OpenRaiser/Intern-Atlas huggingface dataset:
Proof of a Conjecture on the Sequence of Exceptional Numbers, Classifying Cyclic Codes and APN Functions
Venue: arXiv cs.IT 2009
Year: 2009

We prove a conjecture that classifies exceptional numbers. This conjecture arises in two different ways, from cryptography and from coding theory. An odd integer $t\geq 3$ is said to be exceptional if $f(x)=x^t$ is APN (Almost Perfect Nonlinear) over $\mathbb{F}_{2^n}$ for infinitely many values of $n$. Equivalently, $t$ is exceptional if the binary cyclic code of length $2^n-1$ with two zeros $ω, ω^t$ has minimum distance 5 for infinitely many values of $n$. The conjecture we prove states that every exceptional number has the form $2^i+1$ or $4^i-2^i+1$.
Analysis of a Bloom Filter Algorithm via the Supermarket Model
Venue: arXiv cs.DM 2009
Year: 2009

This paper deals with the problem of identifying elephants in the Internet Traffic. The aim is to analyze a new adaptive algorithm based on a Bloom Filter. This algorithm uses a so-called min-rule which can be described as in the supermarket model. This model consists of joining the shortest queue among d queues selected at random in a large number of m queues. In case of equality, one of the shortest queues is chosen at random. An analysis of a simplified model gives an insight of the error generated by the algorithm on the estimation of the number of the elephants. The main conclusion is that, as m gets large, there is a deterministic limit for the empirical distribution of the filter counters. Limit theorems are proved and the limit is identified. It depends on key parameters. The condition for the algorithm to perform well is discussed. Theoretical results are validated by experiments on a traffic trace from France Telecom and by simulations.
Improving Size-Change Analysis in Offline Partial Evaluation
Venue: arXiv cs.PL 2009
Year: 2009

Some recent approaches for scalable offline partial evaluation of logic programs include a size-change analysis for ensuring both so called local and global termination. In this work|inspired by experimental evaluation|we introduce several improvements that may increase the accuracy of the analysis and, thus, the quality of the associated specialized programs. We aim to achieve this while maintaining the same complexity and scalability of the recent works.
Multiagent Learning in Large Anonymous Games
Venue: arXiv cs.MA 2009
Year: 2009

In large systems, it is important for agents to learn to act effectively, but sophisticated multi-agent learning algorithms generally do not scale. An alternative approach is to find restricted classes of games where simple, efficient algorithms converge. It is shown that stage learning efficiently converges to Nash equilibria in large anonymous games if best-reply dynamics converge. Two features are identified that improve convergence. First, rather than making learning more difficult, more agents are actually beneficial in many settings. Second, providing agents with statistical information about the behavior of others can significantly reduce the number of observations needed.
Cooperative Multiplexing: Toward Higher Spectral Efficiency in Multi-antenna Relay Networks
Venue: arXiv cs.IT 2009
Year: 2009

Previous work on cooperative communications has concentrated primarily on the diversity benefits of such techniques. This paper, instead, considers the multiplexing benefits of cooperative communications. First, a new interpretation on the fundamental tradeoff between the transmission rate and outage probability in multi-antenna relay networks is given. It follows that multiplexing gains can be obtained at any finite SNR, in full-duplex multi-antenna relay networks. Thus relaying can offer not only stronger link reliability, but also higher spectral efficiency. Specifically, the decode-and-forward protocol is applied and networks that have one source, one destination, and multiple relays are considered. A receive power gain at the relays, which captures the network large scale fading characteristics, is also considered. It is shown that this power gain can significantly affect the system diversity-multiplexing tradeoff for any finite SNR value. Several relaying protocols are proposed and are shown to offer nearly the same outage probability as if the transmit antennas at the source and the relay(s) were co-located, given certain SNR and receive power gains at the relays. Thus a higher multiplexing gain than that of the direct link can be obtained if the destination has more antennas than the source. Much of the analysis in the paper is valid for arbitrary channel fading statistics. These results point to a view of relay networks as a means for providing higher spectral efficiency, rather than only link reliability.
Parking functions, labeled trees and DCJ sorting scenarios
Venue: arXiv cs.DM 2009
Year: 2009

In genome rearrangement theory, one of the elusive questions raised in recent years is the enumeration of rearrangement scenarios between two genomes. This problem is related to the uniform generation of rearrangement scenarios, and the derivation of tests of statistical significance of the properties of these scenarios. Here we give an exact formula for the number of double-cut-and-join (DCJ) rearrangement scenarios of co-tailed genomes. We also construct effective bijections between the set of scenarios that sort a cycle and well studied combinatorial objects such as parking functions and labeled trees.
Effect of Degree Distribution on Evolutionary Search
Venue: arXiv cs.NE 2009
Year: 2009

This paper introduces a method to generate hierarchically modular networks with prescribed node degree list and proposes a metric to measure network modularity based on the notion of edge distance. The generated networks are used as test problems to explore the effect of modularity and degree distribution on evolutionary algorithm performance. Results from the experiments (i) confirm a previous finding that modularity increases the performance advantage of genetic algorithms over hill climbers, and (ii) support a new conjecture that test problems with modularized constraint networks having heavy-tailed right-skewed degree distributions are more easily solved than test problems with modularized constraint networks having bell-shaped normal degree distributions.
Airport Gate Assignment A Hybrid Model and Implementation
Venue: arXiv cs.AI 2009
Year: 2009

With the rapid development of airlines, airports today become much busier and more complicated than previous days. During airlines daily operations, assigning the available gates to the arriving aircrafts based on the fixed schedule is a very important issue, which motivates researchers to study and solve Airport Gate Assignment Problems (AGAP) with all kinds of state-of-the-art combinatorial optimization techniques. In this paper, we study the AGAP and propose a novel hybrid mathematical model based on the method of constraint programming and 0 - 1 mixed-integer programming. With the objective to minimize the number of gate conflicts of any two adjacent aircrafts assigned to the same gate, we build a mathematical model with logical constraints and the binary constraints. For practical considerations, the potential objective of the model is also to minimize the number of gates that airlines must lease or purchase in order to run their business smoothly. We implement the model in the Optimization Programming Language (OPL) and carry out empirical studies with the data obtained from online timetable of Continental Airlines, Houston Gorge Bush Intercontinental Airport IAH, which demonstrate that our model can provide an efficient evaluation criteria for the airline companies to estimate the efficiency of their current gate assignments.
Multiscale Computations on Neural Networks: From the Individual Neuron Interactions to the Macroscopic-Level Analysis
Venue: arXiv cs.CE 2009
Year: 2009

We show how the Equation-Free approach for multi-scale computations can be exploited to systematically study the dynamics of neural interactions on a random regular connected graph under a pairwise representation perspective. Using an individual-based microscopic simulator as a black box coarse-grained timestepper and with the aid of simulated annealing we compute the coarse-grained equilibrium bifurcation diagram and analyze the stability of the stationary states sidestepping the necessity of obtaining explicit closures at the macroscopic level. We also exploit the scheme to perform a rare-events analysis by estimating an effective Fokker-Planck describing the evolving probability density function of the corresponding coarse-grained observables.
Capacity region of the deterministic multi-pair bi-directional relay network
Venue: arXiv cs.IT 2009
Year: 2009

In this paper we study the capacity region of the multi-pair bidirectional (or two-way) wireless relay network, in which a relay node facilitates the communication between multiple pairs of users. This network is a generalization of the well known bidirectional relay channel, where we have only one pair of users. We examine this problem in the context of the deterministic channel interaction model, which eliminates the channel noise and allows us to focus on the interaction between signals. We characterize the capacity region of this network when the relay is operating at either full-duplex mode or half-duplex mode (with non adaptive listen-transmit scheduling). In both cases we show that the cut-set upper bound is tight and, quite interestingly, the capacity region is achieved by a simple equation-forwarding strategy.
Decoding of MDP Convolutional Codes over the Erasure Channel
Venue: arXiv cs.IT 2009
Year: 2009

This paper studies the decoding capabilities of maximum distance profile (MDP) convolutional codes over the erasure channel and compares them with the decoding capabilities of MDS block codes over the same channel. The erasure channel involving large alphabets is an important practical channel model when studying packet transmissions over a network, e.g, the Internet.
Finding matching initial states for equivalent NLFSRs in the fibonacci and the galois configurations
Venue: arXiv cs.CR 2009
Year: 2009

In this paper, a mapping between initial states of the Fibonacci and the Galois configurations of NLFSRs is established. We show how to choose initial states for two configurations so that the resulting output sequences are equivalent.
A New Local Distance-Based Outlier Detection Approach for Scattered Real-World Data
Venue: arXiv cs.LG 2009
Year: 2009

Detecting outliers which are grossly different from or inconsistent with the remaining dataset is a major challenge in real-world KDD applications. Existing outlier detection methods are ineffective on scattered real-world datasets due to implicit data patterns and parameter setting issues. We define a novel "Local Distance-based Outlier Factor" (LDOF) to measure the {outlier-ness} of objects in scattered datasets which addresses these issues. LDOF uses the relative location of an object to its neighbours to determine the degree to which the object deviates from its neighbourhood. Properties of LDOF are theoretically analysed including LDOF's lower bound and its false-detection probability, as well as parameter settings. In order to facilitate parameter settings in real-world applications, we employ a top-n technique in our outlier detection approach, where only the objects with the highest LDOF values are regarded as outliers. Compared to conventional approaches (such as top-n KNN and top-n LOF), our method top-n LDOF is more effective at detecting outliers in scattered data. It is also easier to set parameters, since its performance is relatively stable over a large range of parameter values, as illustrated by experimental results on both real-world and synthetic datasets.
Hyperbolic Voronoi diagrams made easy
Venue: arXiv cs.CG 2009
Year: 2009

We present a simple framework to compute hyperbolic Voronoi diagrams of finite point sets as affine diagrams. We prove that bisectors in Klein's non-conformal disk model are hyperplanes that can be interpreted as power bisectors of Euclidean balls. Therefore our method simply consists in computing an equivalent clipped power diagram followed by a mapping transformation depending on the selected representation of the hyperbolic space (e.g., Poincaré conformal disk or upper-plane representations). We discuss on extensions of this approach to weighted and $k$-order diagrams, and describe their dual triangulations. Finally, we consider two useful primitives on the hyperbolic Voronoi diagrams for designing tailored user interfaces of an image catalog browsing application in the hyperbolic disk: (1) finding nearest neighbors, and (2) computing smallest enclosing balls.
Distributed and Adaptive Algorithms for Vehicle Routing in a Stochastic and Dynamic Environment
Venue: arXiv cs.RO 2009
Year: 2009

In this paper we present distributed and adaptive algorithms for motion coordination of a group of m autonomous vehicles. The vehicles operate in a convex environment with bounded velocity and must service demands whose time of arrival, location and on-site service are stochastic; the objective is to minimize the expected system time (wait plus service) of the demands. The general problem is known as the m-vehicle Dynamic Traveling Repairman Problem (m-DTRP). The best previously known control algorithms rely on centralized a-priori task assignment and are not robust against changes in the environment, e.g. changes in load conditions; therefore, they are of limited applicability in scenarios involving ad-hoc networks of autonomous vehicles operating in a time-varying environment. First, we present a new class of policies for the 1-DTRP problem that: (i) are provably optimal both in light- and heavy-load condition, and (ii) are adaptive, in particular, they are robust against changes in load conditions. Second, we show that partitioning policies, whereby the environment is partitioned among the vehicles and each vehicle follows a certain set of rules in its own region, are optimal in heavy-load conditions. Finally, by combining the new class of algorithms for the 1-DTRP with suitable partitioning policies, we design distributed algorithms for the m-DTRP problem that (i) are spatially distributed, scalable to large networks, and adaptive to network changes, (ii) are within a constant-factor of optimal in heavy-load conditions and stabilize the system in any load condition. Simulation results are presented and discussed.
Combinatorial Ricci Curvature and Laplacians for Image Processing
Venue: arXiv cs.CV 2009
Year: 2009

A new Combinatorial Ricci curvature and Laplacian operators for grayscale images are introduced and tested on 2D synthetic, natural and medical images. Analogue formulae for voxels are also obtained. These notions are based upon more general concepts developed by R. Forman. Further applications, in particular a fitting Ricci flow, are discussed.
Computations modulo regular chains
Venue: arXiv cs.SC 2009
Year: 2009

The computation of triangular decompositions are based on two fundamental operations: polynomial GCDs modulo regular chains and regularity test modulo saturated ideals. We propose new algorithms for these core operations relying on modular methods and fast polynomial arithmetic. Our strategies take also advantage of the context in which these operations are performed. We report on extensive experimentation, comparing our code to pre-existing Maple implementations, as well as more optimized Magma functions. In most cases, our new code outperforms the other packages by several orders of magnitude.
GeoP2P: An adaptive peer-to-peer overlay for efficient search and update of spatial information
Venue: arXiv cs.NI 2009
Year: 2009

This paper proposes a fully decentralized peer-to-peer overlay structure GeoP2P, to facilitate geographic location based search and retrieval of information. Certain limitations of centralized geographic indexes favor peer-to-peer organization of the information, which, in addition to avoiding performance bottleneck, allows autonomy over local information. Peer-to-peer systems for geographic or multidimensional range queries built on existing DHTs suffer from the inaccuracy in linearization of the multidimensional space. Other overlay structures that are based on hierarchical partitioning of the search space are not scalable because they use special super-peers to represent the nodes in the hierarchy. GeoP2P partitions the search space hierarchically, maintains the overlay structure and performs the routing without the need of any super-peers. Although similar fully-decentralized overlays have been previously proposed, they lack the ability to dynamically grow and retract the partition hierarchy when the number of peers change. GeoP2P provides such adaptive features with minimum perturbation of the system state. Such adaptation makes both the routing delay and the state size of each peer logarithmic to the total number of peers, irrespective of the size of the multidimensional space. Our analysis also reveals that the overlay structure and the routing algorithm are generic and independent of several aspects of the partitioning hierarchy, such as the geometric shape of the zones or the dimensionality of the search space.
Multiple-Input Multiple-Output Gaussian Broadcast Channels with Confidential Messages
Venue: arXiv cs.IT 2009
Year: 2009

This paper considers the problem of secret communication over a two-receiver multiple-input multiple-output (MIMO) Gaussian broadcast channel. The transmitter has two independent messages, each of which is intended for one of the receivers but needs to be kept asymptotically perfectly secret from the other. It is shown that, surprisingly, under a matrix power constraint both messages can be simultaneously transmitted at their respective maximal secrecy rates. To prove this result, the MIMO Gaussian wiretap channel is revisited and a new characterization of its secrecy capacity is provided via a new coding scheme that uses artificial noise and random binning.
Personal report of the 3rd ECMDA-FA'07 conference
Venue: arXiv cs.SE 2009
Year: 2009

Manuscripts notes taken during the conference ECMDA 2008. I give the full conference program (title of the article and name of the person who introduced) detailing some of the presentations.
Gradient-based adaptive interpolation in super-resolution image restoration
Venue: arXiv cs.MM 2009
Year: 2009

This paper presents a super-resolution method based on gradient-based adaptive interpolation. In this method, in addition to considering the distance between the interpolated pixel and the neighboring valid pixel, the interpolation coefficients take the local gradient of the original image into account. The smaller the local gradient of a pixel is, the more influence it should have on the interpolated pixel. And the interpolated high resolution image is finally deblurred by the application of wiener filter. Experimental results show that our proposed method not only substantially improves the subjective and objective quality of restored images, especially enhances edges, but also is robust to the registration error and has low computational complexity.
Feedback control logic synthesis for non safe Petri nets
Venue: arXiv cs.IT 2009
Year: 2009

This paper addresses the problem of forbidden states of non safe Petri Net (PN) modelling discrete events systems. To prevent the forbidden states, it is possible to use conditions or predicates associated with transitions. Generally, there are many forbidden states, thus many complex conditions are associated with the transitions. A new idea for computing predicates in non safe Petri nets will be presented. Using this method, we can construct a maximally permissive controller if it exists.
Sums of powers via integration
Venue: arXiv cs.DM 2009
Year: 2009

Sum of powers 1^p+...+n^p, with n and p being natural numbers and n>=1, can be expressed as a polynomial function of n of degree p+1. Such representations are often called Faulhaber formulae. A simple recursive algorithm for computing coefficients of Faulhaber formulae is presented. The correctness of the algorithm is proved by giving a recurrence relation on Faulhaber formulae.
CliqueStream: an efficient and fault-resilient live streaming network on a clustered peer-to-peer overlay
Venue: arXiv cs.NI 2009
Year: 2009

Several overlay-based live multimedia streaming platforms have been proposed in the recent peer-to-peer streaming literature. In most of the cases, the overlay neighbors are chosen randomly for robustness of the overlay. However, this causes nodes that are distant in terms of proximity in the underlying physical network to become neighbors, and thus data travels unnecessary distances before reaching the destination. For efficiency of bulk data transmission like multimedia streaming, the overlay neighborhood should resemble the proximity in the underlying network. In this paper, we exploit the proximity and redundancy properties of a recently proposed clique-based clustered overlay network, named eQuus, to build efficient as well as robust overlays for multimedia stream dissemination. To combine the efficiency of content pushing over tree structured overlays and the robustness of data-driven mesh overlays, higher capacity stable nodes are organized in tree structure to carry the long haul traffic and less stable nodes with intermittent presence are organized in localized meshes. The overlay construction and fault-recovery procedures are explained in details. Simulation study demonstrates the good locality properties of the platform. The outage time and control overhead induced by the failure recovery mechanism are minimal as demonstrated by the analysis.
Complexity of Fractran and Productivity
Venue: arXiv cs.LO 2009
Year: 2009

In functional programming languages the use of infinite structures is common practice. For total correctness of programs dealing with infinite structures one must guarantee that every finite part of the result can be evaluated in finitely many steps. This is known as productivity. For programming with infinite structures, productivity is what termination in well-defined results is for programming with finite structures. Fractran is a simple Turing-complete programming language invented by Conway. We prove that the question whether a Fractran program halts on all positive integers is Pi^0_2-complete. In functional programming, productivity typically is a property of individual terms with respect to the inbuilt evaluation strategy. By encoding Fractran programs as specifications of infinite lists, we establish that this notion of productivity is Pi^0_2-complete even for the most simple specifications. Therefore it is harder than termination of individual terms. In addition, we explore possible generalisations of the notion of productivity in the framework of term rewriting, and prove that their computational complexity is Pi^1_1-complete, thus exceeding the expressive power of first-order logic.