Classical solutions for a logarithmic fractional diffusion equation

We prove global existence and uniqueness of strong solutions to the logarithmic porous medium type equation with fractional diffusion ?tu + (?)1/2 log(1 + u) = 0, posed for x ? R, with nonnegative initial data in some function space of LlogL type. The solutions are shown to become bounded and C? smooth in (x, t) for all positive times. We also reformulate this equation as a transport equation with nonlocal velocity and critical viscosity, a topic of current relevance. Interesting functional inequalities are involved.

Echo-delay resolution in sonar images of the big brown bat, Eptesicus fuscus

Echolocating big brown bats (Eptesicus fuscus) broadcast ultrasonic frequency-modulated (FM) biosonar sounds (20–100 kHz frequencies; 10–50 μs periods) and perceive target range from echo delay. Knowing the acuity for delay resolution is essential to understand how bats process echoes because they perceive target shape and texture from the delay separation of multiple reflections. Bats can separately perceive the delays of two concurrent electronically generated echoes arriving as little as 2 μs apart, thus resolving reflecting points as close together as 0.3 mm in range (two-point threshold). This two-point resolution is roughly five times smaller than the shortest periods in the bat’s sounds. Because the bat’s broadcasts are 2,000–4,500 μs long, the echoes themselves overlap and interfere with each other, to merge together into a single sound whose spectrum is shaped by their mutual interference depending on the size of the time separation. To separately perceive the delays of overlapping echoes, the bat has to recover information about their very small delay separation that was transferred into the spectrum when the two echoes interfered with each other, thus explicitly reconstructing the range profile of targets from the echo spectrum. However, the bat’s 2-μs resolution limit is so short that the available spectral cues are extremely limited. Resolution of delay seems overly sharp just for interception of flying insects, which suggests that the bat’s biosonar images are of higher quality to suit a wider variety of orientation tasks, and that biosonar echo processing is correspondingly more sophisticated than has been suspected.

A Modified Positive Velocity and Position Feedback scheme with delay compensation for improved nanopositioning performance

Acknowledgments This paper was sponsored by the Spanish FPU12/00984 Program (Ministerio de Educacion, Cultura y Deporte). It was also sponsored by the Spanish Government Research Program with the Project DPI2012-37062-CO2-01 (Ministerio de Economia y Competitividad) and by the European Social Fund.

Continuous and lurching traveling pulses in neuronal networks with delay and spatially decaying connectivity

Propagation of discharges in cortical and thalamic systems, which is used as a probe for examining network circuitry, is studied by constructing a one-dimensional model of integrate-and-fire neurons that are coupled by excitatory synapses with delay. Each neuron fires only one spike. The velocity and stability of propagating continuous pulses are calculated analytically. Above a certain critical value of the constant delay, these pulses lose stability. Instead, lurching pulses propagate with discontinuous and periodic spatio-temporal characteristics. The parameter regime for which lurching occurs is strongly affected by the footprint (connectivity) shape; bistability may occur with a square footprint shape but not with an exponential footprint shape. For strong synaptic coupling, the velocity of both continuous and lurching pulses increases logarithmically with the synaptic coupling strength gsyn for an exponential footprint shape, and it is bounded for a step footprint shape. We conclude that the differences in velocity and shape between the front of thalamic spindle waves in vitro and cortical paroxysmal discharges stem from their different effective delay; in thalamic networks, large effective delay between inhibitory neurons arises from their effective interaction via the excitatory cells which display postinhibitory rebound.

Residual delay maps unveil global patterns of atmospheric nonlinearity and produce improved local forecasts

We use residual-delay maps of observational field data for barometric pressure to demonstrate the structure of latitudinal gradients in nonlinearity in the atmosphere. Nonlinearity is weak and largely lacking in tropical and subtropical sites and increases rapidly into the temperate regions where the time series also appear to be much noisier. The degree of nonlinearity closely follows the meridional variation of midlatitude storm track frequency. We extract the specific functional form of this nonlinearity, a V shape in the lagged residuals that appears to be a basic feature of midlatitude synoptic weather systems associated with frontal passages. We present evidence that this form arises from the relative time scales of high-pressure versus low-pressure events. Finally, we show that this nonlinear feature is weaker in a well regarded numerical forecast model (European Centre for Medium-Range Forecasts) because small-scale temporal and spatial variation is smoothed out in the grided inputs. This is significant, in that it allows us to demonstrate how application of statistical corrections based on the residual-delay map may provide marked increases in local forecast accuracy, especially for severe weather systems.

Light-induced phase-delay of the chicken pineal circadian clock is associated with the induction of cE4bp4, a potential transcriptional repressor of cPer2 gene

The chicken pineal gland contains the autonomous circadian oscillator together with the photic-input pathway. We searched for chicken pineal genes that are induced by light in a time-of-day-dependent manner, and isolated chicken homolog of bZIP transcription factor E4bp4 (cE4bp4) showing high similarity to vrille, one of the Drosophila clock genes. cE4bp4 was expressed rhythmically in the pineal gland with a peak at very early (subjective) night under both 12-h light/12-h dark cycle and constant dark conditions, and the phase was nearly opposite to the expression rhythm of cPer2, a chicken pineal clock gene. Luciferase reporter gene assays showed that cE4BP4 represses cPer2 promoter through a E4BP4-recognition sequence present in the 5′-flanking region, indicating that cE4BP4 can down-regulate the chick pineal cPer2 expression. In vivo light-perturbation studies showed that the prolongation of the light period to early subjective night maintained the high level expression of the pineal cE4bp4, and presumably as a consequence delayed the onset of the induction of the pineal cPer2 expression in the next morning. These light-dependent changes in the mRNA levels of the pineal cE4bp4 and cPer2 were followed by a phase-delay of the subsequent cycles of cE4bp4/cPer2 expression, suggesting that cE4BP4 plays an important role in the phase-delaying process as a light-dependent suppressor of cPer2 gene.

Microsatellite instability in childhood rhabdomyosarcoma is locus specific and correlates with fractional allelic loss.

Replication errors (RERs) were initially identified in hereditary nonpolyposis colon cancer and other tumors of Lynch syndrome II. Mutations in genes involved in mismatch repair give rise to a mutator phenotype, resulting in RERs. The mutator phenotype is thought to predispose to malignant transformation. Here we show that in the embryonal form of childhood rhabdomyosarcoma, RERs also occur, but in contrast to hereditary nonpolyposis colon cancer, only a subset of the microsatellite loci analyzed show RERs. The occurrence of RERs is strongly correlated with increased fractional allelic loss (P < 0.001), suggesting that the occurrence of RERs is a secondary phenomenon in rhabdomyosarcoma. Coincidental loss of genes involved in mismatch repair, possibly due to their proximity to tumor suppressor genes involved in tumor progression of embryonal form of childhood rhabdomyosarcoma, could explain the observed phenomenon.

Viral dynamics in vivo: limitations on estimates of intracellular delay and virus decay.

Anti-viral drug treatment of human immunodeficiency virus type I (HIV-1) and hepatitis B virus (HBV) infections causes rapid reduction in plasma virus load. Viral decline occurs in several phases and provides information on important kinetic constants of virus replication in vivo and pharmacodynamical properties. We develop a mathematical model that takes into account the intracellular phase of the viral life-cycle, defined as the time between infection of a cell and production of new virus particles. We derive analytic solutions for the dynamics following treatment with reverse transcriptase inhibitors, protease inhibitors, or a combination of both. For HIV-1, our results show that the phase of rapid decay in plasma virus (days 2-7) allows precise estimates for the turnover rate of productively infected cells. The initial quasi-stationary phase (days 0-1) and the transition phase (days 1-2) are explained by the combined effects of pharmacological and intracellular delays, the clearance of free virus particles, and the decay of infected cells. Reliable estimates of the first three quantities are not possible from data on virus load only; such estimates require additional measurements. In contrast with HIV-1, for HBV our model predicts that frequent early sampling of plasma virus will lead to reliable estimates of the free virus half-life and the pharmacological properties of the administered drug. On the other hand, for HBV the half-life of infected cells cannot be estimated from plasma virus decay.

Estimating and forecasting generalized fractional Long memory stochastic volatility models

In recent years fractionally differenced processes have received a great deal of attention due to its flexibility in financial applications with long memory. This paper considers a class of models generated by Gegenbauer polynomials, incorporating the long memory in stochastic volatility (SV) components in order to develop the General Long Memory SV (GLMSV) model. We examine the statistical properties of the new model, suggest using the spectral likelihood estimation for long memory processes, and investigate the finite sample properties via Monte Carlo experiments. We apply the model to three exchange rate return series. Overall, the results of the out-of-sample forecasts show the adequacy of the new GLMSV model.

Absence of magnetically induced fractional quantization in atomic contacts

Using the mechanically controlled break junction technique at low temperatures and under cryogenic vacuum conditions we have studied atomic contacts of several magnetic (Fe, Co, and Ni) and nonmagnetic (Pt) metals, which recently were claimed to show fractional conductance quantization. In the case of pure metals we see no quantization of the conductance nor half quantization, even when high magnetic fields are applied. On the other hand, features in the conductance similar to (fractional) quantization are observed when the contact is exposed to gas molecules. Furthermore, the absence of fractional quantization when the contact is bridged by H2 indicates the current is never fully polarized for the metals studied here. Our results are in agreement with recent model calculations.

Stability switches in a first-order complex neutral delay equation

Stability of the first-order neutral delay equation x’ (t) + ax’ (t – τ) = bx(t) + cx(t – τ) with complex coefficients is studied, by analyzing the existence of stability switches.

Local probe of fractional edge states of S=1 Heisenberg spin chains

Spin chains are among the simplest physical systems in which electron-electron interactions induce novel states of matter. Here we propose to combine atomic scale engineering and spectroscopic capabilities of state of the art scanning tunnel microscopy to probe the fractionalized edge states of individual atomic scale S=1 spin chains. These edge states arise from the topological order of the ground state in the Haldane phase. We also show that the Haldane gap and the spin-spin correlation length can be measured with the same technique.

Estimation Models for Nonuniformly Sampled Signals–Application to Multiple Delay Estimation

This letter presents a method to model propagation channels for estimation, in which the sampling scheme can be arbitrary. Additionally, the method yields accurate models, with a size that converges to the channel duration, measured in Nyquist periods. It can be viewed as an improvement on the usual discretization based on regular sampling at the Nyquist rate. The method is introduced in the context of multiple delay estimation using the MUSIC estimator, and is assessed through a numerical example.

Difference schemes for time-dependent heat conduction models with delay

Different non-Fourier models of heat conduction, that incorporate time lags in the heat flux and/or the temperature gradient, have been increasingly considered in the last years to model microscale heat transfer problems in engineering. Numerical schemes to obtain approximate solutions of constant coefficients lagging models of heat conduction have already been proposed. In this work, an explicit finite difference scheme for a model with coefficients variable in time is developed, and their properties of convergence and stability are studied. Numerical computations showing examples of applications of the scheme are presented.