random Perturbation

A simple model with a novel type of dynamics is introduced in order to investigate the emergence of self-ordered motion in systems of particles with biologically motivated interaction. In our model particles are driven with a constant absolute velocity and at each time step assume the average direction of motion of the particles in their neighborhood with some random perturbation ($\eta$) added. We present numerical evidence that this model results in a kinetic phase transition from no transport (zero average velocity, $| {\bf v}_a | =0$) to finite net transport through spontaneous symmetry breaking of the rotational symmetry. The transition is continuous since $| {\bf v}_a |$ is found to scale as $(\eta_c-\eta)^\beta$ with $\beta\simeq 0.45$.

This paper discusses an important issue related to the implementation and interpretation of the analysis scheme in the ensemble Kalman filter. It is shown that the observations must be treated as random variables at the analysis steps. That is, one should add random perturbations with the correct statistics to the observations and generate an ensemble of observations that then is used in updating the ensemble of model states. Traditionally, this has not been done in previous applications of the ensemble Kalman filter and, as will be shown, this has resulted in an updated ensemble with a variance that is too low.

The ensemble Kalman filter (EnKF) is a data assimilation scheme based on the traditional Kalman filter update equation. An ensemble of forecasts are used to estimate the background-error covariances needed to compute the Kalman gain. It is known that if the same observations and the same gain are used to update each member of the ensemble, the ensemble will systematically underestimate analysis-error covariances. This will cause a degradation of subsequent analyses and may lead to filter divergence. For large ensembles, it is known that this problem can be alleviated by treating the observations as random variables, adding random perturbations to them with the correct statistics.

Phase noise is a topic of theoretical and practical interest in electronic circuits, as well as in other fields, such as optics. Although progress has been made in understanding the phenomenon, there still remain significant gaps, both in its fundamental theory and in numerical techniques for its characterization. In this paper, we develop a solid foundation for phase noise that is valid for any oscillator, regardless of operating mechanism. We establish novel results about the dynamics of stable nonlinear oscillators in the presence of perturbations, both deterministic and random. We obtain an exact nonlinear equation for phase error, which we solve without approximations for random perturbations. This leads us to a precise characterization of timing jitter and spectral dispersion, for computing which we develop efficient numerical methods. We demonstrate our techniques on a variety of practical electrical oscillators and obtain good matches with measurements, even at frequencies close to the carrier, where previous techniques break down. Our methods are more than three orders of magnitude faster than the brute-force Monte Carlo approach, which is the only previously available technique that can predict phase noise correctly.

Half century has past since the pioneering works of Anderson and Kubo on the stochastic theory of spectral line shape were published in J. Phys. Soc. Jpn. 9 (1954) 316 and 935, respectively. In this review, we give an overview and extension of the stochastic Liouville equation focusing on its theoretical background and applications to help further the development of their works. With the aid of path integral formalism, we derive the stochastic Liouville equation for density matrices of a system. We then cast the equation into the hierarchy of equations which can be solved analytically or computationally in a nonperturbative manner including the effect of a colored noise. We elucidate the applications of the stochastic theory from the unified theoretical basis to analyze the dynamics of a system as probed by experiments. We illustrate this as a review of several experimental examples including NMR, dielectric relaxation, Mössbauer spectroscopy, neutron scattering, and linear and nonlinear laser spectroscopies. Following the summary of the advantage and limitation of the stochastic theory, we then derive a quantum Fokker-Planck equation and a quantum master equation from a system-bath Hamiltonian with a suitable spectral distribution producing a nearly Markovian random perturbation. By introducing auxiliary parameters that play a role as stochastic variables in an expression for reduced density matrix, we obtain the stochastic Liouville equation including temperature correction terms. The auxiliary parameters may also be interpreted as a random noise that allows us to derive a quantum Langevin equation for non-Markovian noise at any temperature. The results afford a basis for clarifying the relationship between the stochastic and dynamical approaches. Analytical as well as numerical calculations are given as examples and discussed.

We compare the three basic algorithms for model-based clustering on high-dimensional discretevariable datasets. All three algorithms use the same underlying model: a naive-Bayes model with a hidden root node, also known as a multinomial-mixture model. In the first part of the paper, we perform an experimental comparison between three batch algorithms that learn the parameters of this model: the Expectation-Maximization (EM) algorithm, a "winner take all" version of the EM algorithm reminiscent of the K-means algorithm, and modelbased agglomerative clustering. We find that the EM algorithm significantly outperforms the other methods, and proceed to investigate the effect of various initialization methods on the final solution produced by the EM algorithm. The initializations that we consider are (1) parameters sampled from an uninformative prior, (2) random perturbations of the marginal distribution of the data, and (3) the output of agglomerative clustering. Although the methods are substantially different, they lead to learned models that are similar in quality.

We consider the problem of online keyword advertising auctions among multiple bidders with limited budgets, and study a natural bidding heuristic in which advertisers attempt to optimize their utility by equalizing their return-on-investment across all keywords. We show that existing auction mechanisms combined with this heuristic can experience cycling (as has been observed in many current systems), and therefore propose a modified class of mechanisms with small random perturbations. This perturbation is reminiscent of the small time-dependent perturbations employed in the dynamical systems literature to convert many types of chaos into attracting motions. We show that the perturbed mechanism provably converges in the case of first-price auctions and experimentally converges in the case of second-price auctions. Moreover, the point of convergence has a natural economic interpretation as the unique market equilibrium in the case of first-price mechanisms. In the case of second-price auctions, we conjecture that it converges to the "supply-aware" market equilibrium. Thus, our results can be alternatively described as a tâtonnement process for convergence to market equilibrium in which prices are adjusted on the side of the buyers rather than

Privacy is becoming an increasingly important issue in many data-mining applications. This has triggered the development of many privacy-preserving data-mining techniques. A large fraction of them use randomized data-distortion techniques to mask the data for preserving the privacy of sensitive data. This methodology attempts to hide the sensitive data by randomly modifying the data values often using additive noise. This paper questions the utility of the random-value distortion technique in privacy preservation. The paper first notes that random matrices have predictable structures in the spectral domain and then it develops a random matrix-based spectral-filtering technique to retrieve original data from the dataset distorted by adding random values. The proposed method works by comparing the spectrum generated from the observed data with that of random matrices. This paper presents the theoretical foundation and extensive experimental results to demonstrate that, in many cases, random-data distortion preserves very little data privacy. The analytical framework presented in this paper also points out several possible avenues for the development of new privacy-preserving data-mining techniques. Examples include algorithms that explicitly guard against privacy breaches through linear transformations, exploiting multiplicative and colored noise for preserving privacy in data mining applications.

A 2×2 game is played repeatedly by two satisficing players. The game considered includes the Prisoner's Dilemma, as well as games of coordination and common interest. Each player has anaspirationat each date, and takes an action. The action is switched at the subsequent period only if the achieved payoff falls below aspirations; the switching probability depends on the shortfall. Aspirations are periodically updated according to payoff experience, but are occasionally subject to trembles. For sufficiently slow updating of aspirations and small tremble probability, it is shown that both players must ultimately cooperate most of the time.Journal of Economic LiteratureClassification Numbers C72, D83.

We study the following vertex-weighted online bipartite matching problem: G(U, V, E) is a bipartite graph. The vertices in U have weights and are known ahead of time, while the vertices in V arrive online in an arbitrary order and have to be matched upon arrival. The goal is to maximize the sum of weights of the matched vertices in U . When all the weights are equal, this reduces to the classic online bipartite matching problem for which Karp, Vazirani and Vazirani gave an optimal 1 − 1 e -competitive algorithm in their seminal work [KVV90]. Our main result is an optimal 1 − 1 e -competitive randomized algorithm for general vertex weights. We use random perturbations of weights by appropriately chosen multiplicative factors. Our solution constitutes the first known generalization of the algorithm in in this model and provides new insights into the role of randomization in online allocation problems. It also effectively solves the problem of online budgeted allocations [MSVV05] in the case when an agent makes the same bid for any desired item, even if the bid is comparable to his budgetcomplementing the results of [MSVV05, BJN07] which apply when the bids are much smaller than the budgets.

We study small random perturbations by additive white-noise of a spatial discretization of a reaction-diffusion equation with a stable equilibrium and solutions that blow up in finite time. We prove that the perturbed system blows up with total probability and establish its order of magnitude and asymptotic distribution. For initial data in the domain of explosion we prove that the explosion time converges to the deterministic one while for initial data in the domain of attraction of the stable equilibrium we show that the system exhibits metastable behavior.

This paper discusses a randomized nonautonomous logistic equation dN(t) = N(t) a(t) − b(t)N(t) dt + α(t) dB(t) , where B(t) is 1-dimensional standard Brownian motion. We show that E[1/N(t)] has a unique positive T-periodic solution E[1/N p (t)] provided a(t), b(t), and α(t) are continuous T-periodic functions, a(t) > 0, b(t) > 0 and T 0 [a(s) − α 2 (s)] ds > 0.

The naturally coexisting intrinsic mechanical and reflex properties of the human elbow joint were identified simultaneously using nonlinear, time-delay, continuous-time, and dynamic models. Angular random perturbations of small amplitude and low bandwidth were applied to the joint using a computer-controlled servomotor, while the subject maintained various levels of mean background muscle torque. Joint neuromuscular dynamics were identified from the measured elbow angle and torque. Stretch reflexes were modeled nonlinearly with both dynamic and static reflex gains. A continuous-time system identification method was developed to estimate parameters of the nonlinear models directly from sampled data while retaining realistic physical or physiological interpretations. Results from six subjects showed that dynamic stretch reflex gains, joint stiffness, and viscosity generally increased with mean background muscle torque; and that dynamic stretch reflex gain was higher during muscle stretch than that during muscle shortening. More importantly, the study provided realistic simultaneous estimates of the relative contributions of intrinsic mechanical and reflex actions to net joint torque. In particular, reflexively-mediated stiffness generated a significant portion of the total joint stiffness and the percentage varied systematically with background muscle torque.

The identification of general principles relating structure to dynamics has been a major goal in the study of complex networks. We propose that the special case of linear network dynamics provides a natural framework within which a number of interesting yet tractable problems can be defined. We report the emergence of modularity and hierarchical organization in evolved networks supporting asymptotically stable linear dynamics. Numerical experiments demonstrate that linear stability benefits from the presence of a hierarchy of modules and that this architecture improves the robustness of network stability to random perturbations in network structure. This work illustrates an approach to network science which is simultaneously structural and dynamical in nature.

A prerequisite for secure communications between two sensor nodes is that these nodes exclusively share a pairwise key. Although numerous pairwise key establishment (PKE) schemes have been proposed in recent years, most of them have no guarantee for direct key establishment, no resilience to a large number of node compromises, no resilience to dynamic network topology, or high overhead. To address these limitations, we propose a novel random perturbationbased (RPB) scheme in this paper. The scheme guarantees that any two nodes can directly establish a pairwise key without exposing any secret to other nodes. Even after a large number of nodes have been compromised, the pairwise keys shared by non-compromised nodes remain highly secure. Moreover, the scheme adapts to changes in network topology and incurs low computation and communication overhead. To the best of our knowledge, the RPB scheme is the only one that provides all these salient features without relying on public key cryptography. Through prototypebased evaluation, we show that the RPB scheme is highly efficient and practical for current generation of sensor nodes. In particular, to support a sensor network with up to 2 16 nodes, establishing a pairwise key of 80 bits between any two 8-bit, 7.37-MHz MICA2 motes only requires about 0.13 second of CPU time, 0.33 KB RAM space, and 15 KB ROM space per node.

We consider random walks on Zd with transition ratesp(x, y) given by a random matrix. Ifp is a small random perturbation of the simple random walk, we show that the walk remains diffusive for almost all environmentsp ifd>2. The result also holds for a continuous time Markov process with a random drift. The corresponding path space measures converge weakly, in the scaling limit, to the Wiener process, for almost everyp.

Privacy preserving data mining has become increasingly popular because it allows sharing of privacy-sensitive data for analysis purposes. However, existing techniques such as random perturbation do not fare well for simple yet widely used and efficient Euclidean distance-based mining algorithms. Although original data distributions can be pretty accurately reconstructed from the perturbed data, distances between individual data points are not preserved, leading to poor accuracy for the distance-based mining methods. Besides, they do not generally focus on data reduction. Other studies on secure multi-party computation often concentrate on techniques useful to very specific mining algorithms and scenarios such that they require modification of the mining algorithms and are often difficult to generalize to other mining algorithms or scenarios. This paper proposes a novel generalized approach using the well-known energy compaction power of Fourier-related transforms to hide sensitive data values and to approximately preserve Euclidean distances in centralized and distributed scenarios to a great degree of accuracy. Three algorithms to select the most important transform coefficients are presented, one for a centralized database case, the second one for a horizontally partitioned, and the third one for a vertically partitioned database case. Experimental re-sults demonstrate the effectiveness of the proposed approach.

A semilinear parabolic equation on ~J with a non-additive random perturbation is studied. The noise is supposed to be a spatially homogeneous Wiener process. Conditions for the existence and uniqueness of the solution in terms of the spectral measure of the noise are given. Applications to population and geophysical models are indicated. The Freidlin-Wentzell large deviation estimates are obtained as well. © 1997 Elsevier Science B.V.

In this paper, we discuss the two-group SIR model introduced by Guo, Li and Shuai [H.B. Guo, M.Y. Li, Z. Shuai, Global stability of the endemic equilibrium of multigroup SIR epidemic models, Can. Appl. Math. Q. 14 (2006) 259-284], allowing random fluctuation around the endemic equilibrium. We prove the endemic equilibrium of the model with random perturbation is stochastic asymptotically stable in the large. In addition, the stability condition is obtained by the construction of Lyapunov function. Finally, numerical simulations are presented to illustrate our mathematical findings.

The factors affecting vortex growth in convectively stable protoplanetary disks are explored using numerical simulations of a two-dimensional anelastic-gas model that includes baroclinic vorticity production and radiative cooling. The baroclinic feedback, in which anomalous temperature gradients produce vorticity through the baroclinic term and vortices then reinforce these temperature gradients, is found to be an important process in the rate of growth of vortices in the disk. Factors that strengthen the baroclinic feedback include fast radiative cooling, high thermal diffusion, and large radial temperature gradients in the background temperature. When the baroclinic feedback is sufficiently strong, anticyclonic vortices form from initial random perturbations and maintain their strength for the duration of the simulation, for over 600 orbital periods. Based on both simulations and a simple vortex model, we find that the local angular momentum transport due to a single vortex may be inward or outward, depending on its orientation. The global angular momentum transport is highly variable in time and is sometimes negative and sometimes positive. This result is for an anelastic-gas model and does not include shocks that could affect angular momentum transport in a compressible-gas disk.

We calculate the distribution of eigenfunction amplitudes and the variance of the "inverse participation ratio" (IPR) in disordered metallic samples. A relation is established between the distribution function of IPR and that of "level velocities"-parametric derivatives of energy levels with respect to a random perturbation.

Background: One of the mechanisms that ensure cancer robustness is tumor heterogeneity, and its effects on tumor cells dynamics have to be taken into account when studying cancer progression. There is no unifying theoretical framework in mathematical modeling of carcinogenesis that would account for parametric heterogeneity. Results: Here we formulate a modeling approach that naturally takes stock of inherent cancer cell heterogeneity and illustrate it with a model of interaction between a tumor and an oncolytic virus. We show that several phenomena that are absent in homogeneous models, such as cancer recurrence, tumor dormancy, and others, appear in heterogeneous setting. We also demonstrate that, within the applied modeling framework, to overcome the adverse effect of tumor cell heterogeneity on the outcome of cancer treatment, a heterogeneous population of an oncolytic virus must be used. Heterogeneity in parameters of the model, such as tumor cell susceptibility to virus infection and the ability of an oncolytic virus to infect tumor cells, can lead to complex, irregular evolution of the tumor. Thus, quasi-chaotic behavior of the tumor-virus system can be caused not only by random perturbations but also by the heterogeneity of the tumor and the virus. Conclusion: The modeling approach described here reveals the importance of tumor cell and virus heterogeneity for the outcome of cancer therapy. It should be straightforward to apply these techniques to mathematical modeling of other types of anticancer therapy. Reviewers: Leonid Hanin (nominated by Arcady Mushegian), Natalia Komarova (nominated by Orly Alter), and David Krakauer.

In this paper, a hybrid descent method, consisting of a simulated annealing algorithm and a gradient-based method, is proposed. The simulated annealing algorithm is used to locate descent points for previously converged local minima. The combined method has the descent property and the convergence is monotonic. To demonstrate the effectiveness of the proposed hybrid descent method, several multi-dimensional non-convex optimization problems are solved. Numerical examples show that global minimum can be sought via this hybrid descent method.

This article proposes a multi-prize noisy-ranking contest model. Contestants are ranked in descending order based on their perceived performance, which is subject to random perturbation, and they are rewarded based on their ranks. Under plausible conditions, we establish that our noisy performance ranking model is stochastically equivalent to the family of multi-prize lottery contests built upon ratio-form contest success functions. We further establish the equivalence of our model to a contest model that ranks contestants by their best performance out of multiple independent attempts. These results therefore shed light on the micro-foundations of the popularly adopted lottery contest models. The "best-shot ranking rule" reveals a common thread that connects a broad class of seemingly disparate competitive activities (such as rent-seeking contests, patent races, research tournaments), and unifies them through a common performance evaluation mechanism.

Heat flux between fiver water and riverbed contributes significantly to fiver water heat content and river temperature, especially in shallow rivers. A numerical model of heat conduction in a riverbed was verified with detailed temperatures measurements in a fiverbed. Three different methods, the heat budget method, the gradient method, and an inverse method, were used alternatively for the estimation of the riverbed heat flux. Propagation of uncertainty in the fiverbed temperature model was studied using a vector state space perturbation method. Output uncertainty was estimated by random perturbations of the effective thermal conductivity from the main value. The coefficient of variation of effective thermal conductivity was 0.1. Temperatures and heat fluxes in the riverbed were affected by the uncertain thermal conductivity. Introduction Water temperature has a significant influence on the water quality and aquatic life of a river. It controls the solubility of dissolved oxygen, the metabolism and respiration of plants and animals, and the toxicity of pollutants. Temporal and spatial distribution variations of water temperature are required as a boundary condition of ecological models [Brocard and Harleman, 1976; McCutcheon, 1989]. Temperature is one of the most important parameters in river water quality [Bowles et al., 1977; McCutcheon, 1989]. Considerable interest has been shown in the numerical prediction of fiver temperature dynamics [Brocard and

Let A be an arbitrary matrix and let A be a slight random perturbation of A. We prove that it is unlikely that A has large condition number. Using this result, we prove it is unlikely that A has large growth factor under Gaussian elimination without pivoting. By combining these results, we show that the smoothed precision necessary to solve Ax = b, for any b, using Gaussian elimination without pivoting is logarithmic. Moreover, when A is an all-zero square matrix, our results significantly improve the average-case analysis of Gaussian elimination without pivoting performed by Yeung and Chan (SIAM J. Matrix Anal. Appl., 1997).

For the quantum kicked top we study numerically the distribution of Hilbert-space vectors evolving in the presence of a small random perturbation. For an initial coherent state centered in a chaotic region of the classical dynamics, the evolved perturbed vectors are distributed essentially like random vectors in Hilbert space. In contrast, for an initial coherent state centered near an elliptic (regular) fixed point of the classical dynamics, the evolved perturbed vectors remain close together, explore only few dimensions of Hilbert space, and do not explore them randomly. These results support and extend results of earlier studies, thereby providing additional support for a new characterization of quantum chaos that uses concepts from information theory.

This paper presents a technique for creating a smooth, closed surface from a set of 2D contours, which have been extracted from a 3D scan. The technique interprets the pixels that make up the contours as points in R 3 and employs Multi-level Partition of Unity (MPU) implicit models to create a surface that approximately fits to the 3D points. Since MPU implicit models additionally require surface normal information at each point, an algorithm that estimates normals from the contour data is also described. Contour data frequently contains noise from the scanning and delineation process. MPU implicit models provide a superior approach to the problem of contour-based surface reconstruction, especially in the presence of noise, because they are based on adaptive implicit functions that locally approximate the points within a controllable error bound. We demonstrate the effectiveness of our technique with a number of example datasets, providing images and error statistics generated from our results.

We give both sufficient conditions and necessary conditions for the stochastic stability of non-uniformly expanding maps either with or without critical sets. We also show that the number of probability measures describing the statistical asymptotic behaviour of random orbits is bounded by the number of SRB measures if the noise level is small enough.

We present new solutions to the nonautonomous nonlinear Schrödinger equation that may be realized through convenient manipulation of Bose-Einstein condensates. The procedure is based on the modulation of breathers through an analytical study of the one-dimensional Gross-Pitaevskii equation, which is known to offer a good theoretical model to describe quasi-one-dimensional cigar-shaped condensates. Using a specific Ansatz, we transform the nonautonomous nonlinear equation into an autonomous one, which engenders composed states corresponding to solutions localized in space, with an oscillating behavior in time. Numerical simulations confirm stability of the breathers against random perturbation on the input profile of the solutions.

The 17th of the problems proposed by Steve Smale for the 21st century asks for the existence of a deterministic algorithm computing an approximate solution of a system of n complex polynomials in n unknowns in time polynomial, on the average, in the size N of the input system. A partial solution to this problem was given by Carlos Beltrán and Luis Miguel Pardo who exhibited a randomized algorithm doing so. In this paper we further extend this result in several directions. Firstly, we exhibit a linear homotopy algorithm that efficiently implements a non-constructive idea of Mike Shub. This algorithm is then used in a randomized algorithm, call it LV,à la Beltrán-Pardo. Secondly, we perform a smoothed analysis (in the sense of Spielman and Teng) of algorithm LV and prove that its smoothed complexity is polynomial in the input size and σ −1 , where σ controls the size of of the random perturbation of the input systems. Thirdly, we perform a condition-based analysis of LV. That is, we give a bound, for each system f , of the expected running time of LV with input f . In addition to its dependence on N this bound also depends on the condition of f . Fourthly, and to conclude, we return to Smale's 17th problem as originally formulated for deterministic algorithms. We exhibit such an algorithm and show that its average complexity is N O(log log N) . This is nearly a solution to Smale's 17th problem.

Degenerate white noise perturbations of Hamiltonian systems in R 2 are studied. In particular, perturbations of a nonlinear oscillator with 1 degree of freedom are considered. If the oscillator has more than one stable equilibrium, the long time behavior of the system is defined by a diffusion process on a graph. Inside the edges the process is defined by a standard averaging procedure, but to define the process for all t > 0 one should add gluing conditions at the vertices. Calculation of the gluing conditions is based on delicate Hörmander-type estimates.

Clustering algorithms may be applied to the analysis of DNA microarray data to identify novel subgroups that may lead to new taxonomies of diseases defined at bio-molecular level. A major problem related to the identification of biologically meaningful clusters is the assessment of their reliability, since clustering algorithms may find clusters even if no structure is present. Methodology: Recently, methods based on random "perturbations" of the data, such as bootstrapping, noise injections techniques and random subspace methods have been applied to the problem of cluster validity estimation. In this framework, we propose stability measures that exploits the high dimensionality of DNA microarray data and the redundancy of information stored in microarray chips. To this end we randomly project the original gene expression data into lower dimensional subspaces, approximately preserving the distance between the examples according to the Johnson-Lindenstrauss (JL) theory. The stability of the clusters discovered in the original high dimensional space is estimated by comparing them with the clusters discovered in randomly projected lower dimensional subspaces. The proposed cluster-stability measures may be applied to validate and to quantitatively assess the reliability of the clusters obtained by a large class of clustering algorithms. Results and conclusion: We tested the effectiveness of our approach with high dimensional synthetic data, whose distribution is a priori known, showing that the stability measures based on randomized maps correctly predict the number of clusters and the reliability of each individual cluster. Then we showed how to apply the proposed measures to the analysis of DNA microarray data, whose underlying distribution is unknown. We evaluated the validity of clusters discovered by hierarchical clustering algorithms in diffuse large B-cell lymphoma (DLBCL) and malignant melanoma patients, showing that the proposed reliability measures can support bio-medical researchers in the identification of stable clusters of patients and in the discovery of new subtypes of diseases characterized at bio-molecular level.

We develop a neuromechanical model for running insects that includes a simplified hexapedal leg geometry with agonist-antagonist muscle pairs actuating each leg joint. Restricting to dynamics in the horizontal plane and neglecting leg masses, we reduce the model to three degrees of freedom describing translational and yawing motions of the body. Muscles are driven by stylized action potentials characteristic of fast motoneurons, and modeled using an activation function and nonlinear length and shortening velocity dependence. Parameter values are based on measurements from depressor muscles and observations of kinematics and dynamics of the cockroach Blaberus discoidalis; in particular, motoneuronal inputs and muscle force levels are chosen to approximately achieve joint torques that are consistent with measured ground reaction forces. We show that the model has stable double-tripod gaits over the animal's speed range, that its dynamics at preferred speeds matches those observed, and that it maintains stable gaits, with low frequency yaw deviations, when subject to random perturbations in foot touchdown and lift-off timing and action potential input timing. We explain this in terms of the low-dimensional dynamics. (R.P. Kukillaya).

OSCAR II is a twin-engine aerial demonstrator equipped with a monocular visual system, which manages to keep its gaze and its heading steadily fixed on a target (i.e., a dark edge or a bar) in spite of the severe random perturbations applied to its body via a ducted fan. The tethered robot stabilizes its gaze on the basis of two oculomotor reflexes (ORs) inspired by studies on animals: 1) a visual-fixation reflex (VFR) and 2) a vestibulo-ocular reflex (VOR). One of the key features of this robot is that the eye is decoupled mechanically from the body about the vertical (i.e., yaw) axis. To meet the conflicting requirements of high accuracy and fast ocular responses, a miniature (2.4 g) voice-coil motor (VCM) was used, which enables the eye to make a change of orientation with an unusually short rise time (19 ms). The robot, which was equipped with a high-bandwidth (7 Hz) "VOR," which is based on an inertial microrate gyro, is capable of accurate visual fixation as long as there is light. The robot is also able to pursue a moving target in the presence of erratic gusts of wind. Here, we present the two interdependent control schemes driving the eye in the robot and the robot in space with no knowledge of the robot's angular position. This "steering-by-gazing" control strategy, which is implemented on this lightweight (100 g) miniature aerial robot, demonstrates the effectiveness of this biomimetic visual/inertial heading control strategy.

We consider the problem of achieving distributed convergence to coordination in a multiagent environment. Each agent is modeled as a learning automaton which repeatedly interacts with an unknown environment, receives a reward, and updates the probabilities of its next action based on its own previous actions and received rewards. In this class of problems, more than one stable equilibrium (i.e., coordination structure) exists. We analyze the dynamic behavior of the distributed system in terms of convergence to an efficient equilibrium, suitably defined. In particular, we analyze the effect of dynamic processing on convergence properties, where agents include the derivative of their own reward into the decision process (i.e., derivative action). We show that derivative action can be used as an equilibrium selection scheme by appropriately adjusting derivative feedback gains.

Computing the morphological similarity of diffusion tensors (DTs) at neighboring voxels within a DT image, or at corresponding locations across different DT images, is a fundamental and ubiquitous operation in the postprocessing of DT images. The morphological similarity of DTs typically has been computed using either the principal directions (PDs) of DTs (i.e., the direction along which water molecules diffuse preferentially) or their tensor elements. Although comparing PDs allows the similarity of one morphological feature of DTs to be visualized directly in eigenspace, this method takes into account only a single eigenvector, and it is therefore sensitive to the presence of noise in the images that can introduce error intothe estimation of that vector. Although comparing tensor elements, rather than PDs, is comparatively more robust to the effects of noise, the individual elements of a given tensor do not directly reflect the diffusion properties of water molecules. We propose a measure for computing the morphological similarity of DTs that uses both their eigenvalues and eigenvectors, and that also accounts for the noise levels present in DT images. Our measure presupposes that DTs in a homogeneous region within or across DT images are random perturbations of one another in the presence of noise. The similarity values that are computed using our method are smooth (in the sense that small changes in eigenvalues and eigenvectors cause only small changes in similarity), and they are symmetric when differences in eigenvalues and eigenvectors are also symmetric. In addition, our method does not presuppose that the corresponding eigenvectors across two DTs have been identified accurately, an assumption that is problematic in the presence of noise. Because we compute the similarity between DTs using their eigenspace components, our similarity measure relates directly to both the magnitude and the direction of the diffusion of water molecules. The favorable performance characteristics of our measure offer the prospect of substantially improving additional postprocessing operations that are commonly performed on DTI datasets, such as image segmentation, fiber tracking, noise filtering, and spatial normalization.

The mechanisms that regulate the spatial distribution of species are an essential aid to understanding the effects of the environment on the persistence of populations and communities. The effects of spatial structure on the persistence and robustness of ecological communities can, in turn, prove useful in uncovering their functioning, e.g., in the decomposition of leaf detritus. We applied the framework of complex networks to evaluate the effects of spatial structure on the colonization process of leaf detritus in a patchy aquatic environment, with a spatial network of six pools at different salinity. We found three well-defined modules formed by groups of taxa sharing the same pools, observing an association between modularity and spatial proximity of pools. Modules maximize the number of links within modules, and minimize the number of links among modules, showing the presence of a strong site-specific association between taxa and pools. The topological characteristics of the network show robustness against random perturbations and a lower tolerance of targeted perturbations. These findings suggest that random events, such as flooding or heavy rains, slightly affect the robustness of the system, while localized perturbations on the most connected nodes could have a negative effect on the connectivity of the whole network. The consequences could lead to a structural and functional homogenization of the system, with potential effects for the entire trophic chain. Here we discuss the topological properties of the network in relation to the spatial distribution of pools, showing how network analysis can yield valuable insight for conservation and management.

We consider a chance constraint Prob{ξ : A(x, ξ) ∈ K} ≥ 1 − (x is the decision vector, ξ is a random perturbation, K is a closed convex cone, and A(•, •) is bilinear). While important for many applications in Optimization and Control, chance constraints typically are "computationally intractable", which makes it necessary to look for their tractable approximations. We present these approximations for the cases when the underlying conic constraint A(x, ξ) ∈ K is (a) scalar inequality, or (b) conic quadratic inequality, or (c) linear matrix inequality, and discuss the level of conservativeness of the approximations.

The specification of the initial ensemble for ensemble data assimilation is addressed. The presented work examines the impact of ensemble initiation in the Maximum Likelihood Ensemble Filter (MLEF) framework, but is also applicable to other ensemble data assimilation algorithms. Two methods are considered: the first is based on the use of the Kardar-Parisi-Zhang (KPZ) equation to form sparse random perturbations, followed by spatial smoothing to enforce desired correlation structure, while the second is based on the spatial smoothing of initially uncorrelated random perturbations. Data assimilation experiments are conducted using a global shallow-water model and simulated observations. The two proposed methods are compared to the commonly used method of uncorrelated random perturbations. The results indicate that the impact of the initial correlations in ensemble data assimilation is beneficial. The root-mean-square error rate of convergence of the data assimilation is improved, and the positive impact of initial correlations is notable throughout the data assimilation cycles. The sensitivity to the choice of the correlation length scale exists, although it is not very high. The implied computational savings and improvement of the results may be important in future realistic applications of ensemble data assimilation.