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The problem of statistical inference in its various forms has been the subject of decades-long extensive research. Most of the effort has been focused on characterizing the behavior as a function of the number of available samples, with far…
Let $\alpha(x)$ be a measurable function taking values in $ [\alpha_1,\alpha_2]$ for $0<\A_1\le \A_2<2$, and $\kappa(x,z)$ be a positive measurable function that is symmetric in $z$ and bounded between two positive constants. Under a…
The uncertainty principle brings out intrinsic quantum bounds on the precision of measuring non-commuting observables. Statistical outcomes in the measurement of incompatible observables reveal a trade-off on the sum of corresponding…
An evolving problem in the field of spatial and ecological statistics is that of preferential sampling, where biases may be present due to a relationship between sample data locations and a response of interest. This field of research bears…
Nowadays, the numerical models of real-world structures are more precise, more complex and, of course, more time-consuming. Despite the growth of a computational effort, the exploration of model behaviour remains a complex task. The…
Based on gradient estimates for the heat equation by Hamilton, we discover a backward in time Harnack inequality for positive solutions on compact manifolds without further restrictions such as boundedness or vanishing boundary value for…
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…
One of the most used metrics to gauge the effects of climate change is the equilibrium climate sensitivity, defined as the long-term (equilibrium) temperature increase resulting from instantaneous doubling of atmospheric CO$_2$. Since…
The spectrum and coherency are useful quantities for characterizing the temporal correlations and functional relations within and between point processes. This paper begins with a review of these quantities, their interpretation and how…
Estimating thermal expectation values of observables is a fundamental task in quantum physics, quantum chemistry, and materials science. While recent quantum algorithms have enabled efficient quantum preparation of thermal states,…
Imitation from observation is the framework of learning tasks by observing demonstrated state-only trajectories. Recently, adversarial approaches have achieved significant performance improvements over other methods for imitating complex…
While Landauer's Principle sets a lower bound for the work required for a computation, that work is recoverable for efficient computations. However, practical physical computers, such as modern digital computers or biochemical systems, are…
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…
In the present paper we study inverse problems related to determining the time-dependent coefficient and unknown source function of fractional heat equations. Our approach shows that having just one set of data at an observation point…
In this paper, we show that efficient separated sum-of-exponentials approximations can be constructed for the heat kernel in any dimension. In one space dimension, the heat kernel admits an approximation involving a number of terms that is…
We present a novel approach to the parallelization of the parabolic fast multipole method for a space-time boundary element method for the heat equation. We exploit the special temporal structure of the involved operators to provide an…
Heisenberg's uncertainty principle provides a fundamental limitation on an observer's ability to simultaneously predict the outcome when one of two measurements is performed on a quantum system. However, if the observer has access to a…
We investigate temporal correlations in the simplest measurement scenario, i.e., that of a physical system on which the same measurement is performed at different times, producing a sequence of dichotomic outcomes. The resource for…
The estimation of covariance operators of spatio-temporal data is in many applications only computationally feasible under simplifying assumptions, such as separability of the covariance into strictly temporal and spatial factors.Powerful…
A recently proposed method for the characterization and analysis of local equilibrium states in relativistic quantum field theory is applied to a simple model. Within this model states are identified which are locally (but not globally) in…