Fusion Tensor Subspace Transformation Framework

Tensor subspace transformation, a commonly used subspace transformation technique, has gained more and more popularity over the past few years because many objects in the real world can be naturally represented as multidimensional arrays, i.e. tensors. For example, a RGB facial image can be represented as a three-dimensional array (or 3rd-order tensor). The first two dimensionalities (or modes) represent the facial spatial information and the third dimensionality (or mode) represents the color space information. Each mode of the tensor may express a different semantic meaning. Thus different transformation strategies should be applied to different modes of the tensor according to their semantic meanings to obtain the best performance. To the best of our knowledge, there are no existing tensor subspace transformation algorithm which implements different transformation strategies on different modes of a tensor accordingly. In this paper, we propose a fusion tensor subspace transformation framework, a novel idea where different transformation strategies are implemented on separate modes of a tensor. Under the framework, we propose the Fusion Tensor Color Space (FTCS) model for face recognition.     

First capture success in two dimensions: The search for prey by a random walk predator in a comprehensive space of random walks

Random walk models are an important tool used for understanding how complex organisms redistribute themselves through space and time in search of targets such as food, shelter, or mates. These walks are easily studied with agent-based models, which can be used to ask which search strategy is best according to some efficiency metric. Current studies however, generally do not consider the full range of potential random walks, success metrics, and constraints on the walker, and implementation details vary widely. It is therefore difficult to compare results across studies. In this paper, we investigate predator search behaviour in a comprehensive space of key movement variables that allows the predator to select from a continuum of random walks ranging from Brownian walks (BWs) to correlated random walks (CorRWs) which include directional persistence, to composite random walks (ComRWs) which feature intensive and extensive search modes (ISMs and ESMs), and finally to more complex correlated composite random walks (CCRWs). We specifically focus on the search behaviour of a predator between the initiation of a search for a prey item and the first successful acquisition of a prey target: we call this interval the “search-to-capture” event. We measure the predator's success against three metrics of energetic cost: (1) the time elapsed, (2) the distance travelled, and (3) an equally weighted combination of time and distance. In addition, we explore the effect of three different constraints on the predator: (1) hunting success in the extensive search mode, (2) detection radius when in the extensive search mode, and (3) prey density. Our work confirms the broadly held notion that CCRW movement patterns should always outperform BWs, but find instructive cases where other walks are superior. We also show that, within the CCRW category, there is a wide range of possible walks and rank these according to measures of energetic cost. Our work also offers insights into the evolutionary pressures surrounding the “search-to-capture” event, and suggests that CCRW predators with low hunting success in one movement mode experience higher evolutionary pressures and are thus more likely to adopt a nearly optimal random walk. Our work highlights the need for comprehensive studies that examine several aspects of random walks simultaneously.     

Lateral diffusion in an archipelago. Single-particle diffusion.

Several laboratories have measured lateral diffusion of single particles on the cell surface, and these measurements may reveal an otherwise inaccessible level of submicroscopic organization of cell membranes. Pitfalls in the interpretation of these experiments are analyzed. Random walks in unobstructed systems show structure that could be interpreted as free diffusion, obstructed diffusion, directed motion, or trapping in finite domains. To interpret observed trajectories correctly, one must consider not only the trajectories themselves but also the probabilities of occurrence of various trajectories. Measures of the asymmetry of obstructed and unobstructed random walks are calculated, and probabilities are evaluated for random trajectories that resemble either directed motion or diffusion in a bounded region.     

A computational method to detect epistatic effects contributing to a quantitative trait

We develop a new computational method to detect epistatic effects that contribute to a complex quantitative trait. Rather than looking for epistatic effects that show statistical significance when considered in isolation, we search for a close approximation to the quantitative trait by a sum of epistatic effects. Our search algorithm consists of a sequence of random walks around the space of sums of epistatic effects. An important feature of our approach is that there is learning between random walks, i.e. the control mechanism that chooses steps in our random walks adapts to the experiences of earlier random walks. We test the effectiveness of our algorithms by applying them to synthetic datasets where the phenotype is a sum of epistatic effects plus normally distributed noise. Our test statistic is the rate of success that our methods achieve in identifying the underlying epistatic effects. We report on the effectiveness of our methods as we vary parameters that are intrinsic to the computation (length of random walks and degree of learning) as well as parameters that are extrinsic to the computation (number of markers, number of individuals, noise level, architecture of the epistatic effects).     

Scales of orientation, directed walks and movement path structure in sharks

1. Animal search patterns reflect sensory perception ranges combined with memory and knowledge of the surrounding environment. 2. Random walks are used when the locations of resources are unknown, whereas directed walks should be optimal when the location of favourable habitats is known. However, directed walks have been quantified for very few species. 3. We re-analysed tracking data from three shark species to determine whether they were using directed walks, and if so, over which spatial scales. Fractal analysis was used to quantify how movement structure varied with spatial scale and determine whether the sharks were using patches. 4. Tiger sharks performed directed walks at large spatial scales (at least 6-8 km). Thresher sharks also showed directed movement (at scales of 400-1900 m), and adult threshers were able to orient at greater scales than juveniles, which may suggest that learning improves the ability to perform directed walks. Blacktip reef sharks had small home ranges, high site fidelity and showed no evidence of oriented movements at large scales. 5. There were inter- and intraspecific differences in path structure and patch size, although most individuals showed scale-dependent movements. Furthermore, some individuals of each species performed movements similar to a correlated random walk. 6. Sharks can perform directed walks over large spatial scales, with scales of movements reflecting site fidelity and home range size. Understanding when and where directed walks occur is crucial for developing more accurate population-level dispersal models.     

Towards a unified framework for connectivity that disentangles movement and mortality in space and time

Predicting connectivity, or how landscapes alter movement, is essential for understanding the scope for species persistence with environmental change. Although it is well known that movement is risky, connectivity modelling often conflates behavioural responses to the matrix through which animals disperse with mortality risk. We derive new connectivity models using random walk theory, based on the concept of spatial absorbing Markov chains. These models decompose the role of matrix on movement behaviour and mortality risk, can incorporate species distribution to predict the amount of flow, and provide both short‐ and long‐term analytical solutions for multiple connectivity metrics. We validate the framework using data on movement of an insect herbivore in 15 experimental landscapes. Our results demonstrate that disentangling the roles of movement behaviour and mortality risk is fundamental to accurately interpreting landscape connectivity, and that spatial absorbing Markov chains provide a generalisable and powerful framework with which to do so.     

The evolution of an 'intelligent' dispersal strategy: biased, correlated random walks in patchy landscapes

Theoretical work exploring dispersal evolution focuses on the emigration rate of individuals and typically assumes that movement occurs either at random to any other patch or to one of the nearest‐neighbour patches. There is a lack of work exploring the process by which individuals move between patches, and how this process evolves. This is of concern because any organism that can exert control over dispersal direction can potentially evolve efficiencies in locating patches, and the process by which individuals find new patches will potentially have major effects on metapopulation dynamics and gene flow. Here, we take an initial step towards filling this knowledge gap. To do this we constructed a continuous space population model, in which individuals each carry heritable trait values that specify the characteristics of the biased correlated random walk they use to disperse from their natal patch. We explore how the evolution of the random walk depends upon the cost of dispersal, the density of patches in the landscape, and the emigration rate. The clearest result is that highly correlated walks always evolved (individuals tended to disperse in relatively straight lines from their natal patch), reflecting the efficiency of straight‐line movement. In our models, more costly dispersal resulted in walks with higher correlation between successive steps. However, the exact walk that evolved also depended upon the density of suitable habitat patches, with low density habitat evolving more biased walks (individuals which orient towards suitable habitat at quite large distances from that habitat). Thus, low density habitat will tend to develop individuals which disperse efficiently between adjacent habitat patches but which only rarely disperse to more distant patches; a result that has clear implications for metapopulation theory. Hence, an understanding of the movement behaviour of dispersing individuals is critical for robust long‐term predictions of population dynamics in fragmented landscapes.     

Development of EMG-based mode and intent recognition algorithms for a computer-controlled above-knee prosthesis

Conventional above-knee prostheses are unable to replace normal leg function due to the lack of adaptive control. Computer-controlled prostheses offer the possibility to implement such adaptive control. For a particular locomotion mode, control algorithms can generate appropriate damping profiles as a function of selected sensory inputs and stored information on normal walking. However, it is essential in such systems that the locomotor modes can be determined accurately from the inputs of the control system. Recognition of the intent to change from one mode to another is also a necessity because the control system has to account for such transitions. The possibility of using EMG signals from hip muscles and muscle residuals of the stump for this purpose is investigated. The modes tested are level walking, ramp ascent and ramp descent with slopes of 6° and 9°. EMG activity curves for three muscles: gluteus maximus, gluteus medius and tensor fasciae latae, are presented for the different modes. The results are obtained from two reference groups of 12 normal individuals and from a prosthetic patient. The results show the possibility of discriminating between modes. A discussion is made of the implementation of the results obtained by a finite state approach and the difficulties relating to the use of EMG signals for control purposes.     

Integrating multi-attribute similarity networks for robust representation of the protein space

MOTIVATION: A global view of the protein space is essential for functional and evolutionary analysis of proteins. In order to achieve this, a similarity network can be built using pairwise relationships among proteins. However, existing similarity networks employ a single similarity measure and therefore their utility depends highly on the quality of the selected measure. A more robust representation of the protein space can be realized if multiple sources of information are used. RESULTS: We propose a novel approach for analyzing multi-attribute similarity networks by combining random walks on graphs with Bayesian theory. A multi-attribute network is created by combining sequence and structure based similarity measures. For each attribute of the similarity network, one can compute a measure of affinity from a given protein to every other protein in the network using random walks. This process makes use of the implicit clustering information of the similarity network, and we show that it is superior to naive, local ranking methods. We then combine the computed affinities using a Bayesian framework. In particular, when we train a Bayesian model for automated classification of a novel protein, we achieve high classification accuracy and outperform single attribute networks. In addition, we demonstrate the effectiveness of our technique by comparison with a competing kernel-based information integration approach.     

Observations on the flight paths of the day-flying moth Virbia lamae during periods of mate location: do males have a strategy for contacting the pheromone plume?

1. To maximize the probability of rapid contact with a female's pheromone plume, the trajectories of male foraging flights might be expected to be directed with respect to wind flow and also to be energetically efficient. 2. Flights directed either upwind, downwind, or crosswind have been proposed as optimal strategies for rapid and/or energetically efficient plume contact. Other possible strategies are random and Lévy walks, which have trajectories and turn frequencies that are not dictated by the direction of wind flow. 3. The planar flight paths of males of the day-active moth Virbia lamae were recorded during the customary time of its sexual activity. 4. We found no directional preference in these foraging flights with respect to the direction of contemporaneous wind flow, but, because crosswind encompasses twice the possible orientations of either upwind or downwind, a random orientation is in effect a de facto crosswind strategy. 5. A crosswind preference should be favoured when the plume extends farther downwind than crosswind, and this strategy is realized by V. lamae males by a random orientation of their trajectories with respect to current wind direction.     

Random walks, random sequences, and nonlinear dynamics in human optokinetic nystagmus.

Optokinetic nystagmus (OKN) is a reflexive eye movement with target-following slow phases (SP) alternating with oppositely directed fast phases (FP). We measured the following from OKN in three humans: FP beginning and ending positions, amplitudes, and intervals and SP amplitudes and velocities. We sought to predict future values of each parameter on the basis of past values, using state-space representation of the sequence (time-delay embedding) and local second-order approximation of trajectories. Predictability is an indication of determinism: this approach allows us to investigate the relative contributions of random and deterministic dynamics in OKN. FP beginning and ending positions showed good predictability, but SP velocity was less predictable. FP and SP amplitudes and FP intervals had little or no predictability. FP beginnings and endings were as predictable as randomized versions that retain linear autocorrelation; this is typical of random walks. Predictability of FP intervals did not change under random rearrangement, which is characteristic of a random process. Only linear determinism was demonstrated; nonlinear interactions may exist that would not be detected by our present approach.     

Single-particle tracking: models of directed transport.

Single-particle tracking techniques make it possible to measure motion of individual particles on the cell surface. In these experiments, individual trajectories are observed, so the data analysis must take into account the randomness of individual random walks. Methods of data analysis are discussed for models combining diffusion and directed motion. In the uniform flow model, a tracer simultaneously diffuses and undergoes directed motion. In the conveyor belt model, a tracer binds and unbinds to a uniform conveyor belt moving with constant velocity. If a tracer is bound, it moves at the velocity of the conveyor belt; if it is unbound, it diffuses freely. Trajectories are analyzed using parameters that measure the extent and asymmetry of the trajectory. A method of assessing the usefulness of such parameters is presented, and pitfalls in data analysis are discussed. Joint probability distributions of pairs of extent and asymmetry parameters are obtained for a pure random walk. These distributions can be used to show that a trajectory is not likely to have resulted from a pure random walk.     

Speciation and the neutral theory of biodiversity

The neutral theory of biodiversity purports that patterns in the distribution and abundance of species do not depend on adaptive differences between species (i.e. niche differentiation) but solely on random fluctuations in population size (“ecological drift”), along with dispersal and speciation. In this framework, the ultimate driver of biodiversity is speciation. However, the original neutral theory made strongly simplifying assumptions about the mechanisms of speciation, which has led to some clearly unrealistic predictions. In response, several recent studies have combined neutral community models with more elaborate speciation models. These efforts have alleviated some of the problems of the earlier approaches, while confirming the general ability of neutral theory to predict empirical patterns of biodiversity. However, the models also show that the mode of speciation can have a strong impact on relative species abundances. Future work should compare these results to diversity patterns arising from non‐neutral modes of speciation, such as adaptive radiations.     

Human papillomavirus type 16 entry: retrograde cell surface transport along actin-rich protrusions

The lateral mobility of individual, incoming human papillomavirus type 16 pseudoviruses (PsV) bound to live HeLa cells was studied by single particle tracking using fluorescence video microscopy. The trajectories were computationally analyzed in terms of diffusion rate and mode of motion as described by the moment scaling spectrum. Four distinct modes of mobility were seen: confined movement in small zones (30-60 nm in diameter), confined movement with a slow drift, fast random motion with transient confinement, and linear, directed movement for long distances. The directed movement was most prominent on actin-rich cell protrusions such as filopodia or retraction fibres, where the rate was similar to that measured for actin retrograde flow. It was, moreover, sensitive to perturbants of actin retrograde flow such as cytochalasin D, jasplakinolide, and blebbistatin. We found that transport along actin protrusions significantly enhanced HPV-16 infection in sparse tissue culture, cells suggesting a role for in vivo infection of basal keratinocytes during wound healing.     

On the origin and characteristics of noise-induced Lévy walks of E. coli

Lévy walks as a random search strategy have recently attracted a lot of attention, and have been described in many animal species. However, very little is known about one of the most important issues, namely how Lévy walks are generated by biological organisms. We study a model of the chemotaxis signaling pathway of E. coli, and demonstrate that stochastic fluctuations and the specific design of the signaling pathway in concert enable the generation of Lévy walks. We show that Lévy walks result from the superposition of an ensemble of exponential distributions, which occurs due to the shifts in the internal enzyme concentrations following the stochastic fluctuations. With our approach we derive the power-law analytically from a model of the chemotaxis signaling pathway, and obtain a power-law exponent μ ≈ 2.2, which coincides with experimental results. This work provides a means to confirm Lévy walks as natural phenomenon by providing understanding on the process through which they emerge. Furthermore, our results give novel insights into the design aspects of biological systems that are capable of translating additive noise on the microscopic scale into beneficial macroscopic behavior.