Convexification for a 3D inverse scattering problem with the moving point source. (arXiv:1911.10289v1 [math.NA])

For the first time, we develop in this paper the globally convergent convexification numerical method for a Coefficient Inverse Problem for the 3D Helmholtz equation for the case when the backscattering data are generated by a point source running along an interval of a straight line and the wavenumber is fixed. Thus, by varying the…

Nonlocal Poincar\'{e} Inequalities for Integral Operators with Integrable Nonhomogeneous Kernels. (arXiv:1911.10292v1 [math.AP])

The paper provides two versions of nonlocal Poincar\’e-type inequalities for integral operators with a convolution-type structure and functions satisfying a zero-Dirichlet like condition. The inequalities extend existing results to a large class of nonhomogeneous kernels with supports that can vary discontinuously and need not contain a common set throughout the domain. The measure of the…

Solution Curve for Linear Control Systems on Lie Groups. (arXiv:1911.10294v1 [math.OC])

The purpose of this paper is to describe explicitly the solution for linear control systems on Lie groups. In case of linear control systems with inner derivations, the solution is given basically by the product of the exponential of the associated invariant system and the exponential of the associated invariant drift field. We present the…

Predator-Prey Interaction Model with Hunting Cooperation among Predators and Allee Effect in Prey. (arXiv:1911.10299v1 [math.DS])

This paper investigates a dynamical predator-prey interaction model that incorporates: (a) hunting cooperation among predators; (b) Allee effect in prey. We show all possible boundary and interior solutions. In order to analyze the stability of the solution, we make use of the Jacobian matrix and the resultant characteristic polynomial. Particularly, the sign of the eigenvalue…

Dissipative signatures of dynamical phases and transitions. (arXiv:1911.10696v1 [cond-mat.stat-mech])

Living and non-living active matter consumes energy at the microscopic scale to drive emergent, macroscopic behavior including traveling waves and coherent oscillations. Recent work has characterized non-equilibrium systems by their total energy dissipation, but little has been said about how dissipation manifests in distinct spatiotemporal patterns. We introduce a novel measure of dissipation we term…

Spatial self-organisation enables species coexistence in a model for savanna ecosystems. (arXiv:1911.10801v1 [q-bio.PE])

The savanna biome is characterised by a continuous vegetation cover, comprised of herbaceous and woody plants. The coexistence of species in arid savannas, where water availability is the main limiting resource for plant growth, provides an apparent contradiction to the classical principle of competitive exclusion. Previous theoretical work using nonspatial models has focussed on the…

Effects of precipitation intermittency on vegetation patterns in semi-arid landscapes. (arXiv:1911.10878v1 [q-bio.PE])

Patterns of vegetation are a characteristic feature of many semi-arid regions. The limiting resource in these ecosystems is water, which is added to the system through short and intense rainfall events that cause a pulse of biological processes such as plant growth and seed dispersal. We propose an impulsive model based on the Klausmeier reaction-advection-diffusion…

Biologically Plausible Sequence Learning with Spiking Neural Networks. (arXiv:1911.10943v1 [cond-mat.dis-nn])

Motivated by the celebrated discrete-time model of nervous activity outlined by McCulloch and Pitts in 1943, we propose a novel continuous-time model, the McCulloch-Pitts network (MPN), for sequence learning in spiking neural networks. Our model has a local learning rule, such that the synaptic weight updates depend only on the information directly accessible by the…

An integrodifference model for vegetation patterns in semi-arid environments with seasonality. (arXiv:1911.10964v1 [q-bio.PE])

Vegetation patterns are a characteristic feature of semi-deserts occurring on all continents except Antarctica. In some semi-arid regions, the climate is characterised by seasonality, which yields a synchronisation of seed dispersal with the dry season or the beginning of the wet season. We reformulate the Klausmeier model, a reaction-advection-diffusion system that describes the plant-water dynamics…

Metastability as a coexistence mechanism in a model for dryland vegetation patterns. (arXiv:1911.11022v1 [q-bio.PE])

Vegetation patterns are a ubiquitous feature of water-deprived ecosystems. Despite the competition for the same limiting resource, coexistence of several plant species is commonly observed. We propose a two-species reaction-diffusion model based on the single-species Klausmeier model, to analytically investigate the existence of states in which both species coexist. Ecologically, the study finds that coexistence…