A linear subspace E of R has colored local rules if there exists a finite set of decorated tiles whose tilings are digitizations of E. The local rules are weak if the digitizations can slightly wander around E. We prove that a linear subspace has weak colored local rules if and only if it is computable. This goes beyond the previous results, all based on algebraic subspaces. We prove an analogo...

Methods for measuring the weak value of non local variables are investigated. We analyze local (indirect) measurement methods for obtaining the weak values. We also describe some new (direct) methods (Non local weak measurements) for measuring the weak values of some non local variables. Non local variables are variables of a composite system with parts in two or more remote locations. An examp...

We study a class of processes that are akin to the Wright-Fisher model, with transition probabilities weighted in terms of the frequency-dependent fitness of the population types. By considering an approximate weak formulation of the discrete problem, we are able to derive a corresponding continuous weak formulation for the probability density. Therefore, we obtain a family of partial different...

In this paper, we analyze a quasistatic problem modeling frictional contact between viscoplastic body and an obstacle, the so called foundation. The material constitutive relation is assumed to be non-linear. boundary conditions of friction are modeled respectively by \textit{Signorini} generalized Coulomb's non-local law. We derive variational formulation for prove existence its unique weak so...

We present a new reduced scaling multireference singles and doubles configuration interaction ~MRSDCI! algorithm based upon the combination of local correlation and pseudospectral methods. Taking advantage of the locality of the Coulomb potential, the weak-pairs approximation of Saebo” and Pulay is employed to eliminate configurations having simultaneous excitations out of pairs of distant, wea...

Program logics are formal systems for specifying and reasoning about software programs. Most program logics make the strong assumption that all threads agree on the value of shared memory at all times. This assumption can be unsound though for programs with races, like many concurrent data structures. Verification of these difficult programs must take into account the weaker models of memory pr...

We propose a measurement-based method to produce a maximally-entangled state from a partially-entangled pure state. Our goal can be thought of as entanglement distillation from a single copy of a partially-entangled state. The present approach involves local two-outcome weak measurements. We show that the application of these local weak measurements leads to a probabilistic amplification of ent...

We consider the 2 x 2 hyperbolic system of isentropic gas dynamics, in both Eulerian or Lagrangian variables (also called the p-system). We show that they can be reformulated as a kinetic equation, using an additional kinetic variable. Such a formulation was first obtained by the authors in the case of multidimensional scalar conservation laws. A new phenomenon occurs here, namely that the adve...

protein based films used for food packaging despite having numerous benefits like biodegradability and renewability suffer from essential drawbacks of weak mechanical and water vapour barrier properties. in recent years efforts for improving functional properties of such films from various resources, through modifying formulation, molecular crosslinking and promote proteins based composite film...