Global Asymptotic Robust Stability and Global Exponential Robust Stability of Neural Networks with Time-Varying Delays

In this paper, based on nonnegative matrix theory, the Halanay’s inequality and Lyapunov functional, some novel sufficient conditions for global asymptotic robust stability and global exponential robust stability of neural networks with time-varying delays are presented. It is shown that our results improve and generalize several previous results derived in the literatures. From the obtained results, some linear matrix inequality criteria are derived. Finally, a simulation is given to show the effectiveness of the results.     

Broadcasting scheme with low client buffers and bandwidths for video-on-demand applications

Efficient data broadcasting is independent of request arrivals, and is thus highly promising when transmitting popular videos. A conventionally adopted broadcasting method is periodic broadcasting, which divides a popular video into segments, which are then simultaneously broadcast on different data channels. Once clients want to watch the video, they download the segments from these channels. The skyscraper broadcasting (SkB) scheme supports clients with small bandwidths. An SkB client requires only two-channel bandwidths to receive video segments. This work proposes a reverse SkB (RSkB) scheme, which extends SkB by reducing buffering spaces. The RSkB is mathematically shown to achieve on-time video delivery and two-channel client bandwidths. A formula for determining the maximum number of segments buffered by an RSkB client is presented. Finally, an analysis of RSkB reveals that its client buffer requirements are usually 25–37% lower than SkB. Extensive simulations of RSkB further demonstrate that RSkB yields lower client buffer demand than other proposed systems.

Smooth Scheduling under Variable Rates or the Analog-Digital Confinement Game

This work considers non-terminating scheduling problems in which a system of multiple resources serves clients having variable needs. The system has m identical resources and n clients; in each time slot each resource may serve at most one client; in each such slot t each client γ has a rate, a real number ρ _γ (t), that specifies his needs in this slot. The rates satisfy the restriction ∑ _γ ρ _γ (t)≤m for any slot t. Except of this restriction, the rates can vary in arbitrary fashion. (This contrasts most prior works in this area in which the rates of the clients are constant.) The schedule is required to be smooth as follows: a schedule is Δ -smooth if for all time intervals I the absolute difference between the amount of service received by each client γ to his nominal needs of ∑ _t∈I ρ _γ (t) is less than Δ. Our objective are online schedulers that produce Δ-smooth schedules where Δ is a small constant which is independent of m and n. Our paper constructs such schedulers; these are the first online Δ-smooth schedulers, with a constant Δ, for clients with arbitrarily variable rates in a single or multiple resource system. Furthermore, the paper also considers a non-concurrent environment in which there is an additional restriction that each client is served at most once in each time slot; it presents the first online smooth schedulers for variable rates under this restriction. The above non-concurrent restriction is crucial in some applications (e.g., CPU scheduling). It has been pointed out that this restriction “adds a surprising amount of difficulty” to the scheduling problem. However, this observation was never formalized and, of course, was never proved. Our paper formalizes and proves some aspects of this observation. Another contribution of this paper is the introduction of a complete information, two player game called the analog-digital confinement game. In such a game pebbles are located on the real line; the two players, the analog player and the digital player, take alternating turns and each one, in his turn, moves some of the pebbles; the digital player moves the pebbles backwards by discrete distances while the analog player moves the pebbles forward by analog distances; the aim of the analog player is to cause one pebble (or more) to escape a pre-defined real interval while the aim of the digital player is to confine the pebbles into the interval. We demonstrate that this game is a convenient framework to study the general question of how to approximate an analog process by a digital one. All the above scheduling results are established via this game. In this derivation, the pebbles represent the clients, the analog player generates the needs of the clients and the digital player generates the schedule. Dedicated to the memory of Professor Shimon Even for his inspiration and encouragement     

Degree-Optimal Routing for P2P Systems

We define a family of Distributed Hash Table systems whose aim is to combine the routing efficiency of randomized networks—e.g. optimal average path length O(log ² n/δlog δ) with δ degree—with the programmability and startup efficiency of a uniform overlay—that is, a deterministic system in which the overlay network is transitive and greedy routing is optimal. It is known that Ω(log n) is a lower bound on the average path length for uniform overlays with O(log n) degree (Xu et al., IEEE J. Sel. Areas Commun. 22(1), 151–163, 2004). Our work is inspired by neighbor-of-neighbor (NoN) routing, a recently introduced variation of greedy routing that allows us to achieve optimal average path length in randomized networks. The advantage of our proposal is that of allowing the NoN technique to be implemented without adding any overhead to the corresponding deterministic network. We propose a family of networks parameterized with a positive integer c which measures the amount of randomness that is used. By varying the value c, the system goes from the deterministic case (c=1) to an “almost uniform” system. Increasing c to relatively low values allows for routing with asymptotically optimal average path length while retaining most of the advantages of a uniform system, such as easy programmability and quick bootstrap of the nodes entering the system. We also provide a matching lower bound for the average path length of the routing schemes for any c. This work was partially supported by the Italian FIRB project “WEB-MINDS” (Wide-scalE, Broadband MIddleware for Network Distributed Services), .     

A Randomized Algorithm for Online Unit Clustering

In this paper, we consider the online version of the following problem: partition a set of input points into subsets, each enclosable by a unit ball, so as to minimize the number of subsets used. In the one-dimensional case, we show that surprisingly the naïve upper bound of 2 on the competitive ratio can be beaten: we present a new randomized 15/8-competitive online algorithm. We also provide some lower bounds and an extension to higher dimensions.     

On the Black-Box Complexity of Sperner’s Lemma

We present several results on the complexity of various forms of Sperner’s Lemma in the black-box model of computing. We give a deterministic algorithm for Sperner problems over pseudo-manifolds of arbitrary dimension. The query complexity of our algorithm is linear in the separation number of the skeleton graph of the manifold and the size of its boundary. As a corollary we get an deterministic query algorithm for the black-box version of the problem 2D-SPERNER, a well studied member of Papadimitriou’s complexity class PPAD. This upper bound matches the deterministic lower bound of Crescenzi and Silvestri. The tightness of this bound was not known before. In another result we prove for the same problem an lower bound for its probabilistic, and an lower bound for its quantum query complexity, showing that all these measures are polynomially related. Research supported by the European Commission IST Integrated Project Qubit Application (QAP) 015848, the OTKA grants T42559 and T46234, and by the ANR Blanc AlgoQP grant of the French Research Ministry.     

Cryptographic and Physical Zero-Knowledge Proof Systems for Solutions of Sudoku Puzzles

We consider cryptographic and physical zero-knowledge proof schemes for Sudoku, a popular combinatorial puzzle. We discuss methods that allow one party, the prover, to convince another party, the verifier, that the prover has solved a Sudoku puzzle, without revealing the solution to the verifier. The question of interest is how a prover can show: (i) that there is a solution to the given puzzle, and (ii) that he knows the solution, while not giving away any information about the solution to the verifier. In this paper we consider several protocols that achieve these goals. Broadly speaking, the protocols are either cryptographic or physical. By a cryptographic protocol we mean one in the usual model found in the foundations of cryptography literature. In this model, two machines exchange messages, and the security of the protocol relies on computational hardness. By a physical protocol we mean one that is implementable by humans using common objects, and preferably without the aid of computers. In particular, our physical protocols utilize items such as scratch-off cards, similar to those used in lotteries, or even just simple playing cards. The cryptographic protocols are direct and efficient, and do not involve a reduction to other problems. The physical protocols are meant to be understood by “lay-people” and implementable without the use of computers. Research of R. Gradwohl was supported by US-Israel Binational Science Foundation Grant 2002246. Research of M. Naor was supported in part by a grant from the Israel Science Foundation. Research of B. Pinkas was supported in part by the Israel Science Foundation (grant number 860/06). Research of G.N. Rothblum was supported by NSF grant CNS-0430450 and NSF grant CFF-0635297.     

Classification of semantic relations between nominals

The NLP community has shown a renewed interest in deeper semantic analyses, among them automatic recognition of semantic relations in text. We present the development and evaluation of a semantic analysis task: automatic recognition of relations between pairs of nominals in a sentence. The task was part of SemEval-2007, the fourth edition of the semantic evaluation event previously known as SensEval. Apart from the observations we have made, the long-lasting effect of this task may be a framework for comparing approaches to the task. We introduce the problem of recognizing relations between nominals, and in particular the process of drafting and refining the definitions of the semantic relations. We show how we created the training and test data, list and briefly describe the 15 participating systems, discuss the results, and conclude with the lessons learned in the course of this exercise.