OpenRaiser/Intern-Atlas huggingface dataset:
Discrete geometric analysis of message passing algorithm on graphs
Venue: arXiv cs.DM 2011
Year: 2011

We often encounter probability distributions given as unnormalized products of non-negative functions. The factorization structures are represented by hypergraphs called factor graphs. Such distributions appear in various fields, including statistics, artificial intelligence, statistical physics, error correcting codes, etc. Given such a distribution, computations of marginal distributions and the normalization constant are often required. However, they are computationally intractable because of their computational costs. One successful approximation method is Loopy Belief Propagation (LBP) algorithm. The focus of this thesis is an analysis of the LBP algorithm. If the factor graph is a tree, i.e. having no cycle, the algorithm gives the exact quantities. If the factor graph has cycles, however, the LBP algorithm does not give exact results and possibly exhibits oscillatory and non-convergent behaviors. The thematic question of this thesis is "How the behaviors of the LBP algorithm are affected by the discrete geometry of the factor graph?" The primary contribution of this thesis is the discovery of a formula that establishes the relation between the LBP, the Bethe free energy and the graph zeta function. This formula provides new techniques for analysis of the LBP algorithm, connecting properties of the graph and of the LBP and the Bethe free energy. We demonstrate applications of the techniques to several problems including (non) convexity of the Bethe free energy, the uniqueness and stability of the LBP fixed point. We also discuss the loop series initiated by Chertkov and Chernyak. The loop series is a subgraph expansion of the normalization constant, or partition function, and reflects the graph geometry. We investigate theoretical natures of the series. Moreover, we show a partial connection between the loop series and the graph zeta function.
Settling the complexity of local max-cut (almost) completely
Venue: arXiv cs.CC 2011
Year: 2011

We consider the problem of finding a local optimum for Max-Cut with FLIP-neighborhood, in which exactly one node changes the partition. Schaeffer and Yannakakis (SICOMP, 1991) showed PLS-completeness of this problem on graphs with unbounded degree. On the other side, Poljak (SICOMP, 1995) showed that in cubic graphs every FLIP local search takes O(n^2) steps, where n is the number of nodes. Due to the huge gap between degree three and unbounded degree, Ackermann, Roeglin, and Voecking (JACM, 2008) asked for the smallest d for which the local Max-Cut problem with FLIP-neighborhood on graphs with maximum degree d is PLS-complete. In this paper, we prove that the computation of a local optimum on graphs with maximum degree five is PLS-complete. Thus, we solve the problem posed by Ackermann et al. almost completely by showing that d is either four or five (unless PLS is in P). On the other side, we also prove that on graphs with degree O(log n) every FLIP local search has probably polynomial smoothed complexity. Roughly speaking, for any instance, in which the edge weights are perturbated by a (Gaussian) random noise with variance σ^2, every FLIP local search terminates in time polynomial in n and σ^{-1}, with probability 1-n^{-Ω(1)}. Putting both results together, we may conclude that although local Max-Cut is likely to be hard on graphs with bounded degree, it can be solved in polynomial time for slightly perturbated instances with high probability.
High-Rate Vector Quantization for the Neyman-Pearson Detection of Correlated Processes
Venue: arXiv cs.IT 2011
Year: 2011

This paper investigates the effect of quantization on the performance of the Neyman-Pearson test. It is assumed that a sensing unit observes samples of a correlated stationary ergodic multivariate process. Each sample is passed through an N-point quantizer and transmitted to a decision device which performs a binary hypothesis test. For any false alarm level, it is shown that the miss probability of the Neyman-Pearson test converges to zero exponentially as the number of samples tends to infinity, assuming that the observed process satisfies certain mixing conditions. The main contribution of this paper is to provide a compact closed-form expression of the error exponent in the high-rate regime i.e., when the number N of quantization levels tends to infinity, generalizing previous results of Gupta and Hero to the case of non-independent observations. If d represents the dimension of one sample, it is proved that the error exponent converges at rate N^{2/d} to the one obtained in the absence of quantization. As an application, relevant high-rate quantization strategies which lead to a large error exponent are determined. Numerical results indicate that the proposed quantization rule can yield better performance than existing ones in terms of detection error.
A Framework For Fully-Simulatable $h$-Out-Of-$n$ Oblivious Transfer
Venue: arXiv cs.CR 2011
Year: 2011

We present a framework for fully-simulatable $h$-out-of-$n$ oblivious transfer ($OT^{n}_{h}$) with security against non-adaptive malicious adversaries. The framework costs six communication rounds and costs at most $40n$ public-key operations in computational overhead. Compared with the known protocols for fully-simulatable oblivious transfer that works in the plain mode (where there is no trusted common reference string available) and proven to be secure under standard model (where there is no random oracle available), the instantiation based on the decisional Diffie-Hellman assumption of the framework is the most efficient one, no matter seen from communication rounds or computational overhead. Our framework uses three abstract tools, i.e., perfectly binding commitment, perfectly hiding commitment and our new smooth projective hash. This allows a simple and intuitive understanding of its security. We instantiate the new smooth projective hash under the lattice assumption, the decisional Diffie-Hellman assumption, the decisional $N$-th residuosity assumption, the decisional quadratic residuosity assumption. This indeed shows that the folklore that it is technically difficult to instantiate the projective hash framework under the lattice assumption is not true. What's more, by using this lattice-based hash and lattice-based commitment scheme, we gain a concrete protocol for $OT^{n}_{h}$ which is secure against quantum algorithms.
Simultaneous communication in noisy channels
Venue: arXiv cs.IT 2011
Year: 2011

A sender wishes to broadcast a message of length $n$ over an alphabet to $r$ users, where each user $i$, $1 \leq i \leq r$ should be able to receive one of $m_i$ possible messages. The broadcast channel has noise for each of the users (possibly different noise for different users), who cannot distinguish between some pairs of letters. The vector $(m_1, m_2,...s, m_r)_{(n)}$ is said to be feasible if length $n$ encoding and decoding schemes exist enabling every user to decode his message. A rate vector $(R_1, R_2,..., R_r)$ is feasible if there exists a sequence of feasible vectors $(m_1, m_2,..., m_r)_{(n)}$ such that $R_i = \lim_{n \mapsto \infty} \frac {\log_2 m_i} {n}, {for all} i$. We determine the feasible rate vectors for several different scenarios and investigate some of their properties. An interesting case discussed is when one user can only distinguish between all the letters in a subset of the alphabet. Tight restrictions on the feasible rate vectors for some specific noise types for the other users are provided. The simplest non-trivial cases of two users and alphabet of size three are fully characterized. To this end a more general previously known result, to which we sketch an alternative proof, is used. This problem generalizes the study of the Shannon capacity of a graph, by considering more than a single user.
Capacity of a Class of Multicast Tree Networks
Venue: arXiv cs.IT 2011
Year: 2011

In this paper, we characterize the capacity of a new class of single-source multicast discrete memoryless relay networks having a tree topology in which the root node is the source and each parent node in the graph has at most one noisy child node and any number of noiseless child nodes. This class of multicast tree networks includes the class of diamond networks studied by Kang and Ulukus as a special case, where they showed that the capacity can be strictly lower than the cut-set bound. For achievablity, a novel coding scheme is constructed where each noisy relay employs a combination of decode-and-forward (DF) and compress-and-forward (CF) and each noiseless relay performs a random binning such that codebook constructions and relay operations are independent for each node and do not depend on the network topology. For converse, a new technique of iteratively manipulating inequalities exploiting the tree topology is used.
Practical Constructions for the Efficient Cryptographic Enforcement of Interval-Based Access Control Policies
Venue: arXiv cs.CR 2011
Year: 2011

The enforcement of access control policies using cryptography has received considerable attention in recent years and the security of such enforcement schemes is increasingly well understood. Recent work in the area has considered the efficient enforcement of temporal and geo-spatial access control policies, and asymptotic results for the time and space complexity of efficient enforcement schemes have been obtained. However, for practical purposes, it is useful to have explicit bounds for the complexity of enforcement schemes. In this paper, we consider interval-based access control policies, of which temporal and geo-spatial access control policies are special cases. We define enforcement schemes for interval-based access control policies for which it is possible, in almost all cases, to obtain exact values for the schemes' complexity, thereby subsuming a substantial body of work in the literature. Moreover, our enforcement schemes are more practical than existing schemes, in the sense that they operate in the same way as standard cryptographic enforcement schemes, unlike other efficient schemes in the literature. The main difference between our approach and earlier work is that we develop techniques that are specific to the cryptographic enforcement of interval-based access control policies, rather than applying generic techniques that give rise to complex constructions and asymptotic bounds.
The 1958 Pekeris-Accad-WEIZAC Ground-Breaking Collaboration that Computed Ground States of Two-Electron Atoms (and its 2010 Redux)
Venue: arXiv cs.SC 2011
Year: 2011

In order to appreciate how well off we mathematicians and scientists are today, with extremely fast hardware and lots and lots of memory, as well as with powerful software, both for numeric and symbolic computation, it may be a good idea to go back to the early days of electronic computers and compare how things went then. We have chosen, as a case study, a problem that was considered a huge challenge at the time. Namely, we looked at C.L. Pekeris's seminal 1958 work on the ground state energies of two-electron atoms. We went through all the computations ab initio with today's software and hardware, with a special emphasis on the symbolic computations which in 1958 had to be made by hand, and which nowadays can be automated and generalized.
Analysis of a Collaborative Filter Based on Popularity Amongst Neighbors
Venue: arXiv cs.IT 2011
Year: 2011

In this paper, we analyze a collaborative filter that answers the simple question: What is popular amongst your friends? While this basic principle seems to be prevalent in many practical implementations, there does not appear to be much theoretical analysis of its performance. In this paper, we partly fill this gap. While recent works on this topic, such as the low-rank matrix completion literature, consider the probability of error in recovering the entire rating matrix, we consider probability of an error in an individual recommendation (bit error rate (BER)). For a mathematical model introduced in [1],[2], we identify three regimes of operation for our algorithm (named Popularity Amongst Friends (PAF)) in the limit as the matrix size grows to infinity. In a regime characterized by large number of samples and small degrees of freedom (defined precisely for the model in the paper), the asymptotic BER is zero; in a regime characterized by large number of samples and large degrees of freedom, the asymptotic BER is bounded away from 0 and 1/2 (and is identified exactly except for a special case); and in a regime characterized by a small number of samples, the algorithm fails. We also present numerical results for the MovieLens and Netflix datasets. We discuss the empirical performance in light of our theoretical results and compare with an approach based on low-rank matrix completion.
Discovery of a missing disease spreader
Venue: arXiv cs.AI 2011
Year: 2011

This study presents a method to discover an outbreak of an infectious disease in a region for which data are missing, but which is at work as a disease spreader. Node discovery for the spread of an infectious disease is defined as discriminating between the nodes which are neighboring to a missing disease spreader node, and the rest, given a dataset on the number of cases. The spread is described by stochastic differential equations. A perturbation theory quantifies the impact of the missing spreader on the moments of the number of cases. Statistical discriminators examine the mid-body or tail-ends of the probability density function, and search for the disturbance from the missing spreader. They are tested with computationally synthesized datasets, and applied to the SARS outbreak and flu pandemic.
Does Treewidth Help in Modal Satisfiability?
Venue: arXiv cs.LO 2011
Year: 2011

Many tractable algorithms for solving the Constraint Satisfaction Problem (CSP) have been developed using the notion of the treewidth of some graph derived from the input CSP instance. In particular, the incidence graph of the CSP instance is one such graph. We introduce the notion of an incidence graph for modal logic formulae in a certain normal form. We investigate the parameterized complexity of modal satisfiability with the modal depth of the formula and the treewidth of the incidence graph as parameters. For various combinations of Euclidean, reflexive, symmetric and transitive models, we show either that modal satisfiability is FPT, or that it is W[1]-hard. In particular, modal satisfiability in general models is FPT, while it is W[1]-hard in transitive models. As might be expected, modal satisfiability in transitive and Euclidean models is FPT.
Partially Ordered Two-way Büchi Automata
Venue: arXiv cs.FL 2011
Year: 2011

We introduce partially ordered two-way Büchi automata and characterize their expressive power in terms of fragments of first-order logic FO[<]. Partially ordered two-way Büchi automata are Büchi automata which can change the direction in which the input is processed with the constraint that whenever a state is left, it is never re-entered again. Nondeterministic partially ordered two-way Büchi automata coincide with the first-order fragment Sigma2. Our main contribution is that deterministic partially ordered two-way Büchi automata are expressively complete for the first-order fragment Delta2. As an intermediate step, we show that deterministic partially ordered two-way Büchi automata are effectively closed under Boolean operations. A small model property yields coNP-completeness of the emptiness problem and the inclusion problem for deterministic partially ordered two-way Büchi automata.
Base station cooperation on the downlink: Large system analysis
Venue: arXiv cs.IT 2011
Year: 2011

This paper considers maximizing the network-wide minimum supported rate in the downlink of a two-cell system, where each base station (BS) is endowed with multiple antennas. This is done for different levels of cell cooperation. At one extreme, we consider single cell processing where the BS is oblivious to the interference it is creating at the other cell. At the other extreme, we consider full cooperative macroscopic beamforming. In between, we consider coordinated beamforming, which takes account of inter-cell interference, but does not require full cooperation between the BSs. We combine elements of Lagrangian duality and large system analysis to obtain limiting SINRs and bit-rates, allowing comparison between the considered schemes. The main contributions of the paper are theorems which provide concise formulas for optimal transmit power, beamforming vectors, and achieved signal to interference and noise ratio (SINR) for the considered schemes. The formulas obtained are valid for the limit in which the number of users per cell, K, and the number of antennas per base station, N, tend to infinity, with fixed ratio. These theorems also provide expressions for the effective bandwidths occupied by users, and the effective interference caused in the adjacent cell, which allow direct comparisons between the considered schemes.
Methods for Accelerating Conway's Doomsday Algorithm (part 1)
Venue: arXiv cs.DS 2011
Year: 2011

We propose a modification of a key component in the Doomsday Algorithm for calculating the day of the week of any calendar date. In particular, we propose to replace the calculation of the required term: \lfloor \frac{x}{12} \rfloor + x \bmod 12 + \lfloor \frac{x \bmod 12}{4} \rfloor with the term 2y + 10 \, (y \bmod 2) + z + \lfloor \frac{2 \, (y \bmod 2) + z}{4} \rfloor where x is an input 2-digit year; y is the tens digit of x; z is the ones digit of x; We argue the fact that our modification operates on individual base-10 digits makes the algorithm easier to calculate mentally.
Online Identification and Tracking of Subspaces from Highly Incomplete Information
Venue: arXiv cs.IT 2011
Year: 2011

This work presents GROUSE (Grassmanian Rank-One Update Subspace Estimation), an efficient online algorithm for tracking subspaces from highly incomplete observations. GROUSE requires only basic linear algebraic manipulations at each iteration, and each subspace update can be performed in linear time in the dimension of the subspace. The algorithm is derived by analyzing incremental gradient descent on the Grassmannian manifold of subspaces. With a slight modification, GROUSE can also be used as an online incremental algorithm for the matrix completion problem of imputing missing entries of a low-rank matrix. GROUSE performs exceptionally well in practice both in tracking subspaces and as an online algorithm for matrix completion.
Notes on higher-dimensional tarai functions
Venue: arXiv cs.DM 2011
Year: 2011

We proved that for every $n\geq 3$, the $n$-dimensional tarai function terminates with call-by-need. It was also shown that the closed form for the function suggested by T. Bailey and J. Cowles is correct.
Secure rate-adaptive reconciliation
Venue: arXiv cs.IT 2011
Year: 2011

We consider in this paper the problem of information reconciliation in the context of secret key agreement between two legitimate parties, Alice and Bob. Beginning the discussion with the secret key agreement model introduced by Ahlswede and Csiszár, the channel-type model with wiretapper, we study a protocol based on error correcting codes. The protocol can be adapted to changes in the communication channel extending the original source. The efficiency of the reconciliation is only limited by the quality of the code and, while transmitting more information than needed to reconcile Alice's and Bob's sequences, it does not reveal any more information on the original source than an ad-hoc code would have revealed.
A Dense Hierarchy of Sublinear Time Approximation Schemes for Bin Packing
Venue: arXiv cs.CC 2011
Year: 2011

The bin packing problem is to find the minimum number of bins of size one to pack a list of items with sizes $a_1,..., a_n$ in $(0,1]$. Using uniform sampling, which selects a random element from the input list each time, we develop a randomized $O({n(\log n)(\log\log n)\over \sum_{i=1}^n a_i}+({1\over ε})^{O({1\overε})})$ time $(1+ε)$-approximation scheme for the bin packing problem. We show that every randomized algorithm with uniform random sampling needs $Ω({n\over \sum_{i=1}^n a_i})$ time to give an $(1+ε)$-approximation. For each function $s(n): N\rightarrow N$, define $\sum(s(n))$ to be the set of all bin packing problems with the sum of item sizes equal to $s(n)$. For a constant $b\in (0,1)$, every problem in $\sum(n^{b})$ has an $O(n^{1-b}(\log n)(\log\log n)+({1\over ε})^{O({1\overε})})$ time $(1+ε)$-approximation for an arbitrary constant $ε$. On the other hand, there is no $o(n^{1-b})$ time $(1+ε)$-approximation scheme for the bin packing problems in $\sum(n^{b})$ for some constant $ε>0$.
Online Stochastic Matching: Online Actions Based on Offline Statistics
Venue: arXiv cs.DS 2011
Year: 2011

We consider the online stochastic matching problem proposed by Feldman et al. [FMMM09] as a model of display ad allocation. We are given a bipartite graph; one side of the graph corresponds to a fixed set of bins and the other side represents the set of possible ball types. At each time step, a ball is sampled independently from the given distribution and it needs to be matched upon its arrival to an empty bin. The goal is to maximize the number of allocations. We present an online algorithm for this problem with a competitive ratio of 0.702. Before our result, algorithms with a competitive ratio better than $1-1/e$ were known under the assumption that the expected number of arriving balls of each type is integral. A key idea of the algorithm is to collect statistics about the decisions of the optimum offline solution using Monte Carlo sampling and use those statistics to guide the decisions of the online algorithm. We also show that our algorithm achieves a competitive ratio of 0.705 when the rates are integral. On the hardness side, we prove that no online algorithm can have a competitive ratio better than 0.823 under the known distribution model (and henceforth under the permutation model). This improves upon the 5/6 hardness result proved by Goel and Mehta \cite{GM08} for the permutation model.
Quantum Error Correction beyond the Bounded Distance Decoding Limit
Venue: arXiv cs.IT 2011
Year: 2011

In this paper, we consider quantum error correction over depolarizing channels with non-binary low-density parity-check codes defined over Galois field of size $2^p$ . The proposed quantum error correcting codes are based on the binary quasi-cyclic CSS (Calderbank, Shor and Steane) codes. The resulting quantum codes outperform the best known quantum codes and surpass the performance limit of the bounded distance decoder. By increasing the size of the underlying Galois field, i.e., $2^p$, the error floors are considerably improved.
Free Probability based Capacity Calculation of Multiantenna Gaussian Fading Channels with Cochannel Interference
Venue: arXiv cs.IT 2011
Year: 2011

During the last decade, it has been well understood that communication over multiple antennas can increase linearly the multiplexing capacity gain and provide large spectral efficiency improvements. However, the majority of studies in this area were carried out ignoring cochannel interference. Only a small number of investigations have considered cochannel interference, but even therein simple channel models were employed, assuming identically distributed fading coefficients. In this paper, a generic model for a multi-antenna channel is presented incorporating four impairments, namely additive white Gaussian noise, flat fading, path loss and cochannel interference. Both point-to-point and multiple-access MIMO channels are considered, including the case of cooperating Base Station clusters. The asymptotic capacity limit of this channel is calculated based on an asymptotic free probability approach which exploits the additive and multiplicative free convolution in the R- and S-transform domain respectively, as well as properties of the eta and Stieltjes transform. Numerical results are utilized to verify the accuracy of the derived closed-form expressions and evaluate the effect of the cochannel interference.