Related papers: Observability for heat equations with time-depende…
We establish sharp regional observability results for solutions of the wave equation in a bounded domain of $\Omega \subset \mathbb{R}^n$, in case where the geometric control condition is not satisfied. Assuming that the waves are observed…
We consider a quantum system with a time-independent Hamiltonian parametrized by a set of unknown parameters $\alpha$. The system is prepared in a general quantum state by an evolution operator that depends on a set of unknown parameters…
Observations of molecular lines are a key tool to determine the main physical properties of prestellar cores. However, not all the information is retained in the observational process or easily interpretable, especially when a larger number…
We study memory-type null controllability for linear parabolic equations with hereditary terms and time-dependent control regions. In contrast with classical null controllability, systems with memory require the simultaneous annihilation of…
The existence of observables that are incompatible or not jointly measurable is a characteristic feature of quantum mechanics, which lies at the root of a number of nonclassical phenomena, such as uncertainty relations, wave--particle dual…
We introduce an algorithmic model of heat conduction, the thermodynamic graph. The thermodynamic graph is analogous to meshes in the finite difference method in the sense that the calculation of temperature is carried out at the vertices of…
This paper is addressed to establishing an internal observability estimate for some linear stochastic hyperbolic equations. The key is to establish a new global Carleman estimate for forward stochastic hyperbolic equations in the…
We provide algorithmically verifiable necessary and sufficient conditions for fundamental system theoretic properties of discrete time linear systems subject to data losses. More precisely, the systems in our modeling framework are subject…
The presented paper concentrates on the boundary element method (BEM) for the heat equation in three spatial dimensions. In particular, we deal with tensor product space-time meshes allowing for quadrature schemes analytic in time and…
Estimating the free energy, as well as other thermodynamic observables, is a key task in lattice field theories. Recently, it has been pointed out that deep generative models can be used in this context [1]. Crucially, these models allow…
We find new quantitative estimates on the space-time analyticity of solutions to linear parabolic equations with analytic coefficients near the initial time. We apply the estimates to obtain observability inequalities and…
Many diverse phenomena in nature often inherently encode both short- and long-term temporal dependencies, which especially result from the direction of the flow of time. In this respect, we discovered experimental evidence suggesting that…
Reconstructing the states of the nodes of a dynamical network is a problem of fundamental importance in the study of neuronal and genetic networks. An underlying related problem is that of observability, i.e., identifying the conditions…
In this paper we introduce a new dynamical condition, the comb geometric control condition, which is sufficient for observability of the Schr\"odinger equation in Euclidean space. We provide examples which show this condition is strictly…
In this paper, we study the observability and controllability of wave equations coupled by first or zero order terms on a compact manifold. We adopt the approach in Dehman-Lebeau's paper \cite{DehmanLebeau09} to prove that: the weak…
Utilizing the information in observations of a complex system to make accurate predictions through a quantitative model when observations are completed at time $T$, requires an accurate estimate of the full state of the model at time $T$.…
We consider linear control problems for the heat equation of the form $\dot f (t) = -Hf (t) + \mathbf{1}_D u (t)$, $f (0) \in \ell_2 (X,m)$, where $H$ is the weighted Laplacian on a discrete graph $(X,b,m)$, and where $D \subseteq X$ is…
In control theory, researchers need to understand a system's local and global behaviors in relation to its initial conditions. When discussing observability, the main focus is on the ability to analyze the system using an output space…
Three inverse boundary value problems for the heat equations in one space dimension are considered. Those three problems are: extracting an unknown interface in a heat conductive material, an unknown boundary in a layered material or a…
Understanding the emergence of the thermodynamic arrow of time in microscopic systems is of fundamental importance, particularly given that unitary evolution preserves time-reversal symmetry. While projective measurements introduce temporal…