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1105.1733
Linear Hybrid System Falsification With Descent
cs.SY math.OC
In this paper, we address the problem of local search for the falsification of hybrid automata with affine dynamics. Namely, if we are given a sequence of locations and a maximum simulation time, we return the trajectory that comes the closest to the unsafe set. In order to solve this problem, we formulate it as a differentiable optimization problem which we solve using Sequential Quadratic Programming. The purpose of developing such a local search method is to combine it with high level stochastic optimization algorithms in order to falsify hybrid systems with complex discrete dynamics and high dimensional continuous spaces. Experimental results indicate that indeed the local search procedure improves upon the results of pure stochastic optimization algorithms.
1105.1745
Analysis of Alternative Metrics for the PAPR Problem in OFDM Transmission
cs.IT math.IT
The effective PAPR of the transmit signal is the standard metric to capture the effect of nonlinear distortion in OFDM transmission. A common rule of thumb is the log$(N)$ barrier where $N$ is the number of subcarriers which has been theoretically analyzed by many authors. Recently, new alternative metrics have been proposed in practice leading potentially to different system design rules which are theoretically analyzed in this paper. One of the main findings is that, most surprisingly, the log$(N)$ barrier turns out to be much too conservative: e.g. for the so-called amplifier-oriented metric the scaling is rather $\log[ \log(N)]$. To prove this result, new upper bounds on the PAPR distribution for coded systems are presented as well as a theorem relating PAPR results to these alternative metrics.
1105.1749
A Real-Time Model-Based Reinforcement Learning Architecture for Robot Control
cs.AI cs.RO cs.SE
Reinforcement Learning (RL) is a method for learning decision-making tasks that could enable robots to learn and adapt to their situation on-line. For an RL algorithm to be practical for robotic control tasks, it must learn in very few actions, while continually taking those actions in real-time. Existing model-based RL methods learn in relatively few actions, but typically take too much time between each action for practical on-line learning. In this paper, we present a novel parallel architecture for model-based RL that runs in real-time by 1) taking advantage of sample-based approximate planning methods and 2) parallelizing the acting, model learning, and planning processes such that the acting process is sufficiently fast for typical robot control cycles. We demonstrate that algorithms using this architecture perform nearly as well as methods using the typical sequential architecture when both are given unlimited time, and greatly out-perform these methods on tasks that require real-time actions such as controlling an autonomous vehicle.
1105.1767
A projected gradient dynamical system modeling the dynamics of bargaining
q-fin.TR cs.SY math.DS math.OC
We propose a projected gradient dynamical system as a model for a bargaining scheme for an asset for which the two interested agents have personal valuations which do not initially coincide. The personal valuations are formed using subjective beliefs concerning the future states of the world and the reservation prices are calculated using expected utility theory. The agents are not rigid concerning their subjective probabilities and are willing to update them under the pressure to reach finally an agreement concerning the asset. The proposed projected dynamical system, on the space of probability measures, provides a model for the evolution of the agents beliefs during the bargaining period and is constructed so that agreement is reached under the minimum possible deviation of both agents from their initial beliefs. The convergence results are shown using techniques from convex dynamics and Lyapunov function theory.
1105.1822
On the Preliminary Design of Multiple Gravity-Assist Trajectories
math.OC cs.NE cs.SY physics.space-ph
In this paper the preliminary design of multiple gravity-assist trajectories is formulated as a global optimization problem. An analysis of the structure of the solution space reveals a strong multimodality, which is strictly dependent on the complexity of the model. On the other hand it is shown how an oversimplification could prevent finding potentially interesting solutions. A trajectory model, which represents a compromise between model completeness and optimization problem complexity is then presented. The exploration of the resulting solution space is performed through a novel global search approach, which hybridizes an evolutionary based algorithm with a systematic branching strategy. This approach allows an efficient exploration of complex solution domains by automatically balancing local convergence and global search. A number of difficult multiple gravity-assist trajectory design cases demonstrates the effectiveness of the proposed methodology.
1105.1823
Design of Low-Thrust Gravity Assist Trajectories to Europa
math.OC cs.SY
This paper presents the design of a mission to Europa using solar electric propulsion as main source of thrust. A direct transcription method based on Finite Elements in Time was used for the design and optimisation of the entire low-thrust gravity assist transfer from the Earth to Europa. Prior to that, a global search algorithm was used to generate a set of suitable first guess solutions for the transfer to Jupiter, and for the capture in the Jovian system. In particular, a fast deterministic search algorithm was developed to find the most promising set of swing-bys to reach Jupiter A second fast search algorithm was developed to find the best sequence of swing-bys of the Jovian moons. After introducing the global search algorithms and the direct transcription through Finite Elements in Time, the paper presents a number of first guess Solutions and a fully optimised transfer from the Earth to Europa.
1105.1829
Optimizing low-thrust and gravity assist maneuvers to design interplanetary trajectories
math.OC cs.SY
In this paper a direct method based on a transcription by finite elements in time has been used to design optimal interplanetary trajectories, exploiting a combination of gravity assist maneuvers and low-thrust propulsion. A multiphase parametric approach has been used to introduce swing-bys, treated as coast phases between two thrusted or coasting trajectory arcs. Gravity maneuvers are at first modeled with a linked-conic approximation and then introduced through a full three-dimensional propagation including perturbations by the Sun. The method is successfully applied to the design of a mission to planet Mercury, for which different options corresponding to different sequences of gravity maneuvers or launch opportunities are presented.
1105.1853
Feedback Message Passing for Inference in Gaussian Graphical Models
stat.ML cs.AI
While loopy belief propagation (LBP) performs reasonably well for inference in some Gaussian graphical models with cycles, its performance is unsatisfactory for many others. In particular for some models LBP does not converge, and in general when it does converge, the computed variances are incorrect (except for cycle-free graphs for which belief propagation (BP) is non-iterative and exact). In this paper we propose {\em feedback message passing} (FMP), a message-passing algorithm that makes use of a special set of vertices (called a {\em feedback vertex set} or {\em FVS}) whose removal results in a cycle-free graph. In FMP, standard BP is employed several times on the cycle-free subgraph excluding the FVS while a special message-passing scheme is used for the nodes in the FVS. The computational complexity of exact inference is $O(k^2n)$, where $k$ is the number of feedback nodes, and $n$ is the total number of nodes. When the size of the FVS is very large, FMP is intractable. Hence we propose {\em approximate FMP}, where a pseudo-FVS is used instead of an FVS, and where inference in the non-cycle-free graph obtained by removing the pseudo-FVS is carried out approximately using LBP. We show that, when approximate FMP converges, it yields exact means and variances on the pseudo-FVS and exact means throughout the remainder of the graph. We also provide theoretical results on the convergence and accuracy of approximate FMP. In particular, we prove error bounds on variance computation. Based on these theoretical results, we design efficient algorithms to select a pseudo-FVS of bounded size. The choice of the pseudo-FVS allows us to explicitly trade off between efficiency and accuracy. Experimental results show that using a pseudo-FVS of size no larger than $\log(n)$, this procedure converges much more often, more quickly, and provides more accurate results than LBP on the entire graph.
1105.1894
Decoding Cyclic Codes up to a New Bound on the Minimum Distance
cs.IT math.IT
A new lower bound on the minimum distance of q-ary cyclic codes is proposed. This bound improves upon the Bose-Chaudhuri-Hocquenghem (BCH) bound and, for some codes, upon the Hartmann-Tzeng (HT) bound. Several Boston bounds are special cases of our bound. For some classes of codes the bound on the minimum distance is refined. Furthermore, a quadratic-time decoding algorithm up to this new bound is developed. The determination of the error locations is based on the Euclidean Algorithm and a modified Chien search. The error evaluation is done by solving a generalization of Forney's formula.
1105.1901
Convergence Analysis of Differential Evolution Variants on Unconstrained Global Optimization Functions
cs.NE
In this paper, we present an empirical study on convergence nature of Differential Evolution (DE) variants to solve unconstrained global optimization problems. The aim is to identify the competitive nature of DE variants in solving the problem at their hand and compare. We have chosen fourteen benchmark functions grouped by feature: unimodal and separable, unimodal and nonseparable, multimodal and separable, and multimodal and nonseparable. Fourteen variants of DE were implemented and tested on fourteen benchmark problems for dimensions of 30. The competitiveness of the variants are identified by the Mean Objective Function value, they achieved in 100 runs. The convergence nature of the best and worst performing variants are analyzed by measuring their Convergence Speed (Cs) and Quality Measure (Qm).
1105.1917
How citation boosts promote scientific paradigm shifts and Nobel Prizes
physics.soc-ph cs.DL cs.SI
Nobel Prizes are commonly seen to be among the most prestigious achievements of our times. Based on mining several million citations, we quantitatively analyze the processes driving paradigm shifts in science. We find that groundbreaking discoveries of Nobel Prize Laureates and other famous scientists are not only acknowledged by many citations of their landmark papers. Surprisingly, they also boost the citation rates of their previous publications. Given that innovations must outcompete the rich-gets-richer effect for scientific citations, it turns out that they can make their way only through citation cascades. A quantitative analysis reveals how and why they happen. Science appears to behave like a self-organized critical system, in which citation cascades of all sizes occur, from continuous scientific progress all the way up to scientific revolutions, which change the way we see our world. Measuring the "boosting effect" of landmark papers, our analysis reveals how new ideas and new players can make their way and finally triumph in a world dominated by established paradigms. The underlying "boost factor" is also useful to discover scientific breakthroughs and talents much earlier than through classical citation analysis, which by now has become a widespread method to measure scientific excellence, influencing scientific careers and the distribution of research funds. Our findings reveal patterns of collective social behavior, which are also interesting from an attention economics perspective. Understanding the origin of scientific authority may therefore ultimately help to explain, how social influence comes about and why the value of goods depends so strongly on the attention they attract.
1105.1922
Numerical Construction of LISS Lyapunov Functions under a Small Gain Condition
math.NA cs.SY math.OC
In the stability analysis of large-scale interconnected systems it is frequently desirable to be able to determine a decay point of the gain operator, i.e., a point whose image under the monotone operator is strictly smaller than the point itself. The set of such decay points plays a crucial role in checking, in a semi-global fashion, the local input-to-state stability of an interconnected system and in the numerical construction of a LISS Lyapunov function. We provide a homotopy algorithm that computes a decay point of a monotone op- erator. For this purpose we use a fixed point algorithm and provide a function whose fixed points correspond to decay points of the monotone operator. The advantage to an earlier algorithm is demonstrated. Furthermore an example is given which shows how to analyze a given perturbed interconnected system.
1105.1929
The Hidden Web, XML and Semantic Web: A Scientific Data Management Perspective
cs.AI
The World Wide Web no longer consists just of HTML pages. Our work sheds light on a number of trends on the Internet that go beyond simple Web pages. The hidden Web provides a wealth of data in semi-structured form, accessible through Web forms and Web services. These services, as well as numerous other applications on the Web, commonly use XML, the eXtensible Markup Language. XML has become the lingua franca of the Internet that allows customized markups to be defined for specific domains. On top of XML, the Semantic Web grows as a common structured data source. In this work, we first explain each of these developments in detail. Using real-world examples from scientific domains of great interest today, we then demonstrate how these new developments can assist the managing, harvesting, and organization of data on the Web. On the way, we also illustrate the current research avenues in these domains. We believe that this effort would help bridge multiple database tracks, thereby attracting researchers with a view to extend database technology.
1105.1930
Emerging multidisciplinary research across database management systems
cs.DB
The database community is exploring more and more multidisciplinary avenues: Data semantics overlaps with ontology management; reasoning tasks venture into the domain of artificial intelligence; and data stream management and information retrieval shake hands, e.g., when processing Web click-streams. These new research avenues become evident, for example, in the topics that doctoral students choose for their dissertations. This paper surveys the emerging multidisciplinary research by doctoral students in database systems and related areas. It is based on the PIKM 2010, which is the 3rd Ph.D. workshop at the International Conference on Information and Knowledge Management (CIKM). The topics addressed include ontology development, data streams, natural language processing, medical databases, green energy, cloud computing, and exploratory search. In addition to core ideas from the workshop, we list some open research questions in these multidisciplinary areas.
1105.1943
Asymptotic Analysis of Double-Scattering Channels
cs.IT math.IT
We consider a multiple-input multiple-output (MIMO) multiple access channel (MAC), where the channel between each transmitter and the receiver is modeled by the doubly-scattering channel model. Based on novel techniques from random matrix theory, we derive deterministic approximations of the mutual information, the signal-to-noise-plus-interference-ratio (SINR) at the output of the minimum-mean-square-error (MMSE) detector and the sum-rate with MMSE detection which are almost surely tight in the large system limit. Moreover, we derive the asymptotically optimal transmit covariance matrices. Our simulation results show that the asymptotic analysis provides very close approximations for realistic system dimensions.
1105.1950
An analytical framework for data stream mining techniques based on challenges and requirements
cs.DB
A growing number of applications that generate massive streams of data need intelligent data processing and online analysis. Real-time surveillance systems, telecommunication systems, sensor networks and other dynamic environments are such examples. The imminent need for turning such data into useful information and knowledge augments the development of systems, algorithms and frameworks that address streaming challenges. The storage, querying and mining of such data sets are highly computationally challenging tasks. Mining data streams is concerned with extracting knowledge structures represented in models and patterns in non stopping streams of information. Generally, two main challenges are designing fast mining methods for data streams and need to promptly detect changing concepts and data distribution because of highly dynamic nature of data streams. The goal of this article is to analyze and classify the application of diverse data mining techniques in different challenges of data stream mining. In this paper, we present the theoretical foundations of data stream analysis and propose an analytical framework for data stream mining techniques.
1105.1951
Self-configuration from a Machine-Learning Perspective
nlin.AO cs.LG stat.ML
The goal of machine learning is to provide solutions which are trained by data or by experience coming from the environment. Many training algorithms exist and some brilliant successes were achieved. But even in structured environments for machine learning (e.g. data mining or board games), most applications beyond the level of toy problems need careful hand-tuning or human ingenuity (i.e. detection of interesting patterns) or both. We discuss several aspects how self-configuration can help to alleviate these problems. One aspect is the self-configuration by tuning of algorithms, where recent advances have been made in the area of SPO (Sequen- tial Parameter Optimization). Another aspect is the self-configuration by pattern detection or feature construction. Forming multiple features (e.g. random boolean functions) and using algorithms (e.g. random forests) which easily digest many fea- tures can largely increase learning speed. However, a full-fledged theory of feature construction is not yet available and forms a current barrier in machine learning. We discuss several ideas for systematic inclusion of feature construction. This may lead to partly self-configuring machine learning solutions which show robustness, flexibility, and fast learning in potentially changing environments.
1105.1969
Capacity of Discrete Molecular Diffusion Channels
cs.IT math.IT
In diffusion-based molecular communications, messages can be conveyed via the variation in the concentration of molecules in the medium. In this paper, we intend to analyze the achievable capacity in transmission of information from one node to another in a diffusion channel. We observe that because of the molecular diffusion in the medium, the channel possesses memory. We then model the memory of the channel by a two-step Markov chain and obtain the equations describing the capacity of the diffusion channel. By performing a numerical analysis, we obtain the maximum achievable rate for different levels of the transmitter power, i.e., the molecule production rate.
1105.2013
Weyl theory and explicit solutions of direct and inverse problems for a Dirac system with rectangular matrix potential
math.SP cs.SY math.CA math.OC
A non-classical Weyl theory is developed for Dirac systems with rectangular matrix potentials. The notion of the Weyl function is introduced and the corresponding direct problem is treated. Furthermore, explicit solutions of the direct and inverse problems are obtained for the case of rational Weyl matrix functions.
1105.2017
Potential Games for Energy-Efficient Resource Allocation in Multipoint-to-Multipoint CDMA Wireless Data Networks
cs.IT math.IT
The problem of noncooperative resource allocation in a multipoint-to-multipoint cellular network is considered in this paper. The considered scenario is general enough to represent several key instances of modern wireless networks such as a multicellular network, a peer-to-peer network (interference channel), and a wireless network equipped with femtocells. In particular, the problem of joint transmit waveforms adaptation, linear receiver design, and transmit power control is examined. Several utility functions to be maximized are considered, and, among them, we cite the received SINR, and the transmitter energy efficiency, which is measured in bit/Joule, and represents the number of successfully delivered bits for each energy unit used for transmission. Resorting to the theory of potential games, noncooperative games admitting Nash equilibria in multipoint-to-multipoint cellular networks regardless of the channel coefficient realizations are designed. Computer simulations confirm that the considered games are convergent, and show the huge benefits that resource allocation schemes can bring to the performance of wireless data networks.
1105.2054
Generalized Boosting Algorithms for Convex Optimization
cs.LG stat.ML
Boosting is a popular way to derive powerful learners from simpler hypothesis classes. Following previous work (Mason et al., 1999; Friedman, 2000) on general boosting frameworks, we analyze gradient-based descent algorithms for boosting with respect to any convex objective and introduce a new measure of weak learner performance into this setting which generalizes existing work. We present the weak to strong learning guarantees for the existing gradient boosting work for strongly-smooth, strongly-convex objectives under this new measure of performance, and also demonstrate that this work fails for non-smooth objectives. To address this issue, we present new algorithms which extend this boosting approach to arbitrary convex loss functions and give corresponding weak to strong convergence results. In addition, we demonstrate experimental results that support our analysis and demonstrate the need for the new algorithms we present.
1105.2062
Scalar Quantization with Random Thresholds
cs.IT math.IT
The distortion-rate performance of certain randomly-designed scalar quantizers is determined. The central results are the mean-squared error distortion and output entropy for quantizing a uniform random variable with thresholds drawn independently from a uniform distribution. The distortion is at most 6 times that of an optimal (deterministically-designed) quantizer, and for a large number of levels the output entropy is reduced by approximately (1-gamma)/(ln 2) bits, where gamma is the Euler-Mascheroni constant. This shows that the high-rate asymptotic distortion of these quantizers in an entropy-constrained context is worse than the optimal quantizer by at most a factor of 6 exp(-2(1-gamma)).
1105.2096
Sum Capacity of Gaussian Interfering Multiple Access Channels in the Low Interference Regime
cs.IT math.IT
This paper has been withdrawn due to an incorrect proof.
1105.2114
An algebraic look into MAC-DMT of lattice space-time codes
cs.IT math.IT math.NT
In this paper we are concentrating on the diversity-multiplexing gain trade-off (DMT) of some space-time lattice codes. First we give a DMT bound for lattice codes having restricted dimension. We then recover the well known results of the DMT of algebraic number field codes and the Alamouti code by using the union bound and see that these codes do achieve the previously mentioned bound. During our analysis interesting connections to the Dedekind's zeta-function and to the unit group of algebraic number fields are revealed. Finally we prove that both the number field codes and Alamouti code are in some sense optimal codes in the multiple access channel (MAC).
1105.2176
A Framework for Optimization under Limited Information
math.OC cs.IT cs.LG cs.SY math.IT
In many real world problems, optimization decisions have to be made with limited information. The decision maker may have no a priori or posteriori data about the often nonconvex objective function except from on a limited number of points that are obtained over time through costly observations. This paper presents an optimization framework that takes into account the information collection (observation), estimation (regression), and optimization (maximization) aspects in a holistic and structured manner. Explicitly quantifying the information acquired at each optimization step using the entropy measure from information theory, the (nonconvex) objective function to be optimized (maximized) is modeled and estimated by adopting a Bayesian approach and using Gaussian processes as a state-of-the-art regression method. The resulting iterative scheme allows the decision maker to solve the problem by expressing preferences for each aspect quantitatively and concurrently.
1105.2211
Dual Control with Active Learning using Gaussian Process Regression
math.OC cs.IT cs.LG cs.SY math.IT
In many real world problems, control decisions have to be made with limited information. The controller may have no a priori (or even posteriori) data on the nonlinear system, except from a limited number of points that are obtained over time. This is either due to high cost of observation or the highly non-stationary nature of the system. The resulting conflict between information collection (identification, exploration) and control (optimization, exploitation) necessitates an active learning approach for iteratively selecting the control actions which concurrently provide the data points for system identification. This paper presents a dual control approach where the information acquired at each control step is quantified using the entropy measure from information theory and serves as the training input to a state-of-the-art Gaussian process regression (Bayesian learning) method. The explicit quantification of the information obtained from each data point allows for iterative optimization of both identification and control objectives. The approach developed is illustrated with two examples: control of logistic map as a chaotic system and position control of a cart with inverted pendulum.
1105.2214
An improved mathematical model of social group competition
physics.soc-ph cs.SI
An improved mathematical model of social group competition is proposed. The utility obtained by a member of a certain group from each other member is assumed to be group size-dependent. Obtained results are close to available census data. It is shown that a significant fraction of population can be affiliated in a group with lower maximal specific utility.
1105.2254
Symmetries in observer design: review of some recent results and applications to EKF-based SLAM
math.OC cs.RO cs.SY
In this paper, we first review the theory of symmetry-preserving observers and we mention some recent results. Then, we apply the theory to Extended Kalman Filter-based Simultaneous Localization and Mapping (EKF SLAM). It allows to derive a new (symmetry-preserving) Extended Kalman Filter for the non-linear SLAM problem that possesses convergence properties. We also prove a special choice of the gains ensures global exponential convergence.
1105.2255
On the Limitations of Provenance for Queries With Difference
cs.DB
The annotation of the results of database transformations was shown to be very effective for various applications. Until recently, most works in this context focused on positive query languages. The provenance semirings is a particular approach that was proven effective for these languages, and it was shown that when propagating provenance with semirings, the expected equivalence axioms of the corresponding query languages are satisfied. There have been several attempts to extend the framework to account for relational algebra queries with difference. We show here that these suggestions fail to satisfy some expected equivalence axioms (that in particular hold for queries on "standard" set and bag databases). Interestingly, we show that this is not a pitfall of these particular attempts, but rather every such attempt is bound to fail in satisfying these axioms, for some semirings. Finally, we show particular semirings for which an extension for supporting difference is (im)possible.
1105.2257
From brain to earth and climate systems: Small-world interaction networks or not?
physics.data-an cs.SI physics.soc-ph
We consider recent reports on small-world topologies of interaction networks derived from the dynamics of spatially extended systems that are investigated in diverse scientific fields such as neurosciences, geophysics, or meteorology. With numerical simulations that mimic typical experimental situations we have identified an important constraint when characterizing such networks: indications of a small-world topology can be expected solely due to the spatial sampling of the system along with commonly used time series analysis based approaches to network characterization.
1105.2264
Distributed Semantic Web Data Management in HBase and MySQL Cluster
cs.DB cs.PF
Various computing and data resources on the Web are being enhanced with machine-interpretable semantic descriptions to facilitate better search, discovery and integration. This interconnected metadata constitutes the Semantic Web, whose volume can potentially grow the scale of the Web. Efficient management of Semantic Web data, expressed using the W3C's Resource Description Framework (RDF), is crucial for supporting new data-intensive, semantics-enabled applications. In this work, we study and compare two approaches to distributed RDF data management based on emerging cloud computing technologies and traditional relational database clustering technologies. In particular, we design distributed RDF data storage and querying schemes for HBase and MySQL Cluster and conduct an empirical comparison of these approaches on a cluster of commodity machines using datasets and queries from the Third Provenance Challenge and Lehigh University Benchmark. Our study reveals interesting patterns in query evaluation, shows that our algorithms are promising, and suggests that cloud computing has a great potential for scalable Semantic Web data management.
1105.2274
Data-Distributed Weighted Majority and Online Mirror Descent
cs.LG cs.DC
In this paper, we focus on the question of the extent to which online learning can benefit from distributed computing. We focus on the setting in which $N$ agents online-learn cooperatively, where each agent only has access to its own data. We propose a generic data-distributed online learning meta-algorithm. We then introduce the Distributed Weighted Majority and Distributed Online Mirror Descent algorithms, as special cases. We show, using both theoretical analysis and experiments, that compared to a single agent: given the same computation time, these distributed algorithms achieve smaller generalization errors; and given the same generalization errors, they can be $N$ times faster.
1105.2283
The Deterministic Sum Capacity of a Multiple Access Channel Interfering with a Point to Point Link
cs.IT math.IT
In this paper, we use the linear deterministic approximation model to study a two user multiple access channel mutually interfering with a point to point link, which represents a basic setup of a cellular system. We derive outer bounds on the achievable sum rate and construct coding schemes achieving the outer bounds. For a large parameter range, the sum capacity is identical to the sum capacity of the interference channel obtained by silencing the weaker user in the multiple access channel. For other interference configurations, the sum rate can be increased using interference alignment, which exploits the channel gain difference of the users in the multiple access channel. From these results, lower bounds on the generalized degrees of freedom for the Gaussian counterpart are derived.
1105.2291
Proof of a Conjecture of Helleseth: Maximal Linear Recursive Sequences of Period $2^{2^n}-1$ Never Have Three-Valued Cross-Correlation
math.CO cs.IT math.IT
We prove a conjecture of Helleseth that claims that for any $n \geq 0$, a pair of binary maximal linear sequences of period $2^{2^n}-1$ can not have a three-valued cross-correlation function.
1105.2311
An Achievable Rate Region for the Broadcast Channel with Feedback
cs.IT math.IT
A single-letter achievable rate region is proposed for the two-receiver discrete memoryless broadcast channel with generalized feedback. The coding strategy involves block-Markov superposition coding, using Marton's coding scheme for the broadcast channel without feedback as the starting point. If the message rates in the Marton scheme are too high to be decoded at the end of a block, each receiver is left with a list of messages compatible with its output. Resolution information is sent in the following block to enable each receiver to resolve its list. The key observation is that the resolution information of the first receiver is correlated with that of the second. This correlated information is efficiently transmitted via joint source-channel coding, using ideas similar to the Han-Costa coding scheme. Using the result, we obtain an achievable rate region for the stochastically degraded AWGN broadcast channel with noisy feedback from only one receiver. It is shown that this region is strictly larger than the no-feedback capacity region.
1105.2361
A standard form for generator matrices with respect to the Niederreiter-Rosenbloom-Tsfasman metric
cs.IT math.IT math.NT
In this note, we present an analogue for codes in vector spaces with a Rosenbloom-Tsfasman metric of the well-known standard form of generator matrices for codes in spaces with the Hamming metric.
1105.2375
On the DMT of TDD-SIMO Systems with Channel-Dependent Reverse Channel Training
cs.IT math.IT
This paper investigates the Diversity-Multiplexing gain Trade-off (DMT) of a training based reciprocal Single Input Multiple Output (SIMO) system, with (i) perfect Channel State Information (CSI) at the Receiver (CSIR) and noisy CSI at the Transmitter (CSIT), and (ii) noisy CSIR and noisy CSIT. In both the cases, the CSIT is acquired through Reverse Channel Training (RCT), i.e., by sending a training sequence from the receiver to the transmitter. A channel-dependent fixed-power training scheme is proposed for acquiring CSIT, along with a forward-link data transmit power control scheme. With perfect CSIR, the proposed scheme is shown to achieve a diversity order that is quadratically increasing with the number of receive antennas. This is in contrast with conventional orthogonal RCT schemes, where the diversity order is known to saturate as the number of receive antennas is increased, for a given channel coherence time. Moreover, the proposed scheme can achieve a larger DMT compared to the orthogonal training scheme. With noisy CSIR and noisy CSIT, a three-way training scheme is proposed and its DMT performance is analyzed. It is shown that nearly the same diversity order is achievable as in the perfect CSIR case. The time-overhead in the training schemes is explicitly accounted for in this work, and the results show that the proposed channel-dependent RCT and data power control schemes offer a significant improvement in terms of the DMT, compared to channel-agnostic orthogonal RCT schemes. The outage performance of the proposed scheme is illustrated through Monte-Carlo simulations.
1105.2377
Entropy rate calculations of algebraic measures
cs.IT math.IT
Let $K = \{0,1,...,q-1\}$. We use a special class of translation invariant measures on $K^\mathbb{Z}$ called algebraic measures to study the entropy rate of a hidden Markov processes. Under some irreducibility assumptions of the Markov transition matrix we derive exact formulas for the entropy rate of a general $q$ state hidden Markov process derived from a Markov source corrupted by a specific noise model. We obtain upper bounds on the error when using an approximation to the formulas and numerically compute the entropy rates of two and three state hidden Markov models.
1105.2416
PAC-Bayesian Analysis of Martingales and Multiarmed Bandits
cs.LG stat.ML
We present two alternative ways to apply PAC-Bayesian analysis to sequences of dependent random variables. The first is based on a new lemma that enables to bound expectations of convex functions of certain dependent random variables by expectations of the same functions of independent Bernoulli random variables. This lemma provides an alternative tool to Hoeffding-Azuma inequality to bound concentration of martingale values. Our second approach is based on integration of Hoeffding-Azuma inequality with PAC-Bayesian analysis. We also introduce a way to apply PAC-Bayesian analysis in situation of limited feedback. We combine the new tools to derive PAC-Bayesian generalization and regret bounds for the multiarmed bandit problem. Although our regret bound is not yet as tight as state-of-the-art regret bounds based on other well-established techniques, our results significantly expand the range of potential applications of PAC-Bayesian analysis and introduce a new analysis tool to reinforcement learning and many other fields, where martingales and limited feedback are encountered.
1105.2422
Joint Network and LDPC Coding for Bi-directional Relaying
cs.IT math.IT
In this paper, we consider joint network and LDPC coding for practically implementing the denosie-and-forward protocol over bi-directional relaying. the closed-form expressions for computing the log-likelihood ratios of the network-coded codewords have been derived for both real and complex multiple-access channels. It is revealed that the equivalent channel observed at the relay is an asymmetrical channel, where the channel input is the XOR form of the two source nodes.
1105.2434
Diffusion in Social Networks with Competing Products
cs.SI cs.DS physics.soc-ph
We introduce a new threshold model of social networks, in which the nodes influenced by their neighbours can adopt one out of several alternatives. We characterize the graphs for which adoption of a product by the whole network is possible (respectively necessary) and the ones for which a unique outcome is guaranteed. These characterizations directly yield polynomial time algorithms that allow us to determine whether a given social network satisfies one of the above properties. We also study algorithmic questions for networks without unique outcomes. We show that the problem of computing the minimum possible spread of a product is NP-hard to approximate with an approximation ratio better than $\Omega(n)$, in contrast to the maximum spread, which is efficiently computable. We then move on to questions regarding the behavior of a node with respect to adopting some (resp. a given) product. We show that the problem of determining whether a given node has to adopt some (resp. a given) product in all final networks is co-NP-complete.
1105.2441
Science Models as Value-Added Services for Scholarly Information Systems
cs.DL cs.IR
The paper introduces scholarly Information Retrieval (IR) as a further dimension that should be considered in the science modeling debate. The IR use case is seen as a validation model of the adequacy of science models in representing and predicting structure and dynamics in science. Particular conceptualizations of scholarly activity and structures in science are used as value-added search services to improve retrieval quality: a co-word model depicting the cognitive structure of a field (used for query expansion), the Bradford law of information concentration, and a model of co-authorship networks (both used for re-ranking search results). An evaluation of the retrieval quality when science model driven services are used turned out that the models proposed actually provide beneficial effects to retrieval quality. From an IR perspective, the models studied are therefore verified as expressive conceptualizations of central phenomena in science. Thus, it could be shown that the IR perspective can significantly contribute to a better understanding of scholarly structures and activities.
1105.2443
Comparing webometric with web-independent rankings: a case study with German universities
cs.SI cs.DL physics.soc-ph
In this paper we examine if hyperlink-based (webometric) indicators can be used to rank academic websites. Therefore we analyzed the interlinking structure of German university websites and compared our simple hyperlink-based ranking with official and web-independent rankings of universities. We found that link impact could not easily be seen as a prestige factor for universities.
1105.2447
LUNES: Agent-based Simulation of P2P Systems (Extended Version)
cs.DC cs.MA cs.NI
We present LUNES, an agent-based Large Unstructured NEtwork Simulator, which allows to simulate complex networks composed of a high number of nodes. LUNES is modular, since it splits the three phases of network topology creation, protocol simulation and performance evaluation. This permits to easily integrate external software tools into the main software architecture. The simulation of the interaction protocols among network nodes is performed via a simulation middleware that supports both the sequential and the parallel/distributed simulation approaches. In the latter case, a specific mechanism for the communication overhead-reduction is used; this guarantees high levels of performance and scalability. To demonstrate the efficiency of LUNES, we test the simulator with gossip protocols executed on top of networks (representing peer-to-peer overlays), generated with different topologies. Results demonstrate the effectiveness of the proposed approach.
1105.2459
Deciphering Network Community Structure by Surprise
q-bio.MN cs.SI physics.soc-ph
The analysis of complex networks permeates all sciences, from biology to sociology. A fundamental, unsolved problem is how to characterize the community structure of a network. Here, using both standard and novel benchmarks, we show that maximization of a simple global parameter, which we call Surprise (S), leads to a very efficient characterization of the community structure of complex synthetic networks. Particularly, S qualitatively outperforms the most commonly used criterion to define communities, Newman and Girvan's modularity (Q). Applying S maximization to real networks often provides natural, well-supported partitions, but also sometimes counterintuitive solutions that expose the limitations of our previous knowledge. These results indicate that it is possible to define an effective global criterion for community structure and open new routes for the understanding of complex networks.
1105.2461
Optimal grid exploration by asynchronous oblivious robots
cs.DC cs.DM cs.NI cs.RO
We consider a team of {\em autonomous weak robots} that are endowed with visibility sensors and motion actuators. Autonomous means that the team cannot rely on any kind of central coordination mechanism or scheduler. By weak we mean that the robots are devoid of (1) any (observable) IDs allowing to differentiate them (anonymous), (2) means of communication allowing them to communicate directly, and (3) any way to remember any previous observation nor computation performed in any previous step (oblivious). Robots asynchronously operate in cycles of three phases: Look, Compute, and Move. Furthermore, the network is an anonymous unoriented grid. In such settings, the robots must collaborate to solve a collective task, here the terminating grid exploration (exploration for short), despite being limited with respect to input from the environment, asymmetry, memory, etc. Exploration requires that robots explore the grid and stop when the task is complete. We propose optimal (w.r.t. the number of robots) solutions for the deterministic terminating exploration of a grid shaped network by a team of $k$ asynchronous oblivious robots in the fully asynchronous and non-atomic model, so called CORDA. In more details, we first assume the ATOM model in which each Look-Compute-Move cycle execution is executed atomically, ie every robot that is activated at instant t instantaneously executes a full cycle between t and t+1. ATOM being strictly stronger than CORDA, all impossibility results in ATOM also hold in CORDA. We show that it is impossible to explore a grid of at least three nodes with less than three robots in ATOM. (This first result holds for both deterministic and probabilistic settings.) Next, we show that it is impossible to deterministically explore a (2,2)-Grid with less than 4 robots, and a (3,3)-Grid with less than 5 robots, respectively. Then, we propose deterministic algorithms in CORDA to exhibit the optimal number of robots allowing to explore of a given grid. Our results show that except in two particular cases, 3 robots are necessary and sufficient to deterministically explore a grid of at least three nodes. The optimal number of robots for the two remaining cases is: 4 for the (2,2)-Grid and 5 for the (3,3)-Grid.
1105.2470
The game of go as a complex network
cs.GT cond-mat.stat-mech cs.SI physics.soc-ph
We study the game of go from a complex network perspective. We construct a directed network using a suitable definition of tactical moves including local patterns, and study this network for different datasets of professional tournaments and amateur games. The move distribution follows Zipf's law and the network is scale free, with statistical peculiarities different from other real directed networks, such as e. g. the World Wide Web. These specificities reflect in the outcome of ranking algorithms applied to it. The fine study of the eigenvalues and eigenvectors of matrices used by the ranking algorithms singles out certain strategic situations. Our results should pave the way to a better modelization of board games and other types of human strategic scheming.
1105.2491
A Multiple Component Matching Framework for Person Re-Identification
cs.CV
Person re-identification consists in recognizing an individual that has already been observed over a network of cameras. It is a novel and challenging research topic in computer vision, for which no reference framework exists yet. Despite this, previous works share similar representations of human body based on part decomposition and the implicit concept of multiple instances. Building on these similarities, we propose a Multiple Component Matching (MCM) framework for the person re-identification problem, which is inspired by Multiple Component Learning, a framework recently proposed for object detection. We show that previous techniques for person re-identification can be considered particular implementations of our MCM framework. We then present a novel person re-identification technique as a direct, simple implementation of our framework, focused in particular on robustness to varying lighting conditions, and show that it can attain state of the art performances.
1105.2526
Deconvolution of mixing time series on a graph
stat.ME cs.SI
In many applications we are interested in making inference on latent time series from indirect measurements, which are often low-dimensional projections resulting from mixing or aggregation. Positron emission tomography, super-resolution, and network traffic monitoring are some examples. Inference in such settings requires solving a sequence of ill-posed inverse problems, y_t= A x_t, where the projection mechanism provides information on A. We consider problems in which A specifies mixing on a graph of times series that are bursty and sparse. We develop a multilevel state-space model for mixing times series and an efficient approach to inference. A simple model is used to calibrate regularization parameters that lead to efficient inference in the multilevel state-space model. We apply this method to the problem of estimating point-to-point traffic flows on a network from aggregate measurements. Our solution outperforms existing methods for this problem, and our two-stage approach suggests an efficient inference strategy for multilevel models of dependent time series.
1105.2541
Rearranging trees for robust consensus
math.OC cs.SY
In this paper, we use the H2 norm associated with a communication graph to characterize the robustness of consensus to noise. In particular, we restrict our attention to trees and by systematic attention to the effect of local changes in topology, we derive a partial ordering for undirected trees according to the H2 norm. Our approach for undirected trees provides a constructive method for deriving an ordering for directed trees. Further, our approach suggests a decentralized manner in which trees can be rearranged in order to improve their robustness.
1105.2550
A Maximal Large Deviation Inequality for Sub-Gaussian Variables
cs.LG
In this short note we prove a maximal concentration lemma for sub-Gaussian random variables stating that for independent sub-Gaussian random variables we have \[P<(\max_{1\le i\le N}S_{i}>\epsilon>) \le\exp<(-\frac{1}{N^2}\sum_{i=1}^{N}\frac{\epsilon^{2}}{2\sigma_{i}^{2}}>), \] where $S_i$ is the sum of $i$ zero mean independent sub-Gaussian random variables and $\sigma_i$ is the variance of the $i$th random variable.
1105.2614
Growth and Optimality in Network Evolution
cond-mat.dis-nn cs.SI nlin.AO physics.bio-ph
In this paper we investigate networks whose evolution is governed by the interaction of a random assembly process and an optimization process. In the first process, new nodes are added one at a time and form connections to randomly selected old nodes. In between node additions, the network is rewired to minimize its pathlength. For timescales, at which neither the assembly nor the optimization processes are dominant, we find a rich variety of complex networks with power law tails in the degree distributions. These networks also exhibit non-trivial clustering, a hierarchical organization and interesting degree mixing patterns.
1105.2621
A Compressed Sensing Wire-Tap Channel
cs.IT math.IT
A multiplicative Gaussian wire-tap channel inspired by compressed sensing is studied. Lower and upper bounds on the secrecy capacity are derived, and shown to be relatively tight in the large system limit for a large class of compressed sensing matrices. Surprisingly, it is shown that the secrecy capacity of this channel is nearly equal to the capacity without any secrecy constraint provided that the channel of the eavesdropper is strictly worse than the channel of the intended receiver. In other words, the eavesdropper can see almost everything and yet learn almost nothing. This behavior, which contrasts sharply with that of many commonly studied wiretap channels, is made possible by the fact that a small number of linear projections can make a crucial difference in the ability to estimate sparse vectors.
1105.2631
On Pseudocodewords and Decision Regions of Linear Programming Decoding of HDPC Codes
cs.IT math.IT
In this paper we explore the decision regions of Linear Programming (LP) decoding. We compare the decision regions of an LP decoder, a Belief Propagation (BP) decoder and the optimal Maximum Likelihood (ML) decoder. We study the effect of minimal-weight pseudocodewords on LP decoding. We present global optimization as a method for finding the minimal pseudoweight of a given code as well as the number of minimal-weight generators. We present a complete pseudoweight distribution for the [24; 12; 8] extended Golay code, and provide justifications of why the pseudoweight distribution alone cannot be used for obtaining a tight upper bound on the error probability.
1105.2651
A Note on the Entropy/Influence Conjecture
math.CO cs.LG
The entropy/influence conjecture, raised by Friedgut and Kalai in 1996, seeks to relate two different measures of concentration of the Fourier coefficients of a Boolean function. Roughly saying, it claims that if the Fourier spectrum is "smeared out", then the Fourier coefficients are concentrated on "high" levels. In this note we generalize the conjecture to biased product measures on the discrete cube, and prove a variant of the conjecture for functions with an extremely low Fourier weight on the "high" levels.
1105.2707
Generalized Symmetric Divergence Measures and Metric Spaces
cs.IT math.IT
Recently, Taneja studied two one parameter generalizations of J-divergence, Jensen-Shannon divergence and Arithmetic-Geometric divergence. These two generalizations in particular contain measures like: Hellinger discrimination, symmetric chi-square divergence, and triangular discrimination. These measures are well known in the literature of Statistics and Information theory. In this paper our aim is to prove metric space properties for square root of these two symmetric generalized divergence measures.
1105.2760
Amplify-and-Forward in Wireless Relay Networks
cs.IT math.IT
A general class of wireless relay networks with a single source-destination pair is considered. Intermediate nodes in the network employ an amplify-and-forward scheme to relay their input signals. In this case the overall input-output channel from the source via the relays to the destination effectively behaves as an intersymbol interference channel with colored noise. Unlike previous work we formulate the problem of the maximum achievable rate in this setting as an optimization problem with no assumption on the network size, topology, and received signal-to-noise ratio. Previous work considered only scenarios wherein relays use all their power to amplify their received signals. We demonstrate that this may not always maximize the maximal achievable rate in amplify-and-forward relay networks. The proposed formulation allows us to not only recover known results on the performance of the amplify-and-forward schemes for some simple relay networks but also characterize the performance of more complex amplify-and-forward relay networks which cannot be addressed in a straightforward manner using existing approaches. Using cut-set arguments, we derive simple upper bounds on the capacity of general wireless relay networks. Through various examples, we show that a large class of amplify-and-forward relay networks can achieve rates within a constant factor of these upper bounds asymptotically in network parameters.
1105.2782
$\ell_0$ Minimization for Wavelet Frame Based Image Restoration
cs.CV math.FA math.OC
The theory of (tight) wavelet frames has been extensively studied in the past twenty years and they are currently widely used for image restoration and other image processing and analysis problems. The success of wavelet frame based models, including balanced approach and analysis based approach, is due to their capability of sparsely approximating piecewise smooth functions like images. Motivated by the balanced approach and analysis based approach, we shall propose a wavelet frame based $\ell_0$ minimization model, where the $\ell_0$ "norm" of the frame coefficients is penalized. We adapt the penalty decomposition (PD) method to solve the proposed optimization problem. Numerical results showed that the proposed model solved by the PD method can generate images with better quality than those obtained by either analysis based approach or balanced approach in terms of restoring sharp features as well as maintaining smoothness of the recovered images. Some convergence analysis of the PD method will also be provided.
1105.2783
$p$-ary sequences with six-valued cross-correlation function: a new decimation of Niho type
cs.IT cs.DM math.IT
For an odd prime $p$ and $n=2m$, a new decimation $d=\frac{(p^{m}-1)^{2}}{2}+1$ of Niho type of $m$-sequences is presented. Using generalized Niho's Theorem, we show that the cross-correlation function between a $p$-ary $m$-sequence of period $p^{n}-1$ and its decimated sequence by the above $d$ is at most six-valued and we can easily know that the magnitude of the cross correlation is upper bounded by $4\sqrt{p^{n}}-1$.
1105.2786
On the Cross-Correlation of a Ternary $m$-sequence of Period $3^{4k}-1$ and Its Decimated Sequence by $\frac{(3^{2k}+1)^{2}}{20}$
cs.IT math.IT
Let $d=\frac{(3^{2k}+1)^{2}}{20}$, where $k$ is an odd integer. We show that the magnitude of the cross-correlation values of a ternary $m$-sequence $\{s_{t}\}$ of period $3^{4k}-1$ and its decimated sequence $\{s_{dt}\}$ is upper bounded by $5\sqrt{3^{n}}+1$, where $n=4k$.
1105.2790
On the equivalence of Hopfield Networks and Boltzmann Machines
cond-mat.dis-nn cs.AI
A specific type of neural network, the Restricted Boltzmann Machine (RBM), is implemented for classification and feature detection in machine learning. RBM is characterized by separate layers of visible and hidden units, which are able to learn efficiently a generative model of the observed data. We study a "hybrid" version of RBM's, in which hidden units are analog and visible units are binary, and we show that thermodynamics of visible units are equivalent to those of a Hopfield network, in which the N visible units are the neurons and the P hidden units are the learned patterns. We apply the method of stochastic stability to derive the thermodynamics of the model, by considering a formal extension of this technique to the case of multiple sets of stored patterns, which may act as a benchmark for the study of correlated sets. Our results imply that simulating the dynamics of a Hopfield network, requiring the update of N neurons and the storage of N(N-1)/2 synapses, can be accomplished by a hybrid Boltzmann Machine, requiring the update of N+P neurons but the storage of only NP synapses. In addition, the well known glass transition of the Hopfield network has a counterpart in the Boltzmann Machine: It corresponds to an optimum criterion for selecting the relative sizes of the hidden and visible layers, resolving the trade-off between flexibility and generality of the model. The low storage phase of the Hopfield model corresponds to few hidden units and hence a overly constrained RBM, while the spin-glass phase (too many hidden units) corresponds to unconstrained RBM prone to overfitting of the observed data.
1105.2795
View subspaces for indexing and retrieval of 3D models
cs.CV cs.MM
View-based indexing schemes for 3D object retrieval are gaining popularity since they provide good retrieval results. These schemes are coherent with the theory that humans recognize objects based on their 2D appearances. The viewbased techniques also allow users to search with various queries such as binary images, range images and even 2D sketches. The previous view-based techniques use classical 2D shape descriptors such as Fourier invariants, Zernike moments, Scale Invariant Feature Transform-based local features and 2D Digital Fourier Transform coefficients. These methods describe each object independent of others. In this work, we explore data driven subspace models, such as Principal Component Analysis, Independent Component Analysis and Nonnegative Matrix Factorization to describe the shape information of the views. We treat the depth images obtained from various points of the view sphere as 2D intensity images and train a subspace to extract the inherent structure of the views within a database. We also show the benefit of categorizing shapes according to their eigenvalue spread. Both the shape categorization and data-driven feature set conjectures are tested on the PSB database and compared with the competitor view-based 3D shape retrieval algorithms
1105.2796
Salient Local 3D Features for 3D Shape Retrieval
cs.CV cs.MM
In this paper we describe a new formulation for the 3D salient local features based on the voxel grid inspired by the Scale Invariant Feature Transform (SIFT). We use it to identify the salient keypoints (invariant points) on a 3D voxelized model and calculate invariant 3D local feature descriptors at these keypoints. We then use the bag of words approach on the 3D local features to represent the 3D models for shape retrieval. The advantages of the method are that it can be applied to rigid as well as to articulated and deformable 3D models. Finally, this approach is applied for 3D Shape Retrieval on the McGill articulated shape benchmark and then the retrieval results are presented and compared to other methods.
1105.2797
Face Recognition using 3D Facial Shape and Color Map Information: Comparison and Combination
cs.CV
In this paper, we investigate the use of 3D surface geometry for face recognition and compare it to one based on color map information. The 3D surface and color map data are from the CAESAR anthropometric database. We find that the recognition performance is not very different between 3D surface and color map information using a principal component analysis algorithm. We also discuss the different techniques for the combination of the 3D surface and color map information for multi-modal recognition by using different fusion approaches and show that there is significant improvement in results. The effectiveness of various techniques is compared and evaluated on a dataset with 200 subjects in two different positions.
1105.2800
Retrieval and Clustering from a 3D Human Database based on Body and Head Shape
cs.CV cs.CG
In this paper, we describe a framework for similarity based retrieval and clustering from a 3D human database. Our technique is based on both body and head shape representation and the retrieval is based on similarity of both of them. The 3D human database used in our study is the CAESAR anthropometric database which contains approximately 5000 bodies. We have developed a web-based interface for specifying the queries to interact with the retrieval system. Our approach performs the similarity based retrieval in a reasonable amount of time and is a practical approach.
1105.2813
Optimal Upper and Lower Bounds for Boolean Expressions by Dissociation
cs.AI cs.DB cs.LO
This paper develops upper and lower bounds for the probability of Boolean expressions by treating multiple occurrences of variables as independent and assigning them new individual probabilities. Our technique generalizes and extends the underlying idea of a number of recent approaches which are varyingly called node splitting, variable renaming, variable splitting, or dissociation for probabilistic databases. We prove that the probabilities we assign to new variables are the best possible in some sense.
1105.2831
Planar Pixelations and Image Recognition
math.DG cs.CG cs.CV
Any subset of the plane can be approximated by a set of square pixels. This transition from a shape to its pixelation is rather brutal since it destroys geometric and topological information about the shape. Using a technique inspired by Morse Theory, we algorithmically produce a PL approximation of the original shape using only information from its pixelation. This approximation converges to the original shape in a very strong sense: as the size of the pixels goes to zero we can recover important geometric and topological invariants of the original shape such as Betti numbers, area, perimeter and curvature measures.
1105.2858
A Reconstruction Method for Band-Limited Signals on the Hyperbolic Plane
math.FA cs.IT math.IT
A notion of band limited functions is considered in the case of the hyperbolic plane in its Poincare upper half-plane $\mathbb{H}$ realization. The concept of band-limitedness is based on the existence of the Helgason-Fourier transform on $\mathbb{H}$. An iterative algorithm is presented, which allows to reconstruct band-limited functions from some countable sets of their values. It is shown that for sufficiently dense metric lattices a geometric rate of convergence can be guaranteed as long as the sampling density is high enough compared to the band-width of the sampled function.
1105.2864
The Rate-Distortion Function for Product of Two Sources with Side-Information at Decoders
cs.IT math.IT
This paper investigates a lossy source coding problem in which two decoders can access their side-information respectively. The correlated sources are a product of two component correlated sources, and we exclusively investigate the case such that each component is degraded. We show the rate-distortion function for that case, and give the following observations. When the components are degraded in matched order, the rate distortion function of the product sources is equal to the sum of the component-wise rate distortion functions. On the otherhand, the former is strictly smaller than the latter when the component sources are degraded in mismatched order. The converse proof for the mismatched case is motivated by the enhancement technique used for broadcast channels. For binary Hamming and Gaussian examples, we evaluate the rate-distortion functions.
1105.2865
Error Correction for Index Coding with Side Information
cs.IT math.IT
A problem of index coding with side information was first considered by Y. Birk and T. Kol (IEEE INFOCOM, 1998). In the present work, a generalization of index coding scheme, where transmitted symbols are subject to errors, is studied. Error-correcting methods for such a scheme, and their parameters, are investigated. In particular, the following question is discussed: given the side information hypergraph of index coding scheme and the maximal number of erroneous symbols $\delta$, what is the shortest length of a linear index code, such that every receiver is able to recover the required information? This question turns out to be a generalization of the problem of finding a shortest-length error-correcting code with a prescribed error-correcting capability in the classical coding theory. The Singleton bound and two other bounds, referred to as the $\alpha$-bound and the $\kappa$-bound, for the optimal length of a linear error-correcting index code (ECIC) are established. For large alphabets, a construction based on concatenation of an optimal index code with an MDS classical code, is shown to attain the Singleton bound. For smaller alphabets, however, this construction may not be optimal. A random construction is also analyzed. It yields another implicit bound on the length of an optimal linear ECIC. Further, the problem of error-correcting decoding by a linear ECIC is studied. It is shown that in order to decode correctly the desired symbol, the decoder is required to find one of the vectors, belonging to an affine space containing the actual error vector. The syndrome decoding is shown to produce the correct output if the weight of the error pattern is less or equal to the error-correcting capability of the corresponding ECIC. Finally, the notion of static ECIC, which is suitable for use with a family of instances of an index coding problem, is introduced.
1105.2868
Semantic Vector Machines
cs.LG cs.AI
We first present our work in machine translation, during which we used aligned sentences to train a neural network to embed n-grams of different languages into an $d$-dimensional space, such that n-grams that are the translation of each other are close with respect to some metric. Good n-grams to n-grams translation results were achieved, but full sentences translation is still problematic. We realized that learning semantics of sentences and documents was the key for solving a lot of natural language processing problems, and thus moved to the second part of our work: sentence compression. We introduce a flexible neural network architecture for learning embeddings of words and sentences that extract their semantics, propose an efficient implementation in the Torch framework and present embedding results comparable to the ones obtained with classical neural language models, while being more powerful.
1105.2894
Ant Colony Optimization and Hypergraph Covering Problems
cs.NE
Ant Colony Optimization (ACO) is a very popular metaheuristic for solving computationally hard combinatorial optimization problems. Runtime analysis of ACO with respect to various pseudo-boolean functions and different graph based combinatorial optimization problems has been taken up in recent years. In this paper, we investigate the runtime behavior of an MMAS*(Max-Min Ant System) ACO algorithm on some well known hypergraph covering problems that are NP-Hard. In particular, we have addressed the Minimum Edge Cover problem, the Minimum Vertex Cover problem and the Maximum Weak- Independent Set problem. The influence of pheromone values and heuristic information on the running time is analysed. The results indicate that the heuristic information has greater impact towards improving the expected optimization time as compared to pheromone values. For certain instances of hypergraphs, we show that the MMAS* algorithm gives a constant order expected optimization time when the dominance of heuristic information is suitably increased.
1105.2902
A Multi-Purpose Scenario-based Simulator for Smart House Environments
cs.AI
Developing smart house systems has been a great challenge for researchers and engineers in this area because of the high cost of implementation and evaluation process of these systems, while being very time consuming. Testing a designed smart house before actually building it is considered as an obstacle towards an efficient smart house project. This is because of the variety of sensors, home appliances and devices available for a real smart environment. In this paper, we present the design and implementation of a multi-purpose smart house simulation system for designing and simulating all aspects of a smart house environment. This simulator provides the ability to design the house plan and different virtual sensors and appliances in a two dimensional model of the virtual house environment. This simulator can connect to any external smart house remote controlling system, providing evaluation capabilities to their system much easier than before. It also supports detailed adding of new emerging sensors and devices to help maintain its compatibility with future simulation needs. Scenarios can also be defined for testing various possible combinations of device states; so different criteria and variables can be simply evaluated without the need of experimenting on a real environment.
1105.2943
Feature Selection for MAUC-Oriented Classification Systems
cs.LG cs.AI
Feature selection is an important pre-processing step for many pattern classification tasks. Traditionally, feature selection methods are designed to obtain a feature subset that can lead to high classification accuracy. However, classification accuracy has recently been shown to be an inappropriate performance metric of classification systems in many cases. Instead, the Area Under the receiver operating characteristic Curve (AUC) and its multi-class extension, MAUC, have been proved to be better alternatives. Hence, the target of classification system design is gradually shifting from seeking a system with the maximum classification accuracy to obtaining a system with the maximum AUC/MAUC. Previous investigations have shown that traditional feature selection methods need to be modified to cope with this new objective. These methods most often are restricted to binary classification problems only. In this study, a filter feature selection method, namely MAUC Decomposition based Feature Selection (MDFS), is proposed for multi-class classification problems. To the best of our knowledge, MDFS is the first method specifically designed to select features for building classification systems with maximum MAUC. Extensive empirical results demonstrate the advantage of MDFS over several compared feature selection methods.
1105.2952
Bounds on the Bayes Error Given Moments
stat.ML cs.IT math.IT
We show how to compute lower bounds for the supremum Bayes error if the class-conditional distributions must satisfy moment constraints, where the supremum is with respect to the unknown class-conditional distributions. Our approach makes use of Curto and Fialkow's solutions for the truncated moment problem. The lower bound shows that the popular Gaussian assumption is not robust in this regard. We also construct an upper bound for the supremum Bayes error by constraining the decision boundary to be linear.
1105.2965
Generating Similar Graphs From Spherical Features
cs.SI physics.soc-ph stat.AP stat.ME stat.ML
We propose a novel model for generating graphs similar to a given example graph. Unlike standard approaches that compute features of graphs in Euclidean space, our approach obtains features on a surface of a hypersphere. We then utilize a von Mises-Fisher distribution, an exponential family distribution on the surface of a hypersphere, to define a model over possible feature values. While our approach bears similarity to a popular exponential random graph model (ERGM), unlike ERGMs, it does not suffer from degeneracy, a situation when a significant probability mass is placed on unrealistic graphs. We propose a parameter estimation approach for our model, and a procedure for drawing samples from the distribution. We evaluate the performance of our approach both on the small domain of all 8-node graphs as well as larger real-world social networks.
1105.2988
Anatomy of a Bit: Information in a Time Series Observation
cs.IT cond-mat.stat-mech math.IT math.ST nlin.AO stat.TH
Appealing to several multivariate information measures---some familiar, some new here---we analyze the information embedded in discrete-valued stochastic time series. We dissect the uncertainty of a single observation to demonstrate how the measures' asymptotic behavior sheds structural and semantic light on the generating process's internal information dynamics. The measures scale with the length of time window, which captures both intensive (rates of growth) and subextensive components. We provide interpretations for the components, developing explicit relationships between them. We also identify the informational component shared between the past and the future that is not contained in a single observation. The existence of this component directly motivates the notion of a process's effective (internal) states and indicates why one must build models.
1105.2989
Worst-Case Robust Distributed Power Allocation in Shared Unlicensed Spectrum
cs.IT math.IT
This paper considers non-cooperative and fully-distributed power-allocation for selfish transmitter-receiver pairs in shared unlicensed spectrum when normalized-interference to each receiver is uncertain. We model each uncertain parameter by the sum of its nominal (estimated) value and a bounded additive error in a convex set, and show that the allocated power always converges to its equilibrium, called robust Nash equilibrium (RNE). In the case of a bounded and symmetric uncertainty region, we show that the power allocation problem for each user is simplified, and can be solved in a distributed manner. We derive the conditions for RNE's uniqueness and for convergence of the distributed algorithm; and show that the total throughput (social utility) is less than that at NE when RNE is unique. We also show that for multiple RNEs, the social utility may be higher at a RNE as compared to that at the corresponding NE, and demonstrate that this is caused by users' orthogonal utilization of bandwidth at RNE. Simulations confirm our analysis.
1105.3006
The approximate maximum-likelihood certificate
cs.IT math.IT
A new property which relies on the linear programming (LP) decoder, the approximate maximum-likelihood certificate (AMLC), is introduced. When using the belief propagation decoder, this property is a measure of how close the decoded codeword is to the LP solution. Using upper bounding techniques, it is demonstrated that the conditional frame error probability given that the AMLC holds is, with some degree of confidence, below a threshold. In channels with low noise, this threshold is several orders of magnitude lower than the simulated frame error rate, and our bound holds with very high degree of confidence. In contrast, showing this error performance by simulation would require very long Monte Carlo runs. When the AMLC holds, our approach thus provides the decoder with extra error detection capability, which is especially important in applications requiring high data integrity.
1105.3037
Horizon Adaptation for Nonlinear Model Predictive Controllers with guaranteed Degree of Suboptimality
math.OC cs.SY
We propose adaptation strategies to modify the standard constrained model predictive controller scheme in order to guarantee a certain lower bound on the degree of suboptimality. Within this analysis, the length of the optimization horizon is the parameter we wish to adapt. We develop and prove several shortening and prolongation strategies which also allow for an effective implementation. Moreover, extensions of stability results and suboptimality estimates to model predictive controllers with varying optimization horizon are shown.
1105.3040
The transversality conditions for infinite-horizon optimal control problem with a free right endpoint and the stability of the adjoint variable (in Russian)
math.OC cs.SY
An infinite-horizon optimal control problem with a free right endpoint is considered. In this paper we proved that Lyapunov stability of the adjoint variable implying the vanishing of the adjoint variable at infinity along optimal solution.
1105.3042
Parallelizing a State Exchange Strategy for Noncooperative Distributed NMPC
math.OC cs.SY math.DS
We consider a distributed non cooperative control setting in which systems are interconnected via state constraints. Each of these systems is governed by an agent which is responsible for exchanging information with its neighbours and computing a feedback law using a nonlinear model predictive controller to avoid violations of constraints. For this setting we present an algorithm which generates a parallelizable hierarchy among the systems. Moreover, we show both feasibility and stability of the closed loop using only abstract properties of this algorithm. To this end, we utilize a trajectory based stability result which we extend to the distributed setting.
1105.3068
On the Capacity of Noisy Computations
cs.IT math.IT
This paper presents an analysis of the concept of capacity for noisy computations, i.e. algorithms implemented by unreliable computing devices (e.g. noisy Turing Machines). The capacity of a noisy computation is defined and justified by companion coding theorems. Under some constraints on the encoding process, capacity is the upper bound of input rates allowing reliable computation, i.e. decodability of noisy outputs into expected outputs. A model of noisy computation of a perfect function f thanks to an unreliable device F is given together with a model of reliable computation based on input encoding and output decoding. A coding lemma (extending the Feinstein's theorem to noisy computations), a joint source-computation coding theorem and its converse are proved. They apply if the input source, the function f, the noisy device F and the cascade f^{-1}F induce AMS and ergodic one-sided random processes.
1105.3106
Collective stability of networks of winner-take-all circuits
q-bio.NC cond-mat.dis-nn cs.NE
The neocortex has a remarkably uniform neuronal organization, suggesting that common principles of processing are employed throughout its extent. In particular, the patterns of connectivity observed in the superficial layers of the visual cortex are consistent with the recurrent excitation and inhibitory feedback required for cooperative-competitive circuits such as the soft winner-take-all (WTA). WTA circuits offer interesting computational properties such as selective amplification, signal restoration, and decision making. But, these properties depend on the signal gain derived from positive feedback, and so there is a critical trade-off between providing feedback strong enough to support the sophisticated computations, while maintaining overall circuit stability. We consider the question of how to reason about stability in very large distributed networks of such circuits. We approach this problem by approximating the regular cortical architecture as many interconnected cooperative-competitive modules. We demonstrate that by properly understanding the behavior of this small computational module, one can reason over the stability and convergence of very large networks composed of these modules. We obtain parameter ranges in which the WTA circuit operates in a high-gain regime, is stable, and can be aggregated arbitrarily to form large stable networks. We use nonlinear Contraction Theory to establish conditions for stability in the fully nonlinear case, and verify these solutions using numerical simulations. The derived bounds allow modes of operation in which the WTA network is multi-stable and exhibits state-dependent persistent activities. Our approach is sufficiently general to reason systematically about the stability of any network, biological or technological, composed of networks of small modules that express competition through shared inhibition.
1105.3107
Learning to Place New Objects
cs.RO
The ability to place objects in the environment is an important skill for a personal robot. An object should not only be placed stably, but should also be placed in its preferred location/orientation. For instance, a plate is preferred to be inserted vertically into the slot of a dish-rack as compared to be placed horizontally in it. Unstructured environments such as homes have a large variety of object types as well as of placing areas. Therefore our algorithms should be able to handle placing new object types and new placing areas. These reasons make placing a challenging manipulation task. In this work, we propose a supervised learning algorithm for finding good placements given the point-clouds of the object and the placing area. It learns to combine the features that capture support, stability and preferred placements using a shared sparsity structure in the parameters. Even when neither the object nor the placing area is seen previously in the training set, our algorithm predicts good placements. In extensive experiments, our method enables the robot to stably place several new objects in several new placing areas with 98% success-rate; and it placed the objects in their preferred placements in 92% of the cases.
1105.3144
Asynchronous Physical-layer Network Coding
cs.IT cs.NI math.IT
A key issue in physical-layer network coding (PNC) is how to deal with the asynchrony between signals transmitted by multiple transmitters. That is, symbols transmitted by different transmitters could arrive at the receiver with symbol misalignment as well as relative carrier-phase offset. A second important issue is how to integrate channel coding with PNC to achieve reliable communication. This paper investigates these two issues and makes the following contributions: 1) We propose and investigate a general framework for decoding at the receiver based on belief propagation (BP). The framework can effectively deal with symbol and phase asynchronies while incorporating channel coding at the same time. 2) For unchannel-coded PNC, we show that for BPSK and QPSK modulations, our BP method can significantly reduce the asynchrony penalties compared with prior methods. 3) For unchannel-coded PNC, with half symbol offset between the transmitters, our BP method can drastically reduce the performance penalty due to phase asynchrony, from more than 6 dB to no more than 1 dB. 4) For channel-coded PNC, with our BP method, both symbol and phase asynchronies actually improve the system performance compared with the perfectly synchronous case. Furthermore, the performance spread due to different combinations of symbol and phase offsets between the transmitters in channel-coded PNC is only around 1 dB. The implication of 3) is that if we could control the symbol arrival times at the receiver, it would be advantageous to deliberately introduce a half symbol offset in unchannel-coded PNC. The implication of 4) is that when channel coding is used, symbol and phase asynchronies are not major performance concerns in PNC.
1105.3168
Lassoing Line Outages in the Smart Power Grid
cs.SY math.OC stat.AP
Fast and accurate unveiling of power line outages is of paramount importance not only for preventing faults that may lead to blackouts, but also for routine monitoring and control tasks of the smart grid, including state estimation and optimal power flow. Existing approaches are either challenged by the \emph{combinatorial complexity} issues involved, and are thus limited to identifying single- and double-line outages; or, they invoke less pragmatic assumptions such as \emph{conditionally independent} phasor angle measurements available across the grid. Using only a subset of voltage phasor angle data, the present paper develops a near real-time algorithm for identifying multiple line outages at the affordable complexity of solving a quadratic program via block coordinate descent iterations. The novel approach relies on reformulating the DC linear power flow model as a \emph{sparse} overcomplete expansion, and leveraging contemporary advances in compressive sampling and variable selection using the least-absolute shrinkage and selection operator (Lasso). Analysis and simulated tests on the standard IEEE 118-bus system confirm the effectiveness of lassoing line changes in the smart power grid.
1105.3228
The formation of share market prices under heterogeneous beliefs and common knowledge
physics.soc-ph cs.SI q-fin.PR
Financial economic models often assume that investors know (or agree on) the fundamental value of the shares of the firm, easing the passage from the individual to the collective dimension of the financial system generated by the Share Exchange over time. Our model relaxes that heroic assumption of one unique "true value" and deals with the formation of share market prices through the dynamic formation of individual and social opinions (or beliefs) based upon a fundamental signal of economic performance and position of the firm, the forecast revision by heterogeneous individual investors, and their social mood or sentiment about the ongoing state of the market pricing process. Market clearing price formation is then featured by individual and group dynamics that make its collective dimension irreducible to its individual level. This dynamic holistic approach can be applied to better understand the market exuberance generated by the Share Exchange over time.
1105.3259
On R\'enyi and Tsallis entropies and divergences for exponential families
cs.IT cs.LG math.IT
Many common probability distributions in statistics like the Gaussian, multinomial, Beta or Gamma distributions can be studied under the unified framework of exponential families. In this paper, we prove that both R\'enyi and Tsallis divergences of distributions belonging to the same exponential family admit a generic closed form expression. Furthermore, we show that R\'enyi and Tsallis entropies can also be calculated in closed-form for sub-families including the Gaussian or exponential distributions, among others.
1105.3264
Community Detection Using A Neighborhood Strength Driven Label Propagation Algorithm
cs.SI physics.soc-ph
Studies of community structure and evolution in large social networks require a fast and accurate algorithm for community detection. As the size of analyzed communities grows, complexity of the community detection algorithm needs to be kept close to linear. The Label Propagation Algorithm (LPA) has the benefits of nearly-linear running time and easy implementation, thus it forms a good basis for efficient community detection methods. In this paper, we propose new update rule and label propagation criterion in LPA to improve both its computational efficiency and the quality of communities that it detects. The speed is optimized by avoiding unnecessary updates performed by the original algorithm. This change reduces significantly (by order of magnitude for large networks) the number of iterations that the algorithm executes. We also evaluate our generalization of the LPA update rule that takes into account, with varying strength, connections to the neighborhood of a node considering a new label. Experiments on computer generated networks and a wide range of social networks show that our new rule improves the quality of the detected communities compared to those found by the original LPA. The benefit of considering positive neighborhood strength is pronounced especially on real-world networks containing sufficiently large fraction of nodes with high clustering coefficient.
1105.3266
Stability of Constrained Adaptive Model Predictive Control Algorithms
math.OC cs.SY
Recently, suboptimality estimates for model predictive controllers (MPC) have been derived for the case without additional stabilizing endpoint constraints or a Lyapunov function type endpoint weight. The proposed methods yield a posteriori and a priori estimates of the degree of suboptimality with respect to the infinite horizon optimal control and can be evaluated at runtime of the MPC algorithm. Our aim is to design automatic adaptation strategies of the optimization horizon in order to guarantee stability and a predefined degree of suboptimality for the closed loop solution. Here, we present a stability proof for an arbitrary adaptation scheme and state a simple shortening and prolongation strategy which can be used for adapting the optimization horizon.
1105.3267
Reducing the Prediction Horizon in NMPC: An Algorithm Based Approach
math.OC cs.SY math.NA
In order to guarantee stability, known results for MPC without additional terminal costs or endpoint constraints often require rather large prediction horizons. Still, stable behavior of closed loop solutions can often be observed even for shorter horizons. Here, we make use of the recent observation that stability can be guaranteed for smaller prediction horizons via Lyapunov arguments if more than only the first control is implemented. Since such a procedure may be harmful in terms of robustness, we derive conditions which allow to increase the rate at which state measurements are used for feedback while maintaining stability and desired performance specifications. Our main contribution consists in developing two algorithms based on the deduced conditions and a corresponding stability theorem which ensures asymptotic stability for the MPC closed loop for significantly shorter prediction horizons.
1105.3268
Robustness of Prediction Based Delay Compensation for Nonlinear Systems
math.OC cs.SY
Control of systems where the information between the controller, actuator, and sensor can be lost or delayed can be challenging with respect to stability and performance. One way to overcome the resulting problems is the use of prediction based compensation schemes. Instead of a single input, a sequence of (predicted) future controls is submitted and implemented at the actuator. If suitable, so-called prediction consistent compensation and control schemes, such as certain predictive control approaches, are used, stability of the closed loop in the presence of delays and packet losses can be guaranteed. In this paper, we show that control schemes employing prediction based delay compensation approaches do posses inherent robustness properties. Specifically, if the nominal closed loop system without delay compensation is ISS with respect to perturbation and measurement errors, then the closed loop system employing prediction based delay compensation techniques is robustly stable. We analyze the influence of the prediction horizon on the robustness gains and illustrate the results in simulation.
1105.3270
Optimal Camera Placement to measure Distances Conservativly Regarding Static and Dynamic Obstacles
cs.CV cs.RO math.OC
In modern production facilities industrial robots and humans are supposed to interact sharing a common working area. In order to avoid collisions, the distances between objects need to be measured conservatively which can be done by a camera network. To estimate the acquired distance, unmodelled objects, e.g., an interacting human, need to be modelled and distinguished from premodelled objects like workbenches or robots by image processing such as the background subtraction method. The quality of such an approach massively depends on the settings of the camera network, that is the positions and orientations of the individual cameras. Of particular interest in this context is the minimization of the error of the distance using the objects modelled by the background subtraction method instead of the real objects. Here, we show how this minimization can be formulated as an abstract optimization problem. Moreover, we state various aspects on the implementation as well as reasons for the selection of a suitable optimization method, analyze the complexity of the proposed method and present a basic version used for extensive experiments.
1105.3272
Stability of Observer Based Predictive Control for Nonlinear Sampled-data Systems
math.OC cs.SY math.FA
We propose a new model predictive control (MPC) approach which is completely based on an observer for the state system. For this, we show semiglobally practically asymptotic stability of the closed loop for an abstract observer and illustrate our results for a numerical example.
1105.3298
Graphical model approximations of random finite set filters
cs.SY math.OC
Random finite sets (RFSs) has been a fruitful area of research in recent years, yielding new approximate filters such as the probability hypothesis density (PHD), cardinalised PHD (CPHD), and multiple target multi-Bernoulli (MeMBer). These new methods have largely been based on approximations that side-step the need for measurement-to-track association. Comparably, RFS methods that incorporate data association, such as Morelande and Challa's (M-C) method, have received little attention. This paper provides a RFS algorithm that incorporates data association similarly to the M-C method, but retains computational tractability via a recently developed approximation of marginal association weights. We describe an efficient method for resolving the track coalescence phenomenon which is problematic for joint probabilistic data association (JPDA) and related methods (including M-C). The method utilises a network flow optimisation, and thus is tractable for large numbers of targets. Finally, our derivation also shows that it is natural for the multi-target density to incorporate both a Poisson point process (PPP) component (representing targets that have never been detected) and a multi-Bernoulli component (representing targets under track). We describe a method of recycling, in which tracks with a low probability existence are transferred from the multi-Bernoulli component to the PPP component, effectively yielding a hybrid of M-C and PHD.
1105.3299
Compressed Sensing with coherent tight frames via $l_q$-minimization for $0<q\leq1$
math.NA cs.IT math.IT
Our aim of this article is to reconstruct a signal from undersampled data in the situation that the signal is sparse in terms of a tight frame. We present a condition, which is independent of the coherence of the tight frame, to guarantee accurate recovery of signals which are sparse in the tight frame, from undersampled data with minimal $l_1$-norm of transform coefficients. This improves the result in [1]. Also, the $l_q$-minimization $(0<q<1)$ approaches are introduced. We show that under a suitable condition, there exists a value $q_0\in(0,1]$ such that for any $q\in(0,q_0)$, each solution of the $l_q$-minimization is approximately well to the true signal. In particular, when the tight frame is an identity matrix or an orthonormal basis, all results obtained in this paper appeared in [13] and [26].
1105.3316
Affinity Paths and Information Diffusion in Social Networks
physics.soc-ph cs.SI
Widespread interest in the diffusion of information through social networks has produced a large number of Social Dynamics models. A majority of them use theoretical hypothesis to explain their diffusion mechanisms while the few empirically based ones average out their measures over many messages of different content. Our empirical research tracking the step-by-step email propagation of an invariable viral marketing message delves into the content impact and has discovered new and striking features. The topology and dynamics of the propagation cascades display patterns not inherited from the email networks carrying the message. Their disconnected, low transitivity, tree-like cascades present positive correlation between their nodes probability to forward the message and the average number of neighbors they target and show increased participants' involvement as the propagation paths length grows. Such patterns not described before, nor replicated by any of the existing models of information diffusion, can be explained if participants make their pass-along decisions based uniquely on local knowledge of their network neighbors affinity with the message content. We prove the plausibility of such mechanism through a stylized, agent-based model that replicates the \emph{Affinity Paths} observed in real information diffusion cascades.
1105.3326
Xampling at the Rate of Innovation
cs.IT math.IT
We address the problem of recovering signals from samples taken at their rate of innovation. Our only assumption is that the sampling system is such that the parameters defining the signal can be stably determined from the samples, a condition that lies at the heart of every sampling theorem. Consequently, our analysis subsumes previously studied nonlinear acquisition devices and nonlinear signal classes. In particular, we do not restrict attention to memoryless nonlinear distortions or to union-of-subspace models. This allows treatment of various finite-rate-of-innovation (FRI) signals that were not previously studied, including, for example, continuous phase modulation transmissions. Our strategy relies on minimizing the error between the measured samples and those corresponding to our signal estimate. This least-squares (LS) objective is generally non-convex and might possess many local minima. Nevertheless, we prove that under the stability hypothesis, any optimization method designed to trap a stationary point of the LS criterion necessarily converges to the true solution. We demonstrate our approach in the context of recovering pulse streams in settings that were not previously treated. Furthermore, in situations for which other algorithms are applicable, we show that our method is often preferable in terms of noise robustness.
1105.3338
The Power Grid as a Complex Network: a Survey
physics.soc-ph cs.DM cs.SI
The statistical tools of Complex Network Analysis are of great use to understand salient properties of complex systems, may these be natural or pertaining human engineered infrastructures. One of these that is receiving growing attention for its societal relevance is that of electricity distribution. In this paper, we present a survey of the most important scientific studies investigating the properties of different Power Grids infrastructures using Complex Network Analysis techniques and methodologies. We categorize and explore the most relevant literature works considering general topological properties, differences between the various graph-related indicators and reliability aspects.