The Peres-Horodecki criterion of positivity under partial transpose is studied in the context of separability of bipartite continuous variable states. The partial transpose operation admits, in the continuous case, a geometric interpretation as mirror reflection in phase space. This recognition leads to uncertainty principles, stronger than the traditional ones, to be obeyed by all separable st...

We show that if p > pc(Z ), then the unique infinite percolation cluster supports a nonzero flow f with finite q energy for all q > 2. This extends the work of Grimmett, Kesten, and Zhang and Levin and Peres in dimensions d ≥ 3. As an application of our techniques we exhibit a graph that has transient percolation clusters, but does not admit exponential intersection tails. This answers a questi...

In an increasingly human-dominated world, where most of us seem oblivious to the liquidation of Earth’s natural resource capital (Chapters 3 and 4), exploitation of biological populations has become one of the most important threats to the persistence of global biodiversity. Many regional economies, if not entire civilizations, have been built on free-for-all extractive industries, and history ...

Häggström, Peres, and Steif (1997) have introduced a dynamical version of percolation on a graph G. When G is a tree they derived a necessary and sufficient condition for percolation to exist at some time t. In the case that G is a spherically symmetric tree, Peres and Steif (1998) derived a necessary and sufficient condition for percolation to exist at some time t in a given target set D. The ...

YUVAL PERES and WILHELM SCHLAG

Recently Peres and Shields discovered a new method for estimating the order of a stationary fixed order Markov chain [15]. They showed that the estimator is consistent by proving a threshold result. While this threshold is valid asymptotically in the limit, it is not very useful for DNA sequence analysis where data sizes are moderate. In this paper we give a novel interpretation of the Peres-Sh...

It is shown that the 33 complex rays in three dimensions used by Penrose to prove the Bell-Kochen-Specker theorem have the same orthogonality relations as the 33 real rays of Peres, and therefore provide an isomorphic proof of the theorem. It is further shown that the Peres and Penrose rays are just two members of a continuous three-parameter family of unitarily inequivalent rays that prove the...

We report a computation of the exact output rate of recently-discovered generalization of Peres algorithm for generating random bits from loaded dice. Instead of resorting to brute-force computation for all possible inputs, which becomes quickly impractical as the input size increases, we compute the total output length on equiprobable sets of inputs by dynamic programming using a recursive for...

Adders and multipliers are two main units of the computer arithmetic processors and play an important role in reversible computations. The binary multiplier consists of two main parts, the partial products generation circuit (PPGC) and the reversible parallel adders (RPA). This paper introduces a novel reversible 4×4 multiplier circuit that is based on an advanced PPGC with Peres gates only. Ag...