OpenRaiser/Intern-Atlas huggingface dataset:
Some Properties of Large Excursions of a Stationary Gaussian Process
Venue: arXiv cs.IT 2014
Year: 2014

The present work investigates two properties of level crossings of a stationary Gaussian process $X(t)$ with autocorrelation function $R_X(τ)$. We show firstly that if $R_X(τ)$ admits finite second and fourth derivatives at the origin, the length of up-excursions above a large negative level $-γ$ is asymptotically exponential as $-γ\to -\infty$. Secondly, assuming that $R_X(τ)$ admits a finite second derivative at the origin and some defined properties, we derive the mean number of crossings as well as the length of successive excursions above two subsequent large levels. The asymptotic results are shown to be effective even for moderate values of crossing level. An application of the developed results is proposed to derive the probability of successive excursions above adjacent levels during a time window.
Quantifying synergistic mutual information
Venue: arXiv cs.IT 2014
Year: 2014

Quantifying cooperation or synergy among random variables in predicting a single target random variable is an important problem in many complex systems. We review three prior information-theoretic measures of synergy and introduce a novel synergy measure defined as the difference between the whole and the union of its parts. We apply all four measures against a suite of binary circuits to demonstrate that our measure alone quantifies the intuitive concept of synergy across all examples. We show that for our measure of synergy that independent predictors can have positive redundant information.
Rényi Divergence and Kullback-Leibler Divergence
Venue: arXiv cs.IT 2014
Year: 2014

Rényi divergence is related to Rényi entropy much like Kullback-Leibler divergence is related to Shannon's entropy, and comes up in many settings. It was introduced by Rényi as a measure of information that satisfies almost the same axioms as Kullback-Leibler divergence, and depends on a parameter that is called its order. In particular, the Rényi divergence of order 1 equals the Kullback-Leibler divergence. We review and extend the most important properties of Rényi divergence and Kullback-Leibler divergence, including convexity, continuity, limits of $σ$-algebras and the relation of the special order 0 to the Gaussian dichotomy and contiguity. We also show how to generalize the Pythagorean inequality to orders different from 1, and we extend the known equivalence between channel capacity and minimax redundancy to continuous channel inputs (for all orders) and present several other minimax results.
Secure Compute-and-Forward in a Bidirectional Relay
Venue: arXiv cs.IT 2014
Year: 2014

We consider the basic bidirectional relaying problem, in which two users in a wireless network wish to exchange messages through an intermediate relay node. In the compute-and-forward strategy, the relay computes a function of the two messages using the naturally-occurring sum of symbols simultaneously transmitted by user nodes in a Gaussian multiple access (MAC) channel, and the computed function value is forwarded to the user nodes in an ensuing broadcast phase. In this paper, we study the problem under an additional security constraint, which requires that each user's message be kept secure from the relay. We consider two types of security constraints: perfect secrecy, in which the MAC channel output seen by the relay is independent of each user's message; and strong secrecy, which is a form of asymptotic independence. We propose a coding scheme based on nested lattices, the main feature of which is that given a pair of nested lattices that satisfy certain "goodness" properties, we can explicitly specify probability distributions for randomization at the encoders to achieve the desired security criteria. In particular, our coding scheme guarantees perfect or strong secrecy even in the absence of channel noise. The noise in the channel only affects reliability of computation at the relay, and for Gaussian noise, we derive achievable rates for reliable and secure computation. We also present an application of our methods to the multi-hop line network in which a source needs to transmit messages to a destination through a series of intermediate relays.
The Simple Economics of Approximately Optimal Auctions
Venue: arXiv cs.GT 2014
Year: 2014

The intuition that profit is optimized by maximizing marginal revenue is a guiding principle in microeconomics. In the classical auction theory for agents with linear utility and single-dimensional preferences, Bulow and Roberts (1989) show that the optimal auction of Myerson (1981) is in fact optimizing marginal revenue. In particular Myerson's virtual values are exactly the derivative of an appropriate revenue curve. This paper considers mechanism design in environments where the agents have multi-dimensional and non-linear preferences. Understanding good auctions for these environments is considered to be the main challenge in Bayesian optimal mechanism design. In these environments maximizing marginal revenue may not be optimal and there is sometimes no direct way to implement the marginal revenue maximization. Our contributions are three fold: we characterize the settings for which marginal revenue maximization is optimal (by identifying an important condition that we call revenue linearity), we give simple procedures for implementing marginal revenue maximization in general, and we show that marginal revenue maximization is approximately optimal. Our approximation factor smoothly degrades in a term that quantifies how far the environment is from ideal (where marginal revenue maximization is optimal). Because the marginal revenue mechanism is optimal for single-dimensional agents, our generalization immediately approximately extends many results for single-dimensional agents. One of the biggest open questions in Bayesian algorithmic mechanism design is developing methodologies that are not brute-force in the size of the agent type space. Our methods identify a subproblem that, e.g., for unit-demand agents with values drawn from product distributions, enables approximation mechanisms that are polynomial in the dimension.
Locally Repairable Codes
Venue: arXiv cs.IT 2014
Year: 2014

Distributed storage systems for large-scale applications typically use replication for reliability. Recently, erasure codes were used to reduce the large storage overhead, while increasing data reliability. A main limitation of off-the-shelf erasure codes is their high-repair cost during single node failure events. A major open problem in this area has been the design of codes that {\it i)} are repair efficient and {\it ii)} achieve arbitrarily high data rates. In this paper, we explore the repair metric of {\it locality}, which corresponds to the number of disk accesses required during a {\color{black}single} node repair. Under this metric we characterize an information theoretic trade-off that binds together locality, code distance, and the storage capacity of each node. We show the existence of optimal {\it locally repairable codes} (LRCs) that achieve this trade-off. The achievability proof uses a locality aware flow-graph gadget which leads to a randomized code construction. Finally, we present an optimal and explicit LRC that achieves arbitrarily high data-rates. Our locality optimal construction is based on simple combinations of Reed-Solomon blocks.
Adaptive vibration suppression system: An iterative control law for a piezoelectric actuator shunted by a negative capacitor
Venue: arXiv cs.CE 2014
Year: 2014

An adaptive system for the suppression of vibration transmission using a single piezoelectric actuator shunted by a negative capacitance circuit is presented. It is known that using negative capacitance shunt, the spring constant of piezoelectric actuator can be controlled to extreme values of zero or infinity. Since the value of spring constant controls a force transmitted through an elastic element, it is possible to achieve a reduction of transmissibility of vibrations through a piezoelectric actuator by reducing its effective spring constant. The narrow frequency range and broad frequency range vibration isolation systems are analyzed, modeled, and experimentally investigated. The problem of high sensitivity of the vibration control system to varying operational conditions is resolved by applying an adaptive control to the circuit parameters of the negative capacitor. A control law that is based on the estimation of the value of effective spring constant of shunted piezoelectric actuator is presented. An adaptive system, which achieves a self-adjustment of the negative capacitor parameters is presented. It is shown that such an arrangement allows a design of a simple electronic system, which, however, offers a great vibration isolation efficiency in variable vibration conditions.
Tiling $R^{5}$ by Crosses
Venue: arXiv cs.IT 2014
Year: 2014

An $n$-dimensional cross comprises $2n+1$ unit cubes: the center cube and reflections in all its faces. It is well known that there is a tiling of $R^{n}$ by crosses for all $n.$ AlBdaiwi and the first author proved that if $2n+1$ is not a prime then there are $2^{\aleph_{0}}$ \ non-congruent regular (= face-to-face) tilings of $R^{n}$ by crosses, while there is a unique tiling of $R^{n}$ by crosses for $n=2,3$. They conjectured that this is always the case if $2n+1$ is a prime. To support the conjecture we prove in this paper that also for $R^{5}$ there is a unique regular, and no non-regular, tiling by crosses. So there is a unique tiling of $R^{3}$ by crosses, there are $2^{\aleph_{0}}$ tilings of $R^{4},$ but for $R^{5}$ there is again only one tiling by crosses. We guess that this result goes against our intuition that suggests "the higher the dimension of the \ space, the more freedom we get".
Robust statistics, hypothesis testing, and confidence intervals for persistent homology on metric measure spaces
Venue: arXiv cs.CG 2014
Year: 2014

We study distributions of persistent homology barcodes associated to taking subsamples of a fixed size from metric measure spaces. We show that such distributions provide robust invariants of metric measure spaces, and illustrate their use in hypothesis testing and providing confidence intervals for topological data analysis.
Information Networks with in-Block Memory
Venue: arXiv cs.IT 2014
Year: 2014

A class of channels is introduced for which there is memory inside blocks of a specified length and no memory across the blocks. The multi-user model is called an information network with in-block memory (NiBM). It is shown that block-fading channels, channels with state known causally at the encoder, and relay networks with delays are NiBMs. A cut-set bound is developed for NiBMs that unifies, strengthens, and generalizes existing cut bounds for discrete memoryless networks. The bound gives new finite-letter capacity expressions for several classes of networks including point-to-point channels, and certain multiaccess, broadcast, and relay channels. Cardinality bounds on the random coding alphabets are developed that improve on existing bounds for channels with action-dependent state available causally at the encoder and for relays without delay. Finally, quantize-forward network coding is shown to achieve rates within an additive gap of the new cut-set bound for linear, additive, Gaussian noise channels, symmetric power constraints, and a multicast session.
An Analysis of Interactions Within and Between Extreme Right Communities in Social Media
Venue: arXiv cs.SI 2014
Year: 2014

Many extreme right groups have had an online presence for some time through the use of dedicated websites. This has been accompanied by increased activity in social media platforms in recent years, enabling the dissemination of extreme right content to a wider audience. In this paper, we present an analysis of the activity of a selection of such groups on Twitter, using network representations based on reciprocal follower and interaction relationships, while also analyzing topics found in their corresponding tweets. International relationships between certain extreme right groups across geopolitical boundaries are initially identified. Furthermore, we also discover stable communities of accounts within local interaction networks, in addition to associated topics, where the underlying extreme right ideology of these communities is often identifiable.
On the Consistency of AUC Pairwise Optimization
Venue: arXiv cs.LG 2014
Year: 2014

AUC (area under ROC curve) is an important evaluation criterion, which has been popularly used in many learning tasks such as class-imbalance learning, cost-sensitive learning, learning to rank, etc. Many learning approaches try to optimize AUC, while owing to the non-convexity and discontinuousness of AUC, almost all approaches work with surrogate loss functions. Thus, the consistency of AUC is crucial; however, it has been almost untouched before. In this paper, we provide a sufficient condition for the asymptotic consistency of learning approaches based on surrogate loss functions. Based on this result, we prove that exponential loss and logistic loss are consistent with AUC, but hinge loss is inconsistent. Then, we derive the $q$-norm hinge loss and general hinge loss that are consistent with AUC. We also derive the consistent bounds for exponential loss and logistic loss, and obtain the consistent bounds for many surrogate loss functions under the non-noise setting. Further, we disclose an equivalence between the exponential surrogate loss of AUC and exponential surrogate loss of accuracy, and one straightforward consequence of such finding is that AdaBoost and RankBoost are equivalent.
Computing Topological Persistence for Simplicial Maps
Venue: arXiv cs.CG 2014
Year: 2014

Algorithms for persistent homology and zigzag persistent homology are well-studied for persistence modules where homomorphisms are induced by inclusion maps. In this paper, we propose a practical algorithm for computing persistence under $\mathbb{Z}_2$ coefficients for a sequence of general simplicial maps and show how these maps arise naturally in some applications of topological data analysis. First, we observe that it is not hard to simulate simplicial maps by inclusion maps but not necessarily in a monotone direction. This, combined with the known algorithms for zigzag persistence, provides an algorithm for computing the persistence induced by simplicial maps. Our main result is that the above simple minded approach can be improved for a sequence of simplicial maps given in a monotone direction. A simplicial map can be decomposed into a set of elementary inclusions and vertex collapses--two atomic operations that can be supported efficiently with the notion of simplex annotations for computing persistent homology. A consistent annotation through these atomic operations implies the maintenance of a consistent cohomology basis, hence a homology basis by duality. While the idea of maintaining a cohomology basis through an inclusion is not new, maintaining them through a vertex collapse is new, which constitutes an important atomic operation for simulating simplicial maps. Annotations support the vertex collapse in addition to the usual inclusion quite naturally. Finally, we exhibit an application of this new tool in which we approximate the persistence diagram of a filtration of Rips complexes where vertex collapses are used to tame the blow-up in size.
Tenacious tagging of images via Mellin monomials
Venue: arXiv cs.CV 2014
Year: 2014

We describe a method for attaching persistent metadata to an image. The method can be interpreted as a template-based blind watermarking scheme, robust to common editing operations, namely: cropping, rotation, scaling, stretching, shearing, compression, printing, scanning, noise, and color removal. Robustness is achieved through the reciprocity of the embedding and detection invariants. The embedded patterns are real onedimensional Mellin monomial patterns distributed over two-dimensions. The embedded patterns are scale invariant and can be directly embedded in an image by simple pixel addition. Detection achieves rotation and general affine invariance by signal projection using implicit Radon transformation. Embedded signals contract to one-dimension in the two-dimensional Fourier polar domain. The real signals are detected by correlation with complex Mellin monomial templates. Using a unique template of 4 chirp patterns we detect the affine signature with exquisite sensitivity and moderate security. The practical implementation achieves efficiencies through fast Fourier transform (FFT) correspondences such as the projection-slice theorem, the FFT correlation relation, and fast resampling via the chirp-z transform. The overall method utilizes orthodox spread spectrum patterns for the payload and performs well in terms of the classic robustness-capacity-visibility performance triangle. Tags are entirely imperceptible with a mean SSIM greater than 0.988 in all cases tested. Watermarked images survive almost all Stirmark attacks. The method is ideal for attaching metadata robustly to both digital and analogue images.
Distribution of the largest eigenvalue for real Wishart and Gaussian random matrices and a simple approximation for the Tracy-Widom distribution
Venue: arXiv cs.IT 2014
Year: 2014

We derive efficient recursive formulas giving the exact distribution of the largest eigenvalue for finite dimensional real Wishart matrices and for the Gaussian Orthogonal Ensemble (GOE). In comparing the exact distribution with the limiting distribution of large random matrices, we also found that the Tracy-Widom law can be approximated by a properly scaled and shifted Gamma distribution, with great accuracy for the values of common interest in statistical applications.
Capacity Limits and Multiplexing Gains of MIMO Channels with Transceiver Impairments
Venue: arXiv cs.IT 2014
Year: 2014

The capacity of ideal MIMO channels has a high-SNR slope that equals the minimum of the number of transmit and receive antennas. This letter analyzes if this result holds when there are distortions from physical transceiver impairments. We prove analytically that such physical MIMO channels have a finite upper capacity limit, for any channel distribution and SNR. The high-SNR slope thus collapses to zero. This appears discouraging, but we prove the encouraging result that the relative capacity gain of employing MIMO is at least as large as with ideal transceivers.
copulaedas: An R Package for Estimation of Distribution Algorithms Based on Copulas
Venue: arXiv cs.NE 2014
Year: 2014

The use of copula-based models in EDAs (estimation of distribution algorithms) is currently an active area of research. In this context, the copulaedas package for R provides a platform where EDAs based on copulas can be implemented and studied. The package offers complete implementations of various EDAs based on copulas and vines, a group of well-known optimization problems, and utility functions to study the performance of the algorithms. Newly developed EDAs can be easily integrated into the package by extending an S4 class with generic functions for their main components. This paper presents copulaedas by providing an overview of EDAs based on copulas, a description of the implementation of the package, and an illustration of its use through examples. The examples include running the EDAs defined in the package, implementing new algorithms, and performing an empirical study to compare the behavior of different algorithms on benchmark functions and a real-world problem.
A Cookbook for Temporal Conceptual Data Modelling with Description Logics
Venue: arXiv cs.LO 2014
Year: 2014

We design temporal description logics suitable for reasoning about temporal conceptual data models and investigate their computational complexity. Our formalisms are based on DL-Lite logics with three types of concept inclusions (ranging from atomic concept inclusions and disjointness to the full Booleans), as well as cardinality constraints and role inclusions. In the temporal dimension, they capture future and past temporal operators on concepts, flexible and rigid roles, the operators `always' and `some time' on roles, data assertions for particular moments of time and global concept inclusions. The logics are interpreted over the Cartesian products of object domains and the flow of time (Z,<), satisfying the constant domain assumption. We prove that the most expressive of our temporal description logics (which can capture lifespan cardinalities and either qualitative or quantitative evolution constraints) turn out to be undecidable. However, by omitting some of the temporal operators on concepts/roles or by restricting the form of concept inclusions we obtain logics whose complexity ranges between PSpace and NLogSpace. These positive results were obtained by reduction to various clausal fragments of propositional temporal logic, which opens a way to employ propositional or first-order temporal provers for reasoning about temporal data models.
Contributions to Persistence Theory
Venue: arXiv cs.CG 2014
Year: 2014

This paper provides a method to calculate the bar codes of a PCD (point cloud data) with real coefficients in Section 3. With Dan Burghelea and Tamal Dey we developed a persistence theory which involves level sets discussed in Section 4. This paper is the Ph.D thesis written under the direction of Dan Burghelea at OSU.
Oriented Euler Complexes and Signed Perfect Matchings
Venue: arXiv cs.DM 2014
Year: 2014

This paper presents "oriented pivoting systems" as an abstract framework for complementary pivoting. It gives a unified simple proof that the endpoints of complementary pivoting paths have opposite sign. A special case are the Nash equilibria of a bimatrix game at the ends of Lemke-Howson paths, which have opposite index. For Euler complexes or "oiks", an orientation is defined which extends the known concept of oriented abstract simplicial manifolds. Ordered "room partitions" for a family of oriented oiks come in pairs of opposite sign. For an oriented oik of even dimension, this sign property holds also for unordered room partitions. In the case of a two-dimensional oik, these are perfect matchings of an Euler graph, with the sign as defined for Pfaffian orientations of graphs. A near-linear time algorithm is given for the following problem: given a graph with an Eulerian orientation with a perfect matching, find another perfect matching of opposite sign. In contrast, the complementary pivoting algorithm for this problem may be exponential.
On the Power of Conditional Samples in Distribution Testing
Venue: arXiv cs.DS 2014
Year: 2014

In this paper we define and examine the power of the {\em conditional-sampling} oracle in the context of distribution-property testing. The conditional-sampling oracle for a discrete distribution $μ$ takes as input a subset $S \subset [n]$ of the domain, and outputs a random sample $i \in S$ drawn according to $μ$, conditioned on $S$ (and independently of all prior samples). The conditional-sampling oracle is a natural generalization of the ordinary sampling oracle in which $S$ always equals $[n]$. We show that with the conditional-sampling oracle, testing uniformity, testing identity to a known distribution, and testing any label-invariant property of distributions is easier than with the ordinary sampling oracle. On the other hand, we also show that for some distribution properties the sample-complexity remains near-maximal even with conditional sampling.