OpenRaiser/Intern-Atlas huggingface dataset:
Down the Rabbit Hole: Robust Proximity Search and Density Estimation in Sublinear Space
Venue: arXiv cs.CG 2013
Year: 2013

For a set of $n$ points in $\Re^d$, and parameters $k$ and $\eps$, we present a data structure that answers $(1+\eps,k)$-\ANN queries in logarithmic time. Surprisingly, the space used by the data-structure is $\Otilde (n /k)$; that is, the space used is sublinear in the input size if $k$ is sufficiently large. Our approach provides a novel way to summarize geometric data, such that meaningful proximity queries on the data can be carried out using this sketch. Using this, we provide a sublinear space data-structure that can estimate the density of a point set under various measures, including: \begin{inparaenum}[(i)] \item sum of distances of $k$ closest points to the query point, and \item sum of squared distances of $k$ closest points to the query point. \end{inparaenum} Our approach generalizes to other distance based estimation of densities of similar flavor. We also study the problem of approximating some of these quantities when using sampling. In particular, we show that a sample of size $\Otilde (n /k)$ is sufficient, in some restricted cases, to estimate the above quantities. Remarkably, the sample size has only linear dependency on the dimension.
Matrix Inversion Using Cholesky Decomposition
Venue: arXiv cs.MS 2013
Year: 2013

In this paper we present a method for matrix inversion based on Cholesky decomposition with reduced number of operations by avoiding computation of intermediate results; further, we use fixed point simulations to compare the numerical accuracy of the method.
Spatial Throughput of Mobile Ad Hoc Networks Powered by Energy Harvesting
Venue: arXiv cs.IT 2013
Year: 2013

Designing mobiles to harvest ambient energy such as kinetic activities or electromagnetic radiation will enable wireless networks to be self sustaining besides alleviating global warming. In this paper, the spatial throughput of a mobile ad hoc network powered by energy harvesting is analyzed using a stochastic-geometry model. In this model, transmitters are distributed as a Poisson point process and energy arrives at each transmitter randomly with a uniform average rate called the energy arrival rate; upon harvesting sufficient energy, each transmitter transmits with fixed power to an intended receiver under an outage-probability constraint for a target signal-to-interference-and-noise ratio. It is assumed that transmitters store energy in batteries with infinite capacity. By applying the random-walk theory, the probability that a transmitter transmits, called the transmission probability, is proved to be equal to one if the energy-arrival rate exceeds transmission power or otherwise is equal to their ratio. This result and tools from stochastic geometry are applied to maximize the network throughput for a given energy-arrival rate by optimizing transmission power. The maximum network throughput is shown to be proportional to the optimal transmission probability, which is equal to one if the transmitter density is below a derived function of the energy-arrival rate or otherwise is smaller than one and solves a given polynomial equation. Last, the limits of the maximum network throughput are obtained for the extreme cases of high energy-arrival rates and dense networks.
Information-Theoretically Optimal Compressed Sensing via Spatial Coupling and Approximate Message Passing
Venue: arXiv cs.IT 2013
Year: 2013

We study the compressed sensing reconstruction problem for a broad class of random, band-diagonal sensing matrices. This construction is inspired by the idea of spatial coupling in coding theory. As demonstrated heuristically and numerically by Krzakala et al. \cite{KrzakalaEtAl}, message passing algorithms can effectively solve the reconstruction problem for spatially coupled measurements with undersampling rates close to the fraction of non-zero coordinates. We use an approximate message passing (AMP) algorithm and analyze it through the state evolution method. We give a rigorous proof that this approach is successful as soon as the undersampling rate $δ$ exceeds the (upper) Rényi information dimension of the signal, $\uRenyi(p_X)$. More precisely, for a sequence of signals of diverging dimension $n$ whose empirical distribution converges to $p_X$, reconstruction is with high probability successful from $\uRenyi(p_X)\, n+o(n)$ measurements taken according to a band diagonal matrix. For sparse signals, i.e., sequences of dimension $n$ and $k(n)$ non-zero entries, this implies reconstruction from $k(n)+o(n)$ measurements. For `discrete' signals, i.e., signals whose coordinates take a fixed finite set of values, this implies reconstruction from $o(n)$ measurements. The result is robust with respect to noise, does not apply uniquely to random signals, but requires the knowledge of the empirical distribution of the signal $p_X$.
Refactoring Composite to Visitor and Inverse Transformation in Java
Venue: arXiv cs.SE 2013
Year: 2013

We describe how to use refactoring tools to transform a Java program conforming to the Composite design pattern into a program conforming to the Visitor design pattern with the same external behavior. We also describe the inverse transformation. We use the refactoring tool provided by IntelliJ IDEA.
Tight Bounds for Distributed Functional Monitoring
Venue: arXiv cs.DS 2013
Year: 2013

We resolve several fundamental questions in the area of distributed functional monitoring, initiated by Cormode, Muthukrishnan, and Yi (SODA, 2008). In this model there are $k$ sites each tracking their input and communicating with a central coordinator that continuously maintain an approximate output to a function $f$ computed over the union of the inputs. The goal is to minimize the communication. We show the randomized communication complexity of estimating the number of distinct elements up to a $1+\eps$ factor is $\tildeΩ(k/\eps^2)$, improving the previous $Ω(k + 1/\eps^2)$ bound and matching known upper bounds up to a logarithmic factor. For the $p$-th frequency moment $F_p$, $p > 1$, we improve the previous $Ω(k + 1/\eps^2)$ communication bound to $\tildeΩ(k^{p-1}/\eps^2)$. We obtain similar improvements for heavy hitters, empirical entropy, and other problems. We also show that we can estimate $F_p$, for any $p > 1$, using $\tilde{O}(k^{p-1}\poly(\eps^{-1}))$ communication. This greatly improves upon the previous $\tilde{O}(k^{2p+1}N^{1-2/p} \poly(\eps^{-1}))$ bound of Cormode, Muthukrishnan, and Yi for general $p$, and their $\tilde{O}(k^2/\eps + k^{1.5}/\eps^3)$ bound for $p = 2$. For $p = 2$, our bound resolves their main open question. Our lower bounds are based on new direct sum theorems for approximate majority, and yield significant improvements to problems in the data stream model, improving the bound for estimating $F_p, p > 2,$ in $t$ passes from $\tildeΩ(n^{1-2/p}/(\eps^{2/p} t))$ to $\tildeΩ(n^{1-2/p}/(\eps^{4/p} t))$, giving the first bound for estimating $F_0$ in $t$ passes of $Ω(1/(\eps^2 t))$ bits of space that does not use the gap-hamming problem.
On the Hyperbolicity of Small-World and Tree-Like Random Graphs
Venue: arXiv cs.SI 2013
Year: 2013

Hyperbolicity is a property of a graph that may be viewed as being a "soft" version of a tree, and recent empirical and theoretical work has suggested that many graphs arising in Internet and related data applications have hyperbolic properties. We consider Gromov's notion of δ-hyperbolicity, and establish several results for small-world and tree-like random graph models. First, we study the hyperbolicity of Kleinberg small-world random graphs and show that the hyperbolicity of these random graphs is not significantly improved comparing to graph diameter even when it greatly improves decentralized navigation. Next we study a class of tree-like graphs called ringed trees that have constant hyperbolicity. We show that adding random links among the leaves similar to the small-world graph constructions may easily destroy the hyperbolicity of the graphs, except for a class of random edges added using an exponentially decaying probability function based on the ring distance among the leaves. Our study provides one of the first significant analytical results on the hyperbolicity of a rich class of random graphs, which shed light on the relationship between hyperbolicity and navigability of random graphs, as well as on the sensitivity of hyperbolic δ to noises in random graphs.
Comparison of Persistent Homologies for Vector Functions: from continuous to discrete and back
Venue: arXiv cs.CG 2013
Year: 2013

The theory of multidimensional persistent homology was initially developed in the discrete setting, and involved the study of simplicial complexes filtered through an ordering of the simplices. Later, stability properties of multidimensional persistence have been proved to hold when topological spaces are filtered by continuous functions, i.e. for continuous data. This paper aims to provide a bridge between the continuous setting, where stability properties hold, and the discrete setting, where actual computations are carried out. More precisely, a stability preserving method is developed to compare rank invariants of vector functions obtained from discrete data. These advances confirm that multidimensional persistent homology is an appropriate tool for shape comparison in computer vision and computer graphics applications. The results are supported by numerical tests.
Multi-User Scheduling in the 3GPP LTE Cellular Uplink
Venue: arXiv cs.NI 2013
Year: 2013

In this paper, we consider resource allocation in the 3GPP Long Term Evolution (LTE) cellular uplink, which will be the most widely deployed next generation cellular uplink. The key features of the 3GPP LTE uplink (UL) are that it is based on a modified form of the orthogonal frequency division multiplexing based multiple access (OFDMA) which enables channel dependent frequency selective scheduling, and that it allows for multi-user (MU) scheduling wherein multiple users can be assigned the same time-frequency resource. In addition to the considerable spectral efficiency improvements that are possible by exploiting these two features, the LTE UL allows for transmit antenna selection together with the possibility to employ advanced receivers at the base-station, which promise further gains. However, several practical constraints that seek to maintain a low signaling overhead, are also imposed. In this paper, we show that the resulting resource allocation problem is APX-hard and then propose a local ratio test (LRT) based constant-factor polynomial-time approximation algorithm. We then propose two enhancements to this algorithm as well as a sequential LRT based MU scheduling algorithm that offers a constant-factor approximation and is another useful choice in the complexity versus performance tradeoff. Further, user pre-selection, wherein a smaller pool of good users is pre-selected and a sophisticated scheduling algorithm is then employed on the selected pool, is also examined. We suggest several such user pre-selection algorithms, some of which are shown to offer constant-factor approximations to the pre-selection problem. Detailed evaluations reveal that the proposed algorithms and their enhancements offer significant gains.
Participatory Privacy: Enabling Privacy in Participatory Sensing
Venue: arXiv cs.CR 2013
Year: 2013

Participatory Sensing is an emerging computing paradigm that enables the distributed collection of data by self-selected participants. It allows the increasing number of mobile phone users to share local knowledge acquired by their sensor-equipped devices, e.g., to monitor temperature, pollution level or consumer pricing information. While research initiatives and prototypes proliferate, their real-world impact is often bounded to comprehensive user participation. If users have no incentive, or feel that their privacy might be endangered, it is likely that they will not participate. In this article, we focus on privacy protection in Participatory Sensing and introduce a suitable privacy-enhanced infrastructure. First, we provide a set of definitions of privacy requirements for both data producers (i.e., users providing sensed information) and consumers (i.e., applications accessing the data). Then, we propose an efficient solution designed for mobile phone users, which incurs very low overhead. Finally, we discuss a number of open problems and possible research directions.
Constraint Propagation as Information Maximization
Venue: arXiv cs.AI 2013
Year: 2013

This paper draws on diverse areas of computer science to develop a unified view of computation: (1) Optimization in operations research, where a numerical objective function is maximized under constraints, is generalized from the numerical total order to a non-numerical partial order that can be interpreted in terms of information. (2) Relations are generalized so that there are relations of which the constituent tuples have numerical indexes, whereas in other relations these indexes are variables. The distinction is essential in our definition of constraint satisfaction problems. (3) Constraint satisfaction problems are formulated in terms of semantics of conjunctions of atomic formulas of predicate logic. (4) Approximation structures, which are available for several important domains, are applied to solutions of constraint satisfaction problems. As application we treat constraint satisfaction problems over reals. These cover a large part of numerical analysis, most significantly nonlinear equations and inequalities. The chaotic algorithm analyzed in the paper combines the efficiency of floating-point computation with the correctness guarantees of arising from our logico-mathematical model of constraint-satisfaction problems.
Multiple-Source Shortest Paths in Embedded Graphs
Venue: arXiv cs.DS 2013
Year: 2013

Let G be a directed graph with n vertices and non-negative weights in its directed edges, embedded on a surface of genus g, and let f be an arbitrary face of G. We describe a randomized algorithm to preprocess the graph in O(gn log n) time with high probability, so that the shortest-path distance from any vertex on the boundary of f to any other vertex in G can be retrieved in O(log n) time. Our result directly generalizes the O(n log n)-time algorithm of Klein [SODA 2005] for multiple-source shortest paths in planar graphs. Intuitively, our preprocessing algorithm maintains a shortest-path tree as its source point moves continuously around the boundary of f. As an application of our algorithm, we describe algorithms to compute a shortest non-contractible or non-separating cycle in embedded, undirected graphs in O(g^2 n log n) time with high probability. Our high-probability time bounds hold in the worst-case for generic edge weights, or with an additional O(log n) factor for arbitrary edge weights.
Core-Periphery Structure in Networks
Venue: arXiv cs.SI 2013
Year: 2013

Intermediate-scale (or `meso-scale') structures in networks have received considerable attention, as the algorithmic detection of such structures makes it possible to discover network features that are not apparent either at the local scale of nodes and edges or at the global scale of summary statistics. Numerous types of meso-scale structures can occur in networks, but investigations of such features have focused predominantly on the identification and study of community structure. In this paper, we develop a new method to investigate the meso-scale feature known as core-periphery structure, which entails identifying densely-connected core nodes and sparsely-connected periphery nodes. In contrast to communities, the nodes in a core are also reasonably well-connected to those in the periphery. Our new method of computing core-periphery structure can identify multiple cores in a network and takes different possible cores into account. We illustrate the differences between our method and several existing methods for identifying which nodes belong to a core, and we use our technique to examine core-periphery structure in examples of friendship, collaboration, transportation, and voting networks.
Worst-Case Additive Noise in Wireless Networks
Venue: arXiv cs.IT 2013
Year: 2013

A classical result in Information Theory states that the Gaussian noise is the worst-case additive noise in point-to-point channels, meaning that, for a fixed noise variance, the Gaussian noise minimizes the capacity of an additive noise channel. In this paper, we significantly generalize this result and show that the Gaussian noise is also the worst-case additive noise in wireless networks with additive noises that are independent from the transmit signals. More specifically, we show that, if we fix the noise variance at each node, then the capacity region with Gaussian noises is a subset of the capacity region with any other set of noise distributions. We prove this result by showing that a coding scheme that achieves a given set of rates on a network with Gaussian additive noises can be used to construct a coding scheme that achieves the same set of rates on a network that has the same topology and traffic demands, but with non-Gaussian additive noises.
On the complexity of solving linear congruences and computing nullspaces modulo a constant
Venue: arXiv cs.CC 2013
Year: 2013

We consider the problems of determining the feasibility of a linear congruence, producing a solution to a linear congruence, and finding a spanning set for the nullspace of an integer matrix, where each problem is considered modulo an arbitrary constant k>1. These problems are known to be complete for the logspace modular counting classes {Mod_k L} = {coMod_k L} in special case that k is prime (Buntrock et al, 1992). By considering variants of standard logspace function classes --- related to #L and functions computable by UL machines, but which only characterize the number of accepting paths modulo k --- we show that these problems of linear algebra are also complete for {coMod_k L} for any constant k>1. Our results are obtained by defining a class of functions FUL_k which are low for {Mod_k L} and {coMod_k L} for k>1, using ideas similar to those used in the case of k prime in (Buntrock et al, 1992) to show closure of Mod_k L under NC^1 reductions (including {Mod_k L} oracle reductions). In addition to the results above, we briefly consider the relationship of the class FUL_k for arbitrary moduli k to the class {F.coMod_k L} of functions whose output symbols are verifiable by {coMod_k L} algorithms; and consider what consequences such a comparison may have for oracle closure results of the form {Mod_k L}^{Mod_k L} = {Mod_k L} for composite k.
Asynchronous Signal Passing for Tile Self-Assembly: Fuel Efficient Computation and Efficient Assembly of Shapes
Venue: arXiv cs.ET 2013
Year: 2013

In this paper we demonstrate the power of a model of tile self-assembly based on active glues which can dynamically change state. We formulate the Signal-passing Tile Assembly Model (STAM), based on the model of Padilla, Liu, and Seeman to be asynchronous, allowing any action of turning a glue on or off, attaching a new tile, or breaking apart an assembly to happen in any order. Within this highly generalized model we provide three new solutions to tile self-assembly problems that have been addressed within the abstract Tile Assembly Model and its variants, showing that signal passing tiles allow for substantial improvement across multiple complexity metrics. Our first result utilizes a recursive assembly process to achieve tile-type efficient assembly of linear structures, using provably fewer tile types than what is possible in standard tile assembly models. Our second system of signal-passing tiles simulates any Turing machine with high fuel efficiency by using only a constant number of tiles per computation step. Our third system assembles the discrete Sierpinski triangle, demonstrating that this pattern can be strictly self-assembled within the STAM. This result is of particular interest in that it is known that this pattern cannot self-assemble within a number of well studied tile self-assembly models. Notably, all of our constructions are at temperature 1, further demonstrating that signal-passing confers the power to bypass many restrictions found in standard tile assembly models.
Development Trends in Steganography
Venue: arXiv cs.MM 2013
Year: 2013

Steganography is a general term referring to all methods for the embedding of additional secret content into some form of carrier, with the aim of concealment of the introduced alterations. The choice of the carrier is nearly unlimited, it may be an ancient piece of parchment, as well as a network protocol header. Inspired by biological phenomena, adopted by man in the ancient times, it has been developed over the ages. Present day steganographic methods are far more sophisticated than their ancient predecessors, but the main principles have remained unchanged. They typically rely on the utilization of digital media files or network protocols as a carrier, in which secret data is embedded. This paper presents the evolution of the hidden data carrier from the ancient times till the present day and pinpoints the observed development trends, with special emphasis on network steganography.
Monobit Digital Receivers for QPSK: Design, Analysis and Performance
Venue: arXiv cs.IT 2013
Year: 2013

Future communication system requires large bandwidth to achieve high data rate up to multigigabit/ sec, which makes analog-to-digital (ADC) become a key bottleneck for the implementation of digital receivers due to its high complexity and large power consumption. Therefore, monobit receivers for BPSK have been proposed to address this problem. In this work, QPSK modulation is considered for higher data rate. First, the optimal receiver based on monobit ADC with Nyquist sampling is derived, and its corresponding performance in the form of deflection ratio is calculated. Then a suboptimal but more practical monobit receiver is obtained, along with iterative demodulation and small sample removal. The effect of the imbalances between the In-phase (I) and Quadrature-phase (Q) branches, including the amplitude and phase imbalances, is carefully investigated too. To combat the performance loss caused by IQ imbalances, monobit receivers based on double training sequences are proposed. Numerical simulations show that the low-complexity suboptimal receiver suffers only 3dB signal to noise ratio (SNR) loss in AWGN channels and 1dB SNR loss in multipath static channels compared with the matched filter based monobit receiver with full channel state information (CSI). The impact of the phase difference between the transmitter and receiver is presented. It is observed that the performance degradation caused by the amplitude imbalance is negligible. Receivers based on double training sequences can efficiently compensate the performance loss in AWGN channel. Thanks to the diversity offered by the multipath, the effect of imbalances on monobit receivers in fading channels is slight. I
Limits of Reliable Communication with Low Probability of Detection on AWGN Channels
Venue: arXiv cs.IT 2013
Year: 2013

We present a square root limit on the amount of information transmitted reliably and with low probability of detection (LPD) over additive white Gaussian noise (AWGN) channels. Specifically, if the transmitter has AWGN channels to an intended receiver and a warden, both with non-zero noise power, we prove that $o(\sqrt{n})$ bits can be sent from the transmitter to the receiver in $n$ channel uses while lower-bounding $α+β\geq1-ε$ for any $ε>0$, where $α$ and $β$ respectively denote the warden's probabilities of a false alarm when the sender is not transmitting and a missed detection when the sender is transmitting. Moreover, in most practical scenarios, a lower bound on the noise power on the channel between the transmitter and the warden is known and $O(\sqrt{n})$ bits can be sent in $n$ LPD channel uses. Conversely, attempting to transmit more than $O(\sqrt{n})$ bits either results in detection by the warden with probability one or a non-zero probability of decoding error at the receiver as $n\rightarrow\infty$.