Related papers: Renewal theorems in a periodic environment
We consider two different proposals to generate a time series with the same non-Poisson distribution of waiting times, to which we refer to as renewal and modulation. We show that, in spite of the apparent statistical equivalence, the two…
We introduce a formalism for the calculation of the time of arrival t at a space point for particles traveling through interacting media. We develop a general formulation that employs quantum canonical transformations from the free to the…
Functional responses are widely used to describe interactions and resources exchange between individuals in ecology. The form given to functional responses dramatically affects the dynamics and stability of populations and communities.…
The evolution of an isolated quantum system inevitably exhibits recurrence: the state returns to the vicinity of its initial condition after finite time. Despite its fundamental nature, a rigorous quantitative understanding of recurrence…
Natural ecosystems, in particular on the microbial scale, are inhabited by a large number of species. The population size of each species is affected by interactions of individuals with each other and by spatial and temporal changes in…
We consider the problem of learning a set from random samples. We show how relevant geometric and topological properties of a set can be studied analytically using concepts from the theory of reproducing kernel Hilbert spaces. A new kind of…
In this paper we consider finite conditional random quantities and conditional previsions assessments in the setting of coherence. We use a suitable representation for conditional random quantities; in particular the indicator of a…
The formalism of Siegert states to describe the resonant scattering in quantum theory is extended to the resonant scattering of electromagnetic waves on periodic dielectric arrays. The excitation of electromagnetic Siegert states by an…
A renewal system divides the slotted timeline into back to back time periods called renewal frames. At the beginning of each frame, it chooses a policy from a set of options for that frame. The policy determines the duration of the frame,…
This paper presents a framework for time-causal wavelet analysis. It targets real-time processing of temporal signals, where data from the future are not available. The study builds upon temporal scale-space theory, originating from a…
This paper investigates the influence of environmental noise on the characteristic timescale of the dynamics of density-dependent populations. General results are obtained on the statistics of time spent in rarity and time spent in…
Understanding under what conditions populations, whether they be plants, animals, or viral particles, persist is an issue of theoretical and practical importance in population biology. Both biotic interactions and environmental fluctuations…
We show that the mechanism of gap formation has a resonance nature. The special real fundamental solutions were discovered which `paradoxically' have knot distribution with a period coinciding with that of potential at all energies of the…
We unify two different periodicity mechanisms: delayed self-regulation and planar predator-prey feedback. We consider scalar delay differential equations $\dot x(t) = rf(x(t), x(t - 1))$ where $f$ is monotone in the delayed component. Due…
We present an approach for the analytical treatment of excitable systems with noise-induced dynamics in the presence of time delay. An excitable system is modeled as a bistable system with a time delay, while another delay enters as a…
We consider a continuous-space and continuous-time diffusion process under resetting with memory. A particle resets to a position chosen from its trajectory in the past according to a memory kernel. Depending on the form of the memory…
We study Dirichlet-type problems for the simplest third-order linear dispersive PDE, often referred to as the Airy equation. Such problems have not been extensively studied, perhaps due to the complexity of the spectral structure of the…
The need for a time-shift invariant formulation of quantum theory arises from fundamental symmetry principles as well as heuristic cosmological considerations. Such a description then leaves open the question of how to reconcile global…
Temporal reasoning is the task of predicting temporal relations of event pairs. While temporal reasoning models can perform reasonably well on in-domain benchmarks, we have little idea of these systems' generalizability due to existing…
This paper investigates the long time dynamics of interacting particle systems subject to singular interactions. We consider a microscopic system of $N$ interacting point particles, where the time evolution of the joint distribution…