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.

On the geometry of solutions of the quasi-geostrophic and Euler equations

We study solutions of the two-dimensional quasi-geostrophic thermal active scalar equation involving simple hyperbolic saddles. There is a naturally associated notion of simple hyperbolic saddle breakdown. It is proved that such breakdown cannot occur in finite time. At large time, these solutions may grow at most at a quadruple-exponential rate. Analogous results hold for the incompressible three-dimensional Euler equation.

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.

A Molecular Network That Produces Spontaneous Oscillations in Excitable Cells of Dictyostelium

A network of interacting proteins has been found that can account for the spontaneous oscillations in adenylyl cyclase activity that are observed in homogenous populations of Dictyostelium cells 4 h after the initiation of development. Previous biochemical assays have shown that when extracellular adenosine 3′,5′-cyclic monophosphate (cAMP) binds to the surface receptor CAR1, adenylyl cyclase and the MAP kinase ERK2 are transiently activated. A rise in the internal concentration of cAMP activates protein kinase A such that it inhibits ERK2 and leads to a loss-of-ligand binding by CAR1. ERK2 phosphorylates the cAMP phosphodiesterase REG A that reduces the internal concentration of cAMP. A secreted phosphodiesterase reduces external cAMP concentrations between pulses. Numerical solutions to a series of nonlinear differential equations describing these activities faithfully account for the observed periodic changes in cAMP. The activity of each of the components is necessary for the network to generate oscillatory behavior; however, the model is robust in that 25-fold changes in the kinetic constants linking the activities have only minor effects on the predicted frequency. Moreover, constant high levels of external cAMP lead to attenuation, whereas a brief pulse of cAMP can advance or delay the phase such that interacting cells become entrained.

Dynamic regulation of the tryptophan operon: A modeling study and comparison with experimental data

A mathematical model for regulation of the tryptophan operon is presented. This model takes into account repression, feedback enzyme inhibition, and transcriptional attenuation. Special attention is given to model parameter estimation based on experimental data. The model's system of delay differential equations is numerically solved, and the results are compared with experimental data on the temporal evolution of enzyme activity in cultures of Escherichia coli after a nutritional shift (minimal + tryptophan medium to minimal medium). Good agreement is obtained between the numeric simulations and the experimental results for wild-type E. coli, as well as for two different mutant strains.

Behavior of several two-dimensional fluid equations in singular scenarios

We give conditions that rule out formation of sharp fronts for certain two-dimensional incompressible flows. We show that a necessary condition of having a sharp front is that the flow has to have uncontrolled velocity growth. In the case of the quasi-geostrophic equation and two-dimensional Euler equation, we obtain estimates on the formation of semi-uniform fronts.

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.

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.

Quantificação de biomassa e carbono da parte aérea em uma área de Mata Atlântica, na Serra da Cantareira, São Paulo

A atividade humana tem contribuído com as emissões de gases de efeito estufa (GEE) associadas, principalmente, com queima de combustíveis fósseis e mudanças no uso da terra. Assim, se faz necessário que sejam adotadas medidas visando o retardamento dos efeitos das mudanças climáticas. As florestas exercem papel essencial no balanço de carbono principalmente por funcionarem como sumidouros de CO2. Por outro lado, se desmatadas, promovem emissões e liberam parte do carbono estocado. A quantidade de biomassa florestal e o teor de carbono podem variar em função do tipo florestal, bem como de sua localização. Entretanto, fator importante diz respeito à confiabilidade dos dados mensurados neste tipo de pesquisa. A biomassa e o carbono da parte aérea podem ser determinados via método destrutivo, ou estimados via método não destrutivo. A construção do Rodoanel Mário Covas trecho norte e a supressão de uma área de Mata Atlântica possibilitou a realização de estudo de biomassa da parte aérea via método destrutivo. O objetivo deste trabalho foi estudar o tamanho e forma de parcelas, a intensidade amostral, quantificar a biomassa e o carbono na parte aérea, comparar métodos destrutivos e não destrutivos para a quantificação de biomassa e carbono na parte aérea, estudar a variação da densidade básica da madeira das espécies nas diferentes classes de DAP e grupos sucessionais e comparar as medidas de altura total e DAP obtidas a campo no inventário com as medidas coletadas após o corte. O tamanho mais conveniente de parcela foi 400 m 2, com forma retangular e dimensão de 10 x 40 m. A intensidade amostral variou entre 39 e 75 unidades amostrais. A biomassa da parte aérea obtida, via método destrutivo, foi de 188,3 Mg ha-1 e o carbono, 85,1 Mg ha-1. A biomassa estimada por equações alométricas da literatura foi subestimada, quando comparada ao valor real, obtido via método destrutivo. As menores classes de DAP apresentaram as maiores densidades básicas da madeira. A densidade básica foi 0,488 g cm-3 na média das espécies. A porcentagem de carbono contida nos troncos e galhos não diferiu entre as classes de DAP. O teor de carbono foi 45,41%, na média dos troncos e galhos. Espécies pioneiras acumularam maior quantidade de biomassa e carbono nos galhos e apresentaram maior densidade básica que as não pioneiras. A utilização dos dados coletados na fase de inventário e após o corte não afetaram os valores de biomassa estimados.

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.

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.

Introduction to Coding Theory for Flow Equations of Complex Systems Models

The modeling of complex dynamic systems depends on the solution of a differential equations system. Some problems appear because we do not know the mathematical expressions of the said equations. Enough numerical data of the system variables are known. The authors, think that it is very important to establish a code between the different languages to let them codify and decodify information. Coding permits us to reduce the study of some objects to others. Mathematical expressions are used to model certain variables of the system are complex, so it is convenient to define an alphabet code determining the correspondence between these equations and words in the alphabet. In this paper the authors begin with the introduction to the coding and decoding of complex structural systems modeling.

Disipation Functions of Flow Equations in Models of Complex Systems

In an open system, each disequilibrium causes a force. Each force causes a flow process, these being represented by a flow variable formally written as an equation called flow equation, and if each flow tends to equilibrate the system, these equations mathematically represent the tendency to that equilibrium. In this paper, the authors, based on the concepts of forces and conjugated fluxes and dissipation function developed by Onsager and Prigogine, they expose the following hypothesis: Is replaced in Prigogine’s Theorem the flow by its equation or by a flow orbital considering conjugate force as a gradient. This allows to obtain a dissipation function for each flow equation and a function of orbital dissipation.

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.

On the Analytic Solutions of the Functional Equations w 1 f(a 1 z) + w 2 f(a 2 z) + ... + w n f(a n z) = 0

In this paper, it is showed that, given an integer number n ≥ 2, each zero of an exponential polynomial of the form w1az1+w2az2+⋯+wnazn, with non-null complex numbers w 1,w 2,…,w n and a 1,a 2,…,a n , produces analytic solutions of the functional equation w 1 f(a 1 z) + w 2 f(a 2 z) + ... + w n f(a n z) = 0 on certain domains of C, which represents an extension of some existing results in the literature on this functional equation for the case of positive coefficients a j and w j.