We consider the problem of learning an unknown function f⋆ on d-dimensional sphere with respect to square loss, given i.i.d. samples {(yi,xi)}i≤n where xi is a feature vector uniformly distributed and yi=f⋆(xi)+εi. study two popular classes models that can be regarded as linearizations two-layers neural networks around random initialization: features model Rahimi–Recht (RF); tangent Jacot–Gabri...

where f = f(x), g = g(x), h = h(x), A = A(u) and B = B(u) are arbitrary smooth functions of their variables, f(x)g(x)A(u) 6=0. Our aim is not to give a physical interpretation of the solution of diffusion equations (that is too huge and cannot be reached in the scope of a short paper), but to list the already known exact solutions of equations from the class under consideration. However, in som...

The main purpose of this paper is to consider the t-best simultaneousapproximation in fuzzy normed spaces. We develop the theory of t-bestsimultaneous approximation in quotient spaces. Then, we discuss the relationshipin t-proximinality and t-Chebyshevity of a given space and its quotientspace.

Let E be a separable (or the dual of a separable) symmetric function space, let M be a semifinite von Neumann algebra and let E(M) be the associated noncommutative function space. Let (εk)k≥1 be a Rademacher sequence, on some probability space Ω. For finite sequences (xk)k≥1 of E(M), we consider the Rademacher averages ∑ k εk ⊗ xk as elements of the noncommutative function space E(L(Ω)⊗M) and s...

Objective: To design an economic evaluation strategy for general health promotion projects. Method: Identification of key parameters of behavioral health from neuroeconomic studies. Results: The Frontal Power of Concentration (C) is a quadripartite executive integrator depending on four key parameters: 1) The Limbic system originating ambivalent emotions (L). 2) Volition in the Prefrontal Corte...

We provide a data mine of proven results for multiple zeta values (MZVs) of the form ζ(s1,s2, . . . ,sk) = ∑n1>n2>...>nk>0 { 1/(n1 1 ...n sk k ) } with weight w = ∑i=1 si and depth k and for Euler sums of the form ∑n1>n2>...>nk>0 { (ε1 1 ...ε nk 1 )/(n s1 1 ...n sk k ) } with signs εi = ±1. Notably, we achieve explicit proven reductions of all MZVs with weights w≤ 22, and all Euler sums with we...

0