"Euclidean distance geometry is the study of Euclidean geometry based on the concept of distance. This is useful in several applications where the input data consists of an incomplete set of distances, and the output is a set of points in Euclidean space that realizes the given distances. We survey some of the theory of Euclidean distance geometry and some of the most important applications: molecular conformation, localization of sensor networks and statics."

"Another illustration that knowledge comes not through blind adherence to methods, but human reflection."

"In sports competitions, teams can manipulate the result by, for instance, throwing games. We show that we can decide how to manipulate round robin and cup competitions, two of the most popular types of sporting competitions in polynomial time. In addition, we show that finding the minimal number of games that need to be thrown to manipulate the result can also be determined in polynomial time. Finally, we show that there are several different variations of standard cup competitions where manipulation remains polynomial."

"Tetravex is a widely played one person computer game in which you are given $n^2$ unit tiles, each edge of which is labelled with a number. The objective is to place each tile within a $n$ by $n$ square such that all neighbouring edges are labelled with an identical number. Unfortunately, playing Tetravex is computationally hard. More precisely, we prove that deciding if there is a tiling of the Tetravex board is NP-complete. Deciding where to place the tiles is therefore NP-hard. This may help to explain why Tetravex is a good puzzle. This result compliments a number of similar results for one person games involving tiling. For example, NP-completeness results have been shown for: the offline version of Tetris, KPlumber (which involves rotating tiles containing drawings of pipes to make a connected network), and shortest sliding puzzle problems. It raises a number of open questions. For example, is the infinite version Turing-complete? How do we generate Tetravex problems which are truly puzzling as random NP-complete problems are often surprising easy to solve? Can we observe phase transition behaviour? What about the complexity of the problem when it is guaranteed to have an unique solution? How do we generate puzzles with unique solutions?"

"We consider the age-old problem of allocating items among different agents in a way that is efficient and fair. Two papers, by Dolev et al. and Ghodsi et al., have recently studied this problem in the context of computer systems. Both papers had similar models for agent preferences, but advocated different notions of fairness. We formalize both fairness notions in economic terms, extending them to apply to a larger family of utilities. Noting that in settings with such utilities efficiency is easily achieved in multiple ways, we study notions of fairness as criteria for choosing between different efficient allocations. Our technical results are algorithms for finding fair allocations corresponding to two fairness notions: Regarding the notion suggested by Ghodsi et al., we present a polynomial-time algorithm that computes an allocation for a general class of fairness notions, in which their notion is included. For the other, suggested by Dolev et al., we show that a competitive market equilibrium achieves the desired notion of fairness, thereby obtaining a polynomial-time algorithm that computes such a fair allocation and solving the main open problem raised by Dolev et al."

"We investigate higher-order Voronoi diagrams in the city metric. This metric is induced by quickest paths in the L1 metric in the presence of an accelerating transportation network of axis-parallel line segments. …"

"Computer scientists make LDA seem complicated because they care about proving that their algorithms work. And the proof is indeed brain-squashingly hard. But the practice of topic modeling makes good sense on its own, without proof, and does not require you to spend even a second thinking about “Dirichlet distributions.” When the math is approached in a practical way, I think humanists will find it easy, intuitive, and empowering. This post focuses on LDA as shorthand for a broader family of “probabilistic” techniques. I’m going to ask how they work, what they’re for, and what their limits are."

"We present a novel angular fingerprinting algorithm for detecting changes in the direction of rotation of a target with a monostatic, stationary sonar platform. Unlike other approaches, we assume that the target's centroid is stationary, and exploit doppler multipath signals to resolve the otherwise unavoidable ambiguities that arise. Since the algorithm is based on an underlying differential topological theory, it is highly robust to distortions in the collected data. We demonstrate performance of this algorithm experimentally, by exhibiting a pulsed doppler sonar collection system that runs on a smartphone. The performance of this system is sufficiently good to both detect changes in target rotation direction using angular fingerprints, and also to form high-resolution inverse synthetic aperature images of the target."

"This paper gives an introduction to the problem of mapping simple polygons with autonomous agents. We focus on minimalistic agents that move from vertex to vertex along straight lines inside a polygon, using their sensors to gather local observations at each vertex. Our attention revolves around the question whether a given configuration of sensors and movement capabilities of the agents allows them to capture enough data in order to draw conclusions regarding the global layout of the polygon. In particular, we study the problem of reconstructing the visibility graph of a simple polygon by an agent moving either inside or on the boundary of the polygon. Our aim is to provide insight about the algorithmic challenges faced by an agent trying to map a polygon. We present an overview of techniques for solving this problem with agents that are equipped with simple sensorial capabilities. We illustrate these techniques on examples with sensors that mea- sure angles between lines of sight or identify the previous location. We give an overview over related problems in combinatorial geometry as well as graph exploration."

"Determining whether an unordered collection of overlapping substrings (called shingles) can be uniquely decoded into a consistent string is a problem that lies within the foundation of a broad assortment of disciplines ranging from networking and information theory through cryptography and even genetic engineering and linguistics. We present three perspectives on this problem: a graph theoretic framework due to Pevzner, an automata theoretic approach from our previous work, and a new insight that yields a time-optimal streaming algorithm for determining whether a string of $n$ characters over the alphabet $Sigma$ can be uniquely decoded from its two-character shingles. Our algorithm achieves an overall time complexity $Theta(n)$ and space complexity $O(|Sigma|)$. As an application, we demonstrate how this algorithm can be extended to larger shingles for efficient string reconciliation."

On my macbook air (Intel core i7), I get that the unpacking speed is not very sensitive to the specific number of bits: generally, the smaller the bit width, the faster the unpacking. The packing speed is much faster when the bit width is 8 or 16. Even so, the difference is only by a factor of two or so. The results are presented in the next figure. On the y axis, you have the time (smaller is better). On the the x axis, we have the number of bits we packed to. For example, when bit is 1, we pack 32 integers into a single 32-bit word. When the number of bits is set to 32 bits, we have a regular copy.

things I never learned

"Previous researches have demonstrated that the framework of dictionary learning with sparse coding, in which signals are decomposed as linear combinations of a few atoms of a learned dictionary, is well adept to reconstruction issues. This framework has also been used for discrimination tasks such as image classification. To achieve better performances of classification, experts develop several methods to learn a discriminative dictionary in a supervised manner. However, another issue is that when the data become extremely large in scale, these methods will be no longer effective as they are all batch-oriented approaches. For this reason, we propose a novel online algorithm for discriminative dictionary learning, dubbed textbf{ODDL} in this paper. First, we introduce a linear classifier into the conventional dictionary learning formulation and derive a discriminative dictionary learning problem. Then, we exploit an online algorithm to solve the derived problem. Unlike the most existing approaches which update dictionary and classifier alternately via iteratively solving sub-problems, our approach directly explores them jointly. Meanwhile, it can largely shorten the runtime for training and is also particularly suitable for large-scale classification issues. To evaluate the performance of the proposed ODDL approach in image recognition, we conduct some experiments on three well-known benchmarks, and the experimental results demonstrate ODDL is fairly promising for image classification tasks."

"The game of chess as always been viewed as an iconic representation of intellectual prowess. Since the very beginning of computer science, the challenge of being able to program a computer capable of playing chess and beating humans has been alive and used both as a mark to measure hardware/software progresses and as an ongoing programming challenge leading to numerous discoveries. In the early days of computer science it was a topic for specialists. But as computers were democratized, and the strength of chess engines began to increase, chess players started to appropriate to themselves these new tools. We show how these interactions between the world of chess and information technologies have been herald of broader social impacts of information technologies. The game of chess, and more broadly the world of chess (chess players, literature, computer softwares and websites dedicated to chess, etc.), turns out to be a surprisingly and particularly sharp indicator of the changes induced in our everyday life by the information technologies. Moreover, in the same way that chess is a modelization of war that captures the raw features of strategic thinking, chess world can be seen as small society making the study of the information technologies impact easier to analyze and to grasp."

"Network coding is studied when an adversary controls a subset of nodes in the network of limited quantity but unknown location. This problem is shown to be more difficult than when the adversary controls a given number of edges in the network, in that linear codes are insufficient. To solve the node problem, the class of Polytope Codes is introduced. Polytope Codes are constant composition codes operating over bounded polytopes in integer vector fields. The polytope structure creates additional complexity, but it induces properties on marginal distributions of code vectors so that validities of codewords can be checked by internal nodes of the network. It is shown that Polytope Codes achieve a cut-set bound for a class of planar networks. It is also shown that this cut-set bound is not always tight, and a tighter bound is given for an example network."

"Single-particle imaging experiments of biomolecules at x-ray free-electron lasers (XFELs) require processing of hundreds of thousands (or more) of images that contain very few x-rays. Each low-flux image of the diffraction pattern is produced by a single, randomly oriented particle, such as a protein. We demonstrate the feasibility of collecting data at these extremes, averaging only 2.5 photons per frame, where it seems doubtful there could be information about the state of rotation, let alone the image contrast. This is accomplished with an expectation maximization algorithm that processes the low-flux data in aggregate, and without any prior knowledge of the object or its orientation. The versatility of the method promises, more generally, to redefine what measurement scenarios can provide useful signal in the high-noise regime."

"The activities, in project scheduling, can be represented graphically in two different ways, by either assigning the activities to the nodes 'AoN' directed acyclic graph (dag) or to the arcs 'AoA dag'. In this paper, a new algorithm is proposed for generating, for a given project scheduling problem, an Activity-on-Arc dag starting from the Activity-on-Node dag using the concepts of line graphs of graphs."

"...Common misconceptions regarding the embedding approach are addressed including whether or not it results in an average value control model (no), is necessary to "tweak" the algorithm to get bang-bang solutions (no), requires infinite switching (no), has real-time capability (yes), or reduction to a classical nonlinear optimization problem (a desirable yes)."

"This paper proposes a novel adaptive algorithm to extract facial feature points automatically such as eyebrows corners, eyes corners, nostrils, nose tip, and mouth corners in frontal view faces, which is based on cumulative histogram approach by varying different threshold values. At first, the method adopts the Viola-Jones face detector to detect the location of face and also crops the face region in an image. From the concept of the human face structure, the six relevant regions such as right eyebrow, left eyebrow, right eye, left eye, nose, and mouth areas are cropped in a face image. Then the histogram of each cropped relevant region is computed and its cumulative histogram value is employed by varying different threshold values to create a new filtering image in an adaptive way. The connected component of interested area for each relevant filtering image is indicated our respective feature region. A simple linear search algorithm for eyebrows, eyes and mouth filtering images and contour algorithm for nose filtering image are applied to extract our desired corner points automatically. The method was tested on a large BioID frontal face database in different illuminations, expressions and lighting conditions and the experimental results have achieved average success rates of 95.27%."

"We study a character-based phylogeny reconstruction problem when an incomplete set of data is given. More specifically, we consider the situation under the directed perfect phylogeny assumption with binary characters in which for some species the states of some characters are missing. Our main object is to give an efficient algorithm to enumerate (or list) all perfect phylogenies that can be obtained when the missing entries are completed. While a simple branch-and-bound algorithm (B&B) shows a theoretically good performance, we propose another approach based on a zero-suppressed binary decision diagram (ZDD). Experimental results on randomly generated data exhibit that the ZDD approach outperforms B&B. We also prove that counting the number of phylogenetic trees consistent with a given data is #P-complete, thus providing an evidence that an efficient random sampling seems hard."

"In this work we develop an algorithm for signal reconstruction from the magnitude of its Fourier transform in a situation where some (non-zero) parts of the sought signal are known. Although our method does not assume that the known part comprises the boundary of the sought signal, this is often the case in microscopy: a specimen is placed inside a known mask, which can be thought of as a known light source that surrounds the unknown signal. Therefore, in the past, several algorithms were suggested that solve the phase retrieval problem assuming known boundary values. Unlike our method, these methods do rely on the fact that the known part is on the boundary. Besides the reconstruction method we give an explanation of the phenomena observed in previous work: the reconstruction is much faster when there is more energy concentrated in the known part. Quite surprisingly, this can be explained using our previous results on phase retrieval with approximately known Fourier phase."

"We proposed two new exact algorithms to detect network motifs of size 3 and 4. Considering that motifs need to count the isomorphic patterns in the original graph $G(V,E)$ and in a set of randomized graphs, the following complexities concern about count isomorphic patterns in a single graph. Let $m=|E|$ and let $a(G)$ be the arboricity of $G$. Assume $|E|geq|V|$. We describe a $O(a(G)m)$ time complexity algorithm to count isomorphic patterns of size 3. The complexity is a $O({msqrt{m}})$ in the worst graph. The second algorithm is a $O(m^2)$ complexity algorithm to count isomorphic patterns of size 4. The final result was expressive faster when compared with other implemented algorithms."

"This paper presents a study on two data structures that have been used to model several problems in computer science: and/or graphs and x-y graphs. An and/or graph is an acyclic digraph containing a source, such that every vertex v has a label f(v) in {and,or} and edges represent dependency relations between vertices: a vertex labeled and depends on all of its out-neighbors, while a vertex labeled or depends on only one of its out-neighbors. X-y graphs are defined as a natural generalization of and/or graphs: every vertex vi of an x-y graph has a label xi-yi to mean that vi depends on xi of its yi out-neighbors. We analyze the complexity of the optimization problems Min-and/or and Min-x-y, which consist of finding solution subgraphs of optimal weight for and/or and x-y graphs, respectively. Motivated by the large applicability as well as the hardness of Min-and/or and Min-x-y, we study new complexity aspects of such problems, both from a classical and a parameterized point of view. …"

"We examine the history of cake cutting mechanisms and discuss the efficiency of their allocations. In the case of piecewise uniform preferences, we define a game that in the presence of strategic agents has equilibria that are not dominated by the allocations of any mechanism. We identify that the equilibria of this game coincide with the allocations of an existing cake cutting mechanism."

"A characteristic feature of functional data is the presence of time variability in addition to amplitude variability. The existing functional regression methods do not handle time variability in an explicit and efficient way. In this paper we introduce a functional regression method that incorporates time warping as an intrinsic part of the model. The method achieves good predictive power in a parsimonious way, and allows for unified statistical inference of time and amplitude variability. The properties of the estimators are studied by simulation, and an application to the modeling of ground-level ozone trajectories is presented."

"We present a new algorithm to solve polynomial equations, and publish its code, which is 1.6-3 times faster than the ZROOTS subroutine that is commercially available from Numerical Recipes, depending on application. The largest improvement, when compared to naive solvers, comes from a fail-safe procedure that permits us to skip the majority of the calculations in the great majority of cases, without risking catastrophic failure in the few cases that these are actually required. Second, we identify a discriminant that enables a rational choice between Laguerre's Method and Newton's Method (or a new intermediate method) on a case-by-case basis. We briefly review the history of root solving and demonstrate that "Newton's Method" was discovered neither by Newton (1671) nor by Raphson (1690), but only by Simpson (1740). Some of the arguments leading to this conclusion were first given by the British historian of science Nick Kollerstrom in 1992, but these do not appear to have penetrated the astronomical community. Finally, we argue that Numerical Recipes should voluntarily surrender its copyright protection for non-profit applications, despite the fact that, in this particular case, such protection was the major stimulant for developing our improved algorithm."

"In several application domains, high-dimensional observations are collected and then analysed in search for naturally occurring data clusters which might provide further insights about the nature of the problem. In this paper we describe a new approach for partitioning such high-dimensional data. Our assumption is that, within each cluster, the data can be approximated well by a linear subspace estimated by means of a principal component analysis (PCA). The proposed algorithm, Predictive Subspace Clustering (PSC) partitions the data into clusters while simultaneously estimating cluster-wise PCA parameters. The algorithm minimises an objective function that depends upon a new measure of influence for PCA models. A penalised version of the algorithm is also described for carrying our simultaneous subspace clustering and variable selection. The convergence of PSC is discussed in detail, and extensive simulation results and comparisons to competing methods are presented. The comparative performance of PSC has been assessed on six real gene expression data sets for which PSC often provides state-of-art results."

"In this paper we investigate the problem of building a static data structure that represents a string s using space close to its compressed size, and allows fast access to individual characters of s. ..."

"The graph realization problem has received a great deal of attention in recent years, due to its importance in applications such as wireless sensor networks and structural biology.…"

"…In this paper, we introduce a replay method- ology for contextual bandit algorithm evaluation. Different from simulator-based approaches, our method is completely data-driven and very easy to adapt to different applications. More importantly, our method can provide provably unbi- ased evaluations. Our empirical results on a large-scale news article recommendation dataset collected from Yahoo! Front Page conform well with our theoretical results. Furthermore, comparisons between our offline replay and online bucket evaluation of several contextual bandit algorithms show ac- curacy and effectiveness of our offline evaluation method."

"Block Sorting is a well studied problem, motivated by its applications in Optical Character Recognition (OCR), and Computational Biology. Block Sorting has been shown to be NP-Hard, and two separate polynomial time 2-approximation algorithms have been designed for the problem. But questions like whether a better approximation algorithm can be designed, and whether the problem is APX-Hard have been open for quite a while now.
In this work we answer the latter question by proving Block Sorting to be Max-SNP-Hard (APX-Hard). The APX-Hardness result is based on a linear reduction of Max-3SAT to Block Sorting. We also provide a new lower bound for the problem via a new parametrized problem k-Block Merging."

'We show that single-digit "Nishio" subproblems in nxn Sudoku puzzles may be solved in time o(2^n), faster than previous solutions such as the pattern overlay method. We also show that single-digit deduction in Sudoku is NP-hard.'

"A new model for computer simulation of solids, composed of bonded particles, is proposed. Vectors rigidly connected with particles are used for description of deformation of a single bond. The expression for potential energy of the bond and corresponding expressions for forces and moments are proposed. Formulas, connecting parameters of the model with longitudinal, shear, bending and torsional stiffnesses of the bond, are derived. It is shown that the model allows to describe any values of the bond stiffnesses exactly. Two different calibration procedures depending on bond length/thickness ratio are proposed. It is shown that parameters of model can be chosen so that under small deformations the bond is equivalent to either Bernoulli-Euler or Timoshenko rod or short cylinder connecting particles. Simple expressions, connecting parameters of V-model with geometrical and mechanical characteristics of the bond, are derived. Computer simulation of dynamical buckling of the straight discrete rod and discrete half-spherical shell is carried out."

"Inspired by birds flying through cluttered environments such as dense forests, this paper studies the theoretical foundations of a novel motion planning problem: high-speed navigation through a randomly-generated obstacle field when only the statistics of the obstacle generating process are known a priori. Resembling a planar forest environment, the obstacle generating process is assumed to determine the locations and sizes of disk-shaped obstacles. When this process is ergodic, and under mild technical conditions on the dynamics of the bird, it is shown that the existence of an infinite collision-free trajectory through the forest exhibits a phase transition. On one hand, if the bird flies faster than a certain critical speed, then, with probability one, there is no infinite collision-free trajectory, i.e., the bird will eventually collide with some tree, almost surely, regardless of the planning algorithm governing the bird's motion. On the other hand, if the bird flies slower than this critical speed, then there exists at least one infinite collision-free trajectory, almost surely. Lower and upper bounds on the critical speed are derived for the special case of a homogeneous Poisson forest considering a simple model for the bird's dynamics. For the same case, an equivalent percolation model is provided. Using this model, the phase diagram is approximated in Monte-Carlo simulations. This paper also establishes novel connections between robot motion planning and statistical physics through ergodic theory and percolation theory, which may be of independent interest."

"In this paper we propose a method based on interacting particle physics, devised for clustering Euclidean datasets without initial constraints or conditions. We model any dataset as an interacting particle system, whose elements correspond to particles that interact through a simplified version of Lennard-Jones potentials. In so doing, mutual attractive interactions allow to identify groups of proximal particles. The main outcome of this modeling task is an adjacency matrix, taken as input by a community detection algorithm aimed to identify different partitions. The underlying conjecture is that, using a multiresolution analysis, the adopted model allows to find the right number of clusters for any given dataset. Experimental results, performed in comparison with a classical clustering algorithm, confirm this assumption."

"We investigate the ray-length distributions for two different rectangular versions of Gilbert's tessellation. In the full rectangular version, lines extend either horizontally (with east- and west-growing rays) or vertically (north- and south-growing rays) from seed points which form a Poisson point process, each ray stopping when another ray is met. In the half rectangular version, east and south growing rays do not interact with west and north rays. For the half rectangular tessellation we compute analytically, via recursion, a series expansion for the ray-length distribution, whilst for the full rectangular version we develop an accurate simulation technique, based in part on the stopping-set theory of Zuyev, to accomplish the same. We demonstrate the remarkable fact that plots of the two distributions appear to be identical when the intensity of seeds in the half model is twice that in the full model. Our paper explores this coincidence mindful of the fact that, for one model, our results are from a simulation (with inherent sampling error).…"

"In this paper we define what we call an affinity system, which is a set of individuals, each with a vector characterizing its preference for all other individuals in the set. The preference of a member can be given either by a ranking of all members or by a weighted vector that defines the degrees of its affinity to others. Affinity systems are useful for modeling social systems as well as general data sets, as social interactions are often determined by affinities among the members. We also define a natural notion of (potentially overlapping) communities in an affinity system, in which the members of a given community collectively prefer each other to anyone else outside the community. Thus these communities are "self-determined" or "self-certified" by the affinity system. We provide a tight polynomial bound on the number of self-determined communities as a function of the robustness of the community. Moreover, we present a polynomial-time algorithm for enumerating these communities, as well as a local algorithm with a strong stochastic performance guarantee that can find a community in time nearly linear in the of size the community.…"

"We introduce the optimal obstacle placement with disambiguations problem wherein the goal is to place true obstacles in an environment cluttered with false obstacles so as to maximize the total traversal length of a navigating agent (NAVA). Prior to the traversal, NAVA is given location information and probabilistic estimates of each disk-shaped hindrance (hereinafter referred to as disk) being a true obstacle. The NAVA can disambiguate a disk's status only when situated on its boundary. There exists an obstacle placing agent (OPA) that locates obstacles prior to NAVA's traversal. The goal of OPA is to place true obstacles in between the clutter in such a way that NAVA's traversal length is maximized in a game-theoretic sense.…"

"Data collection at a massive scale is becoming ubiquitous in a wide variety of settings, from vast offline databases to streaming real-time information. Learning algorithms deployed in such contexts must rely on single-pass inference, where the data history is never revisited. In streaming contexts, learning must also be temporally adaptive to remain up-to-date against unforeseen changes in the data generating mechanism. Although rapidly growing, the online Bayesian inference literature remains challenged by massive data and transient, evolving data streams. Non-parametric modelling techniques can prove particularly ill-suited, as the complexity of the model is allowed to increase with the sample size. In this work, we take steps to overcome these challenges by porting standard streaming techniques, like data discarding and downweighting, into a fully Bayesian framework via the use of informative priors and active learning heuristics. We showcase our methods by augmenting a modern non-parametric modelling framework, dynamic trees, and illustrate its performance on a number of practical examples. The end product is a powerful streaming regression and classification tool, whose performance compares favourably to the state-of-the-art."

"In this paper, first we give a sequential linear-time algorithm for the longest path problem in meshes. This algorithm can be considered as an improvement of [13]. Then based on this sequential algorithm, we present a constant-time parallel algorithm for the problem which can be run on every parallel machine."

In this paper, we obtain polynomial time algorithms to determine the acyclic chromatic number, the star chromatic number, the Thue chromatic number, the harmonious chromatic number and the clique chromatic number of $P_4$-tidy graphs and $(q,q-4)$-graphs, for every fixed $q$. These classes include cographs, $P_4$-sparse and $P_4$-lite graphs. All these coloring problems are known to be NP-hard for general graphs. These algorithms are fixed parameter tractable on the parameter $q(G)$, which is the minimum $q$ such that $G$ is a $(q,q-4)$-graph. We also prove that every connected $(q,q-4)$-graph with at least $q$ vertices is 2-clique-colorable and that every acyclic coloring of a cograph is also nonrepetitive.

Many features from texts and languages can now be inferred from statistical analyses using concepts from complex networks and dynamical systems. In this paper we quantify how topological properties of word co-occurrence networks and intermittency (or burstiness) in word distribution depend on the style of authors. Our database contains 40 books from 8 authors who lived in the 19th and 20th centuries, for which the following network measurements were obtained: clustering coefficient, average shortest path lengths, and betweenness. We found that the two factors with stronger dependency on the authors were the skewness in the distribution of word intermittency and the average shortest paths. Other factors such as the betweeness and the Zipf's law exponent show only weak dependency on authorship. Also assessed was the contribution from each measurement to authorship recognition using three machine learning methods. The best performance was a ca. 65 % accuracy upon combining complex network and intermittency features with the nearest neighbor algorithm. From a detailed analysis of the interdependence of the various metrics it is concluded that the methods used here are complementary for providing short- and long-scale perspectives of texts, which are useful for applications such as identification of topical words and information retrieval.

For the general problem of minimizing a convex function over a compact convex domain, we will investigate a simple iterative approximation algorithm based on the method by Frank & Wolfe 1956, that does not need projection steps in order to stay inside the optimization domain. Instead of a projection step, the linearized problem defined by a current subgradient is solved, which gives a step direction that will naturally stay in the domain. Our framework generalizes the sparse greedy algorithm of Frank & Wolfe and its primal-dual analysis by Clarkson 2010 (and the low-rank SDP approach by Hazan 2008) to arbitrary convex domains. We give a convergence proof guaranteeing {epsilon}-small duality gap after O(1/{epsilon}) iterations.

The method allows us to understand the sparsity of approximate solutions for any l1-regularized convex optimization problem (and for optimization over the simplex), expressed as a function of the approximation quality. We obtain matching upper and lower bounds of {Theta}(1/{epsilon}) for the sparsity for l1-problems. The same bounds apply to low-rank semidefinite optimization with bounded trace, showing that rank O(1/{epsilon}) is best possible here as well. As another application, we obtain sparse matrices of O(1/{epsilon}) non-zero entries as {epsilon}-approximate solutions when optimizing any convex function over a class of diagonally dominant symmetric matrices.

We show that our proposed first-order method also applies to nuclear norm and max-norm matrix optimization problems. For nuclear norm regularized optimization, such as matrix completion and low-rank recovery, we demonstrate the practical efficiency and scalability of our algorithm for large matrix problems, as e.g. the Netflix dataset. For general convex optimization over bounded matrix max-norm, our algorithm is the first with a convergence guarantee, to the best of our knowledge.

We consider a situation where the state of a system is represented by a real-valued vector. Under normal circumstances, the vector is zero, while an event manifests as non-zero entries in this vector, possibly few. Our interest is in the design of algorithms that can reliably detect events (i.e., test whether the vector is zero or not) with the least amount of information. We place ourselves in a situation, now common in the signal processing literature, where information about the vector comes in the form of noisy linear measurements. We derive information bounds in an active learning setup and exhibit some simple near-optimal algorithms. In particular, our results show that the task of detection within this setting is at once much easier, simpler and different than the tasks of estimation and support recovery.

Many algorithms have been proposed for predicting missing edges in networks, but they do not usually take account of which edges are missing. We focus on networks which have missing edges of the form that is likely to occur in real networks, and compare algorithms that find these missing edges. We also investigate the effect of this kind of missing data on community detection algorithms.

Nested sampling is a Bayesian sampling technique developed to explore probability distributions lo- calised in an exponentially small area of the parameter space. The algorithm provides both posterior samples and an estimate of the evidence (marginal likelihood) of the model. The nested sampling algo- rithm also provides an efficient way to calculate free energies and the expectation value of thermodynamic observables at any temperature, through a simple post-processing of the output. Previous applications of the algorithm have yielded large efficiency gains over other sampling techniques, including parallel tempering (replica exchange). In this paper we describe a parallel implementation of the nested sampling algorithm and its application to the problem of protein folding in a Go-type force field of empirical potentials that were designed to stabilize secondary structure elements in room-temperature simulations. We demonstrate the method by conducting folding simulations on a number of small proteins which are commonly used for testing protein folding procedures: protein G, the SH3 domain of Src tyrosine kinase and chymotrypsin inhibitor 2. A topological analysis of the posterior samples is performed to produce energy landscape charts, which give a high level description of the potential energy surface for the protein folding simulations. These charts provide qualitative insights into both the folding process and the nature of the model and force field used.

We introduce the problem of reconstructing a sequence of multidimensional real vectors where some of the data are missing. This problem contains regression and mapping inversion as particular cases where the pattern of missing data is independent of the sequence index. The problem is hard because it involves possibly multivalued mappings at each vector in the sequence, where the missing variables can take more than one value given the present variables; and the set of missing variables can vary from one vector to the next. To solve this problem, we propose an algorithm based on two redundancy assumptions: vector redundancy (the data live in a low-dimensional manifold), so that the present variables constrain the missing ones; and sequence redundancy (e.g. continuity), so that consecutive vectors constrain each other. We capture the low-dimensional nature of the data in a probabilistic way with a joint density model, here the generative topographic mapping, which results in a Gaussian mixture. Candidate reconstructions at each vector are obtained as all the modes of the conditional distribution of missing variables given present variables. The reconstructed sequence is obtained by minimising a global constraint, here the sequence length, by dynamic programming. We present experimental results for a toy problem and for inverse kinematics of a robot arm.

In many data acquisition systems it is common to observe signals whose amplitudes have been clipped. We present two new algorithms for recovering a clipped signal by leveraging the model assumption that the underlying signal is sparse in the frequency domain. Both algorithms employ ideas commonly used in the field of Compressive Sensing; the first is a modified version of Reweighted $ell_1$ minimization, and the second is a modification of a simple greedy algorithm known as Trivial Pursuit. An empirical investigation shows that both approaches can recover signals with significant levels of clipping

We consider the problem of online audio source separation. Existing algorithms adopt either a sliding block approach or a stochastic gradient approach, which is faster but less accurate. Also, they rely either on spatial cues or on spectral cues and cannot separate certain mixtures. In this paper, we design a general online audio source separation framework that combines both approaches and both types of cues. The model parameters are estimated in the Maximum Likelihood (ML) sense using a Generalised Expectation Maximisation (GEM) algorithm with multiplicative updates. The separation performance is evaluated as a function of the block size and the step size and compared to that of an offline algorithm.

In this work, we have considered a class of smooth nonconvex regularization functions and we have proposed an efficient minimization stategy for solving the associated variational problems in imaging applications. Connections with l0 penalized problems have been shown asymptoti- cally. In addition, a novel convergence proof of the proposed subspace MM algorithm relying on the Kurdyka-L􏰄 ojasiewicz inequality has been given. Numerical experiments have been carried out to compare the proposed approach with other state-of-the art continuous optimization meth- ods (both for nonconvex and convex penalizations) and with discrete optimization approaches dealing with a truncated quadratic penalization. In the four presented image processing exam- ples, we argue that the proposed approach constitutes an appealing alternative to the existing methods in terms of recovered image quality and computational time.

Several algorithms are available in the literature for finding the entire set of Pareto-optimal solutions in MultiObjective Linear Programming (MOLP). However, it has not been proposed so far an interior point algorithm that finds all Pareto-optimal solutions of MOLP. We present an explicit construction, based on a transformation of any MOLP into a finite sequence of SemiDefinite Programs (SDP), the solutions of which give the entire set of Pareto-optimal extreme points solutions of MOLP. These SDP problems are solved by interior point methods; thus our approach provides a pseudo-polynomial interior point methodology to find the set of Pareto-optimal solutions of MOLP.

Recently, Bilu and Linial formalized an implicit assumption often made when choosing a clustering objective: that the optimum clustering to the objective should be preserved under small multiplicative perturbations to distances between points. They showed that for max-cut clustering it is possible to circumvent NP-hardness and obtain polynomial-time algorithms for instances resilient to large (factor $O(sqrt{n})$) perturbations, and subsequently Awasthi et al. considered center-based objectives, giving algorithms for instances resilient to O(1) factor perturbations.
In this paper, we greatly advance this line of work. For center-based objectives, we present an algorithm that can optimally cluster instances resilient to $(1 + sqrt{2})$-factor perturbations, solving an open problem of Awasthi et al. For a commonly used center-based objective $k$-median, we additionally give algorithms for a more relaxed assumption in which we allow the optimal solution to change in a small $epsilon$ fraction of the points after perturbation. We give the first bounds known for this more realistic and more general setting. We also provide positive results for min-sum clustering which is a generally much harder objective than $k$-median (and also non-center-based). Our algorithms are based on new linkage criteria that may be of independent interest.
Additionally, we give sublinear-time algorithms, showing algorithms that can return an implicit clustering from only access to a small random sample.

Matching dependencies (MDs) have been recently introduced as declarative rules for entity resolution (ER), i.e. for identifying and resolving duplicates in relational instance $D$. A set of MDs can be used as the basis for a possibly non-deterministic mechanism that computes a duplicate-free instance from $D$. The possible results of this process are the clean, "minimally resolved instances" (MRIs). There might be several MRIs for $D$, and the "resolved answers" to a query are those that are shared by all the MRIs. We investigate the problem of computing resolved answers. We look at various sets of MDs, developing syntactic criteria for determining (in)tractability of the resolved answer problem, including a dichotomy result. For some tractable classes of MDs and conjunctive queries, we present a query rewriting methodology that can be used to retrieve the resolved answers. We also investigate connections with "consistent query answering", deriving further tractability results for MD-based ER.

Stencil computations, involving operations over the elements of an array, are a common programming pattern in scientific computing, games, and image processing. As a programming pattern, stencil computations are highly regular and amenable to optimisation and parallelisation. However, general-purpose languages obscure this regular pattern from the compiler, and even the programmer, preventing optimisation and obfuscating (in)correctness. This paper furthers our work on the Ypnos domain-specific language for stencil computations embedded in Haskell. Ypnos allows declarative, abstract specification of stencil computations, exposing the structure of a problem to the compiler and to the programmer via specialised syntax. In this paper we show the decidable safety guarantee that well-formed, well-typed Ypnos programs cannot index outside of array boundaries. Thus indexing in Ypnos is safe and run-time bounds checking can be eliminated. Program information is encoded as types, using the advanced type-system features of the Glasgow Haskell Compiler, with the safe-indexing invariant enforced at compile time via type checking.

"Autoencoders are unsupervised machine learning circuits whose learning goal is to minimize a distortion measure between inputs and outputs. Linear autoencoders can be defined over any field and only real-valued linear autoencoder have been studied so far. Here we study complex-valued linear autoencoders where the components of the training vectors and adjustable matrices are defined over the complex field with the $L_2$ norm. We provide simpler and more general proofs that unify the real-valued and complex-valued cases, showing that in both cases the landscape of the error function is invariant under certain groups of transformations. The landscape has no local minima, a family of global minima associated with Principal Component Analysis, and many families of saddle points associated with orthogonal projections onto sub-space spanned by sub-optimal subsets of eigenvectors of the covariance matrix. The theory yields several iterative, convergent, learning algorithms, a clear understanding of the generalization properties of the trained autoencoders, and can equally be applied to the hetero-associative case when external targets are provided. Partial results on deep architecture as well as the differential geometry of autoencoders are also presented. The general framework described here is useful to classify autoencoders and identify general common properties that ought to be investigated for each class, illuminating some of the connections between information theory, unsupervised learning, clustering, Hebbian learning, and auto encoders."

"A simplified model of natural convection, similar to the Lorenz (1963) system, is compared to computational fluid dynamics simulations in order to test data assimilation methods and better understand the dynamics of convection. The thermosyphon is represented by a long time flow simulation, which serves as a reference "truth". Forecasts are then made using the Lorenz-like model and synchronized to noisy and limited observations of the truth using data assimilation. The resulting analysis is observed to infer dynamics absent from the model when using short assimilation windows.

Furthermore, chaotic flow reversal occurrence and residency times in each rotational state are forecast using analysis data. Flow reversals have been successfully forecast in the related Lorenz system, as part of a perfect model experiment, but never in the presence of significant model error or unobserved variables. Finally, we provide new details concerning the fluid dynamical processes present in the thermosyphon during these flow reversals."

"Motivated by the problems of computing sample covariance matrices, and of transforming a collection of vectors to a basis where they are sparse, we present a simple algorithm that computes an approximation of the product of two n-by-n real matrices A and B.…"

"The {em longest common subsequence (LCS)} problem is a classic and well-studied problem in computer science. Palindrome is a word which reads the same forward as it does backward. The {em longest common palindromic subsequence (LCPS)} problem is an interesting variant of the classic LCS problem which finds the longest common subsequence between two given strings such that the computed subsequence is also a palindrome. In this paper, we study the LCPS problem and give efficient algorithms to solve this problem. To the best of our knowledge, this is the first attempt to study and solve this interesting problem."

"We study feature selection for $k$-means clustering. Although the literature contains many methods with good empirical performance, algorithms with provable theoretical behavior have only recently been developed. Unfortunately, these algorithms are randomized and fail with, say, a constant probability. We address this issue by presenting a emph{deterministic} feature selection algorithm for $k$-means with theoretical guarantees. At the heart of our algorithm lies a deterministic method for decompositions of the identity."

"The k-domination number of a graph is the minimum size of a set X such that every vertex of G is in distance at most k from X. We give a linear time constant-factor approximation algorithm for k-domination number in classes of graphs with bounded expansion, which include e.g. proper minor-closed graph classes, classes closed on topological minors or classes of graphs that can be drawn on a fixed surface with bounded number of crossings on each edge.

The algorithm is based on the following approximate min-max characterization. A subset A of vertices of a graph G is d-independent if the distance between each pair of vertices in A is greater than d. Note that the size of the largest 2k-independent set is a lower bound for the k-domination number. We show that every graph from a fixed class with bounded expansion contains a 2k-independent set A and a k-dominating set D such that |D|=O(|A|), and these sets can be found in linear time. For domination number (k=1) the assumptions can be relaxed, and the result holds for all graph classes with arrangeability bounded by a constant."

"Efficient global optimization is the problem of minimizing an unknown function f, using as few evaluations f(x) as possible. It can be considered as a continuum-armed bandit problem, with noiseless data and simple regret. Expected improvement is perhaps the most popular method for solving this problem; the algorithm performs well in experiments, but little is known about its theoretical properties. Implementing expected improvement requires a choice of Gaussian process prior, which determines an associated space of functions, its reproducing-kernel Hilbert space (RKHS). When the prior is fixed, expected improvement is known to converge on the minimum of any function in the RKHS. We begin by providing convergence rates for this procedure. The rates are optimal for functions of low smoothness, and we modify the algorithm to attain optimal rates for smoother functions. For practitioners, however, these results are somewhat misleading. Priors are typically not held fixed, but depend on parameters estimated from the data. For standard estimators, we show this procedure may never discover the minimum of f. We then propose alternative estimators, chosen to minimize the constants in the rate of convergence, and show these estimators retain the convergence rates of a fixed prior."

"Given a set $P$ of $n$ points in the plane, we solve the problems of constructing a geometric planar graph spanning $P$ 1) of minimum degree 2, and 2) which is 2-edge connected, respectively, and has max edge length bounded by a factor of 2 times the optimal; we also show that the factor 2 is best possible given appropriate connectivity conditions on the set $P$, respectively. First, we construct in $O(nlog{n})$ time a geometric planar graph of minimum degree 2 and max edge length bounded by 2 times the optimal. This is then used to construct in $O(nlog n)$ time a 2-edge connected geometric planar graph spanning $P$ with max edge length bounded by $sqrt{5}$ times the optimal, assuming that the set $P$ forms a connected Unit Disk Graph. Second, we prove that 2 times the optimal is always sufficient if the set of points forms a 2 edge connected Unit Disk Graph and give an algorithm that runs in $O(n^2)$ time. We also show that for $k in O(sqrt{n})$, there exists a set $P$ of $n$ points in the plane such that even though the Unit Disk Graph spanning $P$ is $k$-vertex connected, there is no 2-edge connected geometric planar graph spanning $P$ even if the length of its edges is allowed to be up to 17/16."

"We present a $(1+epsilon)$-approximation algorithm running in $O(f(epsilon)cdot n log^2 n)$ time for finding the diameter of an undirected planar graph with non-negative edge lengths."

"We present a procedure to solve the inverse Ising problem, that is to find the interactions between a set of binary variables from the measure of their equilibrium correlations. The method consists in constructing and selecting specific clusters of variables, based on their contributions to the cross-entropy of the Ising model. Small contributions are discarded to avoid overfitting and to make the computation tractable. The properties of the cluster expansion and its performances on synthetic data are studied. To make the implementation easier we give the pseudo-code of the algorithm."

"Let G = (V, E) be a directed acyclic graph with two distinguished vertices s, t and let F be a set of forbidden pairs of vertices. We say that a path in G is safe, if it contains at most one vertex from each pair {u, v} in F. Given G and F, the path avoiding forbidden pairs (PAFP) problem is to find a safe s-t path in G. We systematically study the complexity of different special cases of the PAFP problem defined according to the mutual positions of fobidden pairs. Fix one topological ordering of vertices; we say that pairs {u, v} and {x, y} are disjoint, if u, v < x, y, nested, if u < x, y < v, and halving, if u < x < v < y. The PAFP problem is known to be NP-hard in general or if no two pairs are disjoint; we prove that it remains NP-hard even when no two forbidden pairs are nested. On the other hand, if no two pairs are halving, the problem is known to be solvable in cubic time. We simplify and improve this result by showing an O(M(n)) time algorithm, where M(n) is the time to multiply two n times n boolean matrices."

"In machine learning and computer vision, input images are often filtered to increase data discriminability. In some situations, however, one may wish to purposely decrease discriminability of one classification task (a "distractor" task), while simultaneously preserving information relevant to another (the task-of-interest): For example, it may be important to mask the identity of persons contained in face images before submitting them to a crowdsourcing site (e.g., Mechanical Turk) when labeling them for certain facial attributes. Another example is inter-dataset generalization: when training on a dataset with a particular covariance structure among multiple attributes, it may be useful to suppress one attribute while preserving another so that a trained classifier does not learn spurious correlations between attributes. In this paper we present an algorithm that finds optimal filters to give high discriminability to one task while simultaneously giving low discriminability to a distractor task. We present results showing the effectiveness of the proposed technique on both simulated data and natural face images."

"Optimal power flow (OPF) is an important problem for power generation and it is in general non-convex. With the employment of renewable energy, it will be desirable if OPF can be solved very efficiently so its solution can be used in real time. With some special network structure, e.g. trees, the problem has been shown to have a zero duality gap and the convex dual problem yields the optimal solution. In this paper, we propose a primal and a dual algorithm to coordinate the smaller subproblems decomposed from the convexified OPF. We can arrange the subproblems to be solved sequentially and cumulatively in a central node or solved in parallel in distributed nodes. We test the algorithms on IEEE radial distribution test feeders, some random tree-structured networks, and the IEEE transmission system benchmarks. Simulation results show that the computation time can be improved dramatically with our algorithms over the centralized approach of solving the problem without decomposition, especially in tree-structured problems. The computation time grows linearly with the problem size with the cumulative approach while the distributed one can have size-independent computation time."

"This paper considers the model introduced by Bilu and Linial (2010), who study problems for which the optimal clustering does not change when the distances are perturbed by multiplicative factors. They show that even when a problem is NP-hard, it is sometimes possible to obtain polynomial-time algorithms for instances resilient to large perturbations, e.g. on the order of $O(sqrt{n})$ for max-cut clustering. Awasthi et al. (2010) extend this line of work by considering center-based objectives, and Balcan and Liang (2011) consider the $k$-median and min-sum objectives, giving efficient algorithms for instances resilient to certain constant multiplicative perturbations.

Here, we are motivated by the question of to what extent these assumptions can be relaxed while allowing for efficient algorithms. We show there is little room to improve these results by giving NP-hardness lower bounds for both the $k$-median and min-sum objectives. On the other hand, we show that multiplicative resilience parameters, even only on the order of $Theta(1)$, can be so strong as to make the clustering problem trivial, and we exploit these assumptions to present a simple one pass streaming algorithm for the $k$-median objective. We also consider a model of additive perturbations and give a correspondence between additive and multiplicative notions of stability. Our results provide a close examination of the consequences of assuming, even constant, stability in data."

"Internet-scale distributed systems such as content delivery networks (CDNs) operate hundreds of thousands of servers deployed in thousands of data center locations around the globe. Since the energy costs of operating such a large IT infrastructure are a significant fraction of the total operating costs, we argue for redesigning CDNs to incorporate energy optimizations as a first-order principle. We propose techniques to turn off CDN servers during periods of low load while seeking to balance three key design goals: maximize energy reduction, minimize the impact on client-perceived service availability (SLAs), and limit the frequency of on-off server transitions to reduce wear-and-tear and its impact on hardware reliability. We propose an optimal offline algorithm and an online algorithm to extract energy savings both at the level of local load balancing within a data center and global load balancing across data centers. We evaluate our algorithms using real production workload traces from a large commercial CDN. Our results show that it is possible to reduce the energy consumption of a CDN by more than 55% while ensuring a high level of availability that meets customer SLA requirements and incurring an average of one on-off transition per server per day. Further, we show that keeping even 10% of the servers as hot spares helps absorb load spikes due to global flash crowds with little impact on availability SLAs. Finally, we show that redistributing load across proximal data centers can enhance service availability significantly, but has only a modest impact on energy savings."

"Recently, the face recognizers based on linear representations have been shown to deliver state-of-the-art performance. In real-world applications, however, face images usually suffer from expressions, disguises and random occlusions. The problematic facial parts undermine the validity of the linear-subspace assumption and thus the recognition performance deteriorates significantly. In this work, we address the problem in a learning-inference-mixed fashion. By observing that the linear-subspace assumption is more reliable on certain face patches rather than on the holistic face, some Bayesian Patch Representations (BPRs) are randomly generated and interpreted according to the Bayes' theory. We then train an ensemble model over the patch-representations by minimizing the empirical risk w.r.t the "leave-one-out margins". The obtained model is termed Optimal Representation Ensemble (ORE), since it guarantees the optimality from the perspective of Empirical Risk Minimization. To handle the unknown patterns in test faces, a robust version of BPR is proposed by taking the non-face category into consideration. Equipped with the Robust-BPRs, the inference ability of ORE is increased dramatically and several record-breaking accuracies (99.9% on Yale-B and 99.5% on AR) and desirable efficiencies (below 20 ms per face in Matlab) are achieved. It also overwhelms other modular heuristics on the faces with random occlusions, extreme expressions and disguises. Furthermore, to accommodate immense BPRs sets, a boosting-like algorithm is also derived. The boosted model, a.k.a Boosted-ORE, obtains similar performance to its prototype. Besides the empirical superiorities, two desirable features of the proposed methods, namely, the training-determined model-selection and the data-weight-free boosting procedure, are also theoretically verified."

"This paper proposes a novel approach to image deblurring and digital zooming using sparse local models of image appearance. These models, where small image patches are represented as linear combinations of a few elements drawn from some large set (dictionary) of candidates, have proven well adapted to several image restoration tasks. A key to their success has been to learn dictionaries adapted to the reconstruction of small image patches. In contrast, recent works have proposed instead to learn dictionaries which are not only adapted to data reconstruction, but also tuned for a specific task. We introduce here such an approach to deblurring and digital zoom, using pairs of blurry/sharp (or low-/high-resolution) images for training, as well as an effective stochastic gradient algorithm for solving the corresponding optimization task. Although this learning problem is not convex, once the dictionaries have been learned, the sharp/high-resolution image can be recovered via convex optimization at test time. Experiments with synthetic and real data demonstrate the effectiveness of the proposed approach, leading to state-of-the-art performance for non-blind image deblurring and digital zoom."

"We present a novel distributed evolutionary algorithm, KaFFPaE, to solve the Graph Partitioning Problem, which makes use of KaFFPa (Karlsruhe Fast Flow Partitioner). The use of our multilevel graph partitioner KaFFPa provides new effective crossover and mutation operators. By combining these with a scalable communication protocol we obtain a system that is able to improve the best known partitioning results for many inputs in a very short amount of time. For example, in Walshaw's well known benchmark tables we are able to improve or recompute 76% of entries for the tables with 1%, 3% and 5% imbalance."

"Our result may be generalized to other domains where similar algorithms may apply. Our algorithm is based on the fact that the eigenfunctions are presented as a linear combination of simple plane waves. It is therefore tempting to try and generalize it for other drums with similar property. The equilateral triangle is an immediate candidate (see [29] and references within).

A further, and quite surprising, result is the recursive formula for the number of nodal loops. To our knowledge this is the first known exact formula for the nodal count of a non-separable planar manifold (for certain eigenfunctions of tori exact formulas have been given in [22]). The formula was found by direct inspection of large tables and has been verified for a large bulk of data computationally. An obvious challenge is to prove this formula. In particular, the recursive part of the formula resembles the famous Euclid algorithm for the greatest common divisor. A further investigation of the mentioned formula might therefore expose some new number theoretical properties of the nodal count."

"In this paper, a multi-resolution feature extraction algorithm for face recognition is proposed based on two-dimensional discrete wavelet transform (2D-DWT), which efficiently exploits the local spatial variations in a face image. For the purpose of feature extraction, instead of considering the entire face image, an entropy-based local band selection criterion is developed, which selects high-informative horizontal segments from the face image. In order to capture the local spatial variations within these highinformative horizontal bands precisely, the horizontal band is segmented into several small spatial modules. Dominant wavelet coefficients corresponding to each local region residing inside those horizontal bands are selected as features. In the selection of the dominant coefficients, a threshold criterion is proposed, which not only drastically reduces the feature dimension but also provides high within-class compactness and high between-class separability. A principal component analysis is performed to further reduce the dimensionality of the feature space. Extensive experimentation is carried out upon standard face databases and a very high degree of recognition accuracy is achieved by the proposed method in comparison to those obtained by some of the existing methods."

"This paper describes a new QR factorization algorithm which is especially designed for massively parallel platforms combining parallel distributed multi-core nodes. These platforms make the present and the foreseeable future of high-performance computing. Our new QR factorization algorithm falls in the category of the tile algorithms which naturally enables good data locality for the sequential kernels executed by the cores (high sequential performance), low number of messages in a parallel distributed setting (small latency term), and fine granularity (high parallelism)."

"Graph coloring is used in wireless networks to optimize network resources: bandwidth and energy. Nodes access the medium according to their color. It is the responsibility of the coloring algorithm to ensure that interfering nodes do not have the same color. In this research report, we focus on wireless sensor networks with grid topologies. How does a coloring algorithm take advantage of the regularity of grid topology to provide an optimal periodic coloring, that is a coloring with the minimum number of colors? We propose the Vector-Based Coloring Method, denoted VCM, a new method that is able to provide an optimal periodic coloring for any radio transmission range and for any h-hop coloring, h>=1. This method consists in determining at which grid nodes a color can be reproduced without creating interferences between these nodes while minimizing the number of colors used. We compare the number of colors provided by VCM with the number of colors obtained by a distributed coloring algorithm with line and column priority assignments. We also provide bounds on the number of colors of optimal general colorings of the infinite grid, and show that periodic colorings (and thus VCM) are asymptotically optimal. Finally, we discuss the applicability of this method to a real wireless network."

"We give the first polylogarithmic-competitive randomized online algorithm for the $k$-server problem on an arbitrary finite metric space. In particular, our algorithm achieves a competitive ratio of O(log^3 n log^2 k log log n) for any metric space on n points. Our algorithm improves upon the deterministic (2k-1)-competitive algorithm of Koutsoupias and Papadimitriou [J.ACM'95] whenever n is sub-exponential in k."

"The main cause of wasted energy consumption in wireless sensor networks is packet collision. The packet scheduling algorithm is therefore introduced to solve this problem. Some packet scheduling algorithms can also influence and delay the data transmitting in the real-time wireless sensor networks. This paper presents the packet scheduling algorithm (PSA) in order to reduce the packet congestion in MAC layer leading to reduce the overall of packet collision in the system The PSA is compared with the simple CSMA/CA and other approaches using network topology benchmarks in mathematical method. The performances of our PSA are better than the standard (CSMA/CA). The PSA produces better throughput than other algorithms. On other hand, the average delay of PSA is higher than previous works. However, the PSA utilizes the channel better than all algorithms."

"Topological alignments and snakes are used in image processing, particularly in locating object boundaries. Both of them have their own advantages and limitations. To improve the overall image boundary detection system, we focused on developing a novel algorithm for image processing. The algorithm we propose to develop will based on the active contour method in conjunction with topological alignments method to enhance the image detection approach. The algorithm presents novel technique to incorporate the advantages of both Topological Alignments and snakes. Where the initial segmentation by Topological Alignments is firstly transformed into the input of the snake model and begins its evolvement to the interested object boundary. The results show that the algorithm can deal with low contrast images and shape cells, demonstrate the segmentation accuracy under weak image boundaries, which responsible for lacking accuracy in image detecting techniques. We have achieved better segmentation and boundary detecting for the image, also the ability of the system to improve the low contrast and deal with over and under segmentation."

"…While several practical uses of the method have been proposed in Monte Carlo applications, these require an implementation framework that is flexible, general and efficient. We present such a framework for functions that are either strictly linear, concave, or convex on the unit interval using a series of envelope functions defined through a cascade, and show that this method not only greatly reduces the number of input bits needed in practice compared to other currently proposed solutions for more specific problems, but can easily be coupled to more asymptotically efficient methods to allow for theoretically strong results."