OpenRaiser/Intern-Atlas huggingface dataset:
Locating regions in a sequence under density constraints
Venue: arXiv cs.DS 2013
Year: 2013

Several biological problems require the identification of regions in a sequence where some feature occurs within a target density range: examples including the location of GC-rich regions, identification of CpG islands, and sequence matching. Mathematically, this corresponds to searching a string of 0s and 1s for a substring whose relative proportion of 1s lies between given lower and upper bounds. We consider the algorithmic problem of locating the longest such substring, as well as other related problems (such as finding the shortest substring or a maximal set of disjoint substrings). For locating the longest such substring, we develop an algorithm that runs in O(n) time, improving upon the previous best-known O(n log n) result. For the related problems we develop O(n log log n) algorithms, again improving upon the best-known O(n log n) results. Practical testing verifies that our new algorithms enjoy significantly smaller time and memory footprints, and can process sequences that are orders of magnitude longer as a result.
A Discrete Adapted Hierarchical Basis Solver For Radial Basis Function Interpolation
Venue: arXiv cs.NA 2013
Year: 2013

In this paper we develop a discrete Hierarchical Basis (HB) to efficiently solve the Radial Basis Function (RBF) interpolation problem with variable polynomial order. The HB forms an orthogonal set and is adapted to the kernel seed function and the placement of the interpolation nodes. Moreover, this basis is orthogonal to a set of polynomials up to a given order defined on the interpolating nodes. We are thus able to decouple the RBF interpolation problem for any order of the polynomial interpolation and solve it in two steps: (1) The polynomial orthogonal RBF interpolation problem is efficiently solved in the transformed HB basis with a GMRES iteration and a diagonal, or block SSOR preconditioner. (2) The residual is then projected onto an orthonormal polynomial basis. We apply our approach on several test cases to study its effectiveness, including an application to the Best Linear Unbiased Estimator regression problem.
Computing the Girth of a Planar Graph in Linear Time
Venue: arXiv cs.DS 2013
Year: 2013

The girth of a graph is the minimum weight of all simple cycles of the graph. We study the problem of determining the girth of an n-node unweighted undirected planar graph. The first non-trivial algorithm for the problem, given by Djidjev, runs in O(n^{5/4} log n) time. Chalermsook, Fakcharoenphol, and Nanongkai reduced the running time to O(n log^2 n). Weimann and Yuster further reduced the running time to O(n log n). In this paper, we solve the problem in O(n) time.
Hitting and Harvesting Pumpkins
Venue: arXiv cs.DS 2013
Year: 2013

The "c-pumpkin" is the graph with two vertices linked by c>0 parallel edges. A c-pumpkin-model in a graph G is a pair A,B of disjoint subsets of vertices of G, each inducing a connected subgraph of G, such that there are at least c edges in G between A and B. We focus on covering and packing c-pumpkin-models in a given graph: On the one hand, we provide an FPT algorithm running in time 2^O(k) n^O(1) deciding, for any fixed c>0, whether all c-pumpkin-models can be covered by at most k vertices. This generalizes known single-exponential FPT algorithms for Vertex Cover and Feedback Vertex Set, which correspond to the cases c=1,2 respectively. On the other hand, we present a O(log n)-approximation algorithm for both the problems of covering all c-pumpkin-models with a smallest number of vertices, and packing a maximum number of vertex-disjoint c-pumpkin-models.
An Algorithmic Solution to the Five-Point Pose Problem Based on the Cayley Representation of Rotations
Venue: arXiv cs.CV 2013
Year: 2013

We give a new algorithmic solution to the well-known five-point relative pose problem. Our approach does not deal with the famous cubic constraint on an essential matrix. Instead, we use the Cayley representation of rotations in order to obtain a polynomial system from epipolar constraints. Solving that system, we directly get relative rotation and translation parameters of the cameras in terms of roots of a 10th degree polynomial.
Overcoming Misleads In Logic Programs by Redefining Negation
Venue: arXiv cs.AI 2013
Year: 2013

Negation as failure and incomplete information in logic programs have been studied by many researchers In order to explains HOW a negated conclusion was reached, we introduce and proof a different way for negating facts to overcoming misleads in logic programs. Negating facts can be achieved by asking the user for constants that do not appear elsewhere in the knowledge base.
Optimal Real-time Spectrum Sharing between Cooperative Relay and Ad-hoc Networks
Venue: arXiv cs.IT 2013
Year: 2013

Optimization based spectrum sharing strategies have been widely studied. However, these strategies usually require a great amount of real-time computation and significant signaling delay, and thus are hard to be fulfilled in practical scenarios. This paper investigates optimal real-time spectrum sharing between a cooperative relay network (CRN) and a nearby ad-hoc network. Specifically, we optimize the spectrum access and resource allocation strategies of the CRN so that the average traffic collision time between the two networks can be minimized while maintaining a required throughput for the CRN. The development is first for a frame-level setting, and then is extended to an ergodic setting. For the latter setting, we propose an appealing optimal real-time spectrum sharing strategy via Lagrangian dual optimization. The proposed method only involves a small amount of real-time computation and negligible control delay, and thus is suitable for practical implementations. Simulation results are presented to demonstrate the efficiency of the proposed strategies.
Efficient Transductive Online Learning via Randomized Rounding
Venue: arXiv cs.LG 2013
Year: 2013

Most traditional online learning algorithms are based on variants of mirror descent or follow-the-leader. In this paper, we present an online algorithm based on a completely different approach, tailored for transductive settings, which combines "random playout" and randomized rounding of loss subgradients. As an application of our approach, we present the first computationally efficient online algorithm for collaborative filtering with trace-norm constrained matrices. As a second application, we solve an open question linking batch learning and transductive online learning
Perturbation Analysis of Orthogonal Matching Pursuit
Venue: arXiv cs.IT 2013
Year: 2013

Orthogonal Matching Pursuit (OMP) is a canonical greedy pursuit algorithm for sparse approximation. Previous studies of OMP have mainly considered the exact recovery of a sparse signal $\bm x$ through $\bm Φ$ and $\bm y=\bm Φ\bm x$, where $\bm Φ$ is a matrix with more columns than rows. In this paper, based on Restricted Isometry Property (RIP), the performance of OMP is analyzed under general perturbations, which means both $\bm y$ and $\bm Φ$ are perturbed. Though exact recovery of an almost sparse signal $\bm x$ is no longer feasible, the main contribution reveals that the exact recovery of the locations of $k$ largest magnitude entries of $\bm x$ can be guaranteed under reasonable conditions. The error between $\bm x$ and solution of OMP is also estimated. It is also demonstrated that the sufficient condition is rather tight by constructing an example. When $\bm x$ is strong-decaying, it is proved that the sufficient conditions can be relaxed, and the locations can even be recovered in the order of the entries' magnitude.
Dynamic Range Selection in Linear Space
Venue: arXiv cs.CG 2013
Year: 2013

Given a set $S$ of $n$ points in the plane, we consider the problem of answering range selection queries on $S$: that is, given an arbitrary $x$-range $Q$ and an integer $k > 0$, return the $k$-th smallest $y$-coordinate from the set of points that have $x$-coordinates in $Q$. We present a linear space data structure that maintains a dynamic set of $n$ points in the plane with real coordinates, and supports range selection queries in $O((\lg n / \lg \lg n)^2)$ time, as well as insertions and deletions in $O((\lg n / \lg \lg n)^2)$ amortized time. The space usage of this data structure is an $Θ(\lg n / \lg \lg n)$ factor improvement over the previous best result, while maintaining asymptotically matching query and update times. We also present a succinct data structure that supports range selection queries on a dynamic array of $n$ values drawn from a bounded universe.
Furthering Baseline Core Lucid Standard Specification in the Context of the History of Lucid, Intensional Programming, and Context-Aware Computing
Venue: arXiv cs.PL 2013
Year: 2013

This work is multifold. We review the historical literature on the Lucid programming language, its dialects, intensional logic, intensional programming, the implementing systems, and context-oriented and context-aware computing and so on that provide a contextual framework for the converging Core Lucid standard programming model. We are designing a standard specification of a baseline Lucid virtual machine for generic execution of Lucid programs. The resulting Core Lucid language would inherit the properties of generalization attempts of GIPL (1999-2013) and TransLucid (2008-2013) for all future and recent Lucid implementing systems to follow. We also maintain this work across local research group in order to foster deeper collaboration, maintain a list of recent and historical bibliography and a reference manual and reading list for students. We form a (for now informal) SIGLUCID group to keep track of this standard and historical records with eventual long-term goal through iterative revisions for this work to become a book or an encyclopedia of the referenced topics, and perhaps, an RFC. We first begin small with this initial set of notes.
Bounded Rationality in Concurrent Parity Games
Venue: arXiv cs.GT 2013
Year: 2013

We consider 2-player games played on a finite state space for infinite rounds. The games are concurrent: in each round, the two players choose their moves simultaneously; the current state and the moves determine the successor. We consider omega-regular winning conditions given as parity objectives. We consider the qualitative analysis problems: the computation of the almost-sure and limit-sure winning set of states, where player 1 can ensure to win with probability 1 and with probability arbitrarily close to 1, respectively. In general the almost-sure and limit-sure winning strategies require both infinite-memory and infinite-precision. We study the bounded-rationality problem for qualitative analysis of concurrent parity games, where the strategy set player 1 is restricted to bounded-resource strategies. In terms of precision, strategies can be deterministic, uniform, finite-precision or infinite-precision; and in terms of memory, strategies can be memoryless, finite-memory or infinite-memory. We present a precise and complete characterization of the qualitative winning sets for all combinations of classes of strategies. In particular, we show that uniform memoryless strategies are as powerful as finite-precision infinite-memory strategies, and infinite-precision memoryless strategies are as powerful as infinite-precision finite-memory strategies. We show that the winning sets can be computed in O(n^{2d+3}) time, where n is the size of the game and 2d is the number of priorities, and our algorithms are symbolic. The membership problem of whether a state belongs to a winning set can be decided in NP cap coNP. While this complexity is the same as for the simpler class of turn-based games, where in each state only one of the players has a choice of moves, our algorithms, that are obtained by characterization of the winning sets as mu-calculus formulas, are considerably more involved.
Model Based Synthesis of Control Software from System Level Formal Specifications
Venue: arXiv cs.SE 2013
Year: 2013

Many Embedded Systems are indeed Software Based Control Systems, that is control systems whose controller consists of control software running on a microcontroller device. This motivates investigation on Formal Model Based Design approaches for automatic synthesis of embedded systems control software. We present an algorithm, along with a tool QKS implementing it, that from a formal model (as a Discrete Time Linear Hybrid System) of the controlled system (plant), implementation specifications (that is, number of bits in the Analog-to-Digital, AD, conversion) and System Level Formal Specifications (that is, safety and liveness requirements for the closed loop system) returns correct-by-construction control software that has a Worst Case Execution Time (WCET) linear in the number of AD bits and meets the given specifications. We show feasibility of our approach by presenting experimental results on using it to synthesize control software for a buck DC-DC converter, a widely used mixed-mode analog circuit, and for the inverted pendulum.
Approximate Bregman near neighbors in sublinear time: Beyond the triangle inequality
Venue: arXiv cs.CG 2013
Year: 2013

In this paper we present the first provable approximate nearest-neighbor (ANN) algorithms for Bregman divergences. Our first algorithm processes queries in O(log^d n) time using O(n log^d n) space and only uses general properties of the underlying distance function (which includes Bregman divergences as a special case). The second algorithm processes queries in O(log n) time using O(n) space and exploits structural constants associated specifically with Bregman divergences. An interesting feature of our algorithms is that they extend the ring-tree + quad-tree paradigm for ANN searching beyond Euclidean distances and metrics of bounded doubling dimension to distances that might not even be symmetric or satisfy a triangle inequality.
Novel Analysis of Population Scalability in Evolutionary Algorithms
Venue: arXiv cs.NE 2013
Year: 2013

Population-based evolutionary algorithms (EAs) have been widely applied to solve various optimization problems. The question of how the performance of a population-based EA depends on the population size arises naturally. The performance of an EA may be evaluated by different measures, such as the average convergence rate to the optimal set per generation or the expected number of generations to encounter an optimal solution for the first time. Population scalability is the performance ratio between a benchmark EA and another EA using identical genetic operators but a larger population size. Although intuitively the performance of an EA may improve if its population size increases, currently there exist only a few case studies for simple fitness functions. This paper aims at providing a general study for discrete optimisation. A novel approach is introduced to analyse population scalability using the fundamental matrix. The following two contributions summarize the major results of the current article. (1) We demonstrate rigorously that for elitist EAs with identical global mutation, using a lager population size always increases the average rate of convergence to the optimal set; and yet, sometimes, the expected number of generations needed to find an optimal solution (measured by either the maximal value or the average value) may increase, rather than decrease. (2) We establish sufficient and/or necessary conditions for the superlinear scalability, that is, when the average convergence rate of a $(μ+μ)$ EA (where $μ\ge2$) is bigger than $μ$ times that of a $(1+1)$ EA.
Blending margins: The modal logic K has nullary unification type
Venue: arXiv cs.LO 2013
Year: 2013

We investigate properties of the formula $p \to \Box p$ in the basic modal logic K. We show that K satisfies an infinitary weaker variant of the rule of margins $ϕ\to \Boxϕ/ ϕ, \negϕ$, and as a consequence, we obtain various negative results about admissibility and unification in K. We describe a complete set of unifiers (i.e., substitutions making the formula provable) of $p \to \Box p$, and use it to establish that K has the worst possible unification type: nullary. In well-behaved transitive modal logics, admissibility and unification can be analyzed in terms of projective formulas, introduced by Ghilardi; in particular, projective formulas coincide for these logics with formulas that are admissibly saturated (i.e., derive all their multiple-conclusion admissible consequences) or exact (i.e., axiomatize a theory of a substitution). In contrast, we show that in K, the formula $p \to \Box p$ is admissibly saturated, but neither projective nor exact. All our results for K also apply to the basic description logic ALC.
An Overview of Codes Tailor-made for Better Repairability in Networked Distributed Storage Systems
Venue: arXiv cs.DC 2013
Year: 2013

The continuously increasing amount of digital data generated by today's society asks for better storage solutions. This survey looks at a new generation of coding techniques designed specifically for the needs of distributed networked storage systems, trying to reach the best compromise among storage space efficiency, fault tolerance, and maintenance overheads. Four families of codes tailor-made for distributed settings, namely - pyramid, hierarchical, regenerating and self-repairing codes - are presented at a high level, emphasizing the main ideas behind each of these codes, and discussing their pros and cons, before concluding with a quantitative comparison among them. This survey deliberately excluded technical details for the codes, nor does it provide an exhaustive summary of the numerous works. Instead, it provides an overview of the major code families in a manner easily accessible to a broad audience, by presenting the big picture of advances in coding techniques for distributed storage solutions.
Distributed User Profiling via Spectral Methods
Venue: arXiv cs.LG 2013
Year: 2013

User profiling is a useful primitive for constructing personalised services, such as content recommendation. In the present paper we investigate the feasibility of user profiling in a distributed setting, with no central authority and only local information exchanges between users. We compute a profile vector for each user (i.e., a low-dimensional vector that characterises her taste) via spectral transformation of observed user-produced ratings for items. Our two main contributions follow: i) We consider a low-rank probabilistic model of user taste. More specifically, we consider that users and items are partitioned in a constant number of classes, such that users and items within the same class are statistically identical. We prove that without prior knowledge of the compositions of the classes, based solely on few random observed ratings (namely $O(N\log N)$ such ratings for $N$ users), we can predict user preference with high probability for unrated items by running a local vote among users with similar profile vectors. In addition, we provide empirical evaluations characterising the way in which spectral profiling performance depends on the dimension of the profile space. Such evaluations are performed on a data set of real user ratings provided by Netflix. ii) We develop distributed algorithms which provably achieve an embedding of users into a low-dimensional space, based on spectral transformation. These involve simple message passing among users, and provably converge to the desired embedding. Our method essentially relies on a novel combination of gossiping and the algorithm proposed by Oja and Karhunen.
Verification, Validation and Testing of Kinetic Mechanisms of Hydrogen Combustion in Fluid Dynamic Computations
Venue: arXiv cs.CE 2013
Year: 2013

A one-step, a two-step, an abridged, a skeletal and four detailed kinetic schemes of hydrogen oxidation have been tested. A new skeletal kinetic scheme of hydrogen oxidation has been developed. The CFD calculations were carried out using ANSYS CFX software. Ignition delay times and speeds of flames were derived from the computational results. The computational data obtained using ANSYS CFX and CHEMKIN, and experimental data were compared. The precision, reliability, and range of validity of the kinetic schemes in CFD simulations were estimated. The impact of kinetic scheme on the results of computations was discussed. The relationship between grid spacing, timestep, accuracy, and computational cost were analyzed.
FemtoCaching: Wireless Video Content Delivery through Distributed Caching Helpers
Venue: arXiv cs.NI 2013
Year: 2013

Video on-demand streaming from Internet-based servers is becoming one of the most important services offered by wireless networks today. In order to improve the area spectral efficiency of video transmission in cellular systems, small cells heterogeneous architectures (e.g., femtocells, WiFi off-loading) are being proposed, such that video traffic to nomadic users can be handled by short-range links to the nearest small cell access points (referred to as "helpers"). As the helper deployment density increases, the backhaul capacity becomes the system bottleneck. In order to alleviate such bottleneck we propose a system where helpers with low-rate backhaul but high storage capacity cache popular video files. Files not available from helpers are transmitted by the cellular base station. We analyze the optimum way of assigning files to the helpers, in order to minimize the expected downloading time for files. We distinguish between the uncoded case (where only complete files are stored) and the coded case, where segments of Fountain-encoded versions of the video files are stored at helpers. We show that the uncoded optimum file assignment is NP-hard, and develop a greedy strategy that is provably within a factor 2 of the optimum. Further, for a special case we provide an efficient algorithm achieving a provably better approximation ratio of $1-(1-1/d)^d$, where $d$ is the maximum number of helpers a user can be connected to. We also show that the coded optimum cache assignment problem is convex that can be further reduced to a linear program. We present numerical results comparing the proposed schemes.
Outlier detection in default logics: the tractability/intractability frontier
Venue: arXiv cs.AI 2013
Year: 2013

In default theories, outliers denote sets of literals featuring unexpected properties. In previous papers, we have defined outliers in default logics and investigated their formal properties. Specifically, we have looked into the computational complexity of outlier detection problems and proved that while they are generally intractable, interesting tractable cases can be singled out. Following those results, we study here the tractability frontier in outlier detection problems, by analyzing it with respect to (i) the considered outlier detection problem, (ii) the reference default logic fragment, and (iii) the adopted notion of outlier. As for point (i), we shall consider three problems of increasing complexity, called Outlier-Witness Recognition, Outlier Recognition and Outlier Existence, respectively. As for point (ii), as we look for conditions under which outlier detection can be done efficiently, attention will be limited to subsets of Disjunction-free propositional default theories. As for point (iii), we shall refer to both the notion of outlier of [ABP08] and a new and more restrictive one, called strong outlier. After complexity results, we present a polynomial time algorithm for enumerating all strong outliers of bounded size in an quasi-acyclic normal unary default theory. Some of our tractability results rely on the Incremental Lemma that provides conditions for a deafult logic fragment to have a monotonic behavior. Finally, in order to show that the simple fragments of DL we deal with are still rich enough to solve interesting problems and, therefore, the tractability results that we prove are interesting not only on the mere theoretical side, insights into the expressive capabilities of these fragments are provided, by showing that normal unary theories express all NL queries, hereby indirectly answering a question raised by Kautz and Selman.