OpenRaiser/Intern-Atlas huggingface dataset:
Simple dynamics on graphs
Venue: arXiv cs.DM 2016
Year: 2016

Does the interaction graph of a finite dynamical system can force this system to have a "complex" dynamics ? In other words, given a finite interval of integers $A$, which are the signed digraphs $G$ such that every finite dynamical system $f:A^n\to A^n$ with $G$ as interaction graph has a "complex" dynamics ? If $|A|\geq 3$ we prove that no such signed digraph exists. More precisely, we prove that for every signed digraph $G$ there exists a system $f:A^n\to A^n$ with $G$ as interaction graph that converges toward a unique fixed point in at most $\lfloor\log_2 n\rfloor+2$ steps. The boolean case $|A|=2$ is more difficult, and we provide partial answers instead. We exhibit large classes of unsigned digraphs which admit boolean dynamical systems which converge toward a unique fixed point in polynomial, linear or constant time.
There are no finite partial cubes of girth more than 6 and minimum degree at least 3
Venue: arXiv cs.DM 2016
Year: 2016

Partial cubes are graphs isometrically embeddable into hypercubes. We analyze how isometric cycles in partial cubes behave and derive that every partial cube of girth more than 6 must have vertices of degree less than 3. As a direct corollary we get that every regular partial cube of girth more than 6 is an even cycle. Along the way we prove that every partial cube $G$ with girth more than 6 is a tree-zone graph and therefore $2n(G)-m(G)-i(G)+ce(G)=2$ holds, where $i(G)$ is the isometric dimension of $G$ and $ce(G)$ its convex excess.
Distributed Continuous-time Approximate Projection Protocols for Shortest Distance Optimization Problems
Venue: arXiv cs.SY 2016
Year: 2016

In this paper, we investigate the distributed shortest distance optimization problem for a multi-agent network to cooperatively minimize the sum of the quadratic distances from some convex sets, where each set is only associated with one agent. To deal with the optimization problem with projection uncertainties, we propose a distributed continuous-time dynamical protocol based on a new concept of approximate projection. Here each agent can only obtain an approximate projection point on the boundary of its convex set, and communicate with its neighbors over a time-varying communication graph. First, we show that no matter how large the approximate angle is, the system states are always bounded for any initial condition, and uniformly bounded with respect to all initial conditions if the inferior limit of the stepsize is greater than zero. Then, in the two cases, nonempty intersection and empty intersection of convex sets, we provide stepsize and approximate angle conditions to ensure the optimal convergence, respectively. Moreover, we give some characterizations about the optimal solutions for the empty intersection case and also present the convergence error between agents' estimates and the optimal point in the case of constant stepsizes and approximate angles.
A representation theorem for stratified complete lattices
Venue: arXiv cs.LO 2016
Year: 2016

We consider complete lattices equipped with preorderings indexed by the ordinals less than a given (limit) ordinal subject to certain axioms. These structures, called stratified complete lattices, and weakly monotone functions over them, provide a framework for solving fixed point equations involving non-monotone operations such as negation or complement, and have been used to give semantics to logic programs with negation. More precisely, we consider stratified complete lattices subject to two slightly different systems of axioms defining `models' and `strong models'. We prove that a stratified complete lattice is a model iff it is isomorphic to the stratified complete lattice determined by the limit of an inverse system of complete lattices with `locally completely additive' projections. Moreover, we prove that a stratified complete lattice is a strong model iff it is isomorphic to the stratified complete lattice determined by the limit of an inverse system of complete lattices with completely additive projections. We use the inverse limit representation to give alternative proofs of some recent results and to derive some new ones for models and strong models. In particular, we use the representation theorem to prove that every model gives rise to another complete lattice structure, which in limit models corresponds to the lexicographic order. Moreover, we prove that the set of all fixed points of a weakly monotone function over a model, equipped with the new ordering, is a complete lattice. We also consider symmetric models that satisfy, together with each axiom, the dual axiom, and use the inverse limit representation to prove that every strong model is symmetric.
FFT Algorithm for Binary Extension Finite Fields and its Application to Reed-Solomon Codes
Venue: arXiv cs.IT 2016
Year: 2016

Recently, a new polynomial basis over binary extension fields was proposed such that the fast Fourier transform (FFT) over such fields can be computed in the complexity of order $\mathcal{O}(n\lg(n))$, where $n$ is the number of points evaluated in FFT. In this work, we reformulate this FFT algorithm such that it can be easier understood and be extended to develop frequency-domain decoding algorithms for $(n=2^m,k)$ systematic Reed-Solomon~(RS) codes over $\mathbb{F}_{2^m},m\in \mathbb{Z}^+$, with $n-k$ a power of two. First, the basis of syndrome polynomials is reformulated in the decoding procedure so that the new transforms can be applied to the decoding procedure. A fast extended Euclidean algorithm is developed to determine the error locator polynomial. The computational complexity of the proposed decoding algorithm is $\mathcal{O}(n\lg(n-k)+(n-k)\lg^2(n-k))$, improving upon the best currently available decoding complexity $\mathcal{O}(n\lg^2(n)\lg\lg(n))$, and reaching the best known complexity bound that was established by Justesen in 1976. However, Justesen's approach is only for the codes over some specific fields, which can apply Cooley-Tucky FFTs. As revealed by the computer simulations, the proposed decoding algorithm is $50$ times faster than the conventional one for the $(2^{16},2^{15})$ RS code over $\mathbb{F}_{2^{16}}$.
Algorithmic Bayesian Persuasion
Venue: arXiv cs.GT 2016
Year: 2016

Persuasion, defined as the act of exploiting an informational advantage in order to effect the decisions of others, is ubiquitous. Indeed, persuasive communication has been estimated to account for almost a third of all economic activity in the US. This paper examines persuasion through a computational lens, focusing on what is perhaps the most basic and fundamental model in this space: the celebrated Bayesian persuasion model of Kamenica and Gentzkow. Here there are two players, a sender and a receiver. The receiver must take one of a number of actions with a-priori unknown payoff, and the sender has access to additional information regarding the payoffs. The sender can commit to revealing a noisy signal regarding the realization of the payoffs of various actions, and would like to do so as to maximize her own payoff assuming a perfectly rational receiver. We examine the sender's optimization task in three of the most natural input models for this problem, and essentially pin down its computational complexity in each. When the payoff distributions of the different actions are i.i.d. and given explicitly, we exhibit a polynomial-time (exact) algorithm, and a "simple" $(1-1/e)$-approximation algorithm. Our optimal scheme for the i.i.d. setting involves an analogy to auction theory, and makes use of Border's characterization of the space of reduced-forms for single-item auctions. When action payoffs are independent but non-identical with marginal distributions given explicitly, we show that it is #P-hard to compute the optimal expected sender utility. Finally, we consider a general (possibly correlated) joint distribution of action payoffs presented by a black box sampling oracle, and exhibit a fully polynomial-time approximation scheme (FPTAS) with a bi-criteria guarantee. We show that this result is the best possible in the black-box model for information-theoretic reasons.
On SDoF of Multi-Receiver Wiretap Channel With Alternating CSIT
Venue: arXiv cs.IT 2016
Year: 2016

We study the problem of secure transmission over a Gaussian multi-input single-output (MISO) two receiver channel with an external eavesdropper, under the assumption that the state of the channel which is available to each receiver is conveyed either perfectly ($P$) or with delay ($D$) to the transmitter. Denoting by $S_1$, $S_2$, and $S_3$ the channel state information at the transmitter (CSIT) of user 1, user 2, and eavesdropper, respectively, the overall CSIT can then alternate between eight possible states, i.e., $(S_1,S_2,S_3) \in \{P,D\}^3$. We denote by $λ_{S_1 S_2 S_3}$ the fraction of time during which the state $S_1S_2S_3$ occurs. Under these assumptions, we first consider the Gaussian MISO wiretap channel and characterize the secure degrees of freedom (SDoF). Next, we consider the general multi-receiver setup and characterize the SDoF region of fixed hybrid states $PPD$, $PDP$, and $DDP$. We then focus our attention on the symmetric case in which $λ_{PDD}=λ_{DPD}$. For this case, we establish bounds on SDoF region. The analysis reveals that alternating CSIT allows synergistic gains in terms of SDoF; and shows that, by opposition to encoding separately over different states, joint encoding across the states enables strictly better secure rates. Furthermore, we specialize our results for the two receivers channel with an external eavesdropper to the two-user broadcast channel. We show that, the synergistic gains in terms of SDoF by alternating CSIT is not restricted to multi-receiver wiretap channels; and, can also be harnessed under broadcast setting.
AC OPF in Radial Distribution Networks - Parts I,II
Venue: arXiv cs.SY 2016
Year: 2016

The optimal power-flow problem (OPF) has played a key role in the planning and operation of power systems. Due to the non-linear nature of the AC power-flow equations, the OPF problem is known to be non-convex, therefore hard to solve. Most proposed methods for solving the OPF rely on approximations that render the problem convex, but that may yield inexact solutions. Recently, Farivar and Low proposed a method that is claimed to be exact for radial distribution systems, despite no apparent approximations. In our work, we show that it is, in fact, not exact. On one hand, there is a misinterpretation of the physical network model related to the ampacity constraint of the lines' current flows. On the other hand, the proof of the exactness of the proposed relaxation requires unrealistic assumptions related to the unboundedness of specific control variables. We also show that the extension of this approach to account for exact line models might provide physically infeasible solutions. Recently, several contributions have proposed OPF algorithms that rely on the use of the alternating-direction method of multipliers (ADMM). However, as we show in this work, there are cases for which the ADMM-based solution of the non-relaxed OPF problem fails to converge. To overcome the aforementioned limitations, we propose an algorithm for the solution of a non-approximated, non-convex OPF problem in radial distribution systems that is based on the method of multipliers, and on a primal decomposition of the OPF. This work is divided in two parts. In Part I, we specifically discuss the limitations of BFM and ADMM to solve the OPF problem. In Part II, we provide a centralized version and a distributed asynchronous version of the proposed OPF algorithm and we evaluate its performances using both small-scale electrical networks, as well as a modified IEEE 13-node test feeder.
Building Efficient and Compact Data Structures for Simplicial Complexes
Venue: arXiv cs.CG 2016
Year: 2016

The Simplex Tree (ST) is a recently introduced data structure that can represent abstract simplicial complexes of any dimension and allows efficient implementation of a large range of basic operations on simplicial complexes. In this paper, we show how to optimally compress the Simplex Tree while retaining its functionalities. In addition, we propose two new data structures called the Maximal Simplex Tree (MxST) and the Simplex Array List (SAL). We analyze the compressed Simplex Tree, the Maximal Simplex Tree, and the Simplex Array List under various settings.
On the Multiple Access Channel with Asynchronous Cognition
Venue: arXiv cs.IT 2016
Year: 2016

In this paper we introduce the two-user asynchronous cognitive multiple access channel (ACMAC). This channel model includes two transmitters, an uninformed one, and an informed one which knows prior to the beginning of a transmission the message which the uninformed transmitter is about to send. We assume that the channel from the uninformed transmitter to the receiver suffers a fixed but unknown delay. We further introduce a modified model, referred to as the asynchronous codeword cognitive multiple access channel (ACC-MAC), which differs from the ACMAC in that the informed user knows the signal that is to be transmitted by the other user, rather than the message that it is about to transmit. We state inner and outer bounds on the ACMAC and the ACC-MAC capacity regions, and we specialize the results to the Gaussian case. Further, we characterize the capacity regions of these channels in terms of multi-letter expressions. Finally, we provide an example which instantiates the difference between message side-information and codeword side-information.
Finding a low-rank basis in a matrix subspace
Venue: arXiv cs.NA 2016
Year: 2016

For a given matrix subspace, how can we find a basis that consists of low-rank matrices? This is a generalization of the sparse vector problem. It turns out that when the subspace is spanned by rank-1 matrices, the matrices can be obtained by the tensor CP decomposition. For the higher rank case, the situation is not as straightforward. In this work we present an algorithm based on a greedy process applicable to higher rank problems. Our algorithm first estimates the minimum rank by applying soft singular value thresholding to a nuclear norm relaxation, and then computes a matrix with that rank using the method of alternating projections. We provide local convergence results, and compare our algorithm with several alternative approaches. Applications include data compression beyond the classical truncated SVD, computing accurate eigenvectors of a near-multiple eigenvalue, image separation and graph Laplacian eigenproblems.
Covert Communication over Noisy Channels: A Resolvability Perspective
Venue: arXiv cs.IT 2016
Year: 2016

We consider the situation in which a transmitter attempts to communicate reliably over a discrete memoryless channel while simultaneously ensuring covertness (low probability of detection) with respect to a warden, who observes the signals through another discrete memoryless channel. We develop a coding scheme based on the principle of channel resolvability, which generalizes and extends prior work in several directions. First, it shows that, irrespective of the quality of the channels, it is possible to communicate on the order of $\sqrt{n}$ reliable and covert bits over $n$ channel uses if the transmitter and the receiver share on the order of $\sqrt{n}$ key bits; this improves upon earlier results requiring on the order of $\sqrt{n}\log n$ key bits. Second, it proves that, if the receiver's channel is "better" than the warden's channel in a sense that we make precise, it is possible to communicate on the order of $\sqrt{n}$ reliable and covert bits over $n$ channel uses without a secret key; this generalizes earlier results established for binary symmetric channels. We also identify the fundamental limits of covert and secret communications in terms of the optimal asymptotic scaling of the message size and key size, and we extend the analysis to Gaussian channels. The main technical problem that we address is how to develop concentration inequalities for "low-weight" sequences; the crux of our approach is to define suitably modified typical sets that are amenable to concentration inequalities.
Learning to Understand Phrases by Embedding the Dictionary
Venue: arXiv cs.CL 2016
Year: 2016

Distributional models that learn rich semantic word representations are a success story of recent NLP research. However, developing models that learn useful representations of phrases and sentences has proved far harder. We propose using the definitions found in everyday dictionaries as a means of bridging this gap between lexical and phrasal semantics. Neural language embedding models can be effectively trained to map dictionary definitions (phrases) to (lexical) representations of the words defined by those definitions. We present two applications of these architectures: "reverse dictionaries" that return the name of a concept given a definition or description and general-knowledge crossword question answerers. On both tasks, neural language embedding models trained on definitions from a handful of freely-available lexical resources perform as well or better than existing commercial systems that rely on significant task-specific engineering. The results highlight the effectiveness of both neural embedding architectures and definition-based training for developing models that understand phrases and sentences.
Antisocial Behavior in Online Discussion Communities
Venue: arXiv cs.SI 2016
Year: 2016

User contributions in the form of posts, comments, and votes are essential to the success of online communities. However, allowing user participation also invites undesirable behavior such as trolling. In this paper, we characterize antisocial behavior in three large online discussion communities by analyzing users who were banned from these communities. We find that such users tend to concentrate their efforts in a small number of threads, are more likely to post irrelevantly, and are more successful at garnering responses from other users. Studying the evolution of these users from the moment they join a community up to when they get banned, we find that not only do they write worse than other users over time, but they also become increasingly less tolerated by the community. Further, we discover that antisocial behavior is exacerbated when community feedback is overly harsh. Our analysis also reveals distinct groups of users with different levels of antisocial behavior that can change over time. We use these insights to identify antisocial users early on, a task of high practical importance to community maintainers.
Expanding the Compute-and-Forward Framework: Unequal Powers, Signal Levels, and Multiple Linear Combinations
Venue: arXiv cs.IT 2016
Year: 2016

The compute-and-forward framework permits each receiver in a Gaussian network to directly decode a linear combination of the transmitted messages. The resulting linear combinations can then be employed as an end-to-end communication strategy for relaying, interference alignment, and other applications. Recent efforts have demonstrated the advantages of employing unequal powers at the transmitters and decoding more than one linear combination at each receiver. However, neither of these techniques fit naturally within the original formulation of compute-and-forward. This paper proposes an expanded compute-and-forward framework that incorporates both of these possibilities and permits an intuitive interpretation in terms of signal levels. Within this framework, recent achievability and optimality results are unified and generalized.
Formal Certification of Android Bytecode
Venue: arXiv cs.PL 2016
Year: 2016

Android is an operating system that has been used in a majority of mobile devices. Each application in Android runs in an instance of the Dalvik virtual machine, which is a register-based virtual machine (VM). Most applications for Android are developed using Java, compiled to Java bytecode and then translated to DEX bytecode using the dx tool in the Android SDK. In this work, we aim to develop a type-based method for certifying non-interference properties of DEX bytecode, following a methodology that has been developed for Java bytecode certification by Barthe et al. To this end, we develop a formal operational semantics of the Dalvik VM, a type system for DEX bytecode, and prove the soundness of the type system with respect to a notion of non-interference. We then study the translation process from Java bytecode to DEX bytecode, as implemented in the dx tool in the Android SDK. We show that an abstracted version of the translation from Java bytecode to DEX bytecode preserves the non-interference property. More precisely, we show that if the Java bytecode is typable in Barthe et al's type system (which guarantees non-interference) then its translation is typable in our type system. This result opens up the possibility to leverage existing bytecode verifiers for Java to certify non-interference properties of Android bytecode.
Strategic Interaction Among Different Entities in Internet of Things
Venue: arXiv cs.GT 2016
Year: 2016

The economic model of the Internet of Things (IoT) consists of end users, advertisers and three different kinds of providers--IoT service provider (IoTSP), Wireless service provider (WSP) and cloud service provider (CSP). We investigate three different kinds of interactions among the providers. First, we consider that the IoTSP prices a bundled service to the end-users, and the WSP and CSP pay the IoTSP (push model). Next, we consider the model where the end-users independently pay the each provider (pull model). Finally, we consider a hybrid model of the above two where the IoTSP and WSP quote their prices to the end-users, but the CSP quotes its price to the IoTSP. We characterize and quantify the impact of the advertisement revenue on the equilibrium pricing strategy and payoff of providers, and corresponding demands of end users in each of the above interaction models. Our analysis reveals that the demand of end-users, and the payoffs of the providers are non decreasing functions of the advertisement revenue. For sufficiently high advertisement revenue, the IoTSP will offer its service free of cost in each interaction model. However, the payoffs of the providers, and the demand of end-users vary across different interaction models. Our analysis shows that the demand of end-users, and the payoff of the WSP are the highest in the pull (push, resp.) model in the low (high, resp.) advertisement revenue regime. The payoff of the IoTSP is always higher in the pull model irrespective of the advertisement revenue. The payoff of the CSP is the highest in the hybrid model in the low advertisement revenue regime. However, in the high advertisement revenue regime the payoff of the CSP in the hybrid model or in the push model can be higher depending on the equilibrium chosen in the push model.