OpenRaiser/Intern-Atlas huggingface dataset:
The Cost of Mitigating Power Law Delay in Random Access Networks
Venue: arXiv cs.NI 2013
Year: 2013

Exponential backoff (EB) is a widely adopted collision resolution mechanism in many popular random-access networks including Ethernet and wireless LAN (WLAN). The prominence of EB is primarily attributed to its asymptotic throughput stability, which ensures a non-zero throughput even when the number of users in the network goes to infinity. Recent studies, however, show that EB is fundamentally unsuitable for applications that are sensitive to large delay and delay jitters, as it induces divergent second- and higher-order moments of medium access delay. Essentially, the medium access delay follows a power law distribution, a subclass of heavy-tailed distribution. To understand and alleviate the issue, this paper systematically analyzes the tail delay distribution of general backoff functions, with EB being a special case. In particular, we establish a tradeoff between the tail decaying rate of medium access delay distribution and the stability of throughput. To be more specific, convergent delay moments are attainable only when the backoff functions $g(k)$ grows slower than exponential functions, i.e., when $g(k)\in o(r^k)$ for all $r>1$. On the other hand, non-zero asymptotic throughput is attainable only when backoff functions grow at least as fast as an exponential function, i.e., $g(k)\inΩ(r^k)$ for some $r>1$. This implies that bounded delay moments and stable throughput cannot be achieved at the same time. For practical implementation, we show that polynomial backoff (PB), where $g(k)$ is a polynomial that grows slower than exponential functions, obtains finite delay moments and good throughput performance at the same time within a practical range of user population. This makes PB a better alternative than EB for multimedia applications with stringent delay requirements.
Concepts and Their Dynamics: A Quantum-Theoretic Modeling of Human Thought
Venue: arXiv cs.AI 2013
Year: 2013

We analyze different aspects of our quantum modeling approach of human concepts, and more specifically focus on the quantum effects of contextuality, interference, entanglement and emergence, illustrating how each of them makes its appearance in specific situations of the dynamics of human concepts and their combinations. We point out the relation of our approach, which is based on an ontology of a concept as an entity in a state changing under influence of a context, with the main traditional concept theories, i.e. prototype theory, exemplar theory and theory theory. We ponder about the question why quantum theory performs so well in its modeling of human concepts, and shed light on this question by analyzing the role of complex amplitudes, showing how they allow to describe interference in the statistics of measurement outcomes, while in the traditional theories statistics of outcomes originates in classical probability weights, without the possibility of interference. The relevance of complex numbers, the appearance of entanglement, and the role of Fock space in explaining contextual emergence, all as unique features of the quantum modeling, are explicitly revealed in this paper by analyzing human concepts and their dynamics.
The visible perimeter of an arrangement of disks
Venue: arXiv cs.CG 2013
Year: 2013

Given a collection of n opaque unit disks in the plane, we want to find a stacking order for them that maximizes their visible perimeter---the total length of all pieces of their boundaries visible from above. We prove that if the centers of the disks form a dense point set, i.e., the ratio of their maximum to their minimum distance is O(n^1/2), then there is a stacking order for which the visible perimeter is Omega(n^2/3). We also show that this bound cannot be improved in the case of a sufficiently small n^1/2 by n^1/2 uniform grid. On the other hand, if the set of centers is dense and the maximum distance between them is small, then the visible perimeter is O(n^3/4) with respect to any stacking order. This latter bound cannot be improved either. Finally, we address the case where no more than c disks can have a point in common. These results partially answer some questions of Cabello, Haverkort, van Kreveld, and Speckmann.
DEX: Self-healing Expanders
Venue: arXiv cs.DC 2013
Year: 2013

We present a fully-distributed self-healing algorithm DEX, that maintains a constant degree expander network in a dynamic setting. To the best of our knowledge, our algorithm provides the first efficient distributed construction of expanders --- whose expansion properties hold {\em deterministically} --- that works even under an all-powerful adaptive adversary that controls the dynamic changes to the network (the adversary has unlimited computational power and knowledge of the entire network state, can decide which nodes join and leave and at what time, and knows the past random choices made by the algorithm). Previous distributed expander constructions typically provide only {\em probabilistic} guarantees on the network expansion which {\em rapidly degrade} in a dynamic setting; in particular, the expansion properties can degrade even more rapidly under {\em adversarial} insertions and deletions. Our algorithm provides efficient maintenance and incurs a low overhead per insertion/deletion by an adaptive adversary: only $O(\log n)$ rounds and $O(\log n)$ messages are needed with high probability ($n$ is the number of nodes currently in the network). The algorithm requires only a constant number of topology changes. Moreover, our algorithm allows for an efficient implementation and maintenance of a distributed hash table (DHT) on top of DEX, with only a constant additional overhead. Our results are a step towards implementing efficient self-healing networks that have \emph{guaranteed} properties (constant bounded degree and expansion) despite dynamic changes.
New lower bounds for the rank of matrix multiplication
Venue: arXiv cs.CC 2013
Year: 2013

The rank of the matrix multiplication operator for nxn matrices is one of the most studied quantities in algebraic complexity theory. I prove that the rank is at least n^2-o(n^2). More precisely, for any integer p\leq n -1, the rank is at least (3- 1/(p+1))n^2-(1+2p\binom{2p}{p-1})n. The previous lower bound, due to Blaser, was 5n^2/2-3n (the case p=1). The new bounds improve Blaser's bound for all n>84. I also prove lower bounds for rectangular matrices significantly better than the the previous bound.
Pareto-optimal Nash equilibrium in capacity allocation game for self-managed networks
Venue: arXiv cs.GT 2013
Year: 2013

In this paper we introduce a capacity allocation game which models the problem of maximizing network utility from the perspective of distributed noncooperative agents. Motivated by the idea of self-managed networks, in the developed framework decision-making entities are associated with individual transmission links, deciding on the way they split capacity among concurrent flows. An efficient decentralized algorithm is given for computing strongly Pareto-optimal strategies, constituting a pure Nash equilibrium. Subsequently, we discuss the properties of the introduced game related to the Price of Anarchy and Price of Stability. The paper is concluded with an experimental study.
AnonyControl: Control Cloud Data Anonymously with Multi-Authority Attribute-Based Encryption
Venue: arXiv cs.CR 2013
Year: 2013

Cloud computing is a revolutionary computing paradigm which enables flexible, on-demand and low-cost usage of computing resources. However, those advantages, ironically, are the causes of security and privacy problems, which emerge because the data owned by different users are stored in some cloud servers instead of under their own control. To deal with security problems, various schemes based on the Attribute- Based Encryption (ABE) have been proposed recently. However, the privacy problem of cloud computing is yet to be solved. This paper presents an anonymous privilege control scheme AnonyControl to address the user and data privacy problem in a cloud. By using multiple authorities in cloud computing system, our proposed scheme achieves anonymous cloud data access, finegrained privilege control, and more importantly, tolerance to up to (N -2) authority compromise. Our security and performance analysis show that AnonyControl is both secure and efficient for cloud computing environment.
Broadcasting colourings on trees. A combinatorial view
Venue: arXiv cs.DM 2013
Year: 2013

The broadcasting models on a d-ary tree T arise in many contexts such as biology, information theory, statistical physics and computer science. We consider the k-colouring model, i.e. the root of T is assigned an arbitrary colour and, conditional on this assignment, we take a random colouring of T. A basic question here is whether the information of the assignment at the root affects the distribution of the colourings at the leaves. This is the so-called reconstruction/non-reconstruction problem. It is well known that d/ln d is a threshold function for this problem, i.e. * if k \geq (1+\eps)d/ln d, then the colouring of the root has a vanishing effect on the distribution of the colourings at the leaves, as the height of the tree grows * if $k\leq (1-\eps)d/ln d, then the colouring of the root biases the distribution of the colouring of the leaves regardless of the height of the tree. There is no apparent combinatorial reason why such a result should be true. When k\geq (1+\eps)d/ ln d, the threshold implies the following: We can couple two broadcasting processes that assign the root different colours such that the probability of having disagreement at the leaves reduces with their distance from the root. It is natural to perceive such coupling as a mapping from the colouring of the first broadcasting process to the colouring of the second one. Here, we study how can we have such a mapping "combinatorially". Devising a mapping where the disagreements vanish as we move away from the root turns out to be a non-trivial task to accomplish for any k \leq d. In this work we obtain a coupling which has the aforementioned property for any k>3d/ln d, i.e. much smaller than d. Interestingly enough, the decisions that we make in the coupling are local. We relate our result to sampling k-colourings of sparse random graphs, with expected degree d and k<d.
A Linear-Programming Approximation of AC Power Flows
Venue: arXiv cs.AI 2013
Year: 2013

Linear active-power-only DC power flow approximations are pervasive in the planning and control of power systems. However, these approximations fail to capture reactive power and voltage magnitudes, both of which are necessary in many applications to ensure voltage stability and AC power flow feasibility. This paper proposes linear-programming models (the LPAC models) that incorporate reactive power and voltage magnitudes in a linear power flow approximation. The LPAC models are built on a convex approximation of the cosine terms in the AC equations, as well as Taylor approximations of the remaining nonlinear terms. Experimental comparisons with AC solutions on a variety of standard IEEE and MatPower benchmarks show that the LPAC models produce accurate values for active and reactive power, phase angles, and voltage magnitudes. The potential benefits of the LPAC models are illustrated on two "proof-of-concept" studies in power restoration and capacitor placement.
Block Iterative Eigensolvers for Sequences of Correlated Eigenvalue Problems
Venue: arXiv cs.DS 2013
Year: 2013

In Density Functional Theory simulations based on the LAPW method, each self-consistent field cycle comprises dozens of large dense generalized eigenproblems. In contrast to real-space methods, eigenpairs solving for problems at distinct cycles have either been believed to be independent or at most very loosely connected. In a recent study [7], it was demonstrated that, contrary to belief, successive eigenproblems in a sequence are strongly correlated with one another. In particular, by monitoring the subspace angles between eigenvectors of successive eigenproblems, it was shown that these angles decrease noticeably after the first few iterations and become close to collinear. This last result suggests that we can manipulate the eigenvectors, solving for a specific eigenproblem in a sequence, as an approximate solution for the following eigenproblem. In this work we present results that are in line with this intuition. We provide numerical examples where opportunely selected block iterative eigensolvers benefit from the reuse of eigenvectors by achieving a substantial speed-up. The results presented will eventually open the way to a widespread use of block iterative eigensolvers in ab initio electronic structure codes based on the LAPW approach.
A Linear Approximation to the chi^2 Kernel with Geometric Convergence
Venue: arXiv cs.LG 2013
Year: 2013

We propose a new analytical approximation to the $χ^2$ kernel that converges geometrically. The analytical approximation is derived with elementary methods and adapts to the input distribution for optimal convergence rate. Experiments show the new approximation leads to improved performance in image classification and semantic segmentation tasks using a random Fourier feature approximation of the $\exp-χ^2$ kernel. Besides, out-of-core principal component analysis (PCA) methods are introduced to reduce the dimensionality of the approximation and achieve better performance at the expense of only an additional constant factor to the time complexity. Moreover, when PCA is performed jointly on the training and unlabeled testing data, further performance improvements can be obtained. Experiments conducted on the PASCAL VOC 2010 segmentation and the ImageNet ILSVRC 2010 datasets show statistically significant improvements over alternative approximation methods.
Autocorrelations of Binary Sequences and Run Structure
Venue: arXiv cs.IT 2013
Year: 2013

We analyze the connection between the autocorrelation of a binary sequence and its run structure given by the run length encoding. We show that both the periodic and the aperiodic autocorrelation of a binary sequence can be formulated in terms of the run structure. The run structure is given by the consecutive runs of the sequence. Let C=(C(0), C(1),...,C(n)) denote the autocorrelation vector of a binary sequence. We prove that the kth component of the second order difference operator of C can be directly calculated by using the consecutive runs of total length k. In particular this shows that the kth autocorrelation is already determined by all consecutive runs of total length L<k. In the aperiodic case we show how the run vector R can be efficiently calculated and give a characterization of skew-symmetric sequences in terms of their run length encoding.
Preprocessing Subgraph and Minor Problems: When Does a Small Vertex Cover Help?
Venue: arXiv cs.DS 2013
Year: 2013

We prove a number of results around kernelization of problems parameterized by the size of a given vertex cover of the input graph. We provide three sets of simple general conditions characterizing problems admitting kernels of polynomial size. Our characterizations not only give generic explanations for the existence of many known polynomial kernels for problems like q-Coloring, Odd Cycle Transversal, Chordal Deletion, Eta Transversal, or Long Path, parameterized by the size of a vertex cover, but also imply new polynomial kernels for problems like F-Minor-Free Deletion, which is to delete at most k vertices to obtain a graph with no minor from a fixed finite set F. While our characterization captures many interesting problems, the kernelization complexity landscape of parameterizations by vertex cover is much more involved. We demonstrate this by several results about induced subgraph and minor containment testing, which we find surprising. While it was known that testing for an induced complete subgraph has no polynomial kernel unless NP is in coNP/poly, we show that the problem of testing if a graph contains a complete graph on t vertices as a minor admits a polynomial kernel. On the other hand, it was known that testing for a path on t vertices as a minor admits a polynomial kernel, but we show that testing for containment of an induced path on t vertices is unlikely to admit a polynomial kernel.
A Spectral Graph Uncertainty Principle
Venue: arXiv cs.IT 2013
Year: 2013

The spectral theory of graphs provides a bridge between classical signal processing and the nascent field of graph signal processing. In this paper, a spectral graph analogy to Heisenberg's celebrated uncertainty principle is developed. Just as the classical result provides a tradeoff between signal localization in time and frequency, this result provides a fundamental tradeoff between a signal's localization on a graph and in its spectral domain. Using the eigenvectors of the graph Laplacian as a surrogate Fourier basis, quantitative definitions of graph and spectral "spreads" are given, and a complete characterization of the feasibility region of these two quantities is developed. In particular, the lower boundary of the region, referred to as the uncertainty curve, is shown to be achieved by eigenvectors associated with the smallest eigenvalues of an affine family of matrices. The convexity of the uncertainty curve allows it to be found to within $\varepsilon$ by a fast approximation algorithm requiring $O(\varepsilon^{-1/2})$ typically sparse eigenvalue evaluations. Closed-form expressions for the uncertainty curves for some special classes of graphs are derived, and an accurate analytical approximation for the expected uncertainty curve of Erdős-Rényi random graphs is developed. These theoretical results are validated by numerical experiments, which also reveal an intriguing connection between diffusion processes on graphs and the uncertainty bounds.
An Abstract Approach to Stratification in Linear Logic
Venue: arXiv cs.LO 2013
Year: 2013

We study the notion of stratification, as used in subsystems of linear logic with low complexity bounds on the cut-elimination procedure (the so-called light logics), from an abstract point of view, introducing a logical system in which stratification is handled by a separate modality. This modality, which is a generalization of the paragraph modality of Girard's light linear logic, arises from a general categorical construction applicable to all models of linear logic. We thus learn that stratification may be formulated independently of exponential modalities; when it is forced to be connected to exponential modalities, it yields interesting complexity properties. In particular, from our analysis stem three alternative reformulations of Baillot and Mazza's linear logic by levels: one geometric, one interactive, and one semantic.
Characteristic matrix of covering and its application to boolean matrix decomposition and axiomatization
Venue: arXiv cs.AI 2013
Year: 2013

Covering is an important type of data structure while covering-based rough sets provide an efficient and systematic theory to deal with covering data. In this paper, we use boolean matrices to represent and axiomatize three types of covering approximation operators. First, we define two types of characteristic matrices of a covering which are essentially square boolean ones, and their properties are studied. Through the characteristic matrices, three important types of covering approximation operators are concisely equivalently represented. Second, matrix representations of covering approximation operators are used in boolean matrix decomposition. We provide a sufficient and necessary condition for a square boolean matrix to decompose into the boolean product of another one and its transpose. And we develop an algorithm for this boolean matrix decomposition. Finally, based on the above results, these three types of covering approximation operators are axiomatized using boolean matrices. In a word, this work borrows extensively from boolean matrices and present a new view to study covering-based rough sets.
Kron Reduction of Generalized Electrical Networks
Venue: arXiv cs.SY 2013
Year: 2013

Kron reduction is used to simplify the analysis of multi-machine power systems under certain steady state assumptions that underly the usage of phasors. In this paper we show how to perform Kron reduction for a class of electrical networks without steady state assumptions. The reduced models can thus be used to analyze the transient as well as the steady state behavior of these electrical networks.
The number of distinct distances from a vertex of a convex polygon
Venue: arXiv cs.CG 2013
Year: 2013

Erdős conjectured in 1946 that every n-point set P in convex position in the plane contains a point that determines at least floor(n/2) distinct distances to the other points of P. The best known lower bound due to Dumitrescu (2006) is 13n/36 - O(1). In the present note, we slightly improve on this result to (13/36 + eps)n - O(1) for eps ~= 1/23000. Our main ingredient is an improved bound on the maximum number of isosceles triangles determined by P.
Optimal Deterministic Routing and Sorting on the Congested Clique
Venue: arXiv cs.DC 2013
Year: 2013

Consider a clique of n nodes, where in each synchronous round each pair of nodes can exchange O(log n) bits. We provide deterministic constant-time solutions for two problems in this model. The first is a routing problem where each node is source and destination of n messages of size O(log n). The second is a sorting problem where each node i is given n keys of size O(log n) and needs to receive the ith batch of n keys according to the global order of the keys. The latter result also implies deterministic constant-round solutions for related problems such as selection or determining modes.
A robust Khintchine inequality, and algorithms for computing optimal constants in Fourier analysis and high-dimensional geometry
Venue: arXiv cs.CC 2013
Year: 2013

This paper makes two contributions towards determining some well-studied optimal constants in Fourier analysis \newa{of Boolean functions} and high-dimensional geometry. \begin{enumerate} \item It has been known since 1994 \cite{GL:94} that every linear threshold function has squared Fourier mass at least 1/2 on its degree-0 and degree-1 coefficients. Denote the minimum such Fourier mass by $\w^{\leq 1}[\ltf]$, where the minimum is taken over all $n$-variable linear threshold functions and all $n \ge 0$. Benjamini, Kalai and Schramm \cite{BKS:99} have conjectured that the true value of $\w^{\leq 1}[\ltf]$ is $2/π$. We make progress on this conjecture by proving that $\w^{\leq 1}[\ltf] \geq 1/2 + c$ for some absolute constant $c>0$. The key ingredient in our proof is a "robust" version of the well-known Khintchine inequality in functional analysis, which we believe may be of independent interest. \item We give an algorithm with the following property: given any $η> 0$, the algorithm runs in time $2^{\poly(1/η)}$ and determines the value of $\w^{\leq 1}[\ltf]$ up to an additive error of $\pmη$. We give a similar $2^{\poly(1/η)}$-time algorithm to determine \emph{Tomaszewski's constant} to within an additive error of $\pm η$; this is the minimum (over all origin-centered hyperplanes $H$) fraction of points in $\{-1,1\}^n$ that lie within Euclidean distance 1 of $H$. Tomaszewski's constant is conjectured to be 1/2; lower bounds on it have been given by Holzman and Kleitman \cite{HK92} and independently by Ben-Tal, Nemirovski and Roos \cite{BNR02}. Our algorithms combine tools from anti-concentration of sums of independent random variables, Fourier analysis, and Hermite analysis of linear threshold functions. \end{enumerate}