We investigate the effectiveness of selftraining PCFG grammars with latent annotations (PCFG-LA) for parsing languages with different amounts of labeled training data. Compared to Charniak’s lexicalized parser, the PCFG-LA parser was more effectively adapted to a language for which parsing has been less well developed (i.e., Chinese) and benefited more from selftraining. We show for the first t...

We consider backward stochastic differential equations with convex constraints on the gains (or intensity-of-noise) process. Existence and uniqueness of a minimal solution are established in the case of a drift coefficient which is Lipschitz continuous in the state and gains processes and convex in the gains process. It is also shown that the minimal solution can be characterized as the unique ...

We use the notation A ∈ F to indicate that the set A is in F . Remark that since A∩B = (A ∪B) and more generally ⋂ Ai = ( ⋃ Ai) c (Exercise: Prove this equality) axiom ii) holds with union replaced by intersection. Also we have A−B = A ∩B so if A,B ∈ F then A−B ∈ F . Basically you should think of a σ-algebra as a system of subsets in which you can perform any of the usual set-theoretic operatio...

We describe maximal nilpotent subsemigroups of a given nilpotency class in the semigroup Ωn of all n × n real matrices with nonnegative coefficients and the semigroup Dn of all doubly stochastic real matrices.

In this paper, a comprehensive mathematical model for designing an electric power supply chain network via considering preventive maintenance under risk of network failures is proposed. The risk of capacity disruption of the distribution network is handled via using a two-stage stochastic programming as a framework for modeling the optimization problem. An applied method of planning for the net...

We consider the solution of a system of stochastic generalized equations (SGE) where the underlying functions are mathematical expectation of random set-valued mappings. SGE has many applications such as characterizing optimality conditions of a nonsmooth stochastic optimization problem or equilibrium conditions of a stochastic equilibrium problem. We derive quantitative continuity of expected ...

This paper investigates symmetries of autonomous ordinary stochastic differential equations. Change time includes the process itself, and is uniquely determined by transformation spatial variable. As a particular feature, change an admitted Lie symmetry group may be unrelated with in process. Sufficient conditions for to equation are derived. method can applied second order equations as well sy...

In this paper we present two interesting properties of stochastic cellular automata that can be helpful in analyzing the dynamical behavior of such automata. The first property allows calculating cell-wise probability distributions over the state set of a stochastic cellular automaton, i.e. images that show the average state of each cell during the stochastic cellular automaton evolution. The s...