We extend our previous duality theorem for Markov processes by equipping the processes with a pseudometric and the algebras with a notion of metric diameter. We are able to show that the isomorphisms of our previous duality theorem become isometries in this quantitative setting. This opens the way to developing theories of approximate reasoning for probabilistic systems.

We derive braided C*-tensor categories from gapped ground states on two-dimensional quantum spin systems satisfying some additional condition, which we call the approximate Haag duality.

‎in this paper‎, ‎first we develop the duality concept for $g$-bessel sequences‎ ‎and bessel fusion sequences in hilbert spaces‎. ‎we obtain some results about dual‎, ‎pseudo-dual ‎and approximate dual of frames and fusion frames‎. ‎we also expand every $g$-bessel ‎sequence to a frame by summing some elements‎. ‎we define the restricted isometry property for ‎$g$-frames and generalize some resu...

For a {0, 1}-valued matrixM let CC(M) denote the deterministic communication complexity of the boolean function associated with M . The log-rank conjecture of Lovász and Saks [FOCS 1988] states that CC(M) ≤ logc(rank(M)) for some absolute constant c where rank(M) denotes the rank of M over the field of real numbers. We show that CC(M) ≤ c · rank(M)/ log rank(M) for some absolute constant c, ass...

A branch and bound algorithm is proposed for finding an approximate global optimum of quadratic functions over a bounded polyhedral set. The algorithm uses Lagrangian duality to obtain lower bounds. Preliminary computational results are reported.

We focus on a class of nonconvex cooperative optimization problems that involve multiple participants. We study the duality framework and provide geometric and analytic characterizations of the duality gap. The dual problem is related to a market setting in which each participant pursues self-interests at a given price of common goods. The duality gap is a form of price of anarchy. We prove tha...

We consider a class of doubly nonlinear degenerate hyperbolicparabolic equations with homogeneous Dirichlet boundary conditions, for which we first establish the existence and uniqueness of entropy solutions. We then turn to the construction and analysis of discrete duality finite volume schemes (in the spirit of Domelevo and Omnès [41]) for these problems in two and three spatial dimensions. W...

Approximate inference is an important technique for dealing with large, intractable graphical models based on the exponential family of distributions. We extend the idea of approximate inference to the t-exponential family by defining a new t-divergence. This divergence measure is obtained via convex duality between the log-partition function of the t-exponential family and a new t-entropy. We ...

We consider a class of doubly nonlinear degenerate hyperbolicparabolic equations with homogeneous Dirichlet boundary conditions, for which we first establish the existence and uniqueness of entropy solutions. We then turn to the construction and analysis of discrete duality finite volume schemes (in the spirit of Domelevo and Omnès [41]) for these problems in two and three spatial dimensions. W...