Related papers: Sampling Observability for Heat Equations with Mem…

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 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 demonstrate that the presence of entanglement in macroscopic bodies (e.g. solids) in thermodynamical equilibrium could be revealed by measuring heat-capacity. The idea is that if the system were in a separable state, then for certain…

We find new quantitative estimates on the space-time analyticity of solutions to linear parabolic equations with time-independent coefficients and apply them to obtain observability inequalities for its solutions over measurable sets.

Generative models of complex systems often require post-hoc parameter adjustments to produce useful outputs. For example, energy-based models for protein design are sampled at an artificially low ''temperature'' to generate novel,…

We consider the Gurtin-Pipkin equation of the first order in time. For the kernel as a series of exponentials we obtain the structure of the spectrum of the system.

We develop a method to improve on the statistical errors for higher moments using machine learning techniques. We present here results for the dual representation of the Ising model with an external field, derived via the high temperature…

When a spin glass is cooled down, a memory of the cooling process is imprinted in the spin structure. This memory can be disclosed in a continuous heating measurement of the ac-susceptibility. E.g., if a continuous cooling process is…

The paper deals with point-wise estimates for the heat kernel of a nonlocal convolution type operator with a kernel that decays at least exponentially at infinity. It is shown that the large time behaviour of the heat kernel depends…

We propose a novel witness of temporal quantum entanglement using the imaginary component of the complex heat capacity - a measurable thermodynamic quantity in temperature-modulated calorimetry. By establishing a direct correspondence…

We present a systematic study of the nested sampling algorithm based on the example of the Potts model. This model, which exhibits a first order phase transition for $q>4$, exemplifies a generic numerical challenge in statistical physics:…

Temporal data, obtained in the setting where it is only possible to observe one time point per experiment, is widely used in different research fields, yet remains insufficiently addressed from the statistical point of view. Such data often…

We analyze the control properties of heat equations with memory terms. We recall previous results showing that if the moving support of the control covers the whole domain where heat diffuses, the system is null controllable when the memory…

We consider two related tasks: (a) estimating a parameterisation of a given Gibbs state and expectation values of Lipschitz observables on this state; and (b) learning the expectation values of local observables within a thermal or quantum…

The uncertainty principle sets a bound on our ability to predict the measurement outcomes of two incompatible observables which are measured on a quantum particle simultaneously. In quantum information theory, the uncertainty principle can…

Change point estimation in its offline version is traditionally performed by optimizing over the data set of interest, by considering each data point as the true location parameter and computing a data fit criterion. Subsequently, the data…

Umbrella sampling is an efficient method for the calculation of free energy changes of a system along well-defined reaction coordinates. However, when multiple parallel channels along the reaction coordinate or hidden barriers in directions…

We discuss the application of techniques of quantum estimation theory and quantum metrology to thermometry. The ultimate limit to the precision at which the temperature of a system at thermal equilibrium can be determined is related to the…

In the present paper we identify a rigorous property of a number of tempering-based Monte Carlo sampling methods, including parallel tempering as well as partial and infinite swapping. Based on this property we develop a variety of…

Predictive process monitoring is a subfield of process mining that aims to estimate case or event features for running process instances. Such predictions are of significant interest to the process stakeholders. However, most of the…