Motivated by the importance of contextuality and a work on the robustness of the entanglement of mixed quantum states, the robustness of contextuality (RoC) RC(e) of an empirical model e against non-contextual noises was introduced and discussed in Science China Physics, Mechanics and Astronomy (59(4) and 59(9), 2016). Because noises are not always non-contextual, this paper introduces and disc...

A class of generalized state realizations of codes is introduced. In the graph of such a realization, leaf edges represent symbols, ordinary edges represent states, and vertices represent local constraints on incident edges. Such a graph can be decoded by any version of the sum-product algorithm. Any factor graph representation of a code can be put into this form, and any generalized state real...

The quantitative thermodynamic effect of adding a weak, long-range attraction to inverse-power repUlsive potentials is studied. The resulting phase diagrams exhibit two fluid phases and a solid phase. a critical point, a triple point, and, for sufficiently soft repulsions, an additional solid phase with an additional triple point. The effects of attractions other than van der Waals' are studied...

In this work we study numbers and polynomials generated by two type of composition of generating functions and get their explicit formulae. Furthermore we state an improvementof the composita formulae's given in [6] and [3], using the new composita formula's we construct a variety of combinatorics identities. This study go alone to dene new family of generalized Bernoulli polynomials which incl...

The singlet-triplet splittings of chlorine-substituted methylenes and silylenes have been studied by using the ab initio generalized valence bond (GVB) dissociation-consistent configuration interaction (DCCI) method. All chlorine-substituted methylenes and silylenes have singlet ground states, with calculated singlet-triplet splittings of 6.0, 20.5, 35.8, and 55.2 kcal/mol for CHCI, CCI2, SiHCI...

We provide a dynamic programming principle for stochastic optimal control problems with expectation constraints. A weak formulation, using test functions and a probabilistic relaxation of the constraint, avoids restrictions related to a measurable selection but still implies the Hamilton-Jacobi-Bellman equation in the viscosity sense. We treat open state constraints as a special case of expecta...

Finite State Controllers (FSCs) are an effective way to represent sequential plans compactly. By imposing appropriate conditions on transitions, FSCs can also represent generalized plans that solve a range of planning problems from a given domain. In this paper we introduce the concept of hierarchical FSCs for planning by allowing controllers to call other controllers. We show that hierarchical...

In this paper, an efficient, numerically stable procedure is presented for the computation of irreducible generalized state-space realizations from non-minimal ones. The order reduction is performed by removing successively the uncontrollable and the unobservable parts of the system. Each reduction is accomplished by the same basic algorithm which deflates the uncontrollable part of the system ...