Reasoning about the effects of actions in automated planning systems

This paper describes a temporal reasoning system that supports deductions for modeling the physics (i.e. cause and effect relationships) of a specified planning domain. We demonstrate how the process of planning can be profitably partitioned into two inferential components: one responsible for making choices relevant to the construction of a plan and a second responsible for maintaining an accurate picture of the future that takes into account the planner's intended actions. Causal knowledge about the effects of actions and the behavior of processes is stored apart from knowledge of plans for achieving specific tasks. Using this causal knowledge, the second component is able to predict the consequences of actions proposed by the first component and notice interactions that may affect the success of the plan under construction. By keeping track of the reasons why each prediction and choice is made, the resulting system is able to reason efficiently about the consequences of making new choices and retracting old ones. The system described in this paper makes it particularly simple and efficient to reason about actions whose effects vary depending upon the circumstances in which the actions are executed.     

On normal characterizations by the distribution of linear forms,assuming finite variance

If X₁ and X₂ are independent and identically distributed (i. i. d.) with finite variance, then $\text{(X}{}_1\text{+X}{}_2\text{)}\text{√2}$ has the same distribution as X₁ if and only if X₁ is normal with mean zero (Pólya [9]). The idea of using linear combinations of i. i. d. random variables to characterize the normal has since been extended to the case where σ^∞_i=1a_iX_i has the same distribution as X₁. In particular if at least two of the a_i's are non-zero and X₁ has finite variance, then Laha and Lukacs [8] showed that X₁ is normal. They also [7] established the same result without the assumption of finite variance. The purpose of this note is to present a different and easier proof of the characterization under the assumption of finite variance. The idea of the proof follows closely the approach used by Pólya in [9]. The same technique is also used to give a characterization of the exponential distribution.     

The convergence of Cesaro averages for certain nonstationary Markov chains

If P is a stochastic matrix corresponding to a stationary, irreducible, positive persistent Markov chain of period d>1, the powers Pⁿ will not converge as n → ∞. However, the subsequences P^nd+k for k=0,1,...d-1, and hence Cesaro averages Σⁿ_k-1 P^k/n, will converge. In this paper we determine classes of nonstationary Markov chains for which the analogous subsequences and/or Cesaro averages converge and consider the rates of convergence. The results obtained are then applied to the analysis of expected average cost.     

N-group neutron transport theory: A criticality problem in slab geometry

The steady-state equation for N-group neutron transport in slab geometry is written as an integral equation. A spectral analysis is made of the integral operator and related to the criticality problem. The method depends on a representation for the resolvent kernel for a subcritical slab and on analytic continuation in a complex parameter to characterize eigenvalues in terms of singularities of the resolvent. The analytic continuation is based on a bifurcation analysis of some nonlinear matrix integral equations whose solutions provide a matrix Wiener-Hopf factorization of the Fourier transform of the kernel of the transport operator.     

L 1 ergodic behavior of non-negative kernels

Some results that have been obtained in the study of strongly and weakly ergodic behavior of non-homogeneous stochastic kernels are generalized to the case of non-negative kernels. The first generalization simply involves extending the definitions of weakly and strongly ergiodic behavior to the case of non-negative kernels and using the ergodic coefficient which was first defined for stochastic kernels by Dobrushin and extended to non-negative kernels by Blum and Reichaw. It happens that this straightforward extension excludes many cases of non-negative kernels which do exhibit a types of ergodic behavior. In order to study these cases a definition ofL ₁ weakly and strongly ergodic behavior is given in which normalizing by constants is allowed. Sufficient conditions for these types of ergodic behavior are given.     

Shell-model calculation of the spectral function for l=0 proton states in12C

The spectral function for the removal of l=0 protons in¹²C is calculated within the framework of the shell model. The techniques used in the calculation exploit, in a novel fashion, certain features of the Lanczos method used in obtaining energies and wave-functions. G ross and fine details of the resulting strength distributions are compared against the results from¹²C(e, e′p)¹¹B experiments.