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We study inference in models where a transformation of parameters exhibits first-order degeneracy -- that is, its gradient is zero or close to zero, making the standard delta method invalid. A leading example is causal mediation analysis,…
Modeling how individuals evolve over time is a fundamental problem in the natural and social sciences. However, existing datasets are often cross-sectional with each individual observed only once, making it impossible to apply traditional…
In this paper, we consider a population of individuals who have actions and opinions, which coevolve, mutually influencing one another on a complex network structure. In particular, we formulate a control problem for this social network, in…
This paper is concerned with an age-structured model in population dynamics. We investigate the uniqueness of solution for this type of nonlinear reaction-diffusion problem when the source term depends on the density, indicating the…
We consider a nonlinear coupled discrete-time model of population dynamics. This model describes the movement of populations within a heterogeneous landscape, where the growth of subpopulations are modelled by (possibly different) bounded…
In this work, we address the existence of insensitizing controls for a nonlinear coupled system of fourth- and second-order parabolic equations known as the stabilized Kuramoto-Sivashinsky model. The main idea is to look for controls such…
The cell cycle duration is a variable cellular phenotype that underlies long-term population growth and age structures. By analyzing the stationary solutions of a branching process with heritable cell division times, we demonstrate…
We make two remarks about the null-controllability of the heat equation with Dirichlet condition in unbounded domains. Firstly, we give a geometric necessary condition (for interior null-controllability in the Euclidean setting)which…
We study the interacting dark energy model with time varying dark energy equation of state. We examine the stability in the perturbation formalism and the degeneracy among the coupling between dark sectors, the time-dependent dark energy…
We propose a new controllability property for linear time varying control systems in finite dimension: the nonuniform complete controllability, which is halfway between the classical Kalman's properties of complete controllability and…
A degenerate wave equation with time-varying delay in the boundary control input is considered. The well-posedness of the system is established by applying the semigroup theory. The boundary stabilization of the degenerate wave equation is…
This paper provides a qualitative analysis of a non-uniform Euler-Bernoulli beam with degenerate flexural rigidity, subjected to axial force and boundary control with time delay $\tau > 0$. By reformulating the system as an abstract…
We examine the problem of two-point boundary optimal control of nonlinear systems over finite-horizon time periods with unknown model dynamics by employing reinforcement learning. We use techniques from singular perturbation theory to…
Models of many-species ecosystems, such as the Lotka-Volterra and replicator equations, suggest that these systems generically exhibit near-extinction processes, where population sizes go very close to zero for some time before rebounding,…
We study a constrained optimal control problem with possibly degenerate coefficients arising in models of optimal portfolio liquidation under market impact. The coefficients can be random in which case the value function is described by a…
The main purpose of this work is the mathematical modelling of large populations of cells under different deterministic interactions among themselves, in balance with naturally random diffusion. We focus on cell-cell adhesion mechanisms for…
We consider the problem of damping a control system with delay described by first-order functional-differential equations on a temporal tree. The delay in the system is time-proportional and propagates through the internal vertices. The…
We address the control of the dynamics of both population and coherence phase in an open two-level quantum system employing a single external control field. The system dynamics is described by a Markovian master equation that takes into…
We study spatial decay properties of sensitivities in a nonlinear optimal control problem with a graph-structured interaction topology. For a problem with nonlinear decoupled dynamics and quadratic cost, we show that a perturbation of the…
In this paper we study the controllability and the stability for a degenerate beam equation in divergence form via the energy method. The equation is clamped at the left end and controlled by applying a shearing force or a damping at the…