This work presents a new method for symmetrization of directed graphs that constructs an undirected graph with equivalent pairwise effective resistances as a given directed graph. Consequently a graph metric, square root of effective resistance, is preserved between the directed graph and its symmetrized version. It is shown that the preservation of this metric allows for interpretation of alge...

Given a query patch image, patch matching consists in finding similar patches in a target image. In pattern recognition, patch matching is a fundamental task that is time consuming, specially when zoom factors and symmetries are handled. The matching results heavily depend on the underlying notion of distances, or similarities, between patches. We present a method that consists in modeling patc...

‎let $v$ be an $n$-dimensional complex inner product space‎. ‎suppose‎ ‎$h$ is a subgroup of the symmetric group of degree $m$‎, ‎and‎ ‎$chi‎ :‎hrightarrow mathbb{c} $ is an irreducible character (not‎ ‎necessarily linear)‎. ‎denote by $v_{chi}(h)$ the symmetry class‎ ‎of tensors associated with $h$ and $chi$‎. ‎let $k(t)in‎ (v_{chi}(h))$ be the operator induced by $tin‎ ‎text{end}(v)$‎. ‎the...

Non-commutativity is a common feature in mathematical modeling of reality which, in quantum mechanics, introduces the so-called Heisenberg-Weyl algebra. This new quality does not come without a price − the order of components in operator successions is now relevant and has to be carefully traced in calculations. A traditional solution to this problem is to standardize the notation by fixing the...

We provide an analytical expression for optimal Lewenstein-Sanpera decomposition of Bell decomposable states by using semi-definite programming. Also using the KarushKuhn-Tucker optimization method, the minimum relative entropy of entanglement of Bell decomposable states has been evaluated and it is shown that the same separable Bell decomposable state lying at the boundary of convex set of sep...

While influence diagrams have many ad­ vantages as a representation framework for Bayesian decision problems, they have a se­ rious drawback in handling asymmetric de­ cision problems. To be represented in an influence diagram, an asymmetric decision problem must be symmetrized. A consid­ erable amount of unnecessary computation may be involved when a symmetrized influ­ ence diagram is evaluate...

Flp and Cre-mediated recombination on symmetrized FRT and loxP sites, respectively, in circular plasmid substrates yield both DNA inversion and deletion. However, upon sequestering three negative supercoils outside the recombination complex using the resII-resIII synapse formed by Tn3 resolvase and the LER synapse formed by phage Mu transposase in the case of Flp and Cre, respectively, the reac...

an h-magic labeling in a h-decomposable graph g is a bijection f : v (g) ∪ e(g) → {1, 2, ..., p + q} such that for every copy h in the decomposition, σνεv(h) f(v) +  σeεe(h) f(e) is constant. f is said to be h-e-super magic if f(e(g)) = {1, 2, · · · , q}. a family of subgraphs h1,h2, · · · ,hh of g is a mixed cycle-decomposition of g if every subgraph hi is isomorphic to some cycle ck, for k ≥ ...

We study projective dimension, a graph parameter (denoted by pd(G) for a graph G), introduced by Pudlák and Rödl [13], who showed that proving lower bounds for pd(Gf ) for bipartite graphs Gf associated with a Boolean function f imply size lower bounds for branching programs computing f . Despite several attempts [13, 17], proving super-linear lower bounds for projective dimension of explicit f...