OpenRaiser/Intern-Atlas huggingface dataset:
Spatial mixing and approximation algorithms for graphs with bounded connective constant
Venue: arXiv cs.DM 2014
Year: 2014

The hard core model in statistical physics is a probability distribution on independent sets in a graph in which the weight of any independent set I is proportional to lambda^(|I|), where lambda > 0 is the vertex activity. We show that there is an intimate connection between the connective constant of a graph and the phenomenon of strong spatial mixing (decay of correlations) for the hard core model; specifically, we prove that the hard core model with vertex activity lambda < lambda_c(Delta + 1) exhibits strong spatial mixing on any graph of connective constant Delta, irrespective of its maximum degree, and hence derive an FPTAS for the partition function of the hard core model on such graphs. Here lambda_c(d) := d^d/(d-1)^(d+1) is the critical activity for the uniqueness of the Gibbs measure of the hard core model on the infinite d-ary tree. As an application, we show that the partition function can be efficiently approximated with high probability on graphs drawn from the random graph model G(n,d/n) for all lambda < e/d, even though the maximum degree of such graphs is unbounded with high probability. We also improve upon Weitz's bounds for strong spatial mixing on bounded degree graphs (Weitz, 2006) by providing a computationally simple method which uses known estimates of the connective constant of a lattice to obtain bounds on the vertex activities lambda for which the hard core model on the lattice exhibits strong spatial mixing. Using this framework, we improve upon these bounds for several lattices including the Cartesian lattice in dimensions 3 and higher. Our techniques also allow us to relate the threshold for the uniqueness of the Gibbs measure on a general tree to its branching factor (Lyons, 1989).
Wireless Information and Power Transfer in Multiuser OFDM Systems
Venue: arXiv cs.IT 2014
Year: 2014

In this paper, we study the optimal design for simultaneous wireless information and power transfer (SWIPT) in downlink multiuser orthogonal frequency division multiplexing (OFDM) systems. For information transmission, we consider two types of multiple access schemes, namely, time division multiple access (TDMA) and orthogonal frequency division multiple access (OFDMA). At the receiver side, due to the practical limitation that circuits for harvesting energy from radio signals are not yet able to decode the carried information directly, each user applies either time switching (TS) or power splitting (PS) to coordinate the energy harvesting (EH) and information decoding (ID) processes. For the TDMA-based information transmission, we employ TS at the receivers; for the OFDMA-based information transmission, we employ PS at the receivers. Under the above two scenarios, we address the problem of maximizing the weighted sum-rate over all users by varying the time/frequency power allocation and either TS or PS ratio, subject to a minimum harvested energy constraint on each user as well as a peak and/or total transmission power constraint. For the TS scheme, by an appropriate variable transformation the problem is reformulated as a convex problem, for which the optimal power allocation and TS ratio are obtained by the Lagrange duality method. For the PS scheme, we propose an iterative algorithm to optimize the power allocation, subcarrier (SC) allocation and the PS ratio for each user. The performances of the two schemes are compared numerically as well as analytically for the special case of single-user setup. It is revealed that the peak power constraint imposed on each OFDM SC as well as the number of users in the system play a key role in the rate-energy performance comparison by the two proposed schemes.
The geography and carbon footprint of mobile phone use in Cote d'Ivoire
Venue: arXiv cs.CY 2014
Year: 2014

The newly released Orange D4D mobile phone data base provides new insights into the use of mobile technology in a developing country. Here we perform a series of spatial data analyses that reveal important geographic aspects of mobile phone use in Cote d'Ivoire. We first map the locations of base stations with respect to the population distribution and the number and duration of calls at each base station. On this basis, we estimate the energy consumed by the mobile phone network. Finally, we perform an analysis of inter-city mobility, and identify high-traffic roads in the country.
Combined-Semantics Equivalence Is Decidable for a Practical Class of Conjunctive Queries
Venue: arXiv cs.DB 2014
Year: 2014

In this paper, we focus on the problem of determining whether two conjunctive ("CQ") queries posed on relational data are combined-semantics equivalent [9]. We continue the tradition of [2,5,9] of studying this problem using the tool of containment between queries. We introduce a syntactic necessary and sufficient condition for equivalence of queries belonging to a large natural language of "explicit-wave" combined-semantics CQ queries; this language encompasses (but is not limited to) all set, bag, and bag-set queries, and appears to cover all combined-semantics CQ queries that are expressible in SQL. Our result solves in the positive the decidability problem of determining combined-semantics equivalence for pairs of explicit-wave CQ queries. That is, for an arbitrary pair of combined-semantics CQ queries, it is decidable (i) to determine whether each of the queries is explicit wave, and (ii) to determine, in case both queries are explicit wave, whether or not they are combined-semantics equivalent, by using our syntactic criterion. (The problem of determining equivalence for general combined-semantics CQ queries remains open. Even so, our syntactic sufficient containment condition could still be used to determine that two general CQ queries are combined-semantics equivalent.) Our equivalence test, as well as our general sufficient condition for containment of combined-semantics CQ queries, reduce correctly to the special cases reported in [2,5] for set, bag, and bag-set semantics. Our containment and equivalence conditions also properly generalize the results of [9], provided that the latter are restricted to the language of (combined-semantics) CQ queries.
Efficient estimation of eigenvalue counts in an interval
Venue: arXiv cs.NA 2014
Year: 2014

Estimating the number of eigenvalues located in a given interval of a large sparse Hermitian matrix is an important problem in certain applications and it is a prerequisite of eigensolvers based on a divide-and-conquer paradigm. Often an exact count is not necessary and methods based on stochastic estimates can be utilized to yield rough approximations. This paper examines a number of techniques tailored to this specific task. It reviews standard approaches and explores new ones based on polynomial and rational approximation filtering combined with a stochastic procedure.
AWG-based Non-blocking Clos Networks
Venue: arXiv cs.NI 2014
Year: 2014

The three-stage Clos networks remain the most popular solution to many practical switching systems to date. The aim of this paper is to show that the modular structure of Clos networks is invariant with respect to the technological changes. Due to the wavelength routing property of arrayed-waveguide gratings (AWGs), non-blocking and contention-free wavelength-division-multiplexing (WDM) switches require that two calls carried by the same wavelength must be connected by separated links; otherwise, they must be carried by different wavelengths. Thus, in addition to the non-blocking condition, the challenge of the design of AWG-based multistage switching networks is to scale down the wavelength granularity and to reduce the conversion range of tunable wavelength converters (TWCs). We devise a logic scheme to partition the WDM switch network into wavelength autonomous cells, and show that the wavelength scalability problem can be solved by recursively reusing similar, but smaller, set of wavelengths in different cells. Furthermore, we prove that the rearrangeably non-blocking (RNB) condition and route assignments in these AWG-based three-stage networks are consistent with that of classical Clos networks. Thus, the optimal AWG-based non-blocking Clos networks also can achieve 100% utilization when all input and output wavelength channels are busy.
A Note on Sparsification by Frames
Venue: arXiv cs.IT 2014
Year: 2014

The purpose of this note is to establish a new generalized Dictionary-Restricted Isometry Property (D-RIP) sparsity bound constant for compressed sensing. For fulfilling D-RIP, the constant $δ_k$ is used in the definition: $(1 -δ_k)\|D v\|_2^2 \le \|ΦD v\|_2^2 \le (1 + δ_k)\|D v\|^2$. We prove that signals with $k$-sparse $D$-representation can be reconstructed if $δ_{2k} < \frac{2}3$. The approach in this note can be extended to obtain other D-RIP bounds (i.e., $δ_{tk}$).
Connections Between Construction D and Related Constructions of Lattices
Venue: arXiv cs.IT 2014
Year: 2014

Most practical constructions of lattice codes with high coding gains are multilevel constructions where each level corresponds to an underlying code component. Construction D, Construction D$'$, and Forney's code formula are classical constructions that produce such lattices explicitly from a family of nested binary linear codes. In this paper, we investigate these three closely related constructions along with the recently developed Construction A$'$ of lattices from codes over the polynomial ring $\mathbb{F}_2[u]/u^a$. We show that Construction by Code Formula produces a lattice packing if and only if the nested codes being used are closed under Schur product, thus proving the similarity of Construction D and Construction by Code Formula when applied to Reed-Muller codes. In addition, we relate Construction by Code Formula to Construction A$'$ by finding a correspondence between nested binary codes and codes over $\mathbb{F}_2[u]/u^a$. This proves that any lattice constructible using Construction by Code Formula is also constructible using Construction A$'$. Finally, we show that Construction A$'$ produces a lattice if and only if the corresponding code over $\mathbb{F}_2[u]/u^a$ is closed under shifted Schur product.
Self-stabilizing TDMA Algorithms for Wireless Ad-hoc Networks without External Reference
Venue: arXiv cs.DC 2014
Year: 2014

Time division multiple access (TDMA) is a method for sharing communication media. In wireless communications, TDMA algorithms often divide the radio time into timeslots of uniform size, $ξ$, and then combine them into frames of uniform size, $τ$. We consider TDMA algorithms that allocate at least one timeslot in every frame to every node. Given a maximal node degree, $δ$, and no access to external references for collision detection, time or position, we consider the problem of collision-free self-stabilizing TDMA algorithms that use constant frame size. We demonstrate that this problem has no solution when the frame size is $τ< \max\{2δ,χ_2\}$, where $χ_2$ is the chromatic number for distance-$2$ vertex coloring. As a complement to this lower bound, we focus on proving the existence of collision-free self-stabilizing TDMA algorithms that use constant frame size of $τ$. We consider basic settings (no hardware support for collision detection and no prior clock synchronization), and the collision of concurrent transmissions from transmitters that are at most two hops apart. In the context of self-stabilizing systems that have no external reference, we are the first to study this problem (to the best of our knowledge), and use simulations to show convergence even with computation time uncertainties.
A Low-Dimensional Representation for Robust Partial Isometric Correspondences Computation
Venue: arXiv cs.CV 2014
Year: 2014

Intrinsic isometric shape matching has become the standard approach for pose invariant correspondence estimation among deformable shapes. Most existing approaches assume global consistency, i.e., the metric structure of the whole manifold must not change significantly. While global isometric matching is well understood, only a few heuristic solutions are known for partial matching. Partial matching is particularly important for robustness to topological noise (incomplete data and contacts), which is a common problem in real-world 3D scanner data. In this paper, we introduce a new approach to partial, intrinsic isometric matching. Our method is based on the observation that isometries are fully determined by purely local information: a map of a single point and its tangent space fixes an isometry for both global and the partial maps. From this idea, we develop a new representation for partial isometric maps based on equivalence classes of correspondences between pairs of points and their tangent spaces. From this, we derive a local propagation algorithm that find such mappings efficiently. In contrast to previous heuristics based on RANSAC or expectation maximization, our method is based on a simple and sound theoretical model and fully deterministic. We apply our approach to register partial point clouds and compare it to the state-of-the-art methods, where we obtain significant improvements over global methods for real-world data and stronger guarantees than previous heuristic partial matching algorithms.
On the Complexity of Computing Critical Points with Gröbner Bases
Venue: arXiv cs.SC 2014
Year: 2014

Computing the critical points of a polynomial function $q\in\mathbb Q[X_1,\ldots,X_n]$ restricted to the vanishing locus $V\subset\mathbb R^n$ of polynomials $f_1,\ldots, f_p\in\mathbb Q[X_1,\ldots, X_n]$ is of first importance in several applications in optimization and in real algebraic geometry. These points are solutions of a highly structured system of multivariate polynomial equations involving maximal minors of a Jacobian matrix. We investigate the complexity of solving this problem by using Gröbner basis algorithms under genericity assumptions on the coefficients of the input polynomials. The main results refine known complexity bounds (which depend on the maximum $D=\max(deg(f_1),\ldots,deg(f_p),deg(q))$) to bounds which depend on the list of degrees $(deg(f_1),\ldots,deg(f_p),deg(q))$: we prove that the Gröbner basis computation can be performed in $δ^{O(\log(A)/\log(G))}$ arithmetic operations in $\mathbb Q$, where $δ$ is the algebraic degree of the ideal vanishing on the critical points, and $A$ and $G$ are the arithmetic and geometric average of a multiset constructed from the sequence of degrees. As a by-product, we prove that solving such generic optimization problems with Gröbner bases requires at most $D^{O(n)}$ arithmetic operations in $\mathbb Q$, which meets the best known complexity bound for this problem. Finally, we illustrate these complexity results with experiments, giving evidence that these bounds are relevant for applications.
Enumeration of the adjunctive hierarchy of hereditarily finite sets
Venue: arXiv cs.LO 2014
Year: 2014

Hereditarily finite sets (sets which are finite and have only hereditarily finite sets as members) are basic mathematical and computational objects, and also stand at the basis of some programming languages. This raises the need for efficient representation of such sets, for example by numbers. In 2008, Kirby proposed an adjunctive hierarchy of hereditarily finite sets, based on the fact that they can also be seen as built up from the empty set by repeated adjunction, that is, by the addition of a new single element drawn from the already existing sets to an already existing set. Determining the cardinality $a_n$ of each level of this hierarchy, problem crucial in establishing whether the natural adjunctive hierarchy leads to an efficient encoding by numbers, was left open. In this paper we solve this problem. Our results can be generalized to hereditarily finite sets with atoms, or can be further refined by imposing restrictions on rank, on cardinality, or on the maximum level from where the new adjoined element can be drawn. We also show that $a_n$ satisfies the asymptotic formula $a_n = C^{2^n} + O(C^{2^{n-1}})$, for a constant $C \approx 1.3399$, which is a too fast asymptotic growth for practical purposes. We thus propose a very natural variant of the adjunctive hierarchy, whose asymptotic behavior we prove to be $Θ(2^n)$. To our knowledge, this is the first result of this kind.
Indexing by Latent Dirichlet Allocation and Ensemble Model
Venue: arXiv cs.IR 2014
Year: 2014

The contribution of this paper is two-fold. First, we present Indexing by Latent Dirichlet Allocation (LDI), an automatic document indexing method. The probability distributions in LDI utilize those in Latent Dirichlet Allocation (LDA), a generative topic model that has been previously used in applications for document retrieval tasks. However, the ad hoc applications, or their variants with smoothing techniques as prompted by previous studies in LDA-based language modeling, result in unsatisfactory performance as the document representations do not accurately reflect concept space. To improve performance, we introduce a new definition of document probability vectors in the context of LDA and present a novel scheme for automatic document indexing based on LDA. Second, we propose an Ensemble Model (EnM) for document retrieval. The EnM combines basis indexing models by assigning different weights and attempts to uncover the optimal weights to maximize the Mean Average Precision (MAP). To solve the optimization problem, we propose an algorithm, EnM.B, which is derived based on the boosting method. The results of our computational experiments on benchmark data sets indicate that both the proposed approaches are viable options for document retrieval.
Attribute-Efficient Evolvability of Linear Functions
Venue: arXiv cs.LG 2014
Year: 2014

In a seminal paper, Valiant (2006) introduced a computational model for evolution to address the question of complexity that can arise through Darwinian mechanisms. Valiant views evolution as a restricted form of computational learning, where the goal is to evolve a hypothesis that is close to the ideal function. Feldman (2008) showed that (correlational) statistical query learning algorithms could be framed as evolutionary mechanisms in Valiant's model. P. Valiant (2012) considered evolvability of real-valued functions and also showed that weak-optimization algorithms that use weak-evaluation oracles could be converted to evolutionary mechanisms. In this work, we focus on the complexity of representations of evolutionary mechanisms. In general, the reductions of Feldman and P. Valiant may result in intermediate representations that are arbitrarily complex (polynomial-sized circuits). We argue that biological constraints often dictate that the representations have low complexity, such as constant depth and fan-in circuits. We give mechanisms for evolving sparse linear functions under a large class of smooth distributions. These evolutionary algorithms are attribute-efficient in the sense that the size of the representations and the number of generations required depend only on the sparsity of the target function and the accuracy parameter, but have no dependence on the total number of attributes.
How to Identify an Infection Source with Limited Observations
Venue: arXiv cs.SI 2014
Year: 2014

A rumor spreading in a social network or a disease propagating in a community can be modeled as an infection spreading in a network. Finding the infection source is a challenging problem, which is made more difficult in many applications where we have access only to a limited set of observations. We consider the problem of estimating an infection source for a Susceptible-Infected model, in which not all infected nodes can be observed. When the network is a tree, we show that an estimator for the source node associated with the most likely infection path that yields the limited observations is given by a Jordan center, i.e., a node with minimum distance to the set of observed infected nodes. We also propose approximate source estimators for general networks. Simulation results on various synthetic networks and real world networks suggest that our estimators perform better than distance, closeness, and betweenness centrality based heuristics.
A New Class of Index Coding Instances Where Linear Coding is Optimal
Venue: arXiv cs.IT 2014
Year: 2014

We study index-coding problems (one sender broadcasting messages to multiple receivers) where each message is requested by one receiver, and each receiver may know some messages a priori. This type of index-coding problems can be fully described by directed graphs. The aim is to find the minimum codelength that the sender needs to transmit in order to simultaneously satisfy all receivers' requests. For any directed graph, we show that if a maximum acyclic induced subgraph (MAIS) is obtained by removing two or fewer vertices from the graph, then the minimum codelength (i.e., the solution to the index-coding problem) equals the number of vertices in the MAIS, and linear codes are optimal for this index-coding problem. Our result increases the set of index-coding problems for which linear index codes are proven to be optimal.
Multi-layer graph analysis for dynamic social networks
Venue: arXiv cs.SI 2014
Year: 2014

Modern social networks frequently encompass multiple distinct types of connectivity information; for instance, explicitly acknowledged friend relationships might complement behavioral measures that link users according to their actions or interests. One way to represent these networks is as multi-layer graphs, where each layer contains a unique set of edges over the same underlying vertices (users). Edges in different layers typically have related but distinct semantics; depending on the application multiple layers might be used to reduce noise through averaging, to perform multifaceted analyses, or a combination of the two. However, it is not obvious how to extend standard graph analysis techniques to the multi-layer setting in a flexible way. In this paper we develop latent variable models and methods for mining multi-layer networks for connectivity patterns based on noisy data.
Anticipatory Buffer Control and Quality Selection for Wireless Video Streaming
Venue: arXiv cs.NI 2014
Year: 2014

Video streaming is in high demand by mobile users, as recent studies indicate. In cellular networks, however, the unreliable wireless channel leads to two major problems. Poor channel states degrade video quality and interrupt the playback when a user cannot sufficiently fill its local playout buffer: buffer underruns occur. In contrast to that, good channel conditions cause common greedy buffering schemes to pile up very long buffers. Such over-buffering wastes expensive wireless channel capacity. To keep buffering in balance, we employ a novel approach. Assuming that we can predict data rates, we plan the quality and download time of the video segments ahead. This anticipatory scheduling avoids buffer underruns by downloading a large number of segments before a channel outage occurs, without wasting wireless capacity by excessive buffering. We formalize this approach as an optimization problem and derive practical heuristics for segmented video streaming protocols (e.g., HLS or MPEG DASH). Simulation results and testbed measurements show that our solution essentially eliminates playback interruptions without significantly decreasing video quality.