"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."

"In evaluating prediction markets (and other crowd-prediction mechanisms), investigators have repeatedly observed a so-called "wisdom of crowds" effect, which roughly says that the average of participants performs much better than the average participant. The market price---an average or at least aggregate of traders' beliefs---offers a better estimate than most any individual trader's opinion. In this paper, we ask a stronger question: how does the market price compare to the best trader's belief, not just the average trader. We measure the market's worst-case log regret, a notion common in machine learning theory. To arrive at a meaningful answer, we need to assume something about how traders behave. We suppose that every trader optimizes according to the Kelly criteria, a strategy that provably maximizes the compound growth of wealth over an (infinite) sequence of market interactions. We show several consequences.…"

"A number of representation schemes have been presented for use within Learning Classifier Systems, ranging from binary encodings to neural networks. This paper presents results from an investigation into using discrete and fuzzy dynamical system representations within the XCSF Learning Classifier System. In particular, asynchronous Random Boolean Networks are used to represent the traditional condition-action production system rules in the discrete case and asynchronous Fuzzy Logic Networks in the continuous-valued case. It is shown possible to use self-adaptive, open-ended evolution to design an ensemble of such dynamical systems within XCSF to solve a number of well-known test problems."

"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.…"

"We review the observations and the basic laws describing the essential aspects of collective motion -- being one of the most common and spectacular manifestation of coordinated behavior. Our aim is to provide a balanced discussion of the various facets of this highly multidisciplinary field, including experiments, mathematical methods and models for simulations, so that readers with a variety of background could get both the basics and a broader, more detailed picture of the field. The observations we report on include systems consisting of units ranging from macromolecules through metallic rods and robots to groups of animals and people. Some emphasis is put on models that are simple and realistic enough to reproduce the numerous related observations and are useful for developing concepts for a better understanding of the complexity of systems consisting of many simultaneously moving entities. As such, these models allow the establishing of a few fundamental principles of flocking. In particular, it is demonstrated, that in spite of considerable differences, a number of deep analogies exist between equilibrium statistical physics systems and those made of self-propelled (in most cases living) units. In both cases only a few well defined macroscopic/collective states occur and the transitions between these states follow a similar scenario, involving discontinuity and algebraic divergences."

"In a recent paper, we analyzed the self-assembly of a complex cooperation network. The network was shown to approach a state, where every agent invests the same amount of resources. Nevertheless, highly-connected agents arise that extract extra-ordinarily high payoffs while contributing comparably little to any of their cooperations. Here, we investigate a variant of the model, in which highly-connected agents have access to additional resources. We study analytically and numerically whether these resources are invested in existing collaborations, leading to a fairer load distribution, or in establishing new collaborations, leading to an even less fair distribution of loads and payoffs."

"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."

"We study instabilities and pattern formation in reaction-diffusion layers that are diffusively coupled. For two-layer systems of identical two-component reactions, we analyze the stability of homogeneous steady states by exploiting the block symmetric structure of the linear problem. There are eight possible primary bifurcation scenarios, including a Turing-Turing bifurcation that involves two disparate length scales whose ratio may be tuned via the inter-layer coupling. For systems of $n$-component layers and non-identical layers, the linear problem's block form allows approximate decomposition into lower-dimensional linear problems if the coupling is sufficiently weak. As an example, we apply these results to a two-layer Brusselator system. The competing length scales engineered within the linear problem are readily apparent in numerical simulations of the full system. Selecting a $sqrt{2}$:1 length scale ratio produces an unusual steady square pattern."

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.

We introduce a machine learning model to predict atomization energies of a diverse set of organic molecules, based on nuclear charges and atomic positions only. The problem of solving the molecular Schr"odinger equation is mapped onto a non-linear statistical regression problem of reduced complexity. Regression models are trained on and compared to atomization energies computed with hybrid density-functional theory. Cross-validation over more than seven thousand small organic molecules yields a mean absolute error of ~10 kcal/mol. Applicability is demonstrated for the prediction of molecular atomization potential energy curves.

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