. annua over space and time.

Fréedericksz transition in a periodic magnetic field

We study the Fréedericksz transition in a twist geometry under the effect of a periodic modulation of the magnitude of the applied magnetic field. We find a shift of the effective instability point and a time-periodic state with anomalously large orientational fluctuations. This time-periodic state occurs below threshold and it is accompanied by a dynamically stabilized spatial pattern. Beyond the instability the emergence of a transient pattern can be significantly delayed by a fast modulation, allowing the observation of pattern selection by slowing down the reorientational dynamics.