We study online learning where a decision maker interacts with Nature with the objective of maximizing her long-term average reward subject to some sample path average constraints. We define the reward-in-hindsight as the highest reward the decision maker could have achieved, while satisfying the constraints, had she known Nature’s choices in advance. We show that in general the reward-in-hinds...

The CP 1 model with Hopf interaction is quantised following the Batalin-Tyutin (BT) prescription. In this scheme, extra BT fields are introduced which allow for the existence of only commuting first-class constraints. Explicit expression for the quantum correction to the expectation value of the energy density in the physical sector of this model is derived. The result shows that in the particu...

The Object Constraint Language OCL is an integral part of UML, the Unified Modeling Language standard. It has been added to Rational’s UML core as a logic-based sublanguage for the definition of integrity constraints (invariants) on class diagrams as well as for the definition of preand postconditions of operations. Despite of the fact that OCL is called a statically typed language its type che...

In an earlier paper, we used the absolute grading on Heegaard Floer homology HF to give restrictions on knots in S which admit lens space surgeries. The aim of the present article is to exhibit stronger restrictions on such knots, arising from knot Floer homology. One consequence is that all the non-zero coefficients of the Alexander polynomial of such a knot are ±1. This information in turn ca...

Serious mathematical defect in the important kinematics theorem known in continuum mechanics as Convection (or Transport) Theorem is reported. We claim that the traditional demonstration does not take into account a special constraint on integrand functions given in Lagrangian representation. Thus, we put in doubt that the traditional procedure for the transition from integral formulations of p...

This paper investigates the necessary conditions of optimality for uniformly overtaking optimal control on infinite horizon with free right endpoint. Clarke’s form of the Pontryagin Maximum Principle is proved without the assumption on boundedness of total variation of adjoint variable. The transversality condition for adjoint variable is shown to become necessary if the adjoint variable is par...

In a previous paper) we discussed in the framework of the Poincare-Cartan integral invariant, a method for performing the canonical formalism for constrained systems. The basic idea consists of considering a canonical transformation which brings the constraints into a subset of the canonical variables. Thus the physical variables can be easily obtained by means of a reduction of the phase space...

It is well known that –differing from ordinary gauge systems– canonical gauges are not admissible in the path integral for parametrized systems. This is the case for the relativistic particle and gravitation. However, a time dependent canonical transformation can turn a parametrized system into an ordinary gauge system. It is shown how to build a canonical transformation such that the fixation ...

It is well known that –differing from ordinary gauge systems– canonical gauges are not admissible in the path integral for parametrized systems. This is the case for the relativistic particle and gravitation. However, a time dependent canonical transformation can turn a parametrized system into an ordinary gauge system. It is shown how to build a canonical transformation such that the fixation ...

School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA. Graduate School of Informatics, Kyoto University, Kyoto 6068501, Japan. Abstract In this paper we explore the relationship between dual decomposition and the consensus-based method for distributed optimization. The relationship is developed by examining the similarities between the two approa...