Let $G*H$ be the product $*$ of $G$ and $H$. In this paper we determine the rth power of the graph $G*H$ in terms of $G^r, H^r$ and $G^r*H^r$, when $*$ is the join, Cartesian, symmetric difference, disjunctive, composition, skew and corona product. Then we solve the equation $(G*H)^r=G^r*H^r$. We also compute the Wiener index and Wiener polarity index of the skew product.

This paper concerns with a product of circles induced by the quaternionic product considered in a projective manner. Several properties of this composition law are derived and on this way we arrive at some special numbers as roots or powers of unit. We extend this product to cycles as oriented circles and to pairs of circles by using the algebra of octonions. Three applications of the given pro...

We present a novel message passing algorithm for approximating the MAP problem in graphical models. The algorithm is similar in structure to max-product but unlike max-product it always converges, and can be proven to find the exact MAP solution in various settings. The algorithm is derived via block coordinate descent in a dual of the LP relaxation of MAP, but does not require any tunable para...

In this paper, a new interface for programming multimedia compositions in Max/MSP/Jitter using the Lua scripting language is presented. Lua is extensible and efficient making it an ideal choice for designing a programmatic interface for multimedia compositions. First, we discuss the distinctions of graphical and textual interfaces for composition and the requirements for a productive compositio...

The set of min-max functions F : R n ! R n is the least set containing coordinate substitutions and translations and closed under pointwise max, min, and function composition. The Duality Conjecture asserts that the trajectories of a min-max function, considered as a dynamical system, have a linear growth rate (cycle time) and shows how this can be calculated through a representation of F as an...

typical production objectives in distillation process require the delivery of products whose compositions meet certain specifications. the distillation control system, therefore, must hold product compositions as near the set points as possible in faces of upset. in this project, inferential model predictive control, that utilizes an artificial neural network estimator and model predictive cont...

We report studies of ultrahigh-energy cosmic-ray composition via analysis of depth of air shower maximum (X(max)), for air shower events collected by the High-Resolution Fly's Eye (HiRes) observatory. The HiRes data are consistent with a constant elongation rate d/d[log(E)] of 47.9+/-6.0(stat)+/-3.2(syst) g/cm2/decade for energies between 1.6 and 63 EeV, and are consistent with a predom...

This paper describes a package of extensions (externals) for Cycling ‘74’s Max/MSP software to facilitate the exploration of Ambisonic techniques of up to third order. Areas of exploration well suited to the Max/MSP environment and techniques for composition within the Ambisonic domain using the presented externals are described.

In general, the problem of computing the maximum a posteriori (MAP) assignment in a Bayesian network is computationally intractable. In some cases, such as in tree-structured networks, inference can be done efficiently and exactly. However, there are still practical challenges when trying to do inference in networks containing variables with large cardinalities. In this case, representing and m...