We formulate in this paper the mini-bucket algorithm for approximate inference in terms of exact inference on an approximate model produced by splitting nodes in a Bayesian network. The new formulation leads to a number of theoretical and practical implications. First, we show that branchand-bound search algorithms that use minibucket bounds may operate in a drastically reduced search space. Se...

A new gauge theory of gravity on flat spacetime has recently been developed by Lasenby, Doran, and Gull. Einstein’s principles of equivalence and general relativity are replaced by gauge principles asserting, respectively, local rotation and global displacement gauge invariance. A new unitary formulation of Einstein’s tensor illuminates long-standing problems with energy-momentum conservation i...

Keywords hp-FEM · contact problems This paper presents mixed variational formulation and its discretization with finite elements of higher-order for Signorini's problem with Tresca's friction. To guarantee the unique existence of the discrete saddle point of the mixed method, a discrete inf-sup condition is proven. Moreover, a solution scheme based on the dual formulation of the mixed method is...

A decentralized control algorithm for structural control system design has been developed. This novel approach is termed market-based control. As a potential alternative to the classical Linear Quadratic Regulator (LQR), this method decentralizes the decision process of the control system and allows for independent and autonomous control formulation to occur directly upon the control device. Th...

We develop new stabilized mixed finite element methods for Darcy flow. Stability and an a priori error estimate in the ‘‘stability norm’’ are established. A wide variety of convergent finite elements present themselves, unlike the classical Galerkin formulation which requires highly specialized elements. An interesting feature of the formulation is that there are no mesh-dependent parameters. N...

Improper priors are used frequently, but often formally and without reference to a sound theoretical basis. The present paper demonstrates that Kolmogorov’s (1933) formulation of probability theory admits a minimal generalization which includes improper priors and a general Bayes theorem. The resulting theory is closely related to the theory of conditional probability spaces formulated by Renyi...

We derive a compatible discretization method that relies heavily on the underlying geometric structure, and obeys the topological sequences and commuting properties that are constructed. As a sample problem we consider the vorticityvelocity-pressure formulation of the Stokes problem. We motivate the choice for a mixed variational formulation based on both geometric as well as physical arguments...

This article revisits the case formulation approach to psychotherapy outcome research, first proposed by Persons (1991). Persons asserted that randomized clinical trials (RCTs) of psychotherapy do not test the theoretical underpinnings of psychotherapy models since these trials standardize rather than individualize patient problems, ignore the link between individualized assessment and treatmen...

astigmatism’s defect has not yet been formulated in physics and medical physics books theoretically. in this paper, we are trying to formulate the astigmatism’s defect. the results of formulation show that “the degree of astigmatism is negative reverse the distance that vision’s condition of astigmatism’s chart lines change conditions in dimness angle from dimness condition at infinite distance...