Related papers: Sampling Observability for Heat Equations with Mem…
Heat is a complex quantity to measure in stochastic systems because it requires extremely small sampling timesteps. Unfortunately this is not always possible in real experiments, mainly because experimental setups have technical limits. To…
In this paper characterizations of graphs satisfying heat kernel estimates for a wide class of space-time scaling functions are given. The equivalence of the two-sided heat kernel estimate and the parabolic Harnack inequality is also shown…
Based on the quantum violation of bipartite Bell inequality, it has been demonstrated that the sharing of non-locality can be demonstrated for at most two sequential observers at one end and at most one-pair of observers at both ends. In…
We analyse the emergence of Kovacs-like memory effects in athermal systems within the linear response regime. This is done by starting from both the master equation for the probability distribution and the equations for the physically…
A wide variety of optimization techniques, both exact and heuristic, tend to be biased samplers. This means that when attempting to find multiple uncorrelated solutions of a degenerate Boolean optimization problem a subset of the solution…
Negative sampling approaches are prevalent in implicit collaborative filtering for obtaining negative labels from massive unlabeled data. As two major concerns in negative sampling, efficiency and effectiveness are still not fully achieved…
In this paper, we consider the problem of numerical investigation of the counting statistics for a class of one-dimensional systems. Importance sampling, the cornerstone technique usually implemented for such problems, critically hinges on…
For the model problem of the heat equation discretized by an implicit Euler method in time and a conforming finite element method in space, we prove the efficiency of a posteriori error estimators with respect to the energy norm of the…
Tasks that require information about the world imply a trade-off between the time spent on observation and the variance of the response. In particular, fast decisions need to rely on uncertain information. However, standard estimates of…
We propose to use the effect of measurements instead of their number to study the time evolution of quantum systems under monitoring. This time redefinition acts like a microscope which blows up the inner details of seemingly instantaneous…
In this paper, a quantitative estimate of unique continuation for the stochastic heat equation with bounded potentials on the whole Euclidean space is established. This paper generalizes the earlier results in [29] and [17] from a bounded…
In this article, we propose a novel method for sampling potential functions based on noisy observation data of a finite number of observables in quantum canonical ensembles, which leads to the accurate sampling of a wide class of test…
We estimate the heat conducted by a cluster of many small cavities. We show that the dominating heat is a sum, over the number of the cavities, of the heats generated by each cavity after interacting with each other. This interaction is…
Energy systems modeling frequently relies on time series data, whether observed or forecast. This is particularly the case, for example, in capacity planning models that use hourly production and load data forecast to occur over the coming…
The paper addresses the problem of attitude estimation for rigid bodies using (possibly time-varying) vector measurements, for which we provide a necessary and sufficient condition of distinguishability. Such a condition is shown to be…
We establish an observability inequality from space-time measurable sets for a class of strongly coupled parabolic systems consisting of two equations, where the observation acts on a single-component. The model is motivated by parabolic…
The demand for accurate food quantification has increased in the recent years, driven by the needs of applications in dietary monitoring. At the same time, computer vision approaches have exhibited great potential in automating tasks within…
Spatiotemporal dynamics models are fundamental for various domains, from heat propagation in materials to oceanic and atmospheric flows. However, currently available neural network-based spatiotemporal modeling approaches fall short when…
Quantum measurement is ultimately a physical process, resulting from an interaction between the measured system and a measuring apparatus. Considering the physical process of measurement within a thermodynamic context naturally raises the…
In this work, we investigate the solvability of a heat equation involving the Grushin operator. The equation is perturbed by two nonlinear reaction terms, one of which includes a memory component, introducing nonlocal effects in time. We…