Related papers: Observability for heat equations with time-depende…
This paper examines the coincidence of neural networks with numerical methods for solving spatiotemporal physical problems. Neural networks are used to learn predictive numerical models from trajectory datasets from two well understood 1D…
Adopting the frame of mesoscopic physics, we describe a Bell type experiment involving time-delayed two-particle correlation measurements. The indistinguishability of quantum particles results in a specific interference between different…
Monitoring the dynamics processes in combustors is crucial for safe and efficient operations. However, in practice, only limited data can be obtained due to limitations in the measurable quantities, visualization window, and temporal…
Several concepts on the measure of observability, reachability, and robustness are defined and illustrated for both linear and nonlinear control systems. Defined by using computational dynamic optimization, these concepts are applicable to…
We study heat and wave type equations on a separable Hilbert space $\mathcal{H}$ by considering non-local operators in time with any positive densely defined linear operator with discrete spectrum. We show the explicit representation of the…
In this paper we establish the existence and uniqueness of heat kernels to a large class of time-inhomogenous non-symmetric nonlocal operators with Dini's continuous kernels. Moreover, quantitative estimates including two-sided estimates,…
We study the parameter estimation problem in mixture models with observational nonidentifiability: the full model (also containing hidden variables) is identifiable, but the marginal (observed) model is not. Hence global maxima of the…
The practice of collider physics typically involves the marginalization of multi-dimensional collider data to uni-dimensional observables relevant for some physics task. In any cases, such as classification or anomaly detection, the…
Conditional expectation values of quantum mechanical observables reflect unique non-classical correlations, and are generally sensitive to decoherence. We consider the circumstances under which such sensitivity to decoherence is removed,…
This paper studies the robustness of observability of a linear time-invariant system under sensor failures from a computational perspective. To be precise, the problem of determining the minimum number of sensors whose removal can destroy…
Machine learning models can represent climate processes that are nonlocal in horizontal space, height, and time, often by combining information across these dimensions in highly nonlinear ways. While this can improve predictive skill, it…
Observational studies provide invaluable opportunities to draw causal inference, but they may suffer from biases due to pretreatment difference between treated and control units. Matching is a popular approach to reduce observed covariate…
Central to Earth observation is the trade-off between spatial and temporal resolution. For temperature, this is especially critical because real-world applications require high spatiotemporal resolution data. Current technology allows for…
We study the propagation properties of the solutions of the finite-difference space semi-discrete wave equation on an uniform grid of the whole Euclidean space. We provide a construction of high frequency wave packets that propagate along…
In this paper, we present first-order accurate numerical methods for solution of the heat equation with uncertain temperature-dependent thermal conductivity. Each algorithm yields a shared coefficient matrix for the ensemble set improving…
In the present Letter we present an analytical and numerical solution of the self-consistent mode-coupling equations for the problem of heat conductivity in one-dimensional systems. Such a solution leads us to propose a different scenario…
In this position paper we suggest a possible metric approach to shape comparison that is based on a mathematical formalization of the concept of observer, seen as a collection of suitable operators acting on a metric space of functions.…
Knowledge tracing aims to model students' past answer sequences to track the change in their knowledge acquisition during exercise activities and to predict their future learning performance. Most existing approaches ignore the fact that…
We introduce observables associated with the space-time position of a quantum point defined by the intersection of two light pulses. The time observable is canonically conjugated to the energy. Conformal symmetry of massless quantum fields…
A joint characterisation of the controllability and observability of a particular kind of discrete system has been developed. The key idea of the procedure can be reduced to a correct choice of the sampling sequence. This freedom, owing to…