We show how to obtain the mixture connection in an infinite dimensional information manifold and prove that it is dual to the exponential connection with respect to the Fisher information. We also define the α-connections and prove that they are convex mixtures of the extremal (±1)-connections.

Different versions for defining Ashtekar’s generalized connections are investigated depending on the chosen smoothness category for the paths and graphs – the label set for the projective limit. Our definition covers the analytic case as well as the case of

Generalized Lagrange-Weyl structures and compatible connections are introduced as a natural generalization of similar notions from Riemannian geometry. Exactly as in Riemannian case, the compatible connection is unique if certain symmetry conditions with respect to vertical and horizontal Christoffel symbols are imposed. 2000 Math. Subject Classification: 53C60.

We show how to obtain the mixture connection in an infinite dimensional information manifold and prove that it is dual to the exponential connection with respect to the Fisher information. We also define the α-connections and prove that they are convex mixtures of the extremal (±1)-connections.

This paper reports on my exploration of the connections between the family of algorithms collectively known as the dual-tree approach, and the family of shortest-path problems in graphs. I explain why we might expect connections to exist, and the difficulties I encountered in applying the dual-tree method to shortest-path problems.

Many real-world problems, such as Markov Logic Networks (MLNs) with evidence, can be represented as a highly symmetric graphical model perturbed by additional potentials. In these models, variational inference approaches that exploit exact model symmetries are often forced to ground the entire problem, while methods that exploit approximate symmetries (such as by constructing an over-symmetric ...

The generalized Bernstein basis in the space Πn of polynomials of degree at most n, being an extension of the q-Bernstein basis introduced recently by G.M. Phillips, is given by the formula (see S. Lewanowicz & P. Woźny, BIT 44 (2004), 63–78) Bn i (x;ω| q) := 1 (ω; q)n [ n i ] q x (ωx−1; q)i (x; q)n−i (i = 0, 1, . . . , n). We give explicitly the dual basis functions Dn k (x; a, b, ω| q) for th...

Inverse Multiplexing for ATM (IMA) has been standardized by the ATM Forum to provide a high-capacity logical link by grouping several lower-capacity physical links. IMA is intrinsically point-to-point, assumes congestion-free links, and only tolerates relatively constant differential delays between the links. In this paper, we generalize the notion of inverse multiplexing by introducing switchi...

We use weighted characteristic polynomials to compute Tutte polynomials of generalized parallel connections in the case in which the simplification of the maximal common restriction of the two constituent matroids is a modular flat of the simplifications of both matroids. In particular, this includes cycle matroids of graphs that are identified along complete subgraphs. We also develop formulas...