Homotopy probability theory is a version of probability theory in which the vector space of random variables is replaced with a chain complex. A natural example extends ordinary probability theory on a finite volume Riemannian manifold M . In this example, initial conditions for fluid flow on M are identified with collections of homotopy random variables and solutions to the Euler equation are ...

The technology of support vector machines (SVM) is being widely used in many research fields at present, but standard SVM does not provide posterior probability that is needed in many uncertain classification problems. To solve this problem, a probability SVM model is built firstly, then the cross entropy and relative cross entropy model for classification problems are built. Finally, the metho...

We present a Markov Decision Process (MDP) framework for computing post-fault reconfiguration policies that are optimal with respect to a discounted cost. Our cost function penalizes states that are unsuitable to achieve the remaining objectives of the given mission. The cost function also penalizes states where the necessary goal achievement actions cannot be executed. We incorporate probabili...

High-rate (or asymptotic) quantization theory has found formulas for the average squared length (more generally, the q-th moment of the length) of the error produced by various scalar and vector quantizers with many quantization points. In contrast, this paper finds an asymptotic formula for the probability density of the length of the error and, in certain special cases, for the probability de...

We illustrate a framework for simulating degradation processes in components of energy systems. The logical framework revolves around a multi-state representation of the processes. The physics governing the processes is captured in the transition rates governing the random walk across the degradation states. The computational framework relies on a representation of the process dynamics by stoch...

Abstract The conditional probability formula is supposed to reflect the correct updating of assignments when new information incorporated. Starting from a non-atomic measure, it proved that provides only transformed measure satisfying “minimum requirement” relational assumption. This result applies standard Bayesian parametric model.

The main purpose of this paper is to introduce first a new family of empirical test statistics for testing a simple null hypothesis when the vector of parameters of interest are defined through a specific set of unbiased estimating functions. This family of test statistics is based on a distance between two probability vectors, with the first probability vector obtained by maximizing the empiri...

] , [ b a , ] , [ d c real intervals w ∇ partial derivatives of a quantity according to the weight vector elements i A , i B , i C machining times on machine s A, B, and C respectively j i a jth action in the ith state of the agent α learning rate for " mean value type " action-state values b vector of boundary conditions in flow-shop scheduling β learning rate for " standard deviation type " a...

In this paper a new method is introduced for path planning of an autonomous vehicle. In this method, the environment is considered cluttered and with some uncertainty sources. Thus, the state of detected object should be estimated using an optimal filter. To do so, the state distribution is assumed Gaussian. Thus the state vector is estimated by a Kalman filter at each time step. The estimation...