OpenRaiser/Intern-Atlas huggingface dataset:
The Complexity of Simultaneous Geometric Graph Embedding
Venue: arXiv cs.CG 2015
Year: 2015

Given a collection of planar graphs $G_1,\dots,G_k$ on the same set $V$ of $n$ vertices, the simultaneous geometric embedding (with mapping) problem, or simply $k$-SGE, is to find a set $P$ of $n$ points in the plane and a bijection $ϕ: V \to P$ such that the induced straight-line drawings of $G_1,\dots,G_k$ under $ϕ$ are all plane. This problem is polynomial-time equivalent to weak rectilinear realizability of abstract topological graphs, which Kynčl (doi:10.1007/s00454-010-9320-x) proved to be complete for $\exists\mathbb{R}$, the existential theory of the reals. Hence the problem $k$-SGE is polynomial-time equivalent to several other problems in computational geometry, such as recognizing intersection graphs of line segments or finding the rectilinear crossing number of a graph. We give an elementary reduction from the pseudoline stretchability problem to $k$-SGE, with the property that both numbers $k$ and $n$ are linear in the number of pseudolines. This implies not only the $\exists\mathbb{R}$-hardness result, but also a $2^{2^{Ω(n)}}$ lower bound on the minimum size of a grid on which any such simultaneous embedding can be drawn. This bound is tight. Hence there exists such collections of graphs that can be simultaneously embedded, but every simultaneous drawing requires an exponential number of bits per coordinates. The best value that can be extracted from Kynčl's proof is only $2^{2^{Ω(\sqrt{n})}}$.
Scalable Cost-Aware Multi-Way Influence Maximization
Venue: arXiv cs.DS 2015
Year: 2015

Viral marketing is different from other marketing strategies since it leverages the influence power in intimate relationship, e.g., close friends, family members, couples. Due to the development and popularity of social networking services, such as Facebook, Twitter, and Pinterest, the new notion of "social media marketing" has appeared in recent years and presents new opportunities for enabling large-scale and prevalent viral marketing online. To boost the growth of their sales, business is embracing social media in a big way. According to USA Today, the sales of software to run corporate social networks will grow 61\% a year and be a $6.4$ billion business by 2016.
Diagnosis of Multiple Faults: A Sensitivity Analysis
Venue: arXiv cs.AI 2015
Year: 2015

We compare the diagnostic accuracy of three diagnostic inference models: the simple Bayes model, the multimembership Bayes model, which is isomorphic to the parallel combination function in the certainty-factor model, and a model that incorporates the noisy OR-gate interaction. The comparison is done on 20 clinicopathological conference (CPC) cases from the American Journal of Medicine-challenging cases describing actual patients often with multiple disorders. We find that the distributions produced by the noisy OR model agree most closely with the gold-standard diagnoses, although substantial differences exist between the distributions and the diagnoses. In addition, we find that the multimembership Bayes model tends to significantly overestimate the posterior probabilities of diseases, whereas the simple Bayes model tends to significantly underestimate the posterior probabilities. Our results suggest that additional work to refine the noisy OR model for internal medicine will be worthwhile.
Exact simulation of the GHZ distribution
Venue: arXiv cs.IT 2015
Year: 2015

John Bell has shown that the correlations entailed by quantum mechanics cannot be reproduced by a classical process involving non-communicating parties. But can they be simulated with the help of bounded communication? This problem has been studied for more than two decades and it is now well understood in the case of bipartite entanglement. However, the issue was still widely open for multipartite entanglement, even for the simplest case, which is the tripartite Greenberger-Horne-Zeilinger (GHZ) state. We give an exact simulation of arbitrary independent von Neumann measurements on general n-partite GHZ states. Our protocol requires O(n^2) bits of expected communication between the parties, and O(n log n) expected time is sufficient to carry it out in parallel. Furthermore, we need only an expectation of O(n) independent unbiased random bits, with no need for the generation of continuous real random variables nor prior shared random variables. In the case of equatorial measurements, we improve on the prior art with a protocol that needs only O(n log n) bits of communication and O(log^2 n) parallel time. At the cost of a slight increase in the number of bits communicated, these tasks can be accomplished with a constant expected number of rounds.
Bicompletions of distance matrices
Venue: arXiv cs.LO 2015
Year: 2015

In the practice of information extraction, the input data are usually arranged into pattern matrices, and analyzed by the methods of linear algebra and statistics, such as principal component analysis. In some applications, the tacit assumptions of these methods lead to wrong results. The usual reason is that the matrix composition of linear algebra presents information as flowing in waves, whereas it sometimes flows in particles, which seek the shortest paths. This wave-particle duality in computation and information processing has been originally observed by Abramsky. In this paper we pursue a particle view of information, formalized in *distance spaces*, which generalize metric spaces, but are slightly less general than Lawvere's *generalized metric spaces*. In this framework, the task of extracting the 'principal components' from a given matrix of data boils down to a bicompletio}, in the sense of enriched category theory. We describe the bicompletion construction for distance matrices. The practical goal that motivates this research is to develop a method to estimate the hardness of attack constructions in security.
Recovery of Sparse Signals via Generalized Orthogonal Matching Pursuit: A New Analysis
Venue: arXiv cs.IT 2015
Year: 2015

As an extension of orthogonal matching pursuit (OMP) improving the recovery performance of sparse signals, generalized OMP (gOMP) has recently been studied in the literature. In this paper, we present a new analysis of the gOMP algorithm using restricted isometry property (RIP). We show that if the measurement matrix $\mathbfΦ \in \mathcal{R}^{m \times n}$ satisfies the RIP with $$δ_{\max \left\{9, S + 1 \right\}K} \leq \frac{1}{8},$$ then gOMP performs stable reconstruction of all $K$-sparse signals $\mathbf{x} \in \mathcal{R}^n$ from the noisy measurements $\mathbf{y} = \mathbf{Φx} + \mathbf{v}$ within $\max \left\{K, \left\lfloor \frac{8K}{S} \right\rfloor \right\}$ iterations where $\mathbf{v}$ is the noise vector and $S$ is the number of indices chosen in each iteration of the gOMP algorithm. For Gaussian random measurements, our results indicate that the number of required measurements is essentially $m = \mathcal{O}(K \log \frac{n}{K})$, which is a significant improvement over the existing result $m = \mathcal{O}(K^2 \log \frac{n}{K})$, especially for large $K$.
Power of the interactive proof systems with verifiers modeled by semi-quantum two-way finite automata
Venue: arXiv cs.CC 2015
Year: 2015

In this paper we explore the power of AM for the case that verifiers are {\em two-way finite automata with quantum and classical states} (2QCFA)--introduced by Ambainis and Watrous in 2002--and the communications are classical. It is of interest to consider AM with such "semi-quantum" verifiers because they use only limited quantum resources. Our main result is that such Quantum Arthur-Merlin proof systems (QAM(2QCFA)) with polynomial expected running time are more powerful than in the case verifiers are two-way probabilistic finite automata (AM(2PFA)) with polynomial expected running time. Moreover, we prove that there is a language which can be recognized by an exponential expected running time QAM(2QCFA), but can not be recognized by any AM(2PFA), and that the NP-complete language $L_{knapsack}$ can also be recognized by a QAM(2QCFA) working only on quantum pure states using unitary operators.
Adaptive Video Streaming for Wireless Networks with Multiple Users and Helpers
Venue: arXiv cs.NI 2015
Year: 2015

We consider the optimal design of a scheduling policy for adaptive video streaming in a wireless network formed by several users and helpers. A feature of such networks is that any user is typically in the range of multiple helpers. Hence, in order to cope with user-helper association, load balancing and inter-cell interference, an efficient streaming policy should allow the users to dynamically select the helper node to download from, and determine adaptively the video quality level of the download. In order to obtain a tractable formulation, we follow a "divide and conquer" approach: i) Assuming that each video packet (chunk) is delivered within its playback delay ("smooth streaming regime"), the problem is formulated as a network utility maximization (NUM), subject to queue stability, where the network utility function is a concave and componentwise non-decreasing function of the users' video quality measure. ii) We solve the NUM problem by using a Lyapunov Drift Plus Penalty approach, obtaining a scheme that naturally decomposes into two sub-policies referred to as "congestion control" (adaptive video quality and helper station selection) and "transmission scheduling" (dynamic allocation of the helper-user physical layer transmission rates).Our solution is provably optimal with respect to the proposed NUM problem, in a strong per-sample path sense. iii) Finally, we propose a method to adaptively estimate the maximum queuing delays, such that each user can calculate its pre-buffering and re-buffering time in order to cope with the fluctuations of the queuing delays. Through simulations, we evaluate the performance of the proposed algorithm under realistic assumptions of a network with densely deployed helper nodes, and demonstrate the per-sample path optimality of the proposed solution by considering a non-stationary non-ergodic scenario with user mobility, VBR video coding.
Local Correctability of Expander Codes
Venue: arXiv cs.IT 2015
Year: 2015

In this work, we present the first local-decoding algorithm for expander codes. This yields a new family of constant-rate codes that can recover from a constant fraction of errors in the codeword symbols, and where any symbol of the codeword can be recovered with high probability by reading $N^ε$ symbols from the corrupted codeword, where $N$ is the block-length of the code. Expander codes, introduced by Sipser and Spielman, are formed from an expander graph $G = (V,E)$ of degree $d$, and an inner code of block-length $d$ over an alphabet $Σ$. Each edge of the expander graph is associated with a symbol in $Σ$. A string in $Σ^{E}$ will be a codeword if for each vertex in $V$, the symbols on the adjacent edges form a codeword in the inner code. We show that if the inner code has a smooth reconstruction algorithm in the noiseless setting, then the corresponding expander code has an efficient local-correction algorithm in the noisy setting. Instantiating our construction with inner codes based on finite geometries, we obtain novel locally decodable codes with rate approaching one. This provides an alternative to the multiplicity codes of Kopparty, Saraf and Yekhanin (STOC '11) and the lifted codes of Guo, Kopparty and Sudan (ITCS '13).
Quantum Image Representation Through Two-Dimensional Quantum States and Normalized Amplitude
Venue: arXiv cs.MM 2015
Year: 2015

We propose a novel method for image representation in quantum computers, which uses the two-dimensional (2-D) quantum states to locate each pixel in an image through row-location and column-location vectors for identifying each pixel location. The quantum state of an image is the linear superposition of the tensor product of the m-qubits row-location vector and the n-qubits column-location vector of each pixel. It enables the natural quantum representation of rectangular images that other methods lack. The amplitude/intensity of each pixel is incorporated into the coefficient values of the pixel's quantum state, without using any qubits. Due to the fact that linear superposition, tensor product and qubits form the fundamental basis of quantum computing, the proposed method presents the machine level representation of images on quantum computers. Unlike other methods, this method is a pure quantum representation without any classical components.
Riemannian metrics for neural networks II: recurrent networks and learning symbolic data sequences
Venue: arXiv cs.NE 2015
Year: 2015

Recurrent neural networks are powerful models for sequential data, able to represent complex dependencies in the sequence that simpler models such as hidden Markov models cannot handle. Yet they are notoriously hard to train. Here we introduce a training procedure using a gradient ascent in a Riemannian metric: this produces an algorithm independent from design choices such as the encoding of parameters and unit activities. This metric gradient ascent is designed to have an algorithmic cost close to backpropagation through time for sparsely connected networks. We use this procedure on gated leaky neural networks (GLNNs), a variant of recurrent neural networks with an architecture inspired by finite automata and an evolution equation inspired by continuous-time networks. GLNNs trained with a Riemannian gradient are demonstrated to effectively capture a variety of structures in synthetic problems: basic block nesting as in context-free grammars (an important feature of natural languages, but difficult to learn), intersections of multiple independent Markov-type relations, or long-distance relationships such as the distant-XOR problem. This method does not require adjusting the network structure or initial parameters: the network used is a sparse random graph and the initialization is identical for all problems considered.
Robust multirobot coordination using priority encoded homotopic constraints
Venue: arXiv cs.RO 2015
Year: 2015

We study the problem of coordinating multiple robots along fixed geometric paths. Our contribution is threefold. First we formalize the intuitive concept of priorities as a binary relation induced by a feasible coordination solution, without excluding the case of robots following each other on the same geometric path. Then we prove that two paths in the coordination space are continuously deformable into each other if and only if they induce the \emph{same priority graph}, that is, the priority graph uniquely encodes homotopy classes of coordination solutions. Finally, we give a simple control law allowing to safely navigate into homotopy classes \emph{under kinodynamic constraints} even in the presence of unexpected events, such as a sudden robot deceleration without notice. It appears the freedom within homotopy classes allows to much deviate from any pre-planned trajectory without ever colliding nor having to re-plan the assigned priorities.
CSMA using the Bethe Approximation: Scheduling and Utility Maximization
Venue: arXiv cs.NI 2015
Year: 2015

CSMA (Carrier Sense Multiple Access), which resolves contentions over wireless networks in a fully distributed fashion, has recently gained a lot of attentions since it has been proved that appropriate control of CSMA parameters guarantees optimality in terms of stability (i.e., scheduling) and system- wide utility (i.e., scheduling and congestion control). Most CSMA-based algorithms rely on the popular MCMC (Markov Chain Monte Carlo) technique, which enables one to find optimal CSMA parameters through iterative loops of `simulation-and-update'. However, such a simulation-based approach often becomes a major cause of exponentially slow convergence, being poorly adaptive to flow/topology changes. In this paper, we develop distributed iterative algorithms which produce approximate solutions with convergence in polynomial time for both stability and utility maximization problems. In particular, for the stability problem, the proposed distributed algorithm requires, somewhat surprisingly, only one iteration among links. Our approach is motivated by the Bethe approximation (introduced by Yedidia, Freeman and Weiss in 2005) allowing us to express approximate solutions via a certain non-linear system with polynomial size. Our polynomial convergence guarantee comes from directly solving the non-linear system in a distributed manner, rather than multiple simulation-and-update loops in existing algorithms. We provide numerical results to show that the algorithm produces highly accurate solutions and converges much faster than the prior ones.
The Chills and Thrills of Whole Genome Sequencing
Venue: arXiv cs.CR 2015
Year: 2015

In recent years, Whole Genome Sequencing (WGS) evolved from a futuristic-sounding research project to an increasingly affordable technology for determining complete genome sequences of complex organisms, including humans. This prompts a wide range of revolutionary applications, as WGS promises to improve modern healthcare and provide a better understanding of the human genome -- in particular, its relation to diseases and response to treatments. However, this progress raises worrisome privacy and ethical issues, since, besides uniquely identifying its owner, the genome contains a treasure trove of highly personal and sensitive information. In this article, after summarizing recent advances in genomics, we discuss some important privacy issues associated with human genomic information and identify a number of particularly relevant research challenges.
On the quantifier-free dynamic complexity of Reachability
Venue: arXiv cs.LO 2015
Year: 2015

The dynamic complexity of the reachability query is studied in the dynamic complexity framework of Patnaik and Immerman, restricted to quantifier-free update formulas. It is shown that, with this restriction, the reachability query cannot be dynamically maintained, neither with binary auxiliary relations nor with unary auxiliary functions, and that ternary auxiliary relations are more powerful with respect to graph queries than binary auxiliary relations. Further inexpressibility results are given for the reachability query in a different setting as well as for a syntactical restriction of quantifier-free update formulas. Moreover inexpressibility results for some other queries are presented.
Multi-keyword multi-click advertisement option contracts for sponsored search
Venue: arXiv cs.GT 2015
Year: 2015

In sponsored search, advertisement (abbreviated ad) slots are usually sold by a search engine to an advertiser through an auction mechanism in which advertisers bid on keywords. In theory, auction mechanisms have many desirable economic properties. However, keyword auctions have a number of limitations including: the uncertainty in payment prices for advertisers; the volatility in the search engine's revenue; and the weak loyalty between advertiser and search engine. In this paper we propose a special ad option that alleviates these problems. In our proposal, an advertiser can purchase an option from a search engine in advance by paying an upfront fee, known as the option price. He then has the right, but no obligation, to purchase among the pre-specified set of keywords at the fixed cost-per-clicks (CPCs) for a specified number of clicks in a specified period of time. The proposed option is closely related to a special exotic option in finance that contains multiple underlying assets (multi-keyword) and is also multi-exercisable (multi-click). This novel structure has many benefits: advertisers can have reduced uncertainty in advertising; the search engine can improve the advertisers' loyalty as well as obtain a stable and increased expected revenue over time. Since the proposed ad option can be implemented in conjunction with the existing keyword auctions, the option price and corresponding fixed CPCs must be set such that there is no arbitrage between the two markets. Option pricing methods are discussed and our experimental results validate the development. Compared to keyword auctions, a search engine can have an increased expected revenue by selling an ad option.
Short Term Memory Capacity in Networks via the Restricted Isometry Property
Venue: arXiv cs.IT 2015
Year: 2015

Cortical networks are hypothesized to rely on transient network activity to support short term memory (STM). In this paper we study the capacity of randomly connected recurrent linear networks for performing STM when the input signals are approximately sparse in some basis. We leverage results from compressed sensing to provide rigorous non asymptotic recovery guarantees, quantifying the impact of the input sparsity level, the input sparsity basis, and the network characteristics on the system capacity. Our analysis demonstrates that network memory capacities can scale superlinearly with the number of nodes, and in some situations can achieve STM capacities that are much larger than the network size. We provide perfect recovery guarantees for finite sequences and recovery bounds for infinite sequences. The latter analysis predicts that network STM systems may have an optimal recovery length that balances errors due to omission and recall mistakes. Furthermore, we show that the conditions yielding optimal STM capacity can be embodied in several network topologies, including networks with sparse or dense connectivities.
Distributed Online Learning via Cooperative Contextual Bandits
Venue: arXiv cs.LG 2015
Year: 2015

In this paper we propose a novel framework for decentralized, online learning by many learners. At each moment of time, an instance characterized by a certain context may arrive to each learner; based on the context, the learner can select one of its own actions (which gives a reward and provides information) or request assistance from another learner. In the latter case, the requester pays a cost and receives the reward but the provider learns the information. In our framework, learners are modeled as cooperative contextual bandits. Each learner seeks to maximize the expected reward from its arrivals, which involves trading off the reward received from its own actions, the information learned from its own actions, the reward received from the actions requested of others and the cost paid for these actions - taking into account what it has learned about the value of assistance from each other learner. We develop distributed online learning algorithms and provide analytic bounds to compare the efficiency of these with algorithms with the complete knowledge (oracle) benchmark (in which the expected reward of every action in every context is known by every learner). Our estimates show that regret - the loss incurred by the algorithm - is sublinear in time. Our theoretical framework can be used in many practical applications including Big Data mining, event detection in surveillance sensor networks and distributed online recommendation systems.
Power Control in Networks With Heterogeneous Users: A Quasi-Variational Inequality Approach
Venue: arXiv cs.IT 2015
Year: 2015

This work deals with the power allocation problem in a multipoint-to-multipoint network, which is heterogenous in the sense that each transmit and receiver pair can arbitrarily choose whether to selfishly maximize its own rate or energy efficiency. This is achieved by modeling the transmit and receiver pairs as rational players that engage in a non-cooperative game in which the utility function changes according to each player's nature. The underlying game is reformulated as a quasi variational inequality (QVI) problem using convex fractional program theory. The equivalence between the QVI and the non-cooperative game provides us with all the mathematical tools to study the uniqueness of its Nash equilibrium (NE) points and to derive novel algorithms that allow the network to converge to these points in an iterative manner both with and without the need for a centralized processing. A small-cell network is considered as a possible case study of this heterogeneous scenario. Numerical results are used to validate the proposed solutions in different operating conditions.