OpenRaiser/Intern-Atlas huggingface dataset:
Analysis of Regularized LS Reconstruction and Random Matrix Ensembles in Compressed Sensing
Venue: arXiv cs.IT 2016
Year: 2016

Performance of regularized least-squares estimation in noisy compressed sensing is analyzed in the limit when the dimensions of the measurement matrix grow large. The sensing matrix is considered to be from a class of random ensembles that encloses as special cases standard Gaussian, row-orthogonal, geometric and so-called T-orthogonal constructions. Source vectors that have non-uniform sparsity are included in the system model. Regularization based on l1-norm and leading to LASSO estimation, or basis pursuit denoising, is given the main emphasis in the analysis. Extensions to l2-norm and "zero-norm" regularization are also briefly discussed. The analysis is carried out using the replica method in conjunction with some novel matrix integration results. Numerical experiments for LASSO are provided to verify the accuracy of the analytical results. The numerical experiments show that for noisy compressed sensing, the standard Gaussian ensemble is a suboptimal choice for the measurement matrix. Orthogonal constructions provide a superior performance in all considered scenarios and are easier to implement in practical applications. It is also discovered that for non-uniform sparsity patterns the T-orthogonal matrices can further improve the mean square error behavior of the reconstruction when the noise level is not too high. However, as the additive noise becomes more prominent in the system, the simple row-orthogonal measurement matrix appears to be the best choice out of the considered ensembles.
Packing circles within circular containers: a new heuristic algorithm for the balance constraints case
Venue: arXiv cs.CG 2016
Year: 2016

In this work we propose a heuristic algorithm for the layout optimization for disks installed in a rotating circular container. This is a unequal circle packing problem with additional balance constraints. It proved to be an NP-hard problem, which justifies heuristics methods for its resolution in larger instances. The main feature of our heuristic is based on the selection of the next circle to be placed inside the container according to the position of the system's center of mass. Our approach has been tested on a series of instances up to 55 circles and compared with the literature. Computational results show good performance in terms of solution quality and computational time for the proposed algorithm.
Nonasymptotic noisy lossy source coding
Venue: arXiv cs.IT 2016
Year: 2016

This paper shows new general nonasymptotic achievability and converse bounds and performs their dispersion analysis for the lossy compression problem in which the compressor observes the source through a noisy channel. While this problem is asymptotically equivalent to a noiseless lossy source coding problem with a modified distortion function, nonasymptotically there is a noticeable gap in how fast their minimum achievable coding rates approach the common rate-distortion function, as evidenced both by the refined asymptotic analysis (dispersion) and the numerical results. The size of the gap between the dispersions of the noisy problem and the asymptotically equivalent noiseless problem depends on the stochastic variability of the channel through which the compressor observes the source.
Image Block Loss Restoration Using Sparsity Pattern as Side Information
Venue: arXiv cs.MM 2016
Year: 2016

In this paper, we propose a method for image block loss restoration based on the notion of sparse representation. We use the sparsity pattern as side information to efficiently restore block losses by iteratively imposing the constraints of spatial and transform domains on the corrupted image. Two novel features, including a pre-interpolation and a criterion for stopping the iterations, are proposed to improve the performance. Also, to deal with practical applications, we develop a technique to transmit the side information along with the image. In this technique, we first compress the side information and then embed its LDPC coded version in the least significant bits of the image pixels. This technique ensures the error-free transmission of the side information, while causing only a small perturbation on the transmitted image. Mathematical analysis and extensive simulations are performed to validate the method and investigate the efficiency of the proposed techniques. The results verify that the proposed method outperforms its counterparts for image block loss restoration.
Computing the inverses, their power sums, and extrema for Euler's totient and other multiplicative functions
Venue: arXiv cs.DM 2016
Year: 2016

We propose a generic algorithm for computing the inverses of a multiplicative function under the assumption that the set of inverses is finite. More generally, our algorithm can compute certain functions of the inverses, such as their power sums (e.g., cardinality) or extrema, without direct enumeration of the inverses. We illustrate our algorithm with Euler's totient function $φ(\cdot)$ and the $k$-th power sum of divisors $σ_k(\cdot)$. For example, we can establish that the number of solutions to $σ_1(x) = 10^{1000}$ is 15,512,215,160,488,452,125,793,724,066,873,737,608,071,476, while it is intractable to iterate over the actual solutions.
Separating Regular Languages with First-Order Logic
Venue: arXiv cs.FL 2016
Year: 2016

Given two languages, a separator is a third language that contains the first one and is disjoint from the second one. We investigate the following decision problem: given two regular input languages of finite words, decide whether there exists a first-order definable separator. We prove that in order to answer this question, sufficient information can be extracted from semigroups recognizing the input languages, using a fixpoint computation. This yields an EXPTIME algorithm for checking first-order separability. Moreover, the correctness proof of this algorithm yields a stronger result, namely a description of a possible separator. Finally, we generalize this technique to answer the same question for regular languages of infinite words.
Channel Diversity needed for Vector Space Interference Alignment
Venue: arXiv cs.IT 2016
Year: 2016

We consider vector space interference alignment strategies over the $K$-user interference channel and derive an upper bound on the achievable degrees of freedom as a function of the channel diversity $L$, where the channel diversity is modeled by $L$ real-valued parallel channels with coefficients drawn from a non-degenerate joint distribution. The seminal work of Cadambe and Jafar shows that when $L$ is unbounded, vector space interference alignment can achieve $1/2$ degrees of freedom per user independent of the number of users $K$. However wireless channels have limited diversity in practice, dictated by their coherence time and bandwidth, and an important question is the number of degrees of freedom achievable at finite $L$. When $K=3$ and if $L$ is finite, Bresler et al show that the number of degrees of freedom achievable with vector space interference alignment is bounded away from $1/2$, and the gap decreases inversely proportional to $L$. In this paper, we show that when $K\geq4$, the gap is significantly larger. In particular, the gap to the optimal $1/2$ degrees of freedom per user can decrease at most like $1/\sqrt{L}$, and when $L$ is smaller than the order of $2^{(K-2)(K-3)}$, it decays at most like $1/\sqrt[4]{L}$.
Polcovar: Software for Computing the Mean and Variance of Subgraph Counts in Random Graphs
Venue: arXiv cs.MS 2016
Year: 2016

The mean and variance of the number of appearances of a given subgraph $H$ in an Erdős--Rényi random graph over $n$ nodes are rational polynomials in $n$. We present a piece of software named Polcovar (from "polynomial" and "covariance") that computes the exact rational coefficients of these polynomials in function of $H$.
Cyclic Complexity of Words
Venue: arXiv cs.FL 2016
Year: 2016

We introduce and study a complexity function on words $c_x(n),$ called \emph{cyclic complexity}, which counts the number of conjugacy classes of factors of length $n$ of an infinite word $x.$ We extend the well-known Morse-Hedlund theorem to the setting of cyclic complexity by showing that a word is ultimately periodic if and only if it has bounded cyclic complexity. Unlike most complexity functions, cyclic complexity distinguishes between Sturmian words of different slopes. We prove that if $x$ is a Sturmian word and $y$ is a word having the same cyclic complexity of $x,$ then up to renaming letters, $x$ and $y$ have the same set of factors. In particular, $y$ is also Sturmian of slope equal to that of $x.$ Since $c_x(n)=1$ for some $n\geq 1$ implies $x$ is periodic, it is natural to consider the quantity $\liminf_{n\rightarrow \infty} c_x(n).$ We show that if $x$ is a Sturmian word, then $\liminf_{n\rightarrow \infty} c_x(n)=2.$ We prove however that this is not a characterization of Sturmian words by exhibiting a restricted class of Toeplitz words, including the period-doubling word, which also verify this same condition on the limit infimum. In contrast we show that, for the Thue-Morse word $t$, $\liminf_{n\rightarrow \infty} c_t(n)=+\infty.$
New Ideas for Brain Modelling
Venue: arXiv cs.AI 2016
Year: 2016

This paper describes some biologically-inspired processes that could be used to build the sort of networks that we associate with the human brain. New to this paper, a 'refined' neuron will be proposed. This is a group of neurons that by joining together can produce a more analogue system, but with the same level of control and reliability that a binary neuron would have. With this new structure, it will be possible to think of an essentially binary system in terms of a more variable set of values. The paper also shows how recent research associated with the new model, can be combined with established theories, to produce a more complete picture. The propositions are largely in line with conventional thinking, but possibly with one or two more radical suggestions. An earlier cognitive model can be filled in with more specific details, based on the new research results, where the components appear to fit together almost seamlessly. The intention of the research has been to describe plausible 'mechanical' processes that can produce the appropriate brain structures and mechanisms, but that could be used without the magical 'intelligence' part that is still not fully understood. There are also some important updates from an earlier version of this paper.
Chromatic Dispersion Compensation Using Filter Bank Based Complex-Valued All-Pass Filter
Venue: arXiv cs.IT 2016
Year: 2016

A long-haul transmission of 100 Gb/s without optical chromatic-dispersion (CD) compensation provides a range of benefits regarding cost effectiveness, power budget, and nonlinearity tolerance. The channel memory is largely dominated by CD in this case with an intersymbol-interference spread of more than 100 symbol durations. In this paper, we propose CD equalization technique based on nonmaximally decimated discrete Fourier transform (NMDFT) filter bank (FB) with non-trivial prototype filter and complex-valued infinite impulse response (IIR) all-pass filter per sub-band. The design of the sub-band IIR all-pass filter is based on minimizing the mean square error (MSE) in group delay and phase cost functions in an optimization framework. Necessary conditions are derived and incorporated in a multi-step and multi-band optimization framework to ensure the stability of the resulting IIR filter. It is shown that the complexity of the proposed method grows logarithmically with the channel memory, therefore, larger CD values can be tolerated with our approach.
Occam Bound on Lowest Complexity of Elements
Venue: arXiv cs.CC 2016
Year: 2016

The combined universal probability M(D) of strings x in sets D is close to max_{x \in D} M({x}): their ~ logs differ by at most D's information j = I(D:H) about the halting sequence H. Thus if all x have complexity K(x) > k, D carries > i bits of information on each x where i+j ~ k. Note, there are no ways (whether natural or artificial) to generate D with significant I(D:H).
Generating Preview Tables for Entity Graphs
Venue: arXiv cs.DB 2016
Year: 2016

Users are tapping into massive, heterogeneous entity graphs for many applications. It is challenging to select entity graphs for a particular need, given abundant datasets from many sources and the oftentimes scarce information for them. We propose methods to produce preview tables for compact presentation of important entity types and relationships in entity graphs. The preview tables assist users in attaining a quick and rough preview of the data. They can be shown in a limited display space for a user to browse and explore, before she decides to spend time and resources to fetch and investigate the complete dataset. We formulate several optimization problems that look for previews with the highest scores according to intuitive goodness measures, under various constraints on preview size and distance between preview tables. The optimization problem under distance constraint is NP-hard. We design a dynamic-programming algorithm and an Apriori-style algorithm for finding optimal previews. Results from experiments, comparison with related work and user studies demonstrated the scoring measures' accuracy and the discovery algorithms' efficiency.
Utility Maximization for Uplink MU-MIMO: Combining Spectral-Energy Efficiency and Fairness
Venue: arXiv cs.NI 2016
Year: 2016

Driven by green communications, energy efficiency (EE) has become a new important criterion for designing wireless communication systems. However, high EE often leads to low spectral efficiency (SE), which spurs the research on EE-SE tradeoff. In this paper, we focus on how to maximize the utility in physical layer for an uplink multi-user multiple-input multipleoutput (MU-MIMO) system, where we will not only consider EE-SE tradeoff in a unified way, but also ensure user fairness. We first formulate the utility maximization problem, but it turns out to be non-convex. By exploiting the structure of this problem, we find a convexization procedure to convert the original nonconvex problem into an equivalent convex problem, which has the same global optimum with the original problem. Following the convexization procedure, we present a centralized algorithm to solve the utility maximization problem, but it requires the global information of all users. Thus we propose a primal-dual distributed algorithm which does not need global information and just consumes a small amount of overhead. Furthermore, we have proved that the distributed algorithm can converge to the global optimum. Finally, the numerical results show that our approach can both capture user diversity for EE-SE tradeoff and ensure user fairness, and they also validate the effectiveness of our primal-dual distributed algorithm.
Towards Human Computable Passwords
Venue: arXiv cs.CR 2016
Year: 2016

An interesting challenge for the cryptography community is to design authentication protocols that are so simple that a human can execute them without relying on a fully trusted computer. We propose several candidate authentication protocols for a setting in which the human user can only receive assistance from a semi-trusted computer --- a computer that stores information and performs computations correctly but does not provide confidentiality. Our schemes use a semi-trusted computer to store and display public challenges $C_i\in[n]^k$. The human user memorizes a random secret mapping $σ:[n]\rightarrow\mathbb{Z}_d$ and authenticates by computing responses $f(σ(C_i))$ to a sequence of public challenges where $f:\mathbb{Z}_d^k\rightarrow\mathbb{Z}_d$ is a function that is easy for the human to evaluate. We prove that any statistical adversary needs to sample $m=\tildeΩ(n^{s(f)})$ challenge-response pairs to recover $σ$, for a security parameter $s(f)$ that depends on two key properties of $f$. To obtain our results, we apply the general hypercontractivity theorem to lower bound the statistical dimension of the distribution over challenge-response pairs induced by $f$ and $σ$. Our lower bounds apply to arbitrary functions $f $ (not just to functions that are easy for a human to evaluate), and generalize recent results of Feldman et al. As an application, we propose a family of human computable password functions $f_{k_1,k_2}$ in which the user needs to perform $2k_1+2k_2+1$ primitive operations (e.g., adding two digits or remembering $σ(i)$), and we show that $s(f) = \min\{k_1+1, (k_2+1)/2\}$. For these schemes, we prove that forging passwords is equivalent to recovering the secret mapping. Thus, our human computable password schemes can maintain strong security guarantees even after an adversary has observed the user login to many different accounts.
Constructive discrepancy minimization for convex sets
Venue: arXiv cs.DM 2016
Year: 2016

A classical theorem of Spencer shows that any set system with n sets and n elements admits a coloring of discrepancy O(n^1/2). Recent exciting work of Bansal, Lovett and Meka shows that such colorings can be found in polynomial time. In fact, the Lovett-Meka algorithm finds a half integral point in any "large enough" polytope. However, their algorithm crucially relies on the facet structure and does not apply to general convex sets. We show that for any symmetric convex set K with measure at least exp(-n/500), the following algorithm finds a point y in K \cap [-1,1]^n with Omega(n) coordinates in {-1,+1}: (1) take a random Gaussian vector x; (2) compute the point y in K \cap [-1,1]^n that is closest to x. (3) return y. This provides another truly constructive proof of Spencer's theorem and the first constructive proof of a Theorem of Gluskin and Giannopoulos.
Decentralized and Collaborative Subspace Pursuit: A Communication-Efficient Algorithm for Joint Sparsity Pattern Recovery with Sensor Networks
Venue: arXiv cs.IT 2016
Year: 2016

In this paper, we consider the problem of joint sparsity pattern recovery in a distributed sensor network. The sparse multiple measurement vector signals (MMVs) observed by all the nodes are assumed to have a common (but unknown) sparsity pattern. To accurately recover the common sparsity pattern in a decentralized manner with a low communication overhead of the network, we develop an algorithm named decentralized and collaborative subspace pursuit (DCSP). In DCSP, each node is required to perform three kinds of operations per iteration: 1) estimate the local sparsity pattern by finding the subspace that its measurement vector most probably lies in; 2) share its local sparsity pattern estimate with one-hop neighboring nodes; and 3) update the final sparsity pattern estimate by majority vote based fusion of all the local sparsity pattern estimates obtained in its neighborhood. The convergence of DCSP is proved and its communication overhead is quantitatively analyzed. We also propose another decentralized algorithm named generalized DCSP (GDCSP) by allowing more information exchange among neighboring nodes to further improve the accuracy of sparsity pattern recovery at the cost of increased communication overhead. Experimental results show that, 1) compared with existing decentralized algorithms, DCSP provides much better accuracy of sparsity pattern recovery at a comparable communication cost; and 2) the accuracy of GDCSP is very close to that of centralized processing.
On the Number of Iterations for Convergence of CoSaMP and Subspace Pursuit Algorithms
Venue: arXiv cs.IT 2016
Year: 2016

In compressive sensing, one important parameter that characterizes the various greedy recovery algorithms is the iteration bound which provides the maximum number of iterations by which the algorithm is guaranteed to converge. In this letter, we present a new iteration bound for CoSaMP by certain mathematical manipulations including formulation of appropriate sufficient conditions that ensure passage of a chosen support through the two selection stages of CoSaMP, Augment and Update. Subsequently, we extend the treatment to the subspace pursuit (SP) algorithm. The proposed iteration bounds for both CoSaMP and SP algorithms are seen to be improvements over their existing counterparts, revealing that both CoSaMP and SP algorithms converge in fewer iterations than suggested by results available in literature.
On the Satisfiability of Quantum Circuits of Small Treewidth
Venue: arXiv cs.CC 2016
Year: 2016

It has been known for almost three decades that many $\mathrm{NP}$-hard optimization problems can be solved in polynomial time when restricted to structures of constant treewidth. In this work we provide the first extension of such results to the quantum setting. We show that given a quantum circuit $C$ with $n$ uninitialized inputs, $\mathit{poly}(n)$ gates, and treewidth $t$, one can compute in time $(\frac{n}δ)^{\exp(O(t))}$ a classical assignment $y\in \{0,1\}^n$ that maximizes the acceptance probability of $C$ up to a $δ$ additive factor. In particular, our algorithm runs in polynomial time if $t$ is constant and $1/poly(n) < δ< 1$. For unrestricted values of $t$, this problem is known to be complete for the complexity class $\mathrm{QCMA}$, a quantum generalization of MA. In contrast, we show that the same problem is $\mathrm{NP}$-complete if $t=O(\log n)$ even when $δ$ is constant. On the other hand, we show that given a $n$-input quantum circuit $C$ of treewidth $t=O(\log n)$, and a constant $δ<1/2$, it is $\mathrm{QMA}$-complete to determine whether there exists a quantum state $\mid\!φ\rangle \in (\mathbb{C}^d)^{\otimes n}$ such that the acceptance probability of $C\mid\!φ\rangle$ is greater than $1-δ$, or whether for every such state $\mid\!φ\rangle$, the acceptance probability of $C\mid\!φ\rangle$ is less than $δ$. As a consequence, under the widely believed assumption that $\mathrm{QMA} \neq \mathrm{NP}$, we have that quantum witnesses are strictly more powerful than classical witnesses with respect to Merlin-Arthur protocols in which the verifier is a quantum circuit of logarithmic treewidth.
Polynomial time vertex enumeration of convex polytopes of bounded branch-width
Venue: arXiv cs.CG 2016
Year: 2016

Over the last years the vertex enumeration problem of polyhedra has seen a revival in the study of metabolic networks, which increased the demand for efficient vertex enumeration algorithms for high-dimensional polyhedra given by inequalities. It is a famous and long standing open question in polyhedral theory and computational geometry whether the vertices of a polytope (bounded polyhedron), described by a set of linear constraints, can be enumerated in total polynomial time. In this paper we apply the concept of branch-decomposition to the vertex enumeration problem of polyhedra $P = \{x : Ax = b, x \geq 0\}$. For this purpose, we introduce the concept of $k$-module and show how it relates to the separators of the linear matroid generated by the columns of $A$. We then use this to present a total polynomial time algorithm for polytopes $P$ for which the branch-width of the linear matroid generated by $A$ is bounded by a constant $k$.
A Canonical Semi-Deterministic Transducer
Venue: arXiv cs.LG 2016
Year: 2016

We prove the existence of a canonical form for semi-deterministic transducers with incomparable sets of output strings. Based on this, we develop an algorithm which learns semi-deterministic transducers given access to translation queries. We also prove that there is no learning algorithm for semi-deterministic transducers that uses only domain knowledge.