In this paper we consider the contextual multi-armed bandit problem for linear payoffs under a risk-averse criterion. At each round, contexts are revealed arm, and decision maker chooses one arm to pull receives corresponding reward. particular, mean-variance as risk criterion, best is with largest We apply Thompson sampling algorithm disjoint model, provide comprehensive regret analysis varian...

The Dirac operators Ly = i 1 0 0 −1 dy dx + v(x)y, y = y1 y2 , x ∈ [0, π], with L 2-potentials v(x) = 0 P (x) Q(x) 0 , P,Q ∈ L 2 ([0, π]), considered on [0, π] with periodic, antiperiodic or Dirichlet boundary conditions (bc), have discrete spectra, and the Riesz projections SN = 1 2πi |z|=N− 1 2 (z − L bc) −1 dz, Pn = 1 2πi |z−n|= 1 2 (z − L bc) −1 dz are well-defined for |n| ≥ N if N is suffi...

It is proven that if xQ′(x) is increasing on (0,+∞) and w(x) = exp(−Q) is the corresponding weight on [0,+∞), then every continuous function that vanishes outside the support of the extremal measure associated with w can be uniformly approximated by weighted polynomials of the form wPn. This problem was raised by V. Totik, who proved a similar result (the Borwein-Saff conjecture) for convex Q. ...

The paper is a sequel to the paper [5] by the same author. A new criterion is presented for a PSD linear map L : R[x] → R to correspond to a positive Borel measure on Rn. The criterion is stronger than Nussbaum’s criterion in [6] and is similar in nature to Schmüdgen’s criterion in [5] [7]. It is also explained how the criterion allows one to understand the support of the associated measure in ...

We consider the problem of maximizing a real-valued continuous function f using a Bayesian approach. Since the early work of Jonas Mockus and Antanas Žilinskas in the 70’s, the problem of optimization is usually formulated by considering the loss function max f − Mn (where Mn denotes the best function value observed after n evaluations of f ). This loss function puts emphasis on the value of th...

Let p > 3 be a prime, u, v, d ∈ Z, gcd(u, v) = 1, p u2 − dv2 and (−3d p ) = 1, where ( p ) is the Legendre symbol. In the paper we mainly determine the value of u−v √ d u+v √ d (p−( p3 ))/3 (mod p) by expressing p in terms of appropriate binary quadratic forms. As applications, for p ≡ 1 (mod 3) we obtain a general criterion for m(p−1)/3 (mod p) and a criterion for εd to be a cubic residue of p...

This paper shows how the study of colored compositions of integers reveals some unexpected and original connection with the Invert operator. The Invert operator becomes an important tool to solve the problem of directly counting the number of colored compositions for any coloration. The interesting consequences arising from this relationship also give an immediate and simple criterion to determ...

We develop a quantitative theory of the ratio R of radiative to non-radiative de-excitation based on the Dexter-Klick-Russell criterion for the occurrence of luminescence. The model invokes three essential elements: a promoting mode, an accepting mode, and a set of lattice modes which ultimately absorb the vibrational energy. The ratio R is determined by the relative population of the relaxed e...

In the past years various approaches for assessing bioequivalence of so-called "highly variable drugs" have been debated. These are drugs whose pharmacokinetic profiles vary considerably when given to the same subject. As a consequence of the high variability, average bioequivalence between two such drugs can only be shown with an unfeasibly high number of subjects. Therefore regulatory agencie...