Advances in optimal routing through computer networks

The optimal routing problem is defined. Progress in solving the problem during the previous decade is reviewed, with special emphasis on technical developments made during the last few years. The relationships between the routing, the throughput, and the switching technology used are discussed and their future trends are reviewed. Economic aspects are also briefly considered. Modern technical approaches for handling the routing problems and, more generally, the flow control problems are reviewed

Redundancy of classical and quantum correlations during decoherence

We analyze the time dependence of entanglement and total correlations between a system and fractions of its environment in the course of decoherence. For the quantum Brownian motion model we show that the entanglement and total correlations have rather different dependence on the size of the environmental fraction. Redundancy manifests differently in both types of correlations and can be related with induced--classicality. To study this we introduce a new measure of redundancy and compare it with the existing one.Comment: 6 pages, 4 figure

Decoherence induced by a dynamic spin environment (II): Disentanglement by local system-environment interactions

This article studies the decoherence induced on a system of two qubits by local interactions with a spin chain with nontrivial internal dynamics (governed by an XY Hamiltonian). Special attention is payed to the transition between two limits: one in which both qubits interact with the same site of the chain and another one where they interact with distant sites. The two cases exhibit different behaviours in the weak and strong coupling regimes: when the coupling is weak it is found that decoherence tends to decrease with distance, while for strong coupling the result is the opposite. Also, in the weak coupling case, the long distance limit is rapidly reached, while for strong coupling there is clear evidence of an expected effect: environment-induced interactions between the qubits of the system. A consequence of this is the appearance of quasiperiodic events that can be interpreted as ``sudden deaths'' and ``sudden revivals'' of the entanglement between the qubits, with a time scale related to the distance between them.Comment: 10 pages, 9 figure

Output dynamics in an endogenous growth model

The aim of this paper is to assess the importance of RBC models with endogenous growth in characterizing the observed output dynamics. In particular, this article considers a stochastic version of Lucas' (1988) model in the absence of externalities in discrete time with two modifications: agents do not only derive utility from consumption but also from leisure and labor adjustment costs are included. Results reveal that combining the endogenous character of the engine of growth with labor adjustment costs may help solve the Cogley-Nason (1995) puzzle since, it provides a stronger propagation mechanism and this, in the end, improves the model''s ability to generate realistic output dynamics.

Lattice-Based proof of a shuffle

In this paper we present the first fully post-quantum proof of a shuffle for RLWE encryption schemes. Shuffles are commonly used to construct mixing networks (mix-nets), a key element to ensure anonymity in many applications such as electronic voting systems. They should preserve anonymity even against an attack using quantum computers in order to guarantee long-term privacy. The proof presented in this paper is built over RLWE commitments which are perfectly binding and computationally hiding under the RLWE assumption, thus achieving security in a post-quantum scenario. Furthermore we provide a new definition for a secure mixing node (mix-node) and prove that our construction satisfies this definition.Peer ReviewedPostprint (author's final draft

Gaussian Decoherence and Gaussian Echo from Spin Environments

We examine an exactly solvable model of decoherence -- a spin-system interacting with a collection of environment spins. We show that in this simple model (introduced some time ago to illustrate environment--induced superselection) generic assumptions about the coupling strengths lead to a universal (Gaussian) suppression of coherence between pointer states. We explore the regime of validity of this result and discuss its relation to spectral features of the environment. We also consider its relevance to the experiments on the so-called Loschmidt echo (which measures, in effect, the fidelity between the initial and time-reversed or "echo" signal). In particular, we show that for partial reversals (e.g., when of only a part of the total Hamiltonian changes sign) fidelity will exhibit a Gaussian dependence on the time of reversal. In such cases echo may become independent of the details of the reversal procedure or the specifics of the coupling to the environment. This puzzling behavior was observed in several NMR experiments. Natural candidates for such two environments (one of which is easily reversed, while the other is ``irreversible'') are suggested for the experiment involving ferrocene.Comment: Improved text and figures, to appear in the special issue of Acta Physica Polonica B celebrating the 100th anniversary of Smoluchowski's equation and his paper explaining Brownian motion (in http://th-www.if.uj.edu.pl/acta/vol38/pdf/v38p1685.pdf

Geometric Multi-Model Fitting with a Convex Relaxation Algorithm

We propose a novel method to fit and segment multi-structural data via convex relaxation. Unlike greedy methods --which maximise the number of inliers-- this approach efficiently searches for a soft assignment of points to models by minimising the energy of the overall classification. Our approach is similar to state-of-the-art energy minimisation techniques which use a global energy. However, we deal with the scaling factor (as the number of models increases) of the original combinatorial problem by relaxing the solution. This relaxation brings two advantages: first, by operating in the continuous domain we can parallelize the calculations. Second, it allows for the use of different metrics which results in a more general formulation. We demonstrate the versatility of our technique on two different problems of estimating structure from images: plane extraction from RGB-D data and homography estimation from pairs of images. In both cases, we report accurate results on publicly available datasets, in most of the cases outperforming the state-of-the-art

An Effective Field Theory Look at Deep Inelastic Scattering

This talk discusses the effective field theory view of deep inelastic scattering. In such an approach, the standard factorization formula of a hard coefficient multiplied by a parton distribution function arises from matching of QCD onto an effective field theory. The DGLAP equations can then be viewed as the standard renormalization group equations that determines the cut-off dependence of the non-local operator whose forward matrix element is the parton distribution function. As an example, the non-singlet quark splitting functions is derived directly from the renormalization properties of the non-local operator itself. This approach, although discussed in the literature, does not appear to be well known to the larger high energy community. In this talk we give a pedagogical introduction to this subject.Comment: 11 pages, 1 figure, To appear in Modern Physics Letters

Shapes of clusters and groups of galaxies: Comparison of model predictions with observations

We study the properties of the 3-dimensional and projected shapes of haloes using high resolution numerical simulations and observational data where the latter comes from the 2PIGG (Eke et al. 2004) and SDSS-DR3GC group catalogues (Merchan & Zandivarez 2005). We investigate the dependence of halo shape on characteristics such as mass and number of members. In the 3-dimensional case, we find a significant correlation between the mass and halo shape; massive systems are more prolate than small haloes. We detect a source of strong systematics in estimates of the triaxiality of a halo, which is found to be a strong function of the number of members; LCDM haloes usually characterised by triaxial shapes, slightly bent toward prolate forms, appear more oblate when taking only a small subset of the halo particles. The ellipticities of observed 2PIGG and SDSS-DR3GC groups are found to be strongly dependent on the number of group members, so that poor groups appear more elongated than rich ones. However, this is again an artifact caused by poor statistics and not an intrinsic property of the galaxy groups, nor an effect from observational biases. We interpret these results with the aid of a GALFORM mock 2PIGG catalogue. When comparing the group ellipticities in mock and real catalogues, we find an excellent agreement between the trends of shapes with number of group members. When carefully taking into account the effects of low number statistics, we find that more massive groups are consistent with more elongated shapes. Finally, our studies find no significant correlations between the shape of observed 2PIGG or SDSS-DR3GC groups with the properties of galaxy members such as colour or spectral type index.Comment: 9 pages, 10 figures, submitted to MNRA