Generalized synchronization in directionally coupled systems with identical individual dynamics

A simple chaotic flow is presented, which when driven by an identical copy of itself, for certain initial conditions, is able to display generalized synchronization instead of identical synchronization. Being that the drive and the response are observed in exactly the same coordinate system, generalized synchronization is demonstrated by means of the auxiliary system approach and by the conditional Lyapunov spectrum. This is interpreted in terms of changes in the structure of the system stationary points, caused by the coupling, which modify its global behavior.

Dynamics of multiple lin gene expression in Sphingomonas paucimobilis B90A in response to different hexachlorocyclohexane isomers.

Sphingomonas paucimobilis B90A is able to degrade the alpha-, beta-, gamma-, and delta-isomers of hexachlorocyclohexane (HCH). It contains the genes linA, linB, linC, linD, linE, and linR, which have been implicated in HCH degradation. In this study, dynamic expression of the lin genes was measured in chemostat-grown S. paucimobilis B90A by RNA dot blot hybridization and real-time reverse transcriptase PCR upon exposure to a pulse of different HCH isomers. Irrespective of the addition of HCH, linA, linB, and linC were all expressed constitutively. In contrast, linD and linE were induced with alpha-HCH (2 mg/liter) and gamma-HCH (7 mg/liter). A sharp increase in mRNA levels for linD and linE was observed from 10 to 45 min after the addition of alpha- or gamma-HCH. Induction of linD and linE was not detectable upon the addition of 0.7 mg of gamma-HCH per liter, although the compound was degraded by the cells. The addition of beta-HCH (5 mg/liter) or delta-HCH (20 mg/liter) did not lead to linE and linD induction, despite the fact that 50% of the compounds were degraded. This suggests that degradation of beta- and delta-HCH proceeds by a different pathway than that of alpha- and gamma-HCH.

A fluorescent hormone biosensor reveals the dynamics of jasmonate signalling in plants.

Activated forms of jasmonic acid (JA) are central signals coordinating plant responses to stresses, yet tools to analyse their spatial and temporal distribution are lacking. Here we describe a JA perception biosensor termed Jas9-VENUS that allows the quantification of dynamic changes in JA distribution in response to stress with high spatiotemporal sensitivity. We show that Jas9-VENUS abundance is dependent on bioactive JA isoforms, the COI1 co-receptor, a functional Jas motif and proteasome activity. We demonstrate the utility of Jas9-VENUS to analyse responses to JA in planta at a cellular scale, both quantitatively and dynamically. This included using Jas9-VENUS to determine the cotyledon-to-root JA signal velocities on wounding, revealing two distinct phases of JA activity in the root. Our results demonstrate the value of developing quantitative sensors such as Jas9-VENUS to provide high-resolution spatiotemporal data about hormone distribution in response to plant abiotic and biotic stresses.

Individual-based modelling and simulation: towards a better understanding of growth dynamics from small inocula

Postprint (published version)

A quantitative analysis of L-glutamate-regulated Na+ dynamics in mouse cortical astrocytes: implications for cellular bioenergetics.

The mode of Na+ entry and the dynamics of intracellular Na+ concentration ([Na+]i) changes consecutive to the application of the neurotransmitter glutamate were investigated in mouse cortical astrocytes in primary culture by video fluorescence microscopy. An elevation of [Na+]i was evoked by glutamate, whose amplitude and initial rate were concentration dependent. The glutamate-evoked Na+ increase was primarily due to Na+-glutamate cotransport, as inhibition of non-NMDA ionotropic receptors by 6-cyano-7-nitroquinoxiline-2,3-dione (CNQX) only weakly diminished the response and D-aspartate, a substrate of the glutamate transporter, produced [Na+]i elevations similar to those evoked by glutamate. Non-NMDA receptor activation could nevertheless be demonstrated by preventing receptor desensitization using cyclothiazide. Thus, in normal conditions non-NMDA receptors do not contribute significantly to the glutamate-evoked Na+ response. The rate of Na+ influx decreased during glutamate application, with kinetics that correlate well with the increase in [Na+]i and which depend on the extracellular concentration of glutamate. A tight coupling between Na+ entry and Na+/K+ ATPase activity was revealed by the massive [Na+]i increase evoked by glutamate when pump activity was inhibited by ouabain. During prolonged glutamate application, [Na+]i remains elevated at a new steady-state where Na+ influx through the transporter matches Na+ extrusion through the Na+/K+ ATPase. A mathematical model of the dynamics of [Na+]i homeostasis is presented which precisely defines the critical role of Na+ influx kinetics in the establishment of the elevated steady state and its consequences on the cellular bioenergetics. Indeed, extracellular glutamate concentrations of 10 microM already markedly increase the energetic demands of the astrocytes.

On the inverse windowed Fourier transform

The inversion problem concerning the windowed Fourier transform is considered. It is shown that, out of the infinite solutions that the problem admits, the windowed Fourier transform is the "optimal" solution according to a maximum-entropy selection criterion.

The continuous wavelet transform as a maximum entropy solution of the corresponding inverse problem

The continuous wavelet transform is obtained as a maximumentropy solution of the corresponding inverse problem. It is well knownthat although a signal can be reconstructed from its wavelet transform,the expansion is not unique due to the redundancy of continuous wavelets.Hence, the inverse problem has no unique solution. If we want to recognizeone solution as "optimal", then an appropriate decision criterion hasto be adopted. We show here that the continuous wavelet transform is an"optimal" solution in a maximum entropy sense.

Temporal dynamics of auditory what and where processing in humans

Recent evidence suggests the human auditory system is organized,like the visual system, into a ventral 'what' pathway, devoted toidentifying objects and a dorsal 'where' pathway devoted to thelocalization of objects in space w1x. Several brain regions have beenidentified in these two different pathways, but until now little isknown about the temporal dynamics of these regions. We investigatedthis issue using 128-channel auditory evoked potentials(AEPs).Stimuli were stationary sounds created by varying interaural timedifferences and environmental real recorded sounds. Stimuli ofeach condition (localization, recognition) were presented throughearphones in a blocked design, while subjects determined theirposition or meaning, respectively.AEPs were analyzed in terms of their topographical scalp potentialdistributions (segmentation maps) and underlying neuronalgenerators (source estimation) w2x.Fourteen scalp potential distributions (maps) best explained theentire data set.Ten maps were nonspecific (associated with auditory stimulationin general), two were specific for sound localization and two werespecific for sound recognition (P-values ranging from 0.02 to0.045).Condition-specific maps appeared at two distinct time periods:;200 ms and ;375-550 ms post-stimulus.The brain sources associated with the maps specific for soundlocalization were mainly situated in the inferior frontal cortices,confirming previous findings w3x. The sources associated withsound recognition were predominantly located in the temporal cortices,with a weaker activation in the frontal cortex.The data show that sound localization and sound recognitionengage different brain networks that are apparent at two distincttime periods.References1. Maeder et al. Neuroimage 2001.2. Michel et al. Brain Research Review 2001.3. Ducommun et al. Neuroimage 2002.

A non-extensive maximum entropy based regulations method for bad conditioned inverse problems

A regularization method based on the non-extensive maximum entropy principle is devised. Special emphasis is given to the q=1/2 case. We show that, when the residual principle is considered as constraint, the q=1/2 generalized distribution of Tsallis yields a regularized solution for bad-conditioned problems. The so devised regularized distribution is endowed with a component which corresponds to the well known regularized solution of Tikhonov (1977).

Frames: a maximum entropy statistical estimate of the inverse problem

A maximum entropy statistical treatment of an inverse problem concerning frame theory is presented. The problem arises from the fact that a frame is an overcomplete set of vectors that defines a mapping with no unique inverse. Although any vector in the concomitant space can be expressed as a linear combination of frame elements, the coefficients of the expansion are not unique. Frame theory guarantees the existence of a set of coefficients which is “optimal” in a minimum norm sense. We show here that these coefficients are also “optimal” from a maximum entropy viewpoint.

Soil water dynamics and evapotranspiration of forage cactus clones under rainfed conditions

Abstract: The objective of this work was to evaluate soil water dynamics in areas cultivated with forage cactus clones and to determine how environmental conditions and crop growth affect evapotranspiration. The study was conducted in the municipality of Serra Talhada, in the state of Pernambuco, Brazil. Crop growth was monitored through changes in the cladode area index (CAI) and through the soil cover fraction, calculated at the end of the cycle. Real evapotranspiration (ET) of the three evaluated clones was obtained as the residual term in the soil water balance method. No difference was observed between soil water balance components, even though the evaluated clones were of different genus and had different CAI increments. Accumulated ET was of 1,173 mm during the 499 days of the experiment, resulting in daily average of 2.35 mm. The CAI increases the water consumption of the Orelha de Elefante Mexicana clone. In dry conditions, the water consumption of the Miúda clone responds more slowly to variation in soil water availability. The lower evolution of the CAI of the IPA Sertânia clone, during the rainy season, leads to a higher contribution of the evaporation component in ET. The atmospheric demand controls the ET of clones only when there is higher soil water availability; in this condition, the water consumption of the Miúda clone decreases more rapidly with the increase of atmospheric demand.

Blood-Borne Circadian Signal Stimulates Daily Oscillations in Actin Dynamics and SRF Activity.

In peripheral tissues circadian gene expression can be driven either by local oscillators or by cyclic systemic cues controlled by the master clock in the brain's suprachiasmatic nucleus. In the latter case, systemic signals can activate immediate early transcription factors (IETFs) and thereby control rhythmic transcription. In order to identify IETFs induced by diurnal blood-borne signals, we developed an unbiased experimental strategy, dubbed Synthetic TAndem Repeat PROMoter (STAR-PROM) screening. This technique relies on the observation that most transcription factor binding sites exist at a relatively high frequency in random DNA sequences. Using STAR-PROM we identified serum response factor (SRF) as an IETF responding to oscillating signaling proteins present in human and rodent sera. Our data suggest that in mouse liver SRF is regulated via dramatic diurnal changes of actin dynamics, leading to the rhythmic translocation of the SRF coactivator Myocardin-related transcription factor-B (MRTF-B) into the nucleus.

Federal Dynamics in Times of Economic and Financial Crisis

The global economic and financial crisis is a challenge for all governments, but particularly for federal states because divided and/or shared territorial powers make federations susceptible to coordination problems in fiscal policy making. This article explores the effects of the ongoing crisis on federal relations. Three kinds of problems that may become the cause of federal tensions and conflicts are evoked: opportunism of subgovernments, centralisation and erosion of solidarity among members of the federation. Our analysis of fiscal policies and federal conflicts of 11 federations between 2007 and the present reveals three kinds of coordination problems: shirking in the use of federal government grants, rent-seeking in equalisation payments, and over-borrowing and over-spending. Our results show that shirking remained limited to few cases and occurred only in the first part of the crisis. However, rent-seeking and over-borrowing and over-spending led to a reduction of solidarity among subgovernments and to increased regulation of the fiscal discretion of the members of the federation. Subsequently, tensions in federal relations increased - although only in one case did this challenged the federal order.

Analysis of a finite volume method for a cross-diffusion model in population dynamics

The main goal of this paper is to propose a convergent finite volume method for a reactionâeuro"diffusion system with cross-diffusion. First, we sketch an existence proof for a class of cross-diffusion systems. Then the standard two-point finite volume fluxes are used in combination with a nonlinear positivity-preserving approximation of the cross-diffusion coefficients. Existence and uniqueness of the approximate solution are addressed, and it is also shown that the scheme converges to the corresponding weak solution for the studied model. Furthermore, we provide a stability analysis to study pattern-formation phenomena, and we perform two-dimensional numerical examples which exhibit formation of nonuniform spatial patterns. From the simulations it is also found that experimental rates of convergence are slightly below second order. The convergence proof uses two ingredients of interest for various applications, namely the discrete Sobolev embedding inequalities with general boundary conditions and a space-time $L^1$ compactness argument that mimics the compactness lemma due to Kruzhkov. The proofs of these results are given in the Appendix.