We consider classification problems in a variant of the Probably Approximately Correct (PAC)-learning framework, in which an unsupervised learner creates a discriminant function over each class and observations are labeled by the learner returning the highest value associated with that observation. Consideration is given to whether this approach gains significant advantage over traditional disc...

In a Hamiltonian system with first class constraints observables can be defined as elements of a quotient Poisson bracket algebra. In the gauge fixing approach observables form a quotient Dirac bracket algebra. We show that these two algebras are isomorphic. A new realization of the observable algebras through the original Poisson bracket is found.Generators, brackets and pointwise products of ...

We study a classic Cournot market, which we extend to a two-stage game with endogenous cost formation: the retailers’ marginal cost represents purchases from a price-setting, revenue-maximizing supplier. Any demand uncertainty falls to the supplier, who acts first and sets the wholesale price under incomplete information concerning the retailers’ willingness-to-pay for ordering the product. We ...

In this paper we intend to examine the application of Kullback-Leibler, Hellinger and LINEX loss function in Dynamic Linear Model using the real price of oil for 106 years of data from 1913 to 2018 concerning the asymmetric problem in filtering and forecasting. We use DLM form of the basic Hoteling Model under Quadratic loss function, Kullback-Leibler, Hellinger and LINEX trying to address the ...

Primiparous beef cows produced in 3 calving systems were used in a 2-yr study with a completely random design to measure milk yield throughout a 190-d lactation (2002, n = 20; 2003, n = 24 per calving system). Calving occurred in late winter (average calving date = February 4 +/- 2 d), early spring (average calving date = March 30 +/- 2 d), and late spring (average calving date = May 26 +/- 1 d...

In this paper, we consider a class of stochastic differential variational inequalities (for short, SDVIs) consisting an ordinary equation and inequality. The existence to SDVIs are established under the assumption that leading operator in inequality is $P$-function $P_0$ -function, respectively. Then, by using sample average approximation time stepping methods, two approximated problems corresp...

In this paper we consider the class of polynomial optimization problems with inequality and equality constraints, in which every problem of the class is obtained by perturbations of the objective function, while the constraint functions are kept fixed. Under certain assumptions, we establish some stability properties (e.g., strong Hölder stability with explicitly determined exponents, semiconti...

This paper presents a method for approximating a class of complex transfer function matrices corresponding to physically realizable complex linear quantum systems. The class of linear quantum systems under consideration includes interconnections of passive optical components such as cavities, beam-splitters, phaseshifters and interferometers. This approximation method builds on a previous resul...

Using the linear operator Iλ, μ (λ > −1, μ > 0), we introduce and study a new class Q(λ, μ, α, φ) of analytic functions. We derive inclusion relationship and integral representation. We also show that this class is closed under convolution with a convex function. Some applications of this theorem are also discussed. 2000 Mathematics Subject Classification: 30C45, 30C50.