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1005.0608
Informal Concepts in Machines
cs.AI
This paper constructively proves the existence of an effective procedure generating a computable (total) function that is not contained in any given effectively enumerable set of such functions. The proof implies the existence of machines that process informal concepts such as computable (total) functions beyond the limits of any given Turing machine or formal system, that is, these machines can, in a certain sense, "compute" function values beyond these limits. We call these machines creative. We argue that any "intelligent" machine should be capable of processing informal concepts such as computable (total) functions, that is, it should be creative. Finally, we introduce hypotheses on creative machines which were developed on the basis of theoretical investigations and experiments with computer programs. The hypotheses say that machine intelligence is the execution of a self-developing procedure starting from any universal programming language and any input.
1005.0616
Tracking a Random Walk First-Passage Time Through Noisy Observations
math.ST cs.IT math.IT stat.TH
Given a Gaussian random walk (or a Wiener process), possibly with drift, observed through noise, we consider the problem of estimating its first-passage time $\tau_\ell$ of a given level $\ell$ with a stopping time $\eta$ defined over the noisy observation process. Main results are upper and lower bounds on the minimum mean absolute deviation $\inf_\eta \ex|\eta-\tau_\ell|$ which become tight as $\ell\to\infty$. Interestingly, in this regime the estimation error does not get smaller if we allow $ \eta$ to be an arbitrary function of the entire observation process, not necessarily a stopping time. In the particular case where there is no drift, we show that it is impossible to track $\tau_\ell$: $\inf_\eta \ex|\eta-\tau_\ell|^p=\infty$ for any $\ell>0$ and $p\geq1/2$.
1005.0624
The Gaussian Many-to-1 Interference Channel with Confidential Messages
cs.IT math.IT
The many-to-one interference channel has received interest by virtue of embodying the essence of an interference network while being more tractable than the general K-user interference channel. In this paper, we introduce information theoretic secrecy to this model and consider the many-to-one interference channel with confidential messages, in which each receiver, in particular, the one subject to interference, is also one from which the interfering users' messages need to be kept secret from. We derive the achievable secrecy sum rate for this channel using nested lattice codes, as well as an upper bound on the secrecy sum rate for all possible channel gain configurations. We identify several nontrivial cases where the gap between the upper bound and the achieved secrecy sum rate is only a function of the number of the users K, and is uniform over all possible channel gain configurations in each case. In addition, we identify the secure degree of freedom for this channel and show it to be equivalent to its degree of freedom, i.e., the secrecy in high SNR comes for free.
1005.0662
The B-Skip-List: A Simpler Uniquely Represented Alternative to B-Trees
cs.DS cs.DB
In previous work, the author introduced the B-treap, a uniquely represented B-tree analogue, and proved strong performance guarantees for it. However, the B-treap maintains complex invariants and is very complex to implement. In this paper we introduce the B-skip-list, which has most of the guarantees of the B-treap, but is vastly simpler and easier to implement. Like the B-treap, the B-skip-list may be used to construct strongly history-independent index structures and filesystems; such constructions reveal no information about the historical sequence of operations that led to the current logical state. For example, a uniquely represented filesystem would support the deletion of a file in a way that, in a strong information-theoretic sense, provably removes all evidence that the file ever existed. Like the B-tree, the B-skip-list has depth O(log_B (n)) where B is the block transfer size of the external memory, uses linear space with high probability, and supports efficient one-dimensional range queries.
1005.0677
The Enigma of CDMA Revisited
cs.IT math.IT
In this paper, we explore the mystery of synchronous CDMA as applied to wireless and optical communication systems under very general settings for the user symbols and the signature matrix entries. The channel is modeled with real/complex additive noise of arbitrary distribution. Two problems are addressed. The first problem concerns whether overloaded error free codes exist in the absence of additive noise under these general settings, and if so whether there are any practical optimum decoding algorithms. The second one is about the bounds for the sum channel capacity when user data and signature codes employ any real or complex alphabets (finite or infinite). In response to the first problem, we have developed practical Maximum Likelihood (ML) decoding algorithms for overloaded CDMA systems for a large class of alphabets. In response to the second problem, a general theorem has been developed in which the sum capacity lower bounds with respect to the number of users and spreading gain and Signal-to-Noise Ratio (SNR) can be derived as special cases for a given CDMA system. To show the power and utility of the main theorem, a number of sum capacity bounds for special cases are simulated. An important conclusion of this paper is that the lower and upper bounds of the sum capacity for small/medium size CDMA systems depend on both the input and the signature symbols; this is contrary to the asymptotic results for large scale systems reported in the literature (also confirmed in this paper) where the signature symbols and statistics disappear in the asymptotic sum capacity. Moreover, these questions are investigated for the case when not all users are active. Furthermore, upper and asymptotic bounds are derived and numerically evaluated and compared to other derivations.
1005.0707
The Production of Probabilistic Entropy in Structure/Action Contingency Relations
cs.AI physics.soc-ph
Luhmann (1984) defined society as a communication system which is structurally coupled to, but not an aggregate of, human action systems. The communication system is then considered as self-organizing ("autopoietic"), as are human actors. Communication systems can be studied by using Shannon's (1948) mathematical theory of communication. The update of a network by action at one of the local nodes is then a well-known problem in artificial intelligence (Pearl 1988). By combining these various theories, a general algorithm for probabilistic structure/action contingency can be derived. The consequences of this contingency for each system, its consequences for their further histories, and the stabilization on each side by counterbalancing mechanisms are discussed, in both mathematical and theoretical terms. An empirical example is elaborated.
1005.0732
Outage rates and outage durations of opportunistic relaying systems
cs.IT math.IT
Opportunistic relaying is a simple yet efficient cooperation scheme that achieves full diversity and preserves the spectral efficiency among the spatially distributed stations. However, the stations' mobility causes temporal correlation of the system's capacity outage events, which gives rise to its important second-order outage statistical parameters, such as the average outage rate (AOR) and the average outage duration (AOD). This letter presents exact analytical expressions for the AOR and the AOD of an opportunistic relaying system, which employs a mobile source and a mobile destination (without a direct path), and an arbitrary number of (fixed-gain amplify-and-forward or decode-and-forward) mobile relays in Rayleigh fading environment.
1005.0734
An efficient approximation to the correlated Nakagami-m sums and its application in equal gain diversity receivers
cs.IT math.IT
There are several cases in wireless communications theory where the statistics of the sum of independent or correlated Nakagami-m random variables (RVs) is necessary to be known. However, a closed-form solution to the distribution of this sum does not exist when the number of constituent RVs exceeds two, even for the special case of Rayleigh fading. In this paper, we present an efficient closed-form approximation for the distribution of the sum of arbitrary correlated Nakagami-m envelopes with identical and integer fading parameters. The distribution becomes exact for maximal correlation, while the tightness of the proposed approximation is validated statistically by using the Chi-square and the Kolmogorov-Smirnov goodness-of-fit tests. As an application, the approximation is used to study the performance of equal-gain combining (EGC) systems operating over arbitrary correlated Nakagami-m fading channels, by utilizing the available analytical results for the error-rate performance of an equivalent maximal-ratio combining (MRC) system.
1005.0749
Integrating multiple sources to answer questions in Algebraic Topology
cs.SC cs.AI cs.HC
We present in this paper an evolution of a tool from a user interface for a concrete Computer Algebra system for Algebraic Topology (the Kenzo system), to a front-end allowing the interoperability among different sources for computation and deduction. The architecture allows the system not only to interface several systems, but also to make them cooperate in shared calculations.
1005.0766
Learning High-Dimensional Markov Forest Distributions: Analysis of Error Rates
cs.IT math.IT stat.ML
The problem of learning forest-structured discrete graphical models from i.i.d. samples is considered. An algorithm based on pruning of the Chow-Liu tree through adaptive thresholding is proposed. It is shown that this algorithm is both structurally consistent and risk consistent and the error probability of structure learning decays faster than any polynomial in the number of samples under fixed model size. For the high-dimensional scenario where the size of the model d and the number of edges k scale with the number of samples n, sufficient conditions on (n,d,k) are given for the algorithm to satisfy structural and risk consistencies. In addition, the extremal structures for learning are identified; we prove that the independent (resp. tree) model is the hardest (resp. easiest) to learn using the proposed algorithm in terms of error rates for structure learning.
1005.0794
Active Learning for Hidden Attributes in Networks
stat.ML cond-mat.stat-mech cs.IT cs.LG math.IT physics.soc-ph
In many networks, vertices have hidden attributes, or types, that are correlated with the networks topology. If the topology is known but these attributes are not, and if learning the attributes is costly, we need a method for choosing which vertex to query in order to learn as much as possible about the attributes of the other vertices. We assume the network is generated by a stochastic block model, but we make no assumptions about its assortativity or disassortativity. We choose which vertex to query using two methods: 1) maximizing the mutual information between its attributes and those of the others (a well-known approach in active learning) and 2) maximizing the average agreement between two independent samples of the conditional Gibbs distribution. Experimental results show that both these methods do much better than simple heuristics. They also consistently identify certain vertices as important by querying them early on.
1005.0813
TSDS: high-performance merge, subset, and filter software for time series-like data
cs.DB
Time Series Data Server (TSDS) is a software package for implementing a server that provides fast super-setting, sub-setting, filtering, and uniform gridding of time series-like data. TSDS was developed to respond quickly to requests for long time spans of data. Data may be served from a fast database, typically created by aggregating granules (e.g., data files) from a remote data source and storing them in a local cache that is optimized for serving time series. The system was designed specifically for time series data, and is optimized for requests where the longest dimension of the requested data structure is time. Scalar, vector, and spectrogram time series types are supported. The user can interact with the server by requesting a time series, a date range, and an optional filter to apply to the data. Available filters include strides, block average/minimum/maximum, exclude, and inequality. Constraint expressions are supported, which allow such operations as a request for data from one time series when a different time series satisfied a specified relationship. TSDS builds upon DAP (Data Access Protocol), NcML (netCDF Mark-up language) and related software libraries. In this work, we describe the current design of this server, as well as planned features and potential implementation strategies.
1005.0826
Clustering processes
cs.LG cs.IT math.IT stat.ML
The problem of clustering is considered, for the case when each data point is a sample generated by a stationary ergodic process. We propose a very natural asymptotic notion of consistency, and show that simple consistent algorithms exist, under most general non-parametric assumptions. The notion of consistency is as follows: two samples should be put into the same cluster if and only if they were generated by the same distribution. With this notion of consistency, clustering generalizes such classical statistical problems as homogeneity testing and process classification. We show that, for the case of a known number of clusters, consistency can be achieved under the only assumption that the joint distribution of the data is stationary ergodic (no parametric or Markovian assumptions, no assumptions of independence, neither between nor within the samples). If the number of clusters is unknown, consistency can be achieved under appropriate assumptions on the mixing rates of the processes. (again, no parametric or independence assumptions). In both cases we give examples of simple (at most quadratic in each argument) algorithms which are consistent.
1005.0855
On Capacity Scaling of Underwater Networks: An Information-Theoretic Perspective
cs.IT math.IT
Capacity scaling laws are analyzed in an underwater acoustic network with $n$ regularly located nodes on a square. A narrow-band model is assumed where the carrier frequency is allowed to scale as a function of $n$. In the network, we characterize an attenuation parameter that depends on the frequency scaling as well as the transmission distance. A cut-set upper bound on the throughput scaling is then derived in extended networks. Our result indicates that the upper bound is inversely proportional to the attenuation parameter, thus resulting in a highly power-limited network. Interestingly, it is seen that unlike the case of wireless radio networks, our upper bound is intrinsically related to the attenuation parameter but not the spreading factor. Furthermore, we describe an achievable scheme based on the simple nearest neighbor multi-hop (MH) transmission. It is shown under extended networks that the MH scheme is order-optimal as the attenuation parameter scales exponentially with $\sqrt{n}$ (or faster). Finally, these scaling results are extended to a random network realization.
1005.0858
Randomized hybrid linear modeling by local best-fit flats
cs.CV
The hybrid linear modeling problem is to identify a set of d-dimensional affine sets in a D-dimensional Euclidean space. It arises, for example, in object tracking and structure from motion. The hybrid linear model can be considered as the second simplest (behind linear) manifold model of data. In this paper we will present a very simple geometric method for hybrid linear modeling based on selecting a set of local best fit flats that minimize a global l1 error measure. The size of the local neighborhoods is determined automatically by the Jones' l2 beta numbers; it is proven under certain geometric conditions that good local neighborhoods exist and are found by our method. We also demonstrate how to use this algorithm for fast determination of the number of affine subspaces. We give extensive experimental evidence demonstrating the state of the art accuracy and speed of the algorithm on synthetic and real hybrid linear data.
1005.0879
From Skew-Cyclic Codes to Asymmetric Quantum Codes
cs.IT math.IT
We introduce an additive but not $\mathbb{F}_4$-linear map $S$ from $\mathbb{F}_4^{n}$ to $\mathbb{F}_4^{2n}$ and exhibit some of its interesting structural properties. If $C$ is a linear $[n,k,d]_4$-code, then $S(C)$ is an additive $(2n,2^{2k},2d)_4$-code. If $C$ is an additive cyclic code then $S(C)$ is an additive quasi-cyclic code of index $2$. Moreover, if $C$ is a module $\theta$-cyclic code, a recently introduced type of code which will be explained below, then $S(C)$ is equivalent to an additive cyclic code if $n$ is odd and to an additive quasi-cyclic code of index $2$ if $n$ is even. Given any $(n,M,d)_4$-code $C$, the code $S(C)$ is self-orthogonal under the trace Hermitian inner product. Since the mapping $S$ preserves nestedness, it can be used as a tool in constructing additive asymmetric quantum codes.
1005.0896
A two-step fusion process for multi-criteria decision applied to natural hazards in mountains
cs.AI
Mountain river torrents and snow avalanches generate human and material damages with dramatic consequences. Knowledge about natural phenomenona is often lacking and expertise is required for decision and risk management purposes using multi-disciplinary quantitative or qualitative approaches. Expertise is considered as a decision process based on imperfect information coming from more or less reliable and conflicting sources. A methodology mixing the Analytic Hierarchy Process (AHP), a multi-criteria aid-decision method, and information fusion using Belief Function Theory is described. Fuzzy Sets and Possibilities theories allow to transform quantitative and qualitative criteria into a common frame of discernment for decision in Dempster-Shafer Theory (DST ) and Dezert-Smarandache Theory (DSmT) contexts. Main issues consist in basic belief assignments elicitation, conflict identification and management, fusion rule choices, results validation but also in specific needs to make a difference between importance and reliability and uncertainty in the fusion process.
1005.0897
The Complex Gaussian Kernel LMS algorithm
cs.LG
Although the real reproducing kernels are used in an increasing number of machine learning problems, complex kernels have not, yet, been used, in spite of their potential interest in applications such as communications. In this work, we focus our attention on the complex gaussian kernel and its possible application in the complex Kernel LMS algorithm. In order to derive the gradients needed to develop the complex kernel LMS (CKLMS), we employ the powerful tool of Wirtinger's Calculus, which has recently attracted much attention in the signal processing community. Writinger's calculus simplifies computations and offers an elegant tool for treating complex signals. To this end, the notion of Writinger's calculus is extended to include complex RKHSs. Experiments verify that the CKLMS offers significant performance improvements over the traditional complex LMS or Widely Linear complex LMS (WL-LMS) algorithms, when dealing with nonlinearities.
1005.0902
Extension of Wirtinger Calculus in RKH Spaces and the Complex Kernel LMS
cs.LG
Over the last decade, kernel methods for nonlinear processing have successfully been used in the machine learning community. However, so far, the emphasis has been on batch techniques. It is only recently, that online adaptive techniques have been considered in the context of signal processing tasks. To the best of our knowledge, no kernel-based strategy has been developed, so far, that is able to deal with complex valued signals. In this paper, we take advantage of a technique called complexification of real RKHSs to attack this problem. In order to derive gradients and subgradients of operators that need to be defined on the associated complex RKHSs, we employ the powerful tool ofWirtinger's Calculus, which has recently attracted much attention in the signal processing community. Writinger's calculus simplifies computations and offers an elegant tool for treating complex signals. To this end, in this paper, the notion of Writinger's calculus is extended, for the first time, to include complex RKHSs and use it to derive the Complex Kernel Least-Mean-Square (CKLMS) algorithm. Experiments verify that the CKLMS can be used to derive nonlinear stable algorithms, which offer significant performance improvements over the traditional complex LMS orWidely Linear complex LMS (WL-LMS) algorithms, when dealing with nonlinearities.
1005.0907
Multistage Hybrid Arabic/Indian Numeral OCR System
cs.CV
The use of OCR in postal services is not yet universal and there are still many countries that process mail sorting manually. Automated Arabic/Indian numeral Optical Character Recognition (OCR) systems for Postal services are being used in some countries, but still there are errors during the mail sorting process, thus causing a reduction in efficiency. The need to investigate fast and efficient recognition algorithms/systems is important so as to correctly read the postal codes from mail addresses and to eliminate any errors during the mail sorting stage. The objective of this study is to recognize printed numerical postal codes from mail addresses. The proposed system is a multistage hybrid system which consists of three different feature extraction methods, i.e., binary, zoning, and fuzzy features, and three different classifiers, i.e., Hamming Nets, Euclidean Distance, and Fuzzy Neural Network Classifiers. The proposed system, systematically compares the performance of each of these methods, and ensures that the numerals are recognized correctly. Comprehensive results provide a very high recognition rate, outperforming the other known developed methods in literature.
1005.0917
On Building a Knowledge Base for Stability Theory
cs.AI
A lot of mathematical knowledge has been formalized and stored in repositories by now: different mathematical theorems and theories have been taken into consideration and included in mathematical repositories. Applications more distant from pure mathematics, however --- though based on these theories --- often need more detailed knowledge about the underlying theories. In this paper we present an example Mizar formalization from the area of electrical engineering focusing on stability theory which is based on complex analysis. We discuss what kind of special knowledge is necessary here and which amount of this knowledge is included in existing repositories.
1005.0945
An Efficient Vein Pattern-based Recognition System
cs.CV
This paper presents an efficient human recognition system based on vein pattern from the palma dorsa. A new absorption based technique has been proposed to collect good quality images with the help of a low cost camera and light source. The system automatically detects the region of interest from the image and does the necessary preprocessing to extract features. A Euclidean Distance based matching technique has been used for making the decision. It has been tested on a data set of 1750 image samples collected from 341 individuals. The accuracy of the verification system is found to be 99.26% with false rejection rate (FRR) of 0.03%.
1005.0957
ECG Feature Extraction Techniques - A Survey Approach
cs.NE cs.AI physics.med-ph
ECG Feature Extraction plays a significant role in diagnosing most of the cardiac diseases. One cardiac cycle in an ECG signal consists of the P-QRS-T waves. This feature extraction scheme determines the amplitudes and intervals in the ECG signal for subsequent analysis. The amplitudes and intervals value of P-QRS-T segment determines the functioning of heart of every human. Recently, numerous research and techniques have been developed for analyzing the ECG signal. The proposed schemes were mostly based on Fuzzy Logic Methods, Artificial Neural Networks (ANN), Genetic Algorithm (GA), Support Vector Machines (SVM), and other Signal Analysis techniques. All these techniques and algorithms have their advantages and limitations. This proposed paper discusses various techniques and transformations proposed earlier in literature for extracting feature from an ECG signal. In addition this paper also provides a comparative study of various methods proposed by researchers in extracting the feature from ECG signal.
1005.0961
Performance Oriented Query Processing In GEO Based Location Search Engines
cs.IR
Geographic location search engines allow users to constrain and order search results in an intuitive manner by focusing a query on a particular geographic region. Geographic search technology, also called location search, has recently received significant interest from major search engine companies. Academic research in this area has focused primarily on techniques for extracting geographic knowledge from the web. In this paper, we study the problem of efficient query processing in scalable geographic search engines. Query processing is a major bottleneck in standard web search engines, and the main reason for the thousands of machines used by the major engines. Geographic search engine query processing is different in that it requires a combination of text and spatial data processing techniques. We propose several algorithms for efficient query processing in geographic search engines, integrate them into an existing web search query processor, and evaluate them on large sets of real data and query traces.
1005.0965
Artificial Neural Network based Diagnostic Model For Causes of Success and Failures
cs.NE
In this paper an attempt has been made to identify most important human resource factors and propose a diagnostic model based on the back-propagation and connectionist model approaches of artificial neural network (ANN). The focus of the study is on the mobile -communication industry of India. The ANN based approach is particularly important because conventional approaches (such as algorithmic) to the problem solving have their inherent disadvantages. The algorithmic approach is well-suited to the problems that are well-understood and known solution(s). On the other hand the ANNs have learning by example and processing capabilities similar to that of a human brain. ANN has been followed due to its inherent advantage over conversion algorithmic like approaches and having capabilities, training and human like intuitive decision making capabilities. Therefore, this ANN based approach is likely to help researchers and organizations to reach a better solution to the problem of managing the human resource. The study is particularly important as many studies have been carried in developed countries but there is a shortage of such studies in developing nations like India. Here, a model has been derived using connectionist-ANN approach and improved and verified via back-propagation algorithm. This suggested ANN based model can be used for testing the success and failure human factors in any of the communication Industry. Results have been obtained on the basis of connectionist model, which has been further refined by BPNN to an accuracy of 99.99%. Any company to predict failure due to HR factors can directly deploy this model.
1005.0972
Adaptive Tuning Algorithm for Performance tuning of Database Management System
cs.DB
Performance tuning of Database Management Systems(DBMS) is both complex and challenging as it involves identifying and altering several key performance tuning parameters. The quality of tuning and the extent of performance enhancement achieved greatly depends on the skill and experience of the Database Administrator (DBA). As neural networks have the ability to adapt to dynamically changing inputs and also their ability to learn makes them ideal candidates for employing them for tuning purpose. In this paper, a novel tuning algorithm based on neural network estimated tuning parameters is presented. The key performance indicators are proactively monitored and fed as input to the Neural Network and the trained network estimates the suitable size of the buffer cache, shared pool and redo log buffer size. The tuner alters these tuning parameters using the estimated values using a rate change computing algorithm. The preliminary results show that the proposed method is effective in improving the query response time for a variety of workload types. .
1005.1062
Asymptotically Regular LDPC Codes with Linear Distance Growth and Thresholds Close to Capacity
cs.IT math.IT
Families of "asymptotically regular" LDPC block code ensembles can be formed by terminating (J,K)-regular protograph-based LDPC convolutional codes. By varying the termination length, we obtain a large selection of LDPC block code ensembles with varying code rates and substantially better iterative decoding thresholds than those of (J,K)-regular LDPC block code ensembles, despite the fact that the terminated ensembles are almost regular. Also, by means of an asymptotic weight enumerator analysis, we show that minimum distance grows linearly with block length for all of the ensembles in these families, i.e., the ensembles are asymptotically good. We find that, as the termination length increases, families of "asymptotically regular" codes with capacity approaching iterative decoding thresholds and declining minimum distance growth rates are obtained, allowing a code designer to trade-off between distance growth rate and threshold. Further, we show that the thresholds and the distance growth rates can be improved by carefully choosing the component protographs used in the code construction.
1005.1065
New Families of LDPC Block Codes Formed by Terminating Irregular Protograph-Based LDPC Convolutional Codes
cs.IT math.IT
In this paper, we present a method of constructing new families of LDPC block code ensembles formed by terminating irregular protograph-based LDPC convolutional codes. Using the accumulate-repeat-by-4-jagged-accumulate (AR4JA) protograph as an example, a density evolution analysis for the binary erasure channel shows that this flexible design technique gives rise to a large selection of LDPC block code ensembles with varying code rates and thresholds close to capacity. Further, by means of an asymptotic weight enumerator analysis, we show that all the ensembles in this family also have minimum distance that grows linearly with block length, i.e., they are asymptotically good.
1005.1120
Estimating small moments of data stream in nearly optimal space-time
cs.DS cs.LG
For each $p \in (0,2]$, we present a randomized algorithm that returns an $\epsilon$-approximation of the $p$th frequency moment of a data stream $F_p = \sum_{i = 1}^n \abs{f_i}^p$. The algorithm requires space $O(\epsilon^{-2} \log (mM)(\log n))$ and processes each stream update using time $O((\log n) (\log \epsilon^{-1}))$. It is nearly optimal in terms of space (lower bound $O(\epsilon^{-2} \log (mM))$ as well as time and is the first algorithm with these properties. The technique separates heavy hitters from the remaining items in the stream using an appropriate threshold and estimates the contribution of the heavy hitters and the light elements to $F_p$ separately. A key component is the design of an unbiased estimator for $\abs{f_i}^p$ whose data structure has low update time and low variance.
1005.1155
Decentralized Estimation over Orthogonal Multiple-access Fading Channels in Wireless Sensor Networks - Optimal and Suboptimal Estimators
cs.IT math.IT stat.ME
Optimal and suboptimal decentralized estimators in wireless sensor networks (WSNs) over orthogonal multiple-access fading channels are studied in this paper. Considering multiple-bit quantization before digital transmission, we develop maximum likelihood estimators (MLEs) with both known and unknown channel state information (CSI). When training symbols are available, we derive a MLE that is a special case of the MLE with unknown CSI. It implicitly uses the training symbols to estimate the channel coefficients and exploits the estimated CSI in an optimal way. To reduce the computational complexity, we propose suboptimal estimators. These estimators exploit both signal and data level redundant information to improve the estimation performance. The proposed MLEs reduce to traditional fusion based or diversity based estimators when communications or observations are perfect. By introducing a general message function, the proposed estimators can be applied when various analog or digital transmission schemes are used. The simulations show that the estimators using digital communications with multiple-bit quantization outperform the estimator using analog-and-forwarding transmission in fading channels. When considering the total bandwidth and energy constraints, the MLE using multiple-bit quantization is superior to that using binary quantization at medium and high observation signal-to-noise ratio levels.
1005.1252
Universal algorithms, mathematics of semirings and parallel computations
math.NA cs.DS cs.MS cs.NE
This is a survey paper on applications of mathematics of semirings to numerical analysis and computing. Concepts of universal algorithm and generic program are discussed. Relations between these concepts and mathematics of semirings are examined. A very brief introduction to mathematics of semirings (including idempotent and tropical mathematics) is presented. Concrete applications to optimization problems, idempotent linear algebra and interval analysis are indicated. It is known that some nonlinear problems (and especially optimization problems) become linear over appropriate semirings with idempotent addition (the so-called idempotent superposition principle). This linearity over semirings is convenient for parallel computations.
1005.1284
Approximately achieving Gaussian relay network capacity with lattice codes
cs.IT math.IT
Recently, it has been shown that a quantize-map-and-forward scheme approximately achieves (within a constant number of bits) the Gaussian relay network capacity for arbitrary topologies. This was established using Gaussian codebooks for transmission and random mappings at the relays. In this paper, we show that the same approximation result can be established by using lattices for transmission and quantization along with structured mappings at the relays.
1005.1292
Broadcast gossip averaging algorithms: interference and asymptotical error in large networks
math.OC cs.SY
In this paper we study two related iterative randomized algorithms for distributed computation of averages. The first one is the recently proposed Broadcast Gossip Algorithm, in which at each iteration one randomly selected node broadcasts its own state to its neighbors. The second algorithm is a novel de-synchronized version of the previous one, in which at each iteration every node is allowed to broadcast, with a given probability: hence this algorithm is affected by interference among messages. Both algorithms are proved to converge, and their performance is evaluated in terms of rate of convergence and asymptotical error: focusing on the behavior for large networks, we highlight the role of topology and design parameters on the performance. Namely, we show that on fully-connected graphs the rate is bounded away from one, whereas the asymptotical error is bounded away from zero. On the contrary, on a wide class of locally-connected graphs, the rate goes to one and the asymptotical error goes to zero, as the size of the network grows larger.
1005.1339
Coordination and Bargaining over the Gaussian Interference Channel
cs.IT math.IT
This work considers coordination and bargaining between two selfish users over a Gaussian interference channel using game theory. The usual information theoretic approach assumes full cooperation among users for codebook and rate selection. In the scenario investigated here, each selfish user is willing to coordinate its actions only when an incentive exists and benefits of cooperation are fairly allocated. To improve communication rates, the two users are allowed to negotiate for the use of a simple Han-Kobayashi type scheme with fixed power split and conditions for which users have incentives to cooperate are identified. The Nash bargaining solution (NBS) is used as a tool to get fair information rates. The operating point is obtained as a result of an optimization problem and compared with a TDM-based one in the literature.
1005.1340
Distribution of Cognitive Load in Web Search
cs.HC cs.IR
The search task and the system both affect the demand on cognitive resources during information search. In some situations, the demands may become too high for a person. This article has a three-fold goal. First, it presents and critiques methods to measure cognitive load. Second, it explores the distribution of load across search task stages. Finally, it seeks to improve our understanding of factors affecting cognitive load levels in information search. To this end, a controlled Web search experiment with forty-eight participants was conducted. Interaction logs were used to segment search tasks semi-automatically into task stages. Cognitive load was assessed using a new variant of the dual-task method. Average cognitive load was found to vary by search task stages. It was significantly higher during query formulation and user description of a relevant document as compared to examining search results and viewing individual documents. Semantic information shown next to the search results lists in one of the studied interfaces was found to decrease mental demands during query formulation and examination of the search results list. These findings demonstrate that changes in dynamic cognitive load can be detected within search tasks. Dynamic assessment of cognitive load is of core interest to information science because it enriches our understanding of cognitive demands imposed on people engaged in the search process by a task and the interactive information retrieval system employed.
1005.1349
On Holant Theorem and Its Proof
cs.IT math.IT
Holographic algorithms are a recent breakthrough in computer science and has found applications in information theory. This paper provides a proof to the central component of holographic algorithms, namely, the Holant theorem. Compared with previous works, the proof appears simpler and more direct. Along the proof, we also develop a mathematical tool, which we call c-tensor. We expect the notion of c-tensor may be applicable over a wide range of analysis.
1005.1364
Cognitive Radio Transmission under QoS Constraints and Interference Limitations
cs.IT math.IT
In this paper, the performance of cognitive transmission under quality of service (QoS)constraints and interference limitations is studied. Cognitive secondary users are assumed to initially perform sensing over multiple frequency bands (or equivalently channels) to detect the activities of primary users. Subsequently, they perform transmission in a single channel at variable power and rates depending on the channel sensing decisions and the fading environment. A state transition model is constructed to model this cognitive operation. Statistical limitations on the buffer lengths are imposed to take into account the QoS constraints of the cognitive secondary users. Under such QoS constraints and limitations on the interference caused to the primary users, the maximum throughput is identified by finding the effective capacity of the cognitive radio channel. Optimal power allocation strategies are obtained and the optimal channel selection criterion is identified. The intricate interplay between effective capacity, interference and QoS constraints, channel sensing parameters and reliability, fading, and the number of available frequency bands is investigated through numerical results.
1005.1365
Cooperative Sequential Spectrum Sensing Algorithms for OFDM
cs.IT math.IT
This paper considers the problem of spectrum sensing in cognitive radio networks when the primary user employs Orthogonal Frequency Division Multiplexing (OFDM). We develop cooperative sequential detection algorithms based on energy detectors and the autocorrelation property of cyclic prefix (CP) used in OFDM systems and compare their performances. We show that sequential detection provides much better performance than the traditional fixed sample size (snapshot) based detectors. We also study the effect of model uncertainties such as timing and frequency offset, IQ-imbalance and uncertainty in noise and transmit power on the performance of the detectors. We modify the detectors to mitigate the effects of these impairments. The performance of the proposed algorithms are studied via simulations. It is shown that energy detector performs significantly better than the CP-based detector, except in case of a snapshot detector with noise power uncertainty. Also, unlike for the CP-based detector, most of the above mentioned impairments have no effect on the energy detector.
1005.1369
Simultaneous communication in noisy channels
cs.IT math.IT
A sender wishes to broadcast a message of length $n$ over an alphabet to $r$ users, where each user $i$, $1 \leq i \leq r$ should be able to receive one of $m_i$ possible messages. The broadcast channel has noise for each of the users (possibly different noise for different users), who cannot distinguish between some pairs of letters. The vector $(m_1, m_2,...s, m_r)_{(n)}$ is said to be feasible if length $n$ encoding and decoding schemes exist enabling every user to decode his message. A rate vector $(R_1, R_2,..., R_r)$ is feasible if there exists a sequence of feasible vectors $(m_1, m_2,..., m_r)_{(n)}$ such that $R_i = \lim_{n \mapsto \infty} \frac {\log_2 m_i} {n}, {for all} i$. We determine the feasible rate vectors for several different scenarios and investigate some of their properties. An interesting case discussed is when one user can only distinguish between all the letters in a subset of the alphabet. Tight restrictions on the feasible rate vectors for some specific noise types for the other users are provided. The simplest non-trivial cases of two users and alphabet of size three are fully characterized. To this end a more general previously known result, to which we sketch an alternative proof, is used. This problem generalizes the study of the Shannon capacity of a graph, by considering more than a single user.
1005.1391
Solution to the Counterfeit Coin Problem and its Generalization
cs.IT math.IT
This work deals with a classic problem: "Given a set of coins among which there is a counterfeit coin of a different weight, find this counterfeit coin using ordinary balance scales, with the minimum number of weighings possible, and indicate whether it weighs less or more than the rest". The method proposed here not only calculates the minimum number of weighings necessary, but also indicates how to perform these weighings, it is easily mechanizeable and valid for any number of coins. Instructions are also given as to how to generalize the procedure to include cases where there is more than one counterfeit coin.
1005.1395
Fractal Weyl law for Linux Kernel Architecture
cs.CE cond-mat.dis-nn nlin.CD physics.data-an
We study the properties of spectrum and eigenstates of the Google matrix of a directed network formed by the procedure calls in the Linux Kernel. Our results obtained for various versions of the Linux Kernel show that the spectrum is characterized by the fractal Weyl law established recently for systems of quantum chaotic scattering and the Perron-Frobenius operators of dynamical maps. The fractal Weyl exponent is found to be $\nu \approx 0.63$ that corresponds to the fractal dimension of the network $d \approx 1.2$. The eigenmodes of the Google matrix of Linux Kernel are localized on certain principal nodes. We argue that the fractal Weyl law should be generic for directed networks with the fractal dimension $d<2$.
1005.1471
Classification via Incoherent Subspaces
cs.CV
This article presents a new classification framework that can extract individual features per class. The scheme is based on a model of incoherent subspaces, each one associated to one class, and a model on how the elements in a class are represented in this subspace. After the theoretical analysis an alternate projection algorithm to find such a collection is developed. The classification performance and speed of the proposed method is tested on the AR and YaleB databases and compared to that of Fisher's LDA and a recent approach based on on $\ell_1$ minimisation. Finally connections of the presented scheme to already existing work are discussed and possible ways of extensions are pointed out.
1005.1475
How to correctly prune tropical trees
cs.AI cs.DM cs.GT cs.SC
We present tropical games, a generalization of combinatorial min-max games based on tropical algebras. Our model breaks the traditional symmetry of rational zero-sum games where players have exactly opposed goals (min vs. max), is more widely applicable than min-max and also supports a form of pruning, despite it being less effective than alpha-beta. Actually, min-max games may be seen as particular cases where both the game and its dual are tropical: when the dual of a tropical game is also tropical, the power of alpha-beta is completely recovered. We formally develop the model and prove that the tropical pruning strategy is correct, then conclude by showing how the problem of approximated parsing can be modeled as a tropical game, profiting from pruning.
1005.1516
An Agent-based Simulation of the Effectiveness of Creative Leadership
cs.MA cs.NE cs.SI
This paper investigates the effectiveness of creative versus uncreative leadership using EVOC, an agent-based model of cultural evolution. Each iteration, each agent in the artificial society invents a new action, or imitates a neighbor's action. Only the leader's actions can be imitated by all other agents, referred to as followers. Two measures of creativity were used: (1) invention-to-imitation ratio, iLeader, which measures how often an agent invents, and (2) rate of conceptual change, cLeader, which measures how creative an invention is. High iLeader increased mean fitness of ideas, but only when creativity of followers was low. High iLeader was associated with greater diversity of ideas in the early stage of idea generation only. High cLeader increased mean fitness of ideas in the early stage of idea generation; in the later stage it decreased idea fitness. Reasons for these findings and tentative implications for creative leadership in human society are discussed.
1005.1518
Recognizability of Individual Creative Style Within and Across Domains: Preliminary Studies
cs.AI
It is hypothesized that creativity arises from the self-mending capacity of an internal model of the world, or worldview. The uniquely honed worldview of a creative individual results in a distinctive style that is recognizable within and across domains. It is further hypothesized that creativity is domaingeneral in the sense that there exist multiple avenues by which the distinctiveness of one's worldview can be expressed. These hypotheses were tested using art students and creative writing students. Art students guessed significantly above chance both which painting was done by which of five famous artists, and which artwork was done by which of their peers. Similarly, creative writing students guessed significantly above chance both which passage was written by which of five famous writers, and which passage was written by which of their peers. These findings support the hypothesis that creative style is recognizable. Moreover, creative writing students guessed significantly above chance which of their peers produced particular works of art, supporting the hypothesis that creative style is recognizable not just within but across domains.
1005.1524
Cumulative-Separable Codes
cs.IT math.IT
q-ary cumulative-separable $\Gamma(L,G^{(j)})$-codes $L=\{ \alpha \in GF(q^{m}):G(\alpha )\neq 0 \}$ and $G^{(j)}(x)=G(x)^{j}, 1 \leq i\leq q$ are considered. The relation between different codes from this class is demonstrated. Improved boundaries of the minimum distance and dimension are obtained.
1005.1545
Improving Semi-Supervised Support Vector Machines Through Unlabeled Instances Selection
cs.LG
Semi-supervised support vector machines (S3VMs) are a kind of popular approaches which try to improve learning performance by exploiting unlabeled data. Though S3VMs have been found helpful in many situations, they may degenerate performance and the resultant generalization ability may be even worse than using the labeled data only. In this paper, we try to reduce the chance of performance degeneration of S3VMs. Our basic idea is that, rather than exploiting all unlabeled data, the unlabeled instances should be selected such that only the ones which are very likely to be helpful are exploited, while some highly risky unlabeled instances are avoided. We propose the S3VM-\emph{us} method by using hierarchical clustering to select the unlabeled instances. Experiments on a broad range of data sets over eighty-eight different settings show that the chance of performance degeneration of S3VM-\emph{us} is much smaller than that of existing S3VMs.
1005.1560
Computation using Noise-based Logic: Efficient String Verification over a Slow Communication Channel
cs.IT math.IT physics.gen-ph
Utilizing the hyperspace of noise-based logic, we show two string verification methods with low communication complexity. One of them is based on continuum noise-based logic. The other one utilizes noise-based logic with random telegraph signals where a mathematical analysis of the error probability is also given. The last operation can also be interpreted as computing universal hash functions with noise-based logic and using them for string comparison. To find out with 10^-25 error probability that two strings with arbitrary length are different (this value is similar to the error probability of an idealistic gate in today's computer) Alice and Bob need to compare only 83 bits of the noise-based hyperspace.
1005.1567
On The Power of Tree Projections: Structural Tractability of Enumerating CSP Solutions
cs.AI cs.DB
The problem of deciding whether CSP instances admit solutions has been deeply studied in the literature, and several structural tractability results have been derived so far. However, constraint satisfaction comes in practice as a computation problem where the focus is either on finding one solution, or on enumerating all solutions, possibly projected to some given set of output variables. The paper investigates the structural tractability of the problem of enumerating (possibly projected) solutions, where tractability means here computable with polynomial delay (WPD), since in general exponentially many solutions may be computed. A general framework based on the notion of tree projection of hypergraphs is considered, which generalizes all known decomposition methods. Tractability results have been obtained both for classes of structures where output variables are part of their specification, and for classes of structures where computability WPD must be ensured for any possible set of output variables. These results are shown to be tight, by exhibiting dichotomies for classes of structures having bounded arity and where the tree decomposition method is considered.
1005.1594
Channel State Feedback over the MIMO-MAC
cs.IT math.IT
We consider the problem of designing low latency and low complexity schemes for channel state feedback over the MIMO-MAC (multiple-input multiple-output multiple access channel). We develop a framework for analyzing this problem in terms of minimizing the MSE distortion, and come up with separated source-channel schemes and joint source-channel schemes that perform better than analog feedback. We also develop a strikingly simple code design based on scalar quantization and uncoded QAM modulation that achieves the theoretical asymptotic performance limit of the separated approach with very low complexity and latency, in the case of single-antenna users.
1005.1625
On Some Results Related to Napoleon's Configurations
math.MG cs.IT math.GM math.IT
The goal of this paper is to give a purely geometric proof of a theorem by Branko Gr\"unbaum concerning configuration of triangles coming from the classical Napoleon's theorem in planar Euclidean geometry.
1005.1634
Interference Alignment in Regenerating Codes for Distributed Storage: Necessity and Code Constructions
cs.IT cs.DC cs.NI math.IT
Regenerating codes are a class of recently developed codes for distributed storage that, like Reed-Solomon codes, permit data recovery from any arbitrary k of n nodes. However regenerating codes possess in addition, the ability to repair a failed node by connecting to any arbitrary d nodes and downloading an amount of data that is typically far less than the size of the data file. This amount of download is termed the repair bandwidth. Minimum storage regenerating (MSR) codes are a subclass of regenerating codes that require the least amount of network storage; every such code is a maximum distance separable (MDS) code. Further, when a replacement node stores data identical to that in the failed node, the repair is termed as exact. The four principal results of the paper are (a) the explicit construction of a class of MDS codes for d = n-1 >= 2k-1 termed the MISER code, that achieves the cut-set bound on the repair bandwidth for the exact-repair of systematic nodes, (b) proof of the necessity of interference alignment in exact-repair MSR codes, (c) a proof showing the impossibility of constructing linear, exact-repair MSR codes for d < 2k-3 in the absence of symbol extension, and (d) the construction, also explicit, of MSR codes for d = k+1. Interference alignment (IA) is a theme that runs throughout the paper: the MISER code is built on the principles of IA and IA is also a crucial component to the non-existence proof for d < 2k-3. To the best of our knowledge, the constructions presented in this paper are the first, explicit constructions of regenerating codes that achieve the cut-set bound.
1005.1635
The Approximate Capacity Region of the Gaussian Z-Interference Channel with Conferencing Encoders
cs.IT math.IT
A two-user Gaussian Z-Interference Channel (GZIC) is considered, in which encoders are connected through noiseless links with finite capacities. In this setting, prior to each transmission block the encoders communicate with each other over the cooperative links. The capacity region and the sum-capacity of the channel are characterized within 1.71 bits per user and 2 bits in total, respectively. It is also established that properly sharing the total limited cooperation capacity between the cooperative links may enhance the achievable region, even when compared to the case of unidirectional transmitter cooperation with infinite cooperation capacity. To obtain the results, genie-aided upper bounds on the sum-capacity and cut-set bounds on the individual rates are compared with the achievable rate region. In the interference-limited regime, the achievable scheme enjoys a simple type of Han-Kobayashi signaling, together with the zero-forcing, and basic relaying techniques. In the noise-limited regime, it is shown that treating interference as noise achieves the capacity region up to a single bit per user.
1005.1684
On Macroscopic Complexity and Perceptual Coding
cs.IT cs.AI cs.MM cs.SD math.IT
The theoretical limits of 'lossy' data compression algorithms are considered. The complexity of an object as seen by a macroscopic observer is the size of the perceptual code which discards all information that can be lost without altering the perception of the specified observer. The complexity of this macroscopically observed state is the simplest description of any microstate comprising that macrostate. Inference and pattern recognition based on macrostate rather than microstate complexities will take advantage of the complexity of the macroscopic observer to ignore irrelevant noise.
1005.1711
On Design of Distributed Beamforming for Two-Way Relay Networks
cs.IT math.IT
We consider a two-way relay network, where two source nodes, S1 and S2, exchange information through a cluster of relay nodes. The relay nodes receive the sum signal from S1 and S2 in the first time slot. In the second time slot, each relay node multiplies its received signal by a complex coefficient and retransmits the signal to the two source nodes, which leads to a distributed two-way beamforming system. By applying the principle of analog network coding, each receiver at S1 and S2 cancels the ``self-interference'' in the received signal from the relay cluster and decodes the message. This paper studies the 2-dimensional achievable rate region for such a two-way relay network with distributed beamforming. With different assumptions of channel reciprocity between the source-relay and relay-source channels, the achievable rate region is characterized under two setups. First, with reciprocal channels, we investigate the achievable rate regions when the relay cluster is subject to a sum-power constraint or individual-power constraints. We show that the optimal beamforming vectors obtained from solving the weighted sum inverse-SNR minimization (WSISMin) problems are sufficient to characterize the corresponding achievable rate region. Furthermore, we derive the closed form solutions for those optimal beamforming vectors and consequently propose the partially distributed algorithms to implement the optimal beamforming, where each relay node only needs the local channel information and one global parameter. Second, with the non-reciprocal channels, the achievable rate regions are also characterized for both the sum-power constraint case and the individual-power constraint case. Although no closed-form solutions are available under this setup, we present efficient algorithms to compute the optimal beamforming vectors, which are attained by solving SDP problems after semi-definite relaxation.
1005.1715
Degrees of Freedom Region of a Class of Multi-source Gaussian Relay Networks
cs.IT math.IT
We study a layered $K$-user $M$-hop Gaussian relay network consisting of $K_m$ nodes in the $m^{\operatorname{th}}$ layer, where $M\geq2$ and $K=K_1=K_{M+1}$. We observe that the time-varying nature of wireless channels or fading can be exploited to mitigate the inter-user interference. The proposed amplify-and-forward relaying scheme exploits such channel variations and works for a wide class of channel distributions including Rayleigh fading. We show a general achievable degrees of freedom (DoF) region for this class of Gaussian relay networks. Specifically, the set of all $(d_1,..., d_K)$ such that $d_i\leq 1$ for all $i$ and $\sum_{i=1}^K d_i\leq K_{\Sigma}$ is achievable, where $d_i$ is the DoF of the $i^{\operatorname{th}}$ source--destination pair and $K_{\Sigma}$ is the maximum integer such that $K_{\Sigma}\leq \min_m\{K_m\}$ and $M/K_{\Sigma}$ is an integer. We show that surprisingly the achievable DoF region coincides with the cut-set outer bound if $M/\min_m\{K_m\}$ is an integer, thus interference-free communication is possible in terms of DoF. We further characterize an achievable DoF region assuming multi-antenna nodes and general message set, which again coincides with the cut-set outer bound for a certain class of networks.
1005.1716
Heuristics in Conflict Resolution
cs.AI cs.LO
Modern solvers for Boolean Satisfiability (SAT) and Answer Set Programming (ASP) are based on sophisticated Boolean constraint solving techniques. In both areas, conflict-driven learning and related techniques constitute key features whose application is enabled by conflict analysis. Although various conflict analysis schemes have been proposed, implemented, and studied both theoretically and practically in the SAT area, the heuristic aspects involved in conflict analysis have not yet received much attention. Assuming a fixed conflict analysis scheme, we address the open question of how to identify "good'' reasons for conflicts, and we investigate several heuristics for conflict analysis in ASP solving. To our knowledge, a systematic study like ours has not yet been performed in the SAT area, thus, it might be beneficial for both the field of ASP as well as the one of SAT solving.
1005.1785
Sidelobe Suppression for Robust Beamformer via The Mixed Norm Constraint
cs.IT math.IT
Applying a sparse constraint on the beam pattern has been suggested to suppress the sidelobe of the minimum variance distortionless response (MVDR) beamformer recently. To further improve the performance, we add a mixed norm constraint on the beam pattern. It matches the beam pattern better and encourages dense distribution in mainlobe and sparse distribution in sidelobe. The obtained beamformer has a lower sidelobe level and deeper nulls for interference avoidance than the standard sparse constraint based beamformer. Simulation demonstrates that the SINR gain is considerable for its lower sidelobe level and deeper nulling for interference, while the robustness against the mismatch between the steering angle and the direction of arrival (DOA) of the desired signal, caused by imperfect estimation of DOA, is maintained too.
1005.1800
Power-Efficient Ultra-Wideband Waveform Design Considering Radio Channel Effects
cs.IT math.IT
This paper presents a power-efficient mask-constrained ultra-wideband (UWB) waveform design with radio channel effects taken into consideration. Based on a finite impulse response (FIR) filter, we develop a convex optimization model with respect to the autocorrelation of the filter coefficients to optimize the transmitted signal power spectrum, subject to a regulatory emission mask. To improve power efficiency, effects of transmitter radio frequency (RF) components are included in the optimization of the transmitter-output waveform, and radio propagation effects are considered for optimizing at the receiver. Optimum coefficients of the FIR filter are obtained through spectral factorization of their autocorrelations. Simulation results show that the proposed method is able to maximize the transmitted UWB signal power under mask constraints set by regulatory authorities, while mitigating the power loss caused by channel attenuations.
1005.1801
Sparse Support Recovery with Phase-Only Measurements
cs.IT math.IT math.NA
Sparse support recovery (SSR) is an important part of the compressive sensing (CS). Most of the current SSR methods are with the full information measurements. But in practice the amplitude part of the measurements may be seriously destroyed. The corrupted measurements mismatch the current SSR algorithms, which leads to serious performance degeneration. This paper considers the problem of SSR with only phase information. In the proposed method, the minimization of the l1 norm of the estimated sparse signal enforces sparse distribution, while a nonzero constraint of the uncorrupted random measurements' amplitudes with respect to the reconstructed sparse signal is introduced. Because it only requires the phase components of the measurements in the constraint, it can avoid the performance deterioration by corrupted amplitude components. Simulations demonstrate that the proposed phase-only SSR is superior in the support reconstruction accuracy when the amplitude components of the measurements are contaminated.
1005.1803
Anti-Sampling-Distortion Compressive Wideband Spectrum Sensing for Cognitive Radio
cs.IT math.IT
Too high sampling rate is the bottleneck to wideband spectrum sensing for cognitive radio in mobile communication. Compressed sensing (CS) is introduced to transfer the sampling burden. The standard sparse signal recovery of CS does not consider the distortion in the analogue-to-information converter (AIC). To mitigate performance degeneration casued by the mismatch in least square distortionless constraint which doesn't consider the AIC distortion, we define the sparse signal with the sampling distortion as a bounded additive noise, and An anti-sampling-distortion constraint (ASDC) is deduced. Then we combine the \ell1 norm based sparse constraint with the ASDC to get a novel robust sparse signal recovery operator with sampling distortion. Numerical simulations demonstrate that the proposed method outperforms standard sparse wideband spectrum sensing in accuracy, denoising ability, etc.
1005.1804
Compressive Wideband Spectrum Sensing for Fixed Frequency Spectrum Allocation
cs.IT math.IT
Too high sampling rate is the bottleneck to wideband spectrum sensing for cognitive radio (CR). As the survey shows that the sensed signal has a sparse representation in frequency domain in the mass, compressed sensing (CS) can be used to transfer the sampling burden to the digital signal processor. An analog to information converter (AIC) can randomly sample the received signal with sub-Nyquist rate to obtained the random measurements. Considering that the static frequency spectrum allocation of primary radios means the bounds between different primary radios is known in advance, here we incorporate information of the spectrum boundaries between different primary user as a priori information to obtain a mixed l2/l1 norm denoising operator (MNDO). In the MNDO, the estimated power spectrum density (PSD) vector is divided into block sections with bounds corresponding different allocated primary radios. Different from previous standard l1-norm constraint on the whole PSD vector, a sum of the l2 norm of each section of the PSD vector is minimized to encourage the local grouping distribution while the sparse distribution in mass, while a relaxed constraint is used to improve the denoising performance. Simulation demonstrates that the proposed method outperforms standard sparse spectrum estimation in accuracy, denoising ability, etc.
1005.1853
Lattice model refinement of protein structures
cs.CE physics.comp-ph q-bio.QM
To find the best lattice model representation of a given full atom protein structure is a hard computational problem. Several greedy methods have been suggested where results are usually biased and leave room for improvement. In this paper we formulate and implement a Constraint Programming method to refine such lattice structure models. We show that the approach is able to provide better quality solutions. The prototype is implemented in COLA and is based on limited discrepancy search. Finally, some promising extensions based on local search are discussed.
1005.1860
Feature Selection Using Regularization in Approximate Linear Programs for Markov Decision Processes
cs.AI
Approximate dynamic programming has been used successfully in a large variety of domains, but it relies on a small set of provided approximation features to calculate solutions reliably. Large and rich sets of features can cause existing algorithms to overfit because of a limited number of samples. We address this shortcoming using $L_1$ regularization in approximate linear programming. Because the proposed method can automatically select the appropriate richness of features, its performance does not degrade with an increasing number of features. These results rely on new and stronger sampling bounds for regularized approximate linear programs. We also propose a computationally efficient homotopy method. The empirical evaluation of the approach shows that the proposed method performs well on simple MDPs and standard benchmark problems.
1005.1871
Subfield-Subcodes of Generalized Toric codes
cs.IT math.IT
We study subfield-subcodes of Generalized Toric (GT) codes over $\mathbb{F}_{p^s}$. These are the multidimensional analogues of BCH codes, which may be seen as subfield-subcodes of generalized Reed-Solomon codes. We identify polynomial generators for subfield-subcodes of GT codes which allows us to determine the dimensions and obtain bounds for the minimum distance. We give several examples of binary and ternary subfield-subcodes of GT codes that are the best known codes of a given dimension and length.
1005.1918
Prediction with Expert Advice under Discounted Loss
cs.LG
We study prediction with expert advice in the setting where the losses are accumulated with some discounting---the impact of old losses may gradually vanish. We generalize the Aggregating Algorithm and the Aggregating Algorithm for Regression to this case, propose a suitable new variant of exponential weights algorithm, and prove respective loss bounds.
1005.1934
Scalable Probabilistic Databases with Factor Graphs and MCMC
cs.DB cs.AI
Probabilistic databases play a crucial role in the management and understanding of uncertain data. However, incorporating probabilities into the semantics of incomplete databases has posed many challenges, forcing systems to sacrifice modeling power, scalability, or restrict the class of relational algebra formula under which they are closed. We propose an alternative approach where the underlying relational database always represents a single world, and an external factor graph encodes a distribution over possible worlds; Markov chain Monte Carlo (MCMC) inference is then used to recover this uncertainty to a desired level of fidelity. Our approach allows the efficient evaluation of arbitrary queries over probabilistic databases with arbitrary dependencies expressed by graphical models with structure that changes during inference. MCMC sampling provides efficiency by hypothesizing {\em modifications} to possible worlds rather than generating entire worlds from scratch. Queries are then run over the portions of the world that change, avoiding the onerous cost of running full queries over each sampled world. A significant innovation of this work is the connection between MCMC sampling and materialized view maintenance techniques: we find empirically that using view maintenance techniques is several orders of magnitude faster than naively querying each sampled world. We also demonstrate our system's ability to answer relational queries with aggregation, and demonstrate additional scalability through the use of parallelization.
1005.2012
Dual Averaging for Distributed Optimization: Convergence Analysis and Network Scaling
math.OC cs.SY stat.ML
The goal of decentralized optimization over a network is to optimize a global objective formed by a sum of local (possibly nonsmooth) convex functions using only local computation and communication. It arises in various application domains, including distributed tracking and localization, multi-agent co-ordination, estimation in sensor networks, and large-scale optimization in machine learning. We develop and analyze distributed algorithms based on dual averaging of subgradients, and we provide sharp bounds on their convergence rates as a function of the network size and topology. Our method of analysis allows for a clear separation between the convergence of the optimization algorithm itself and the effects of communication constraints arising from the network structure. In particular, we show that the number of iterations required by our algorithm scales inversely in the spectral gap of the network. The sharpness of this prediction is confirmed both by theoretical lower bounds and simulations for various networks. Our approach includes both the cases of deterministic optimization and communication, as well as problems with stochastic optimization and/or communication.
1005.2061
Cooperative Diversity with Mobile Nodes: Capacity Outage Rate and Duration
cs.IT math.IT
The outage probability is an important performance measure for cooperative diversity schemes. However, in mobile environments, the outage probability does not completely describe the behavior of cooperative diversity schemes since the mobility of the involved nodes introduces variations in the channel gains. As a result, the capacity outage events are correlated in time and second-order statistical parameters of the achievable information-theoretic capacity such as the average capacity outage rate (AOR) and the average capacity outage duration (AOD) are required to obtain a more complete description of the properties of cooperative diversity protocols. In this paper, assuming slow Rayleigh fading, we derive exact expressions for the AOR and the AOD of three well-known cooperative diversity protocols: variable-gain amplify-and-forward, decode-and-forward, and selection decode-and-forward relaying. Furthermore, we develop asymptotically tight high signal-to-noise ratio (SNR) approximations, which offer important insights into the influence of various system and channel parameters on the AOR and AOD. In particular, we show that on a double-logarithmic scale, similar to the outage probability, the AOR asymptotically decays with the SNR with a slope that depends on the diversity gain of the cooperative protocol, whereas the AOD asymptotically decays with a slope of -1/2 independent of the diversity gain.
1005.2146
On the Finite Time Convergence of Cyclic Coordinate Descent Methods
cs.LG cs.NA
Cyclic coordinate descent is a classic optimization method that has witnessed a resurgence of interest in machine learning. Reasons for this include its simplicity, speed and stability, as well as its competitive performance on $\ell_1$ regularized smooth optimization problems. Surprisingly, very little is known about its finite time convergence behavior on these problems. Most existing results either just prove convergence or provide asymptotic rates. We fill this gap in the literature by proving $O(1/k)$ convergence rates (where $k$ is the iteration counter) for two variants of cyclic coordinate descent under an isotonicity assumption. Our analysis proceeds by comparing the objective values attained by the two variants with each other, as well as with the gradient descent algorithm. We show that the iterates generated by the cyclic coordinate descent methods remain better than those of gradient descent uniformly over time.
1005.2179
Detecting Blackholes and Volcanoes in Directed Networks
cs.LG
In this paper, we formulate a novel problem for finding blackhole and volcano patterns in a large directed graph. Specifically, a blackhole pattern is a group which is made of a set of nodes in a way such that there are only inlinks to this group from the rest nodes in the graph. In contrast, a volcano pattern is a group which only has outlinks to the rest nodes in the graph. Both patterns can be observed in real world. For instance, in a trading network, a blackhole pattern may represent a group of traders who are manipulating the market. In the paper, we first prove that the blackhole mining problem is a dual problem of finding volcanoes. Therefore, we focus on finding the blackhole patterns. Along this line, we design two pruning schemes to guide the blackhole finding process. In the first pruning scheme, we strategically prune the search space based on a set of pattern-size-independent pruning rules and develop an iBlackhole algorithm. The second pruning scheme follows a divide-and-conquer strategy to further exploit the pruning results from the first pruning scheme. Indeed, a target directed graphs can be divided into several disconnected subgraphs by the first pruning scheme, and thus the blackhole finding can be conducted in each disconnected subgraph rather than in a large graph. Based on these two pruning schemes, we also develop an iBlackhole-DC algorithm. Finally, experimental results on real-world data show that the iBlackhole-DC algorithm can be several orders of magnitude faster than the iBlackhole algorithm, which has a huge computational advantage over a brute-force method.
1005.2243
Robustness and Generalization
cs.LG
We derive generalization bounds for learning algorithms based on their robustness: the property that if a testing sample is "similar" to a training sample, then the testing error is close to the training error. This provides a novel approach, different from the complexity or stability arguments, to study generalization of learning algorithms. We further show that a weak notion of robustness is both sufficient and necessary for generalizability, which implies that robustness is a fundamental property for learning algorithms to work.
1005.2249
Sparse Recovery with Orthogonal Matching Pursuit under RIP
cs.IT math.IT
This paper presents a new analysis for the orthogonal matching pursuit (OMP) algorithm. It is shown that if the restricted isometry property (RIP) is satisfied at sparsity level $O(\bar{k})$, then OMP can recover a $\bar{k}$-sparse signal in 2-norm. For compressed sensing applications, this result implies that in order to uniformly recover a $\bar{k}$-sparse signal in $\Real^d$, only $O(\bar{k} \ln d)$ random projections are needed. This analysis improves earlier results on OMP that depend on stronger conditions such as mutual incoherence that can only be satisfied with $\Omega(\bar{k}^2 \ln d)$ random projections.
1005.2251
Interference Channel with a Half-Duplex Out-of-Band Relay
cs.IT math.IT
A Gaussian interference channel (IC) aided by a half-duplex relay is considered, in which the relay receives and transmits in an orthogonal band with respect to the IC. The system thus consists of two parallel channels, the IC and the channel over which the relay is active, which is referred to as Out-of-Band Relay Channel (OBRC). The OBRC is operated by separating a multiple access phase from the sources to the relay and a broadcast phase from the relay to the destinations. Conditions under which the optimal operation, in terms of the sum-capacity, entails either signal relaying and/or interference forwarding by the relay are identified. These conditions also assess the optimality of either separable or non-separable transmission over the IC and OBRC. Specifically, the optimality of signal relaying and separable coding is established for scenarios where the relay-to-destination channels set the performance bottleneck with respect to the source-to-relay channels on the OBRC. Optimality of interference forwarding and non-separable operation is also established in special cases.
1005.2254
On Universal Complexity Measures
cs.IT cs.CC math.IT
We relate the computational complexity of finite strings to universal representations of their underlying symmetries. First, Boolean functions are classified using the universal covering topologies of the circuits which enumerate them. A binary string is classified as a fixed point of its automorphism group; the irreducible representation of this group is the string's universal covering group. Such a measure may be used to test the quasi-randomness of binary sequences with regard to first-order set membership. Next, strings over general alphabets are considered. The complexity of a general string is given by a universal representation which recursively factors the codeword number associated with a string. This is the complexity of the representation recursively decoding a Godel number having the value of the string; the result is a tree of prime numbers which forms a universal representation of the string's group symmetries.
1005.2263
Context models on sequences of covers
stat.ML cs.LG
We present a class of models that, via a simple construction, enables exact, incremental, non-parametric, polynomial-time, Bayesian inference of conditional measures. The approach relies upon creating a sequence of covers on the conditioning variable and maintaining a different model for each set within a cover. Inference remains tractable by specifying the probabilistic model in terms of a random walk within the sequence of covers. We demonstrate the approach on problems of conditional density estimation, which, to our knowledge is the first closed-form, non-parametric Bayesian approach to this problem.
1005.2267
A Fast Compressive Channel Estimation with Modified Smoothed L0 Algorithm
cs.IT math.IT
Broadband wireless channel is a time dispersive and becomes strongly frequency selective. In most cases, the channel is composed of a few dominant coefficients and a large part of coefficients is approximately zero or zero. To exploit the sparsity of multi-path channel (MPC), there are various methods have been proposed. They are, namely, greedy algorithms, iterative algorithms, and convex program. The former two algorithms are easy to be implemented but not stable; on the other hand, the last method is stable but difficult to be implemented as practical channel estimation problems because of computational complexity. In this paper, we proposed a novel channel estimation strategy by using modified smoothed (MSL0) algorithm which combines stable and low complexity. Computer simulations confirm the effectiveness of the introduced algorithm comparisons with the existing methods. We also give
1005.2269
Sparse Multipath Channel Estimation using DS Algorithm in Wideband Communication Systems
cs.IT cs.NI math.IT
Wideband wireless channel is a time dispersive channel and becomes strongly frequency-selective. However, in most cases, the channel is composed of a few dominant taps and a large part of taps is approximately zero or zero. They are often called sparse multi-path channels (MPC). Conventional linear MPC methods, such as the least squares (LS), do not exploit the sparsity of MPC. In general, accurate sparse MPC estimator can be obtained by solving a LASSO problem even in the presence of noise. In this paper, a novel CS-based sparse MPC method by using Dantzig selector (DS) [1] is introduced. This method exploits a channel's sparsity to reduce the number of training sequence and, hence, increase spectral efficiency when compared to existed methods with computer simulations.
1005.2270
Sparse Multipath Channel Estimation Using Compressive Sampling Matching Pursuit Algorithm
cs.IT math.IT
Wideband wireless channel is a time dispersive channel and becomes strongly frequency-selective. However, in most cases, the channel is composed of a few dominant taps and a large part of taps is approximately zero or zero. To exploit the sparsity of multi-path channel (MPC), two methods have been proposed. They are, namely, greedy algorithm and convex program. Greedy algorithm is easy to be implemented but not stable; on the other hand, the convex program method is stable but difficult to be implemented as practical channel estimation problems. In this paper, we introduce a novel channel estimation strategy using compressive sampling matching pursuit (CoSaMP) algorithm which was proposed in [1]. This algorithm will combine the greedy algorithm with the convex program method. The effectiveness of the proposed algorithm will be confirmed through comparisons with the existing methods.
1005.2296
Online Learning of Noisy Data with Kernels
cs.LG
We study online learning when individual instances are corrupted by adversarially chosen random noise. We assume the noise distribution is unknown, and may change over time with no restriction other than having zero mean and bounded variance. Our technique relies on a family of unbiased estimators for non-linear functions, which may be of independent interest. We show that a variant of online gradient descent can learn functions in any dot-product (e.g., polynomial) or Gaussian kernel space with any analytic convex loss function. Our variant uses randomized estimates that need to query a random number of noisy copies of each instance, where with high probability this number is upper bounded by a constant. Allowing such multiple queries cannot be avoided: Indeed, we show that online learning is in general impossible when only one noisy copy of each instance can be accessed.
1005.2303
Towards Physarum Binary Adders
nlin.PS cs.AI physics.bio-ph q-bio.CB
Plasmodium of \emph{Physarum polycephalum} is a single cell visible by unaided eye. The plasmodium's foraging behaviour is interpreted in terms of computation. Input data is a configuration of nutrients, result of computation is a network of plasmodium's cytoplasmic tubes spanning sources of nutrients. Tsuda et al (2004) experimentally demonstrated that basic logical gates can be implemented in foraging behaviour of the plasmodium. We simplify the original designs of the gates and show --- in computer models --- that the plasmodium is capable for computation of two-input two-output gate $<x, y> \to <xy, x+y>$ and three-input two-output $<x, y, z> \to < \bar{x}yz, x+y+z>$. We assemble the gates in a binary one-bit adder and demonstrate validity of the design using computer simulation.
1005.2308
Finding Your Literature Match -- A Recommender System
cs.DL cs.IR
The universe of potentially interesting, searchable literature is expanding continuously. Besides the normal expansion, there is an additional influx of literature because of interdisciplinary boundaries becoming more and more diffuse. Hence, the need for accurate, efficient and intelligent search tools is bigger than ever. Even with a sophisticated search engine, looking for information can still result in overwhelming results. An overload of information has the intrinsic danger of scaring visitors away, and any organization, for-profit or not-for-profit, in the business of providing scholarly information wants to capture and keep the attention of its target audience. Publishers and search engine engineers alike will benefit from a service that is able to provide visitors with recommendations that closely meet their interests. Providing visitors with special deals, new options and highlights may be interesting to a certain degree, but what makes more sense (especially from a commercial point of view) than to let visitors do most of the work by the mere action of making choices? Hiring psychics is not an option, so a technological solution is needed to recommend items that a visitor is likely to be looking for. In this presentation we will introduce such a solution and argue that it is practically feasible to incorporate this approach into a useful addition to any information retrieval system with enough usage.
1005.2321
Typical Sequences for Polish Alphabets
cs.IT math.IT
The notion of typical sequences plays a key role in the theory of information. Central to the idea of typicality is that a sequence $x_1, x_2, ..., x_n$ that is $P_X$-typical should, loosely speaking, have an empirical distribution that is in some sense close to the distribution $P_X$. The two most common notions of typicality are that of strong (letter) typicality and weak (entropy) typicality. While weak typicality allows one to apply many arguments that can be made with strongly typical arguments, some arguments for strong typicality cannot be generalized to weak typicality. In this paper, we consider an alternate definition of typicality, namely one based on the weak* topology and that is applicable to Polish alphabets (which includes $\reals^n$). This notion is a generalization of strong typicality in the sense that it degenerates to strong typicality in the finite alphabet case, and can also be applied to mixed and continuous distributions. Furthermore, it is strong enough to prove a Markov lemma, and thus can be used to directly prove a more general class of results than weak typicality. As an example of this technique, we directly prove achievability for Gel'fand-Pinsker channels with input constraints for a large class of alphabets and channels without first proving a finite alphabet result and then resorting to delicate quantization arguments. While this large class does not include Gaussian distributions with power constraints, it is shown to be straightforward to recover this case by considering a sequence of truncated Gaussian distributions.
1005.2364
A Short Introduction to Model Selection, Kolmogorov Complexity and Minimum Description Length (MDL)
cs.LG cs.CC
The concept of overfitting in model selection is explained and demonstrated with an example. After providing some background information on information theory and Kolmogorov complexity, we provide a short explanation of Minimum Description Length and error minimization. We conclude with a discussion of the typical features of overfitting in model selection.
1005.2443
Network Coded Transmission of Fountain Codes over Cooperative Relay Networks
cs.IT math.IT
In this paper, a transmission strategy of fountain codes over cooperative relay networks is proposed. When more than one relay nodes are available, we apply network coding to fountain-coded packets. By doing this, partial information is made available to the destination node about the upcoming message block. It is therefore able to reduce the required number of transmissions over erasure channels, hence increasing the effective throughput. Its application to wireless channels with Rayleigh fading and AWGN noise is also analysed, whereby the role of analogue network coding and optimal weight selection is demonstrated.
1005.2533
Dynamics underlying Box-office: Movie Competition on Recommender Systems
physics.soc-ph cs.IR
We introduce a simple model to study movie competition in the recommender systems. Movies of heterogeneous quality compete against each other through viewers' reviews and generate interesting dynamics of box-office. By assuming mean-field interactions between the competing movies, we show that run-away effect of popularity spreading is triggered by defeating the average review score, leading to hits in box-office. The average review score thus characterizes the critical movie quality necessary for transition from box-office bombs to blockbusters. The major factors affecting the critical review score are examined. By iterating the mean-field dynamical equations, we obtain qualitative agreements with simulations and real systems in the dynamical forms of box-office, revealing the significant role of competition in understanding box-office dynamics.
1005.2544
Channel Estimation for Opportunistic Spectrum Access: Uniform and Random Sensing
cs.IT math.IT
The knowledge of channel statistics can be very helpful in making sound opportunistic spectrum access decisions. It is therefore desirable to be able to efficiently and accurately estimate channel statistics. In this paper we study the problem of optimally placing sensing times over a time window so as to get the best estimate on the parameters of an on-off renewal channel. We are particularly interested in a sparse sensing regime with a small number of samples relative to the time window size. Using Fisher information as a measure, we analytically derive the best and worst sensing sequences under a sparsity condition. We also present a way to derive the best/worst sequences without this condition using a dynamic programming approach. In both cases the worst turns out to be the uniform sensing sequence, where sensing times are evenly spaced within the window. With these results we argue that without a priori knowledge, a robust sensing strategy should be a randomized strategy. We then compare different random schemes using a family of distributions generated by the circular $\beta$ ensemble, and propose an adaptive sensing scheme to effectively track time-varying channel parameters. We further discuss the applicability of compressive sensing for this problem.
1005.2603
Eigenvectors for clustering: Unipartite, bipartite, and directed graph cases
cs.LG math.SP
This paper presents a concise tutorial on spectral clustering for broad spectrum graphs which include unipartite (undirected) graph, bipartite graph, and directed graph. We show how to transform bipartite graph and directed graph into corresponding unipartite graph, therefore allowing a unified treatment to all cases. In bipartite graph, we show that the relaxed solution to the $K$-way co-clustering can be found by computing the left and right eigenvectors of the data matrix. This gives a theoretical basis for $K$-way spectral co-clustering algorithms proposed in the literatures. We also show that solving row and column co-clustering is equivalent to solving row and column clustering separately, thus giving a theoretical support for the claim: ``column clustering implies row clustering and vice versa''. And in the last part, we generalize the Ky Fan theorem---which is the central theorem for explaining spectral clustering---to rectangular complex matrix motivated by the results from bipartite graph analysis.
1005.2613
Compressed Sensing with Coherent and Redundant Dictionaries
math.NA cs.IT math.IT
This article presents novel results concerning the recovery of signals from undersampled data in the common situation where such signals are not sparse in an orthonormal basis or incoherent dictionary, but in a truly redundant dictionary. This work thus bridges a gap in the literature and shows not only that compressed sensing is viable in this context, but also that accurate recovery is possible via an L1-analysis optimization problem. We introduce a condition on the measurement/sensing matrix, which is a natural generalization of the now well-known restricted isometry property, and which guarantees accurate recovery of signals that are nearly sparse in (possibly) highly overcomplete and coherent dictionaries. This condition imposes no incoherence restriction on the dictionary and our results may be the first of this kind. We discuss practical examples and the implications of our results on those applications, and complement our study by demonstrating the potential of L1-analysis for such problems.
1005.2633
A Distributed Newton Method for Network Utility Maximization
math.OC cs.SY
Most existing work uses dual decomposition and subgradient methods to solve Network Utility Maximization (NUM) problems in a distributed manner, which suffer from slow rate of convergence properties. This work develops an alternative distributed Newton-type fast converging algorithm for solving network utility maximization problems with self-concordant utility functions. By using novel matrix splitting techniques, both primal and dual updates for the Newton step can be computed using iterative schemes in a decentralized manner with limited information exchange. Similarly, the stepsize can be obtained via an iterative consensus-based averaging scheme. We show that even when the Newton direction and the stepsize in our method are computed within some error (due to finite truncation of the iterative schemes), the resulting objective function value still converges superlinearly to an explicitly characterized error neighborhood. Simulation results demonstrate significant convergence rate improvement of our algorithm relative to the existing subgradient methods based on dual decomposition.
1005.2638
Hierarchical Clustering for Finding Symmetries and Other Patterns in Massive, High Dimensional Datasets
stat.ML cs.CV cs.LG
Data analysis and data mining are concerned with unsupervised pattern finding and structure determination in data sets. "Structure" can be understood as symmetry and a range of symmetries are expressed by hierarchy. Such symmetries directly point to invariants, that pinpoint intrinsic properties of the data and of the background empirical domain of interest. We review many aspects of hierarchy here, including ultrametric topology, generalized ultrametric, linkages with lattices and other discrete algebraic structures and with p-adic number representations. By focusing on symmetries in data we have a powerful means of structuring and analyzing massive, high dimensional data stores. We illustrate the powerfulness of hierarchical clustering in case studies in chemistry and finance, and we provide pointers to other published case studies.
1005.2646
An Algebraic Approach to Physical-Layer Network Coding
cs.IT math.IT
The problem of designing new physical-layer network coding (PNC) schemes via lattice partitions is considered. Building on a recent work by Nazer and Gastpar, who demonstrated its asymptotic gain using information-theoretic tools, we take an algebraic approach to show its potential in non-asymptotic settings. We first relate Nazer-Gastpar's approach to the fundamental theorem of finitely generated modules over a principle ideal domain. Based on this connection, we generalize their code construction and simplify their encoding and decoding methods. This not only provides a transparent understanding of their approach, but more importantly, it opens up the opportunity to design efficient and practical PNC schemes. Finally, we apply our framework for PNC to a Gaussian relay network and demonstrate its advantage over conventional PNC schemes.
1005.2662
Fastest Distributed Consensus Averaging Problem on Perfect and Complete n-ary Tree networks
cs.IT cs.DC cs.NI math.IT
Solving fastest distributed consensus averaging problem (i.e., finding weights on the edges to minimize the second-largest eigenvalue modulus of the weight matrix) over networks with different topologies is one of the primary areas of research in the field of sensor networks and one of the well known networks in this issue is tree network. Here in this work we present analytical solution for the problem of fastest distributed consensus averaging algorithm by means of stratification and semidefinite programming, for two particular types of tree networks, namely perfect and complete n-ary tree networks. Our method in this paper is based on convexity of fastest distributed consensus averaging problem, and inductive comparing of the characteristic polynomials initiated by slackness conditions in order to find the optimal weights. Also the optimal weights for the edges of certain types of branches such as perfect and complete n-ary tree branches are determined independently of rest of the network.
1005.2704
Characterizing and modeling the dynamics of online popularity
physics.soc-ph cs.CY cs.SI
Online popularity has enormous impact on opinions, culture, policy, and profits. We provide a quantitative, large scale, temporal analysis of the dynamics of online content popularity in two massive model systems, the Wikipedia and an entire country's Web space. We find that the dynamics of popularity are characterized by bursts, displaying characteristic features of critical systems such as fat-tailed distributions of magnitude and inter-event time. We propose a minimal model combining the classic preferential popularity increase mechanism with the occurrence of random popularity shifts due to exogenous factors. The model recovers the critical features observed in the empirical analysis of the systems analyzed here, highlighting the key factors needed in the description of popularity dynamics.
1005.2710
Capacity of a Class of Multicast Tree Networks
cs.IT math.IT
In this paper, we characterize the capacity of a new class of single-source multicast discrete memoryless relay networks having a tree topology in which the root node is the source and each parent node in the graph has at most one noisy child node and any number of noiseless child nodes. This class of multicast tree networks includes the class of diamond networks studied by Kang and Ulukus as a special case, where they showed that the capacity can be strictly lower than the cut-set bound. For achievablity, a novel coding scheme is constructed where each noisy relay employs a combination of decode-and-forward (DF) and compress-and-forward (CF) and each noiseless relay performs a random binning such that codebook constructions and relay operations are independent for each node and do not depend on the network topology. For converse, a new technique of iteratively manipulating inequalities exploiting the tree topology is used.
1005.2714
Structural Drift: The Population Dynamics of Sequential Learning
q-bio.PE cs.LG
We introduce a theory of sequential causal inference in which learners in a chain estimate a structural model from their upstream teacher and then pass samples from the model to their downstream student. It extends the population dynamics of genetic drift, recasting Kimura's selectively neutral theory as a special case of a generalized drift process using structured populations with memory. We examine the diffusion and fixation properties of several drift processes and propose applications to learning, inference, and evolution. We also demonstrate how the organization of drift process space controls fidelity, facilitates innovations, and leads to information loss in sequential learning with and without memory.
1005.2715
On the Subspace of Image Gradient Orientations
cs.CV
We introduce the notion of Principal Component Analysis (PCA) of image gradient orientations. As image data is typically noisy, but noise is substantially different from Gaussian, traditional PCA of pixel intensities very often fails to estimate reliably the low-dimensional subspace of a given data population. We show that replacing intensities with gradient orientations and the $\ell_2$ norm with a cosine-based distance measure offers, to some extend, a remedy to this problem. Our scheme requires the eigen-decomposition of a covariance matrix and is as computationally efficient as standard $\ell_2$ PCA. We demonstrate some of its favorable properties on robust subspace estimation.
1005.2731
Cross-Band Interference Considered Harmful in OFDM Based Distributed Spectrum Sharing
cs.IT math.IT
In the past few years we have witnessed the paradigm shift from static spectrum allocation to dynamic spectrum access/sharing. Orthogonal Frequency-Division Multiple Access (OFDMA) is a promising mechanism to implement the agile spectrum access. However, in wireless distributed networks where tight synchronization is infeasible, OFDMA faces the problem of cross-band interference. Subcarriers used by different users are no longer orthogonal, and transmissions operating on non-overlapping subcarriers can interfere with each other. In this paper, we explore the cause of cross-band interference and analytically quantify its strength and impact on packet transmissions. Our analysis captures three key practical artifacts: inter-link frequency offset, temporal sampling mismatch and power heterogeneity. To our best knowledge, this work is the first to systematically analyze the cause and impact of cross-band interference. Using insights from our analysis, we then build and compared three mitigating methods to combat cross-band interference. Analytical and simulation results show that placing frequency guardband at link boundaries is the most effective solution in distributed spectrum sharing, while the other two frequency-domain methods are sensitive to either temporal sampling mismatch or inter-link frequency offset. We find that the proper guardband size depends heavily on power heterogeneity. Consequently, protocol designs for dynamic spectrum access should carefully take into account the cross-band interference when configuring spectrum usage.
1005.2759
Secrecy-Achieving Polar-Coding for Binary-Input Memoryless Symmetric Wire-Tap Channels
cs.IT cs.CR math.IT
A polar coding scheme is introduced in this paper for the wire-tap channel. It is shown that the provided scheme achieves the entire rate-equivocation region for the case of symmetric and degraded wire-tap channel, where the weak notion of secrecy is assumed. For the particular case of binary erasure wire-tap channel, an alternative proof is given. The case of general non-degraded wire-tap channels is also considered.
1005.2770
Capacity-Achieving Polar Codes for Arbitrarily-Permuted Parallel Channels
cs.IT math.IT
Channel coding over arbitrarily-permuted parallel channels was first studied by Willems et al. (2008). This paper introduces capacity-achieving polar coding schemes for arbitrarily-permuted parallel channels where the component channels are memoryless, binary-input and output-symmetric.