OpenRaiser/Intern-Atlas huggingface dataset:
Tight exponential analysis of universally composable privacy amplification and its applications
Venue: arXiv cs.IT 2013
Year: 2013

Motivated by the desirability of universal composability, we analyze in terms of L_1 distinguishability the task of secret key generation from a joint random variable. Under this secrecy criterion, using the Renyi entropy of order 1+s for s in [0,1, we derive a new upper bound of Eve's distinguishability under the application of the universal2 hash functions. It is also shown that this bound gives the tight exponential rate of decrease in the case of independent and identical distributions. The result is applied to the wire-tap channel model and to secret key generation (distillation) by public discussion.
Fixed-parameter tractability of multicut parameterized by the size of the cutset
Venue: arXiv cs.DS 2013
Year: 2013

Given an undirected graph $G$, a collection $\{(s_1,t_1),..., (s_k,t_k)\}$ of pairs of vertices, and an integer $p$, the Edge Multicut problem ask if there is a set $S$ of at most $p$ edges such that the removal of $S$ disconnects every $s_i$ from the corresponding $t_i$. Vertex Multicut is the analogous problem where $S$ is a set of at most $p$ vertices. Our main result is that both problems can be solved in time $2^{O(p^3)}... n^{O(1)}$, i.e., fixed-parameter tractable parameterized by the size $p$ of the cutset in the solution. By contrast, it is unlikely that an algorithm with running time of the form $f(p)... n^{O(1)}$ exists for the directed version of the problem, as we show it to be W[1]-hard parameterized by the size of the cutset.
Short-circuit logic
Venue: arXiv cs.LO 2013
Year: 2013

Short-circuit evaluation denotes the semantics of propositional connectives in which the second argument is evaluated only if the first argument does not suffice to determine the value of the expression. In programming, short-circuit evaluation is widely used, with sequential conjunction and disjunction as primitive connectives. A short-circuit logic is a variant of propositional logic (PL) that can be defined with help of Hoare's conditional, a ternary connective comparable to if-then-else, and that implies all identities that follow from four basic axioms for the conditional and can be expressed in PL (e.g., axioms for associativity of conjunction and double negation shift). In the absence of side effects, short-circuit evaluation characterizes PL. However, short-circuit evaluation admits the possibility to model side effects and gives rise to various different short-circuit logics. The first extreme case is FSCL (free short-circuit logic), which characterizes the setting in which evaluation of each atom (propositional variable) can yield a side effect. The other extreme case is MSCL (memorizing short-circuit logic), the most identifying variant we distinguish below PL. In MSCL, only a very restricted type of side effects can be modelled, while sequential conjunction is non-commutative. We provide axiomatizations for FSCL and MSCL. Extending MSCL with one simple axiom yields SSCL (static short-circuit logic, or sequential PL), for which we also provide a completeness result. We briefly discuss two variants in between FSCL and MSCL, among which a logic that admits contraction of atoms and of their negations.
Multiarmed Bandit Problems with Delayed Feedback
Venue: arXiv cs.DS 2013
Year: 2013

In this paper we initiate the study of optimization of bandit type problems in scenarios where the feedback of a play is not immediately known. This arises naturally in allocation problems which have been studied extensively in the literature, albeit in the absence of delays in the feedback. We study this problem in the Bayesian setting. In presence of delays, no solution with provable guarantees is known to exist with sub-exponential running time. We show that bandit problems with delayed feedback that arise in allocation settings can be forced to have significant structure, with a slight loss in optimality. This structure gives us the ability to reason about the relationship of single arm policies to the entangled optimum policy, and eventually leads to a O(1) approximation for a significantly general class of priors. The structural insights we develop are of key interest and carry over to the setting where the feedback of an action is available instantaneously, and we improve all previous results in this setting as well.
On Balanced Separators, Treewidth, and Cycle Rank
Venue: arXiv cs.DM 2013
Year: 2013

We investigate relations between different width parameters of graphs, in particular balanced separator number, treewidth, and cycle rank. Our main result states that a graph with balanced separator number k has treewidth at least k but cycle rank at most k(1 + log (n/k)), thus refining the previously known bounds, as stated by Robertson and Seymour (1986) and by Bodlaender et al. (1995). Furthermore, we show that the improved bounds are best possible.
Prognostic Watch of the Electric Power System
Venue: arXiv cs.SI 2013
Year: 2013

A prognostic watch of the electric power system (EPS)is framed up, which detects the threat to EPS for a day ahead according to the characteristic times for a day ahead and according to the droop for a day ahead. Therefore, a prognostic analysis of the EPS development for a day ahead is carried out. Also the power grid, the electricity marker state, the grid state and the level of threat for a power grid are found for a day ahead. The accuracy of the built up prognostic watch is evaluated.
GMRES-based multigrid for the complex scaled preconditoner for the indefinite Helmholtz equation
Venue: arXiv cs.NA 2013
Year: 2013

Multigrid preconditioners and solvers for the indefinite Helmholtz equation suffer from non-stability of the stationary smoothers due to the indefinite spectrum of the operator. In this paper we explore GMRES as a replacement for the stationary smoothers of the standard multigrid method. This results in a robust and efficient solver for a complex shifted or stretched Helmholtz problem that can be used as a preconditioner. Very few GMRES iterations are required on each level to build a good multigrid method. The convergence behavior is compared to a theoretically derived stable polynomial smoother. We test this method on some benchmark problems and report on the observed convergence behavior.
The Complexity of 3SAT_N and the P versus NP Problem
Venue: arXiv cs.CC 2013
Year: 2013

We introduce the NP-complete problem 3SAT_N and extend Tovey's results to a classification theorem for this problem. This theorem leads us to generalize the concept of truth assignments for SAT to aggressive truth assignments for 3SAT_N. We introduce the concept of a set compatible with the P and NP problem, and prove that all aggressive truth assignments are pseudo-algorithms. We combine algorithm, pseudo-algorithm and diagonalization method to study the complexity of 3SAT_N and the P versus NP problem. The main result is P != NP.
Fundamental Limits of Infinite Constellations in MIMO Fading Channels
Venue: arXiv cs.IT 2013
Year: 2013

The fundamental and natural connection between the infinite constellation (IC) dimension and the best diversity order it can achieve is investigated in this paper. In the first part of this work we develop an upper bound on the diversity order of IC's for any dimension and any number of transmit and receive antennas. By choosing the right dimensions, we prove in the second part of this work that IC's in general and lattices in particular can achieve the optimal diversity-multiplexing tradeoff of finite constellations. This work gives a framework for designing lattices for multiple-antenna channels using lattice decoding.
Spatially-Coupled MacKay-Neal Codes and Hsu-Anastasopoulos Codes
Venue: arXiv cs.IT 2013
Year: 2013

Kudekar et al. recently proved that for transmission over the binary erasure channel (BEC), spatial coupling of LDPC codes increases the BP threshold of the coupled ensemble to the MAP threshold of the underlying LDPC codes. One major drawback of the capacity-achieving spatially-coupled LDPC codes is that one needs to increase the column and row weight of parity-check matrices of the underlying LDPC codes. It is proved, that Hsu-Anastasopoulos (HA) codes and MacKay-Neal (MN) codes achieve the capacity of memoryless binary-input symmetric-output channels under MAP decoding with bounded column and row weight of the parity-check matrices. The HA codes and the MN codes are dual codes each other. The aim of this paper is to present an empirical evidence that spatially-coupled MN (resp. HA) codes with bounded column and row weight achieve the capacity of the BEC. To this end, we introduce a spatial coupling scheme of MN (resp. HA) codes. By density evolution analysis, we will show that the resulting spatially-coupled MN (resp. HA) codes have the BP threshold close to the Shannon limit.
Preprocessing for Treewidth: A Combinatorial Analysis through Kernelization
Venue: arXiv cs.DS 2013
Year: 2013

The notion of treewidth plays an important role in theoretical and practical studies of graph problems. It has been recognized that, especially in practical environments, when computing the treewidth of a graph it is invaluable to first apply an array of preprocessing rules that simplify and shrink it. This work seeks to prove rigorous performance guarantees for such preprocessing rules, both known and new ones, by studying them in the framework of kernelization from parameterized complexity. It is known that the NP-complete problem of determining whether a given graph G has treewidth at most k admits no polynomial-time preprocessing algorithm that reduces any input instance to size polynomial in k, unless NP is in coNP/poly and the polynomial hierarchy collapses to its third level. In this paper we therefore consider structural graph measures larger than treewidth, and determine whether efficient preprocessing can shrink the instance size to a polynomial in such a parameter value. We prove that given an instance (G,k) of treewidth we can efficiently reduce its size to O(fvs(G)^4) vertices, where fvs(G) is the size of a minimum feedback vertex set in G. We can also prove a size reduction to O(vc(G)^3) vertices, where vc(G) is the size of a minimum vertex cover. Phrased in the language of parameterized complexity, we show that Treewidth has a polynomial kernel when parameterized by the size of a given feedback vertex set, and also by the size of a vertex cover. In contrast we show that Treewidth parameterized by the vertex-deletion distance to a single clique, and Weighted Treewidth parameterized by the size of a vertex cover, do not admit polynomial kernelizations unless NP is in coNP/poly.
Universally Typical Sets for Ergodic Sources of Multidimensional Data
Venue: arXiv cs.IT 2013
Year: 2013

We lift important results about universally typical sets, typically sampled sets, and empirical entropy estimation in the theory of samplings of discrete ergodic information sources from the usual one-dimensional discrete-time setting to a multidimensional lattice setting. We use techniques of packings and coverings with multidimensional windows to construct sequences of multidimensional array sets which in the limit build the generated samples of any ergodic source of entropy rate below an $h_0$ with probability one and whose cardinality grows at most at exponential rate $h_0$.
On the Degree Distribution of Faulty Peer-to-Peer Overlays
Venue: arXiv cs.DC 2013
Year: 2013

This paper presents an analytical framework to model fault-tolerance in unstructured peer-to-peer overlays, represented as complex networks. We define a distributed protocol peers execute for managing the overlay and reacting to node faults. Based on the protocol, evolution equations are defined and manipulated by resorting to generating functions. Obtained outcomes provide insights on the nodes' degree probability distribution. From the study of the degree distribution, it is possible to estimate other important metrics of the peer-to-peer overlay, such as the diameter of the network. We study different networks, characterized by three specific desired degree distributions, i.e. nets with nodes having a fixed desired degree, random graphs and scale-free networks. All these networks are assessed via the analytical tool and simulation as well. Results show that the approach can be factually employed to dynamically tune the average attachment rate at peers so that they maintain their own desired degree and, in general, the desired network topology.
Cuts in Cartesian Products of Graphs
Venue: arXiv cs.DM 2013
Year: 2013

The k-fold Cartesian product of a graph G is defined as a graph on k-tuples of vertices, where two tuples are connected if they form an edge in one of the positions and are equal in the rest. Starting with G as a single edge gives G^k as a k-dimensional hypercube. We study the distributions of edges crossed by a cut in G^k across the copies of G in different positions. This is a generalization of the notion of influences for cuts on the hypercube. We show the analogues of results of Kahn, Kalai, and Linial (KKL Theorem [KahnKL88]) and that of Friedgut (Friedgut's Junta theorem [Friedgut98]), for the setting of Cartesian products of arbitrary graphs. Our proofs extend the arguments of Rossignol [Rossignol06] and of Falik and Samorodnitsky [FalikS07], to the case of arbitrary Cartesian products. We also extend the work on studying isoperimetric constants for these graphs [HoudreT96, ChungT98] to the value of semidefinite relaxations for edge-expansion. We connect the optimal values of the relaxations for computing expansion, given by various semidefinite hierarchies, for G and G^k.
Link Delay Estimation via Expander Graphs
Venue: arXiv cs.NI 2013
Year: 2013

One of the purposes of network tomography is to infer the status of parameters (e.g., delay) for the links inside a network through end-to-end probing between (external) boundary nodes along predetermined routes. In this work, we apply concepts from compressed sensing and expander graphs to the delay estimation problem. We first show that a relative majority of network topologies are not expanders for existing expansion criteria. Motivated by this challenge, we then relax such criteria, enabling us to acquire simulation evidence that link delays can be estimated for 30% more networks. That is, our relaxation expands the list of identifiable networks with bounded estimation error by 30%. We conduct a simulation performance analysis of delay estimation and congestion detection on the basis of l1 minimization, demonstrating that accurate estimation is feasible for an increasing proportion of networks.
Structural Controllability of Switched Linear Systems
Venue: arXiv cs.SY 2013
Year: 2013

This paper studies the structural controllability of a class of uncertain switched linear systems, where the parameters of subsystems state matrices are either unknown or zero. The structural controllability is a generalization of the traditional controllability concept for dynamical systems, and purely based on the interconnection relation between the state variables and inputs through non-zero elements in the state matrices. In order to illustrate such a relationship, two kinds of graphic representations of switched linear systems are proposed, based on which graph theory based necessary and sufficient characterizations of the structural controllability for switched linear systems are presented. Finally, the paper concludes with discussions on the results and future work.
Censored Truncated Sequential Spectrum Sensing for Cognitive Radio Networks
Venue: arXiv cs.SY 2013
Year: 2013

Reliable spectrum sensing is a key functionality of a cognitive radio network. Cooperative spectrum sensing improves the detection reliability of a cognitive radio system but also increases the system energy consumption which is a critical factor particularly for low-power wireless technologies. A censored truncated sequential spectrum sensing technique is considered as an energy-saving approach. To design the underlying sensing parameters, the maximum energy consumption per sensor is minimized subject to a lower bounded global probability of detection and an upper bounded false alarm rate. This way both the interference to the primary user due to miss detection and the network throughput as a result of a low false alarm rate is controlled. We compare the performance of the proposed scheme with a fixed sample size censoring scheme under different scenarios. It is shown that as the sensing cost of the cognitive radios increases, the energy efficiency of the censored truncated sequential approach grows significantly.
From Causal Models To Counterfactual Structures
Venue: arXiv cs.AI 2013
Year: 2013

Galles and Pearl claimed that "for recursive models, the causal model framework does not add any restrictions to counterfactuals, beyond those imposed by Lewis's [possible-worlds] framework." This claim is examined carefully, with the goal of clarifying the exact relationship between causal models and Lewis's framework. Recursive models are shown to correspond precisely to a subclass of (possible-world) counterfactual structures. On the other hand, a slight generalization of recursive models, models where all equations have unique solutions, is shown to be incomparable in expressive power to counterfactual structures, despite the fact that the Galles and Pearl arguments should apply to them as well. The problem with the Galles and Pearl argument is identified: an axiom that they viewed as irrelevant, because it involved disjunction (which was not in their language), is not irrelevant at all.
Stable Restoration and Separation of Approximately Sparse Signals
Venue: arXiv cs.IT 2013
Year: 2013

This paper develops new theory and algorithms to recover signals that are approximately sparse in some general dictionary (i.e., a basis, frame, or over-/incomplete matrix) but corrupted by a combination of interference having a sparse representation in a second general dictionary and measurement noise. The algorithms and analytical recovery conditions consider varying degrees of signal and interference support-set knowledge. Particular applications covered by the proposed framework include the restoration of signals impaired by impulse noise, narrowband interference, or saturation/clipping, as well as image in-painting, super-resolution, and signal separation. Two application examples for audio and image restoration demonstrate the efficacy of the approach.
Decoding of Matrix-Product Codes
Venue: arXiv cs.IT 2013
Year: 2013

We propose a decoding algorithm for the $(u\mid u+v)$-construction that decodes up to half of the minimum distance of the linear code. We extend this algorithm for a class of matrix-product codes in two different ways. In some cases, one can decode beyond the error correction capability of the code.
Nearly Doubling the Throughput of Multiuser MIMO Systems Using Codebook Tailored Limited Feedback Protocol
Venue: arXiv cs.IT 2013
Year: 2013

We present and analyze a new robust feedback and transmit strategy for multiuser MIMO downlink communication systems, termed Rate Approximation (RA). RA combines the flexibility and robustness needed for reliable communications with the user terminal under a limited feedback constraint. It responds to two important observations. First, it is not so significant to approximate the channel but rather the rate, such that the optimal scheduling decision can be mimicked at the base station. Second, a fixed transmit codebook at the transmitter is often better when therefore the channel state information is more accurate. In the RA scheme the transmit and feedback codebook are separated and user rates are delivered to the base station subject to a controlled uniform error. The scheme is analyzed and proved to have better performance below a certain interference plus noise margin and better behavior than the classical Jindal formula. LTE system simulations sustain the analytic results showing performance gains of up to 50% or 70% compared to zeroforcing when using multiple antennas at the base station and multiple antennas or a single antenna at the terminals, respectively. A new feedback protocol is developed which inherently considers the transmit codebook and which is able to deal with the complexity issue at the terminal.
Relay Selection with Channel Probing in Sleep-Wake Cycling Wireless Sensor Networks
Venue: arXiv cs.NI 2013
Year: 2013

In geographical forwarding of packets in a large wireless sensor network (WSN) with sleep-wake cycling nodes, we are interested in the local decision problem faced by a node that has custody of a packet and has to choose one among a set of next-hop relay nodes to forward the packet towards the sink. Each relay is associated with a reward that summarizes the benefit of forwarding the packet through that relay. We seek a solution to this local problem, the idea being that such a solution, if adopted by every node, could provide a reasonable heuristic for the end-to-end forwarding problem. Towards this end, we propose a relay selection problem comprising a forwarding node and a collection of relay nodes, with the relays waking up sequentially at random times. At each relay wake-up instant the forwarder can choose to probe a relay to learn its reward value, based on which the forwarder can then decide whether to stop (and forward its packet to the chosen relay) or to continue to wait for further relays to wake-up. The forwarder's objective is to select a relay so as to minimize a combination of waiting-delay, reward and probing cost. Our problem can be considered as a variant of the asset selling problem studied in the operations research literature. We formulate our relay selection problem as a Markov decision process (MDP) and obtain some interesting structural results on the optimal policy (namely, the threshold and the stage-independence properties). We also conduct simulation experiments and gain valuable insights into the performance of our local forwarding-solution.
A Kalman Decomposition for Possibly Controllable Uncertain Linear Systems
Venue: arXiv cs.SY 2013
Year: 2013

This paper considers the structure of uncertain linear systems building on concepts of robust unobservability and possible controllability which were introduced in previous papers. The paper presents a new geometric characterization of the possibly controllable states. When combined with previous geometric results on robust unobservability, the results of this paper lead to a general Kalman type decomposition for uncertain linear systems which can be applied to the problem of obtaining reduced order uncertain system models.
Multi-channel Hybrid Access Femtocells: A Stochastic Geometric Analysis
Venue: arXiv cs.NI 2013
Year: 2013

For two-tier networks consisting of macrocells and femtocells, the channel access mechanism can be configured to be open access, closed access, or hybrid access. Hybrid access arises as a compromise between open and closed access mechanisms, in which a fraction of available spectrum resource is shared to nonsubscribers while the remaining reserved for subscribers. This paper focuses on a hybrid access mechanism for multi-channel femtocells which employ orthogonal spectrum access schemes. Considering a randomized channel assignment strategy, we analyze the performance in the downlink. Using stochastic geometry as technical tools, we model the distribution of femtocells as Poisson point process or Neyman-Scott cluster process and derive the distributions of signal-to-interference-plus-noise ratios, and mean achievable rates, of both nonsubscribers and subscribers. The established expressions are amenable to numerical evaluation, and shed key insights into the performance tradeoff between subscribers and nonsubscribers. The analytical results are corroborated by numerical simulations.