We present two general sequences of positive linear operators. The first is introduced by using a class of dependent random variables, and the second is a mixture between two linear operators of discrete type. Our goal is to study their statistical convergence to the approximated function. This type of convergence can replace classical results provided by Bohman-Korovkin theorem. A particular c...

This paper proposes a hierarchical nonlinear approximation scheme for scalar-valued multivariate functions, where the main objective is to obtain an accurate approximation with using only very few function evaluations. To this end, our iterative method combines at any refinement step the selection of suitable evaluation points with kriging, a standard method for statistical data analysis. Parti...

Reinforcement learning (RL) is a machine learning answer to the optimal control problem. It consists in learning an optimal control policy through interactions with the system to be controlled, the quality of this policy being quantified by the so-called value function. An important RL subtopic is to approximate this function when the system is too large for an exact representation. This paper ...

New modified Schurer-type q-Bernstein Kantorovich operators are introduced. The local theorem and statistical Korovkin-type approximation properties of these operators are investigated. Furthermore, the rate of approximation is examined in terms of the modulus of continuity and the elements of Lipschitz class functions.

We show that the probabilistic formalism of QM can be obtained as a special projection of classical statistical mechanics for systems with an infinite number of degrees of freedom. Such systems can be interpreted as classical fields. Thus in our approach QM is a projection of (prequantum) classical statistical field theory (PCSFT). This projection is based on the Taylor expansion of classical p...

We consider an interacting system of spin variables on a loopy interaction graph, identified by a tree graph and a set of loopy interactions. We start from a high-temperature expansion for loopy interactions represented by a sum of non-negative contributions from all the possible frustration-free loop configurations. We then compute the loop corrections using different approximations for the no...

, where C0 = ∫ 1 0 f(t)dt. j ∼ scale, k ∼ position. Key properties: 1. vanishing moments: We say ψ has M vanishing moments when ∫ 1 0 tψj,k(t)dt = 0 form = 0, 1, . . . ,M− 1 This means the wavelet is “blind” to polynomial segment with degree α ≤M − 1 2. compact support: a daubechies wavelet with M vanishing moments has support ∝ 2M. Together, these properties imply that only O(l log n) nonzero ...

While it is known that the kinematical approximation works poorly if at all for transmission electron diffraction, substantial success has been achieved over the last few years in applying it via direct methods to determine atomic structures. This raises an interesting quandary; is the established theory of electron diffraction wrong, or are the apparent successes mirages? The intention of this...

A hospital Emergency Department’s (ED’s) wait times can be driven by high occupancy in its downstream InPatient hospital (IP). ED patients not admitted to the IP due to high IP occupancy or transfer delays are termed to be 'boarding' in the ED. ED boarding causes a decrease in ED service capacity, longer ED wait times, increased fractions of patients that leave without treatment, and increased ...