OpenRaiser/Intern-Atlas huggingface dataset:
On a Connection Between Small Set Expansions and Modularity Clustering in Social Networks
Venue: arXiv cs.SI 2014
Year: 2014

In this paper we explore a connection between two seemingly different problems from two different domains: the small-set expansion problem studied in unique games conjecture, and a popular community finding approach for social networks known as the modularity clustering approach. We show that a sub-exponential time algorithm for the small-set expansion problem leads to a sub-exponential time constant factor approximation for some hard input instances of the modularity clustering problem.
Small Jump with Negation-UTM Trampoline
Venue: arXiv cs.CC 2014
Year: 2014

This paper divide some complexity class by using fixpoint and fixpointless area of Decidable Universal Turing Machine (UTM). Decidable Deterministic Turing Machine (DTM) have fixpointless combinator that add no extra resources (like Negation), but UTM makes some fixpoint in the combinator. This means that we can jump out of the fixpointless combinator system by making more complex problem from diagonalisation argument of UTM. As a concrete example, we proof L is not P . We can make Polynomial time UTM that emulate all Logarithm space DTM (LDTM). LDTM set close under Negation, therefore UTM does not close under LDTM set. (We can proof this theorem like halting problem and time/space hierarchy theorem, and also we can extend this proof to divide time/space limited DTM set.) In the same way, we proof P is not NP. These are new hierarchy that use UTM and Negation.
Towards Optimal and Expressive Kernelization for d-Hitting Set
Venue: arXiv cs.DM 2014
Year: 2014

d-Hitting Set is the NP-hard problem of selecting at most k vertices of a hypergraph so that each hyperedge, all of which have cardinality at most d, contains at least one selected vertex. The applications of d-Hitting Set are, for example, fault diagnosis, automatic program verification, and the noise-minimizing assignment of frequencies to radio transmitters. We show a linear-time algorithm that transforms an instance of d-Hitting Set into an equivalent instance comprising at most O(k^d) hyperedges and vertices. In terms of parameterized complexity, this is a problem kernel. Our kernelization algorithm is based on speeding up the well-known approach of finding and shrinking sunflowers in hypergraphs, which yields problem kernels with structural properties that we condense into the concept of expressive kernelization. We conduct experiments to show that our kernelization algorithm can kernelize instances with more than 10^7 hyperedges in less than five minutes. Finally, we show that the number of vertices in the problem kernel can be further reduced to O(k^{d-1}) with additional O(k^{1.5 d}) processing time by nontrivially combining the sunflower technique with d-Hitting Set problem kernels due to Abu-Khzam and Moser.
A Geometric Approach For Fully Automatic Chromosome Segmentation
Venue: arXiv cs.CV 2014
Year: 2014

A fundamental task in human chromosome analysis is chromosome segmentation. Segmentation plays an important role in chromosome karyotyping. The first step in segmentation is to remove intrusive objects such as stain debris and other noises. The next step is detection of touching and overlapping chromosomes, and the final step is separation of such chromosomes. Common methods for separation between touching chromosomes are interactive and require human intervention for correct separation between touching and overlapping chromosomes. In this paper, a geometric-based method is used for automatic detection of touching and overlapping chromosomes and separating them. The proposed scheme performs segmentation in two phases. In the first phase, chromosome clusters are detected using three geometric criteria, and in the second phase, chromosome clusters are separated using a cut-line. Most of earlier methods did not work properly in case of chromosome clusters that contained more than two chromosomes. Our method, on the other hand, is quite efficient in separation of such chromosome clusters. At each step, one separation will be performed and this algorithm is repeated until all individual chromosomes are separated. Another important point about the proposed method is that it uses the geometric features of chromosomes which are independent of the type of images and it can easily be applied to any type of images such as binary images and does not require multispectral images as well. We have applied our method to a database containing 62 touching and partially overlapping chromosomes and a success rate of 91.9% is achieved.
On Conditional Decomposability
Venue: arXiv cs.SY 2014
Year: 2014

The requirement of a language to be conditionally decomposable is imposed on a specification language in the coordination supervisory control framework of discrete-event systems. In this paper, we present a polynomial-time algorithm for the verification whether a language is conditionally decomposable with respect to given alphabets. Moreover, we also present a polynomial-time algorithm to extend the common alphabet so that the language becomes conditionally decomposable. A relationship of conditional decomposability to nonblockingness of modular discrete-event systems is also discussed in this paper in the general settings. It is shown that conditional decomposability is a weaker condition than nonblockingness.
Imperfect Secrecy in Wiretap Channel II
Venue: arXiv cs.IT 2014
Year: 2014

In a point-to-point communication system which consists of a sender, a receiver and a set of noiseless channels, the sender wishes to transmit a private message to the receiver through the channels which may be eavesdropped by a wiretapper. The set of wiretap sets is arbitrary. The wiretapper can access any one but not more than one wiretap set. From each wiretap set, the wiretapper can obtain some partial information about the private message which is measured by the equivocation of the message given the symbols obtained by the wiretapper. The security strategy is to encode the message with some random key at the sender. Only the message is required to be recovered at the receiver. Under this setting, we define an achievable rate tuple consisting of the size of the message, the size of the key, and the equivocation for each wiretap set. We first prove a tight rate region when both the message and the key are required to be recovered at the receiver. Then we extend the result to the general case when only the message is required to be recovered at the receiver. Moreover, we show that even if stochastic encoding is employed at the sender, the message rate cannot be increased.
Low-distortion Inference of Latent Similarities from a Multiplex Social Network
Venue: arXiv cs.SI 2014
Year: 2014

Much of social network analysis is - implicitly or explicitly - predicated on the assumption that individuals tend to be more similar to their friends than to strangers. Thus, an observed social network provides a noisy signal about the latent underlying "social space:" the way in which individuals are similar or dissimilar. Many research questions frequently addressed via social network analysis are in reality questions about this social space, raising the question of inverting the process: Given a social network, how accurately can we reconstruct the social structure of similarities and dissimilarities? We begin to address this problem formally. Observed social networks are usually multiplex, in the sense that they reflect (dis)similarities in several different "categories," such as geographical proximity, kinship, or similarity of professions/hobbies. We assume that each such category is characterized by a latent metric capturing (dis)similarities in this category. Each category gives rise to a separate social network: a random graph parameterized by this metric. For a concrete model, we consider Kleinberg's small world model and some variations thereof. The observed social network is the unlabeled union of these graphs, i.e., the presence or absence of edges can be observed, but not their origins. Our main result is an algorithm which reconstructs each metric with provably low distortion.
On the Capacity Region of Cognitive Multiple Access over White Space Channels
Venue: arXiv cs.IT 2014
Year: 2014

Opportunistically sharing the white spaces, or the temporarily unoccupied spectrum licensed to the primary user (PU), is a practical way to improve the spectrum utilization. In this paper, we consider the fundamental problem of rate regions achievable for multiple secondary users (SUs) which send their information to a common receiver over such a white space channel. In particular, the PU activities are treated as on/off side information, which can be obtained causally or non-causally by the SUs. The system is then modeled as a multi-switch channel and its achievable rate regions are characterized in some scenarios. Explicit forms of outer and inner bounds of the rate regions are derived by assuming additional side information, and they are shown to be tight in some special cases. An optimal rate and power allocation scheme that maximizes the sum rate is also proposed. The numerical results reveal the impacts of side information, channel correlation and PU activity on the achievable rates, and also verify the effectiveness of our rate and power allocation scheme. Our work may shed some light on the fundamental limit and design tradeoffs in practical cognitive radio systems.
Gossip-based Information Spreading in Mobile Networks
Venue: arXiv cs.SI 2014
Year: 2014

Mobile networks receive increasing research interest recently due to their increasingly wide applications in various areas; mobile ad hoc networks (MANET) and Vehicular ad hoc networks (VANET) are two prominent examples. Mobility introduces challenges as well as opportunities: it is known to improve the network throughput as shown in [1]. In this paper, we analyze the effect of mobility on the information spreading based on gossip algorithms. Our contributions are twofold. Firstly, we propose a new performance metric, mobile conductance, which allows us to separate the details of mobility models from the study of mobile spreading time. Secondly, we explore the mobile conductances of several popular mobility models, and offer insights on the corresponding results. Large scale network simulation is conducted to verify our analysis.
Information Transmission using the Nonlinear Fourier Transform, Part I: Mathematical Tools
Venue: arXiv cs.IT 2014
Year: 2014

The nonlinear Fourier transform (NFT), a powerful tool in soliton theory and exactly solvable models, is a method for solving integrable partial differential equations governing wave propagation in certain nonlinear media. The NFT decorrelates signal degrees-of-freedom in such models, in much the same way that the Fourier transform does for linear systems. In this three-part series of papers, this observation is exploited for data transmission over integrable channels such as optical fibers, where pulse propagation is governed by the nonlinear Schrödinger equation. In this transmission scheme, which can be viewed as a nonlinear analogue of orthogonal frequency-division multiplexing commonly used in linear channels, information is encoded in the nonlinear frequencies and their spectral amplitudes. Unlike most other fiber-optic transmission schemes, this technique deals with both dispersion and nonlinearity directly and unconditionally without the need for dispersion or nonlinearity compensation methods. This first paper explains the mathematical tools that underlie the method.
Robust computation of linear models by convex relaxation
Venue: arXiv cs.IT 2014
Year: 2014

Consider a dataset of vector-valued observations that consists of noisy inliers, which are explained well by a low-dimensional subspace, along with some number of outliers. This work describes a convex optimization problem, called REAPER, that can reliably fit a low-dimensional model to this type of data. This approach parameterizes linear subspaces using orthogonal projectors, and it uses a relaxation of the set of orthogonal projectors to reach the convex formulation. The paper provides an efficient algorithm for solving the REAPER problem, and it documents numerical experiments which confirm that REAPER can dependably find linear structure in synthetic and natural data. In addition, when the inliers lie near a low-dimensional subspace, there is a rigorous theory that describes when REAPER can approximate this subspace.
Bounded Termination of Monotonicity-Constraint Transition Systems
Venue: arXiv cs.LO 2014
Year: 2014

Intuitively, if we can prove that a program terminates, we expect some conclusion regarding its complexity. But the passage from termination proofs to complexity bounds is not always clear. In this work we consider Monotonicity Constraint Transition Systems, a program abstraction where termination is decidable (based on the size-change termination principle). We show that these programs also have a decidable complexity property: one can determine whether the length of all transition sequences can be bounded in terms of the initial state. This is the Bounded Termination problem. Interestingly, if a bound exists, it must be polynomial. We prove that the bounded termination problem is PSPACE-complete. We also discuss, theoretically, the use of bounds on the abstract program to infer conclusions on a concrete program that has been abstracted. The conclusion maybe a polynomial time bound, or in other cases polynomial space or exponential time. We argue that the monotonicity-constraint abstraction promises to be useful for practical complexity analysis of programs.
Induced Disjoint Paths in Claw-Free Graphs
Venue: arXiv cs.DM 2014
Year: 2014

Paths P1,...,Pk in a graph G=(V,E) are said to be mutually induced if for any 1 <= i < j <= k, Pi and Pj have neither common vertices nor adjacent vertices (except perhaps their end-vertices). The Induced Disjoint Paths problem is to test whether a graph G with k pairs of specified vertices (si,ti) contains k mutually induced paths Pi such that Pi connects si and ti for i=1,...,k. We show that this problem is fixed-parameter tractable for claw-free graphs when parameterized by k. Several related problems, such as the k-in-a-Path problem, are proven to be fixed-parameter tractable for claw-free graphs as well. We show that an improvement of these results in certain directions is unlikely, for example by noting that the Induced Disjoint Paths problem cannot have a polynomial kernel for line graphs (a type of claw-free graphs), unless NP \subseteq coNP/poly. Moreover, the problem becomes NP-complete, even when k=2, for the more general class of K_1,4-free graphs. Finally, we show that the n^O(k)-time algorithm of Fiala et al. for testing whether a claw-free graph contains some k-vertex graph H as a topological induced minor is essentially optimal by proving that this problem is W[1]-hard even if G and H are line graphs.
Distributed Private Heavy Hitters
Venue: arXiv cs.DS 2014
Year: 2014

In this paper, we give efficient algorithms and lower bounds for solving the heavy hitters problem while preserving differential privacy in the fully distributed local model. In this model, there are n parties, each of which possesses a single element from a universe of size N. The heavy hitters problem is to find the identity of the most common element shared amongst the n parties. In the local model, there is no trusted database administrator, and so the algorithm must interact with each of the $n$ parties separately, using a differentially private protocol. We give tight information-theoretic upper and lower bounds on the accuracy to which this problem can be solved in the local model (giving a separation between the local model and the more common centralized model of privacy), as well as computationally efficient algorithms even in the case where the data universe N may be exponentially large.
Some results on more flexible versions of Graph Motif
Venue: arXiv cs.CC 2014
Year: 2014

The problems studied in this paper originate from Graph Motif, a problem introduced in 2006 in the context of biological networks. Informally speaking, it consists in deciding if a multiset of colors occurs in a connected subgraph of a vertex-colored graph. Due to the high rate of noise in the biological data, more flexible definitions of the problem have been outlined. We present in this paper two inapproximability results for two different optimization variants of Graph Motif: one where the size of the solution is maximized, the other when the number of substitutions of colors to obtain the motif from the solution is minimized. We also study a decision version of Graph Motif where the connectivity constraint is replaced by the well known notion of graph modularity. While the problem remains NP-complete, it allows algorithms in FPT for biologically relevant parameterizations.
Autocalibration with the Minimum Number of Cameras with Known Pixel Shape
Venue: arXiv cs.CV 2014
Year: 2014

In 3D reconstruction, the recovery of the calibration parameters of the cameras is paramount since it provides metric information about the observed scene, e.g., measures of angles and ratios of distances. Autocalibration enables the estimation of the camera parameters without using a calibration device, but by enforcing simple constraints on the camera parameters. In the absence of information about the internal camera parameters such as the focal length and the principal point, the knowledge of the camera pixel shape is usually the only available constraint. Given a projective reconstruction of a rigid scene, we address the problem of the autocalibration of a minimal set of cameras with known pixel shape and otherwise arbitrarily varying intrinsic and extrinsic parameters. We propose an algorithm that only requires 5 cameras (the theoretical minimum), thus halving the number of cameras required by previous algorithms based on the same constraint. To this purpose, we introduce as our basic geometric tool the six-line conic variety (SLCV), consisting in the set of planes intersecting six given lines of 3D space in points of a conic. We show that the set of solutions of the Euclidean upgrading problem for three cameras with known pixel shape can be parameterized in a computationally efficient way. This parameterization is then used to solve autocalibration from five or more cameras, reducing the three-dimensional search space to a two-dimensional one. We provide experiments with real images showing the good performance of the technique.
A Fast Algorithm Finding the Shortest Reset Words
Venue: arXiv cs.FL 2014
Year: 2014

In this paper we present a new fast algorithm finding minimal reset words for finite synchronizing automata. The problem is know to be computationally hard, and our algorithm is exponential. Yet, it is faster than the algorithms used so far and it works well in practice. The main idea is to use a bidirectional BFS and radix (Patricia) tries to store and compare resulted subsets. We give both theoretical and practical arguments showing that the branching factor is reduced efficiently. As a practical test we perform an experimental study of the length of the shortest reset word for random automata with $n$ states and 2 input letters. We follow Skvorsov and Tipikin, who have performed such a study using a SAT solver and considering automata up to $n=100$ states. With our algorithm we are able to consider much larger sample of automata with up to $n=300$ states. In particular, we obtain a new more precise estimation of the expected length of the shortest reset word $\approx 2.5\sqrt{n-5}$.
Information Transmission using the Nonlinear Fourier Transform, Part II: Numerical Methods
Venue: arXiv cs.IT 2014
Year: 2014

In this paper, numerical methods are suggested to compute the discrete and the continuous spectrum of a signal with respect to the Zakharov-Shabat system, a Lax operator underlying numerous integrable communication channels including the nonlinear Schrödinger channel, modeling pulse propagation in optical fibers. These methods are subsequently tested and their ability to estimate the spectrum are compared against each other. These methods are used to compute the spectrum of various signals commonly used in the optical fiber communications. It is found that the layer-peeling and the spectral methods are suitable schemes to estimate the nonlinear spectra with good accuracy. To illustrate the structure of the spectrum, the locus of the eigenvalues is determined under amplitude and phase modulation in a number of examples. It is observed that in some cases, as signal parameters vary, eigenvalues collide and change their course of motion. The real axis is typically the place from which new eigenvalues originate or are absorbed into after traveling a trajectory in the complex plane.
Towards A Generic Formal Framework for Access Control Systems
Venue: arXiv cs.CR 2014
Year: 2014

There have been many proposals for access control models and authorization policy languages, which are used to inform the design of access control systems. Most, if not all, of these proposals impose restrictions on the implementation of access control systems, thereby limiting the type of authorization requests that can be processed or the structure of the authorization policies that can be specified. In this paper, we develop a formal characterization of the features of an access control model that imposes few restrictions of this nature. Our characterization is intended to be a generic framework for access control, from which we may derive access control models and reason about the properties of those models. In this paper, we consider the properties of monotonicity and completeness, the first being particularly important for attribute-based access control systems. XACML, an XML-based language and architecture for attribute-based access control, is neither monotonic nor complete. Using our framework, we define attribute-based access control models, in the style of XACML, that are, respectively, monotonic and complete.
Channel Capacity under Sub-Nyquist Nonuniform Sampling
Venue: arXiv cs.IT 2014
Year: 2014

This paper investigates the effect of sub-Nyquist sampling upon the capacity of an analog channel. The channel is assumed to be a linear time-invariant Gaussian channel, where perfect channel knowledge is available at both the transmitter and the receiver. We consider a general class of right-invertible time-preserving sampling methods which include irregular nonuniform sampling, and characterize in closed form the channel capacity achievable by this class of sampling methods, under a sampling rate and power constraint. Our results indicate that the optimal sampling structures extract out the set of frequencies that exhibits the highest signal-to-noise ratio among all spectral sets of measure equal to the sampling rate. This can be attained through filterbank sampling with uniform sampling at each branch with possibly different rates, or through a single branch of modulation and filtering followed by uniform sampling. These results reveal that for a large class of channels, employing irregular nonuniform sampling sets, while typically complicated to realize, does not provide capacity gain over uniform sampling sets with appropriate preprocessing. Our findings demonstrate that aliasing or scrambling of spectral components does not provide capacity gain, which is in contrast to the benefits obtained from random mixing in spectrum-blind compressive sampling schemes.