Related papers: Observability for heat equations with time-depende…

We establish boundary observability and control for the fractional heat equation over arbitrary time horizons $T > 0$, within the optimal range of fractional exponents $s \in (1/2, 1)$. Our approach introduces a novel synthesis of…

We introduce a new technique to visualize complex flowing phenomena by using concepts from shape analysis. Our approach uses techniques that examine the intrinsic geometry of manifolds through their heat kernel, to obtain representations of…

It is necessary to use more general models than the classical Fourier heat conduction law to describe small-scale thermal conductivity processes. The effects of heat flow memory and heat capacity memory (internal energy) in solids are…

The goal of this paper is to analyze control properties of the parabolic equation with variable coefficients in the principal part and with a singular inverse-square potential:\,$\partial_tu(x,t)-{\rm div}(p(x)\nabla…

For $d\geq 2$, we establish the existence and uniqueness of heat kernels for a large class of time-dependent second order diffusion operator with jumps, which is the sum of time-dependent of a second order elliptic differential operators…

We consider rough metrics on smooth manifolds and corresponding Laplacians induced by such metrics. We demonstrate that globally continuous heat kernels exist and are H\"older continuous locally in space and time. This is done via local…

Identifying coherent spatiotemporal patterns generated by complex dynamical systems is a central problem in many science and engineering disciplines. Here, we combine ideas from the theory of operator-valued kernels with delay-embedding…

We analyze the observability of motion estimates from the fusion of visual and inertial sensors. Because the model contains unknown parameters, such as sensor biases, the problem is usually cast as a mixed identification/filtering, and the…

Real-world problems often involve complex and unstructured sets of measurements, which occur when sensors are sparsely placed in either space or time. Being able to model this irregular spatiotemporal data and extract meaningful forecasts…

Singular statistical models arise whenever different parameter values induce the same distribution, leading to non-identifiability and a breakdown of classical asymptotic theory. While existing approaches analyze these phenomena in…

We prove some estimations of the correlation of two local observables in quantum spin systems (with Schr\"odinger equations) at large temperature. For that, we describe the heat kernel of the Hamiltonian for a finite subset of the lattice,…

We introduce Bell-type inequalities allowing for non-locality and entanglement tests with two cold heteronuclear molecules. The proposed inequalities are based on correlations between each molecule spatial orientation, an observable which…

We consider solutions of the linear heat equation with time-dependent singularities. It is shown that if a singularity is weaker than the order of the fundamental solution of the Laplace equation, then it is removable. We also consider the…

Local observation is an important problem both for the foundations of a quantum theory of gravity and for applications to quantum-cosmological problems such as eternal inflation. While gauge invariant local observables can't be defined, it…

Entropic uncertainty relations are universal quantifiers of fundamental uncertainties of quantum measurements and are widely discussed in the quantum metrology literature. Quantum memory is a phenomenon related to the specific type of…

We study a general class of control systems with memory, which in particular includes systems with fractional derivatives and integrals and also the standard heat equation. We prove that the approximate controllability property of the heat…

The fields of quantum non-locality in physics, and causal discovery in machine learning, both face the problem of deciding whether observed data is compatible with a presumed causal relationship between the variables (for example a local…

Heat capacity measurements are a powerful tool that researchers rely on when studying the relationship between microscopic degrees of freedom and macroscopic behavior in condensed matter. This uniqueness stems from heat capacity capturing…

In this note we apply heat kernels to derive some localization formula in sympletcic geometry, to study moduli spaces of flat connections on a Riemann surface, to obtain the push-forward measures for certain maps between Lie groups and to…

We consider inverse problems for the Einstein equation with a time-depending metric on a 4-dimensional globally hyperbolic Lorentzian manifold $(M,g)$. We formulate the concept of active measurements for relativistic models. We do this by…