On localized vegetation patterns, fairy circles and localized patches in arid landscapes

We investigate the formation of localized structures with a varying width in one and two-dimensional systems. The mechanism of stabilization is attributed to strong nonlocal coupling mediated by a Lorentzian type of Kernel. We show that, in addition to stable dips found recently [see, e.g., C. Fernandez-Oto, M. G. Clerc, D. Escaff, and M. Tlidi, Phys. Rev. Lett. {\bf{110}}, 174101 (2013)], exist stable localized peaks which appear as a result of strong nonlocal coupling, i.e. mediated by a coupling that decays with the distance slower than an exponential. We applied this mechanism to arid ecosystems by considering a prototype model of a Nagumo type. In one-dimension, we study the front that connects the stable uniformly vegetated state with the bare one under the effect of strong nonlocal coupling. We show that strong nonlocal coupling stabilizes both---dip and peak---localized structures. We show analytically and numerically that the width of localized dip, which we interpret as fairy circle, increases strongly with the aridity parameter. This prediction is in agreement with filed observations. In addition, we predict that the width of localized patch decreases with the degree of aridity. Numerical results are in close agreement with analytical predictions

Stochastic thermodynamics for Ising chain and symmetric exclusion process

We verify the finite time fluctuation theorem for a linear Ising chain at its ends in contact with heat reservoirs. Analytic results are derived for a chain consisting of only two spins. The system can be mapped onto a model for particle transport, namely the symmetric exclusion process, in contact with thermal and particle reservoirs. We modify the symmetric exclusion process to represent a thermal engine and reproduce universal features of the efficiency at maximum power

Plant clonal morphologies and spatial patterns as self-organized responses to resource-limited environments

We propose here to interpret and model peculiar plant morphologies (cushions, tussocks) observed in the Andean altiplano as localized structures. Such structures resulting in a patchy, aperiodic aspect of the vegetation cover are hypothesized to self-organize thanks to the interplay between facilitation and competition processes occurring at the scale of basic plant components biologically referred to as 'ramets'. (Ramets are often of clonal origin.) To verify this interpretation, we applied a simple, fairly generic model (one integro-differential equation) emphasizing via Gaussian kernels non-local facilitative and competitive feedbacks of the vegetation biomass density on its own dynamics. We show that under realistic assumptions and parameter values relating to ramet scale, the model can reproduce some macroscopic features of the observed systems of patches and predict values for the inter-patch distance that match the distances encountered in the reference area (Sajama National Park in Bolivia). Prediction of the model can be confronted in the future to data on vegetation patterns along environmental gradients as to anticipate the possible effect of global change on those vegetation systems experiencing constraining environmental conditions.Comment: 14 pages, 6figure

Synchronization of globally coupled two-state stochastic oscillators with a state dependent refractory period

We present a model of identical coupled two-state stochastic units each of which in isolation is governed by a fixed refractory period. The nonlinear coupling between units directly affects the refractory period, which now depends on the global state of the system and can therefore itself become time dependent. At weak coupling the array settles into a quiescent stationary state. Increasing coupling strength leads to a saddle node bifurcation, beyond which the quiescent state coexists with a stable limit cycle of nonlinear coherent oscillations. We explicitly determine the critical coupling constant for this transition

Changes in plasma biomarkers following treatment with cabozantinib in metastatic castration-resistant prostate cancer: a post hoc analysis of an extension cohort of a phase II trial

BACKGROUND: Cabozantinib is an orally available inhibitor of tyrosine kinases including VEGFR2 and c-MET. We performed a post hoc analysis to find associations between select plasma biomarkers and treatment response in patients (pts) with metastatic castration resistant prostate cancer (mCRPC) who received cabozantinib 100 mg daily as part of a phase 2 non-randomized expansion cohort (NCT00940225). METHODS: Plasma samples were collected at baseline, 6 weeks and at time of maximal response from 81 mCRPC pts with bone metastases, of which 33 also had measurable soft-tissue disease. Levels of 27 biomarkers were measured in duplicate using enzyme-linked immunosorbent assay. Spearman correlation coefficients were calculated for the association between biomarker levels or their change on treatment and either bone scan response (BSR) or soft tissue response according to RECIST. RESULTS: A BSR and RECIST response were seen in 66/81 pts (81 %) and 6/33 pts (18 %) respectively. No significant associations were found between any biomarker at any time point and either type of response. Plasma concentrations of VEGFA, FLT3L, c-MET, AXL, Gas6A, bone-specific alkaline phosphatase, interleukin-8 and the hypoxia markers CA9 and clusterin significantly increased during treatment with cabozantinib irrespective of response. The plasma concentrations of VEGFR2, Trap5b, Angiopoietin-2, TIMP-2 and TIE-2 significantly decreased during treatment with caboznatinib. CONCLUSIONS: Our data did not reveal plasma biomarkers associated with response to cabozantinib. The observed alterations in several biomarkers during treatment with cabozantinib may provide insights on the effects of cabozantinib on tumor cells and on tumor micro-environment and may help point to potential co-targeting approaches

Non-local defect interaction in one-dimension: weak versus strong non-locality

Defect interaction (kink-antikink interaction) is studied for a prototypical model for non-local interaction. Mathematically, it is a bistable integrodifferential model, where the non-local interaction is performed due to an integral kernel. The system is able to establish domains where it is in one of its two equilibria, separated by defects. It is shown that the defect interaction depends on the asymptotical behavior of the integral kernel. In the weak non-local regime, when the integral kernel decays faster than an exponential at infinitum, the defect interaction is exponentially weak. Hence, this case is qualitatively similar to the local one. On the other hand, in the strong non-local regime, when the integral kernel decays slower than an exponential at infinitum, the defect interaction is ruled by the asymptotical behavior of the integral kernel. In this case, the defect interaction is stronger, and could be characterized, for instance, by a power law. The effect of this transition (from the weak to strong non-locality) on the domain dynamics is discussed

Mean field model for synchronization of coupled two-state units and the effect of memory

A prototypical model for a mean field second order transition is presented, which is based on an ensemble of coupled two-states units. This system is used as a basic model to study the effect of memory. To wit, we distinguish two types of memories: weak and strong, depending on the feasibility of linearizing the generalized mean field master equation. For weak memory we find static solutions that behave much like those of the memoryless (Markovian) system. The latter exhibits a pitchfork bifurcation as the control parameter is increased, with two stable and one unstable solution. The former exhibits an imperfect pitchfork bifurcation to states with the same behaviors. In both cases, the stability of the static solutions is analyzed via the usual linearization around the equilibrium solution. For strong memories we again find an imperfect pitchfork bifurcation, with two stable and one unstable branch. However, it is no longer possible to analyze these behaviors via the usual linearization, which is local in time, because a strong memory requires knowledge of the system for its entire past. Finally, we are pleased to dedicate this publication to Helmut Brand on the occasion of his 60th birthday