Localized systems coupled to small baths: from Anderson_{nderson} to Zeno_{eno}

We investigate what happens if an Anderson localized system is coupled to a small bath, with a discrete spectrum, when the coupling between system and bath is specially chosen so as to never localize the bath. We find that the effect of the bath on localization in the system is a non-monotonic function of the coupling between system and bath. At weak couplings, the bath facilitates transport by allowing the system to 'borrow' energy from the bath. But above a certain coupling the bath produces localization, because of an orthogonality catastrophe, whereby the bath 'dresses' the system and hence suppresses the hopping matrix element. We call this last regime the regime of "Zeno-localization", since the physics of this regime is akin to the quantum Zeno effect, where frequent measurements of the position of a particle impede its motion. We confirm our results by numerical exact diagonalization

Entanglement spectrum degeneracy and the Cardy formula in 1+1 dimensional conformal field theories

We investigate the effect of a global degeneracy in the distribution of the entanglement spectrum in conformal field theories in one spatial dimension. We relate the recently found universal expression for the entanglement Hamiltonian to the distribution of the entanglement spectrum. The main tool to establish this connection is the Cardy formula. It turns out that the Affleck-Ludwig non-integer degeneracy, appearing because of the boundary conditions induced at the entangling surface, can be directly read from the entanglement spectrum distribution. We also clarify the effect of the noninteger degeneracy on the spectrum of the partial transpose, which is the central object for quantifying the entanglement in mixed states. We show that the exact knowledge of the entanglement spectrum in some integrable spinchains provides strong analytical evidences corroborating our results

A practical constructive scheme for deterministic shared-memory access

Abstract. We present three explicit schemes for distributing M variables among N memory modules, where M = �(N 1.5), M = �(N 2), and M = �(N 3), respectively. Each variable is replicated into a constant number of copies stored in distinct modules. We show that N processors, directly accessing the memories through a complete interconnection, can read/write any set of N variables in worstcase time O(N 1/3), O(N 1/2), and O(N 2/3), respectively for the three schemes. The access times for the last two schemes are optimal with respect to the particular redundancy values used by such schemes. The address computation can be carried out efficiently by each processor without recourse to a complete memory map and requiring only O(1) internal storage. 1

Constructive Deterministic PRAM Simulation on a Mesh-Connected Computer

The PRAM model of computation consists of a collection of sequential RAM machines accessing a shared memory in lock-step fashion. The PRAM is a very high-level abstraction of a parallel computer, and its direct realization in hardware is beyond reach of the current (or even foreseeable) technology. In this paper we present a deterministic simulation scheme to emulate PRAM computation on a mesh-connected computer, a feasible machine where each processor has its own memory module and is connected to at most four other processors via point-to-point links. In order to achieve a good worst-case performance, any deterministic simulation scheme has to replicate each variable in a number of copies. Such copies are stored in the local memory modules according to a Memory Organization Scheme (MOS), which is known to all the processors. A variable is then accessed by routing packets to its copies. All deterministic schemes in the literature make use of a MOS whose existence is proved via the prob..

Dimensionality-adaptive k-center in sliding windows

In this paper we present a novel streaming algorithm for the k-center clustering problem for general metric spaces under the sliding window model. The algorithm maintains a small coreset which, at any time, allows to compute a solution to the k-center problem on the current window with an approximation quality that can be made arbitrarily close to the best approximation attainable by a sequential algorithm running on the entire window. Remarkably, the size of our coreset is independent of the window size and can be upper bounded by a function of k, of the desired accuracy, and of the doubling dimension of the metric space induced by the stream. For streams of bounded doubling dimension, the coreset size is merely linear in k. One of the major strengths of our algorithm is that it is fully oblivious to the doubling dimension of the stream, and it adapts to the characteristics of each individual window. Also, unlike previous works, the algorithm can be made oblivious to the aspect ratio of the metric space, a parameter related to the spread of distances. We also provide experimental evidence of the practical viability of the approach and its superiority over the current state of the art

A General Coreset-Based Approach to Diversity Maximization under Matroid Constraints

Diversity maximization is a fundamental problem in web search and data mining. For a given dataset S of n elements, the problem requires to determine a subset of S containing kg n "representatives"which maximize some diversity function expressed in terms of pairwise distances, where distance models dissimilarity. An important variant of the problem prescribes that the solution satisfy an additional orthogonal requirement, which can be specified as a matroid constraint (i.e., a feasible solution must be an independent set of size k of a given matroid). While unconstrained diversity maximization admits efficient coreset-based strategies for several diversity functions, known approaches dealing with the additional matroid constraint apply only to one diversity function (sum of distances), and are based on an expensive, inherently sequential, local search over the entire input dataset. We devise the first coreset-based algorithms for diversity maximization under matroid constraints for various diversity functions, together with efficient sequential, MapReduce, and Streaming implementations. Technically, our algorithms rely on the construction of a small coreset, that is, a subset of S containing a feasible solution which is no more than a factor 1-I away from the optimal solution for S. While our algorithms are fully general, for the partition and transversal matroids, if I is a constant in (0,1) and S has bounded doubling dimension, the coreset size is independent of n and it is small enough to afford the execution of a slow sequential algorithm to extract a final, accurate, solution in reasonable time. Extensive experiments show that our algorithms are accurate, fast, and scalable, and therefore they are capable of dealing with the large input instances typical of the big data scenario