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The aim of this work is to ascertain the characterization of the existence of coexistence states for a class of cooperative systems supported by the study of an associated non--local equation through classical variational methods. Thanks to…
Cell type (e.g. pluripotent cell, fibroblast) is the end result of many complex processes that unfold due to evolutionary, developmental, and transformational stimuli. A cell's phenotype and the discrete, a priori states that define various…
A theory is developed and applied to the study of opportunities and specific features of coherent control of four-wave mixing as well as of the accompanying processes in the continuous-wave regime, which involve transitions between bound…
We study theoretically the simultaneous, photo-induced two-particle excitations of strongly correlated systems on the basis of the Hubbard model. Under certain conditions specified in this work, the corre- sponding transition probability is…
Topological pumping and duality transformations are paradigmatic concepts in condensed matter and statistical mechanics. In this paper, we extend the concept of topological pumping of particles to topological pumping of quantum…
Stochastic Spatio-Temporal processes are prevalent across domains ranging from modeling of plasma to the turbulence in fluids to the wave function of quantum systems. This letter studies a measure-theoretic description of such systems by…
The paper deals with disorders detection in the multivariate stochastic process. We consider the multidimensional Poisson process or the multivariate renewal process. This class of processes can be used as a description of the distributed…
A continuous time mixed state branching process is constructed as the scaling limits of two-type Galton-Watson processes. The process can also be obtained by the pathwise unique solution to a stochastic equation system. From the stochastic…
We consider a class of density-dependent branching processes which generalises exponential, logistic and Gompertz growth. A population begins with a single individual, grows exponentially initially, and then growth may slow down as the…
The Mamba layer offers an efficient selective state space model (SSM) that is highly effective in modeling multiple domains, including NLP, long-range sequence processing, and computer vision. Selective SSMs are viewed as dual models, in…
A multi-type branching process is defined as a random tree with labeled vertices, where each vertex produces offspring independently according to the same multivariate probability distribution. We demonstrate that in realizations of the…
We derive the asymptotic behavior of the total, active and inactive branch lengths of the seed bank coalescent, when the size of the initial sample grows to infinity. Those random variables have important applications for populations…
We investigate steady-state properties of a two-dimensional incoherent-pumped dissipative Bose-Hubbard model, which describes a photon square lattice. This incoherent pumping exhibits an important environment-induced higher-order…
A general framework to describe a vast majority of biology-inspired systems is to model them as stochastic processes in which multiple couplings are in play at the same time. Molecular motors, chemical reaction networks, catalytic enzymes,…
The multiscattering problem is studied in the matrix density formalism. We study how to isolate the quasi-classical degrees of freedom in order to connect with a cascade approach. The different problems that arise, as well as their possible…
It is well understood that a supercritical continuous-state branching process (CSBP) is equal in law to a discrete continuous-time Galton Watson process (the skeleton of prolific individuals) whose edges are dressed in a Poissonian way with…
We consider a continuous population whose dynamics is described by the standard stationary Fleming-Viot process, so that the genealogy of $n$ uniformly sampled individuals is distributed as the Kingman $n$-coalescent. In this note, we study…
We study three classes of continuous time Markov processes (inclusion process, exclusion process, independent walkers) and a family of interacting diffusions (Brownian energy process). For each model we define a boundary driven process…
We explore the possibilities of creating radiatively stable entangled states of two three-level dipole-interacting atoms in a $\Lambda$ configuration by means of laser biharmonic continuous driving or pulses. We propose three schemes for…
Dualities are hidden symmetries that map seemingly unrelated physical systems onto each other. The goal of this work is to systematically construct families of Hamiltonians endowed with a given duality and to provide a universal description…