Goal-oriented sensitivity analysis for lattice kinetic Monte Carlo simulations

In this paper we propose a new class of coupling methods for the sensitivity analysis of high dimensional stochastic systems and in particular for lattice Kinetic Monte Carlo. Sensitivity analysis for stochastic systems is typically based on approximating continuous derivatives with respect to model parameters by the mean value of samples from a finite difference scheme. Instead of using independent samples the proposed algorithm reduces the variance of the estimator by developing a strongly correlated-"coupled"- stochastic process for both the perturbed and unperturbed stochastic processes, defined in a common state space. The novelty of our construction is that the new coupled process depends on the targeted observables, e.g. coverage, Hamiltonian, spatial correlations, surface roughness, etc., hence we refer to the proposed method as em goal-oriented sensitivity analysis. In particular, the rates of the coupled Continuous Time Markov Chain are obtained as solutions to a goal-oriented optimization problem, depending on the observable of interest, by considering the minimization functional of the corresponding variance. We show that this functional can be used as a diagnostic tool for the design and evaluation of different classes of couplings. Furthermore the resulting KMC sensitivity algorithm has an easy implementation that is based on the Bortz-Kalos-Lebowitz algorithm's philosophy, where here events are divided in classes depending on level sets of the observable of interest. Finally, we demonstrate in several examples including adsorption, desorption and diffusion Kinetic Monte Carlo that for the same confidence interval and observable, the proposed goal-oriented algorithm can be two orders of magnitude faster than existing coupling algorithms for spatial KMC such as the Common Random Number approach

Hierarchical fractional-step approximations and parallel kinetic Monte Carlo algorithms

We present a mathematical framework for constructing and analyzing parallel algorithms for lattice Kinetic Monte Carlo (KMC) simulations. The resulting algorithms have the capacity to simulate a wide range of spatio-temporal scales in spatially distributed, non-equilibrium physiochemical processes with complex chemistry and transport micro-mechanisms. The algorithms can be tailored to specific hierarchical parallel architectures such as multi-core processors or clusters of Graphical Processing Units (GPUs). The proposed parallel algorithms are controlled-error approximations of kinetic Monte Carlo algorithms, departing from the predominant paradigm of creating parallel KMC algorithms with exactly the same master equation as the serial one. Our methodology relies on a spatial decomposition of the Markov operator underlying the KMC algorithm into a hierarchy of operators corresponding to the processors' structure in the parallel architecture. Based on this operator decomposition, we formulate Fractional Step Approximation schemes by employing the Trotter Theorem and its random variants; these schemes, (a) determine the communication schedule} between processors, and (b) are run independently on each processor through a serial KMC simulation, called a kernel, on each fractional step time-window. Furthermore, the proposed mathematical framework allows us to rigorously justify the numerical and statistical consistency of the proposed algorithms, showing the convergence of our approximating schemes to the original serial KMC. The approach also provides a systematic evaluation of different processor communicating schedules.Comment: 34 pages, 9 figure

Investigating the Behavior of Compact Composite Descriptors in Early Fusion, Late Fusion and Distributed Image Retrieval

In Content-Based Image Retrieval (CBIR) systems, the visual content of the images is mapped into a new space named the feature space. The features that are chosen must be discriminative and sufficient for the description of the objects. The key to attaining a successful retrieval system is to choose the right features that represent the images as unique as possible. A feature is a set of characteristics of the image, such as color, texture, and shape. In addition, a feature can be enriched with information about the spatial distribution of the characteristic that it describes. Evaluation of the performance of low-level features is usually done on homogenous benchmarking databases with a limited number of images. In real-world image retrieval systems, databases have a much larger scale and may be heterogeneous. This paper investigates the behavior of Compact Composite Descriptors (CCDs) on heterogeneous databases of a larger scale. Early and late fusion techniques are tested and their performance in distributed image retrieval is calculated. This study demonstrates that, even if it is not possible to overcome the semantic gap in image retrieval by feature similarity, it is still possible to increase the retrieval effectiveness

PLASTICITY OF HUMAN TENDON’S MECHANICAL PROPERTIES: EFFECTS ON SPORT PERFORMANCE

INTRODUCTION: In the literature it is often mentioned, that the tendon is very relevant for the work producing capability of the muscle fibers and for the motion and the performance of the human body. During a given movement, strain energy can be stored in the tendon and this way the whole energy delivery of the muscle can be enhanced. Further, the higher elongation capability of the tendon with respect to the muscle fiber, allows a bigger change in length of the muscle-tendon unit. Therefore, the muscle fibers may work on a lower shortening velocity and as a consequence of the force-velocity relationship their force producing potential will be higher. Generally, the main functions of the tendon during locomotion are: (a) to transfer muscle forces to the skeleton (b) to store mechanical energy coming from the human body or/and from muscular work as strain energy and (c) to create favorable conditions for the muscle fibers to produce force as a result of the force-length-velocity relationship. A higher force potential of the muscle fibers due to the force-length-velocity relationship during submaximal contractions would decrease the volume of active muscle at a given force or a given rate of force generation and consequently would decrease the cost of force production. In the same manner during maximal muscle contractions (maximal activation level) the higher force potential of the muscle fibers will allow the muscles to exert higher forces. The reports about the influence of the non rigidity of the tendon on the effectivity of muscle force production reveal the expectation that sport performance during submaximal as well as maximal running intensities may be affected by the mechanical and morphological properties of the tendon. In a series of experiments we examined the mechanical properties of the lower extremities muscle-tendon units (MTU) from athletes displaying different running economy and sprint performance. The most economical runners showed a higher contractile strength and a higher tendon stiffness in the triceps surae MTU and a higher compliance of the quadriceps tendon and aponeurosis at low level tendon forces (Arampatzis et al., 2006). The faster sprinters exhibited a higher elongation of the vastus lateralis (VL) tendon and aponeurosis at a given tendon force and a higher maximal elongation of the VL tendon and aponeurosis during the MVC (Stafilidis and Arampatzis, 2007). Furthermore, the maximal elongation of the VL tendon and aponeurosis showed a significant correlation with the 100 m sprint times (r = -0.567, P = 0.003). It has been supposed that, the more compliant quadriceps tendon and aponeurosis will increase the energy storage and return as well as the force potential of the muscle due to the force-velocity relationship. These studies provide evidence that the mechanical properties of the tendons at the lower extremity at least partially explain the performance of the human musculoskeletal system during running activities. However, until now no study exist in reference to the potential for improving running performance by manipulating the tendon mechanical properties. Mechanical load induced as cyclic strain on connective soft tissues such as tendons is an important regulator of fibroblast metabolic activity as well as for the maintenance of tendon matrix (Chiquet et al., 2003). An increased loading typically stimulates cells for remodelling and, therefore, for increasing the mechanical properties of the tissue (Arnoczky et al., 2002). Whereas, a decreased loading leads to tissue destruction and weak mechanical properties of the tissue (Arnoczky et al., 2004). These reports demonstrate the highly plastic nature of tendons within the muscle-tendon unit of mammals and give evidence that tendon strain is an important mechanical factor regulating tendon properties. Generally, from a mechanobiological point of view strain magnitude, strain frequency, strain rate and strain duration of cells influence the cellular biochemical responses and the mechanical properties of collagen fascicles. Although it is known that mechanical loading induced as cyclic strain affects the mechanical properties of human tendons in vivo, the effect of a controlled modulation in cyclic strain magnitude, frequency, rate or duration applied to the tendon on the plasticity of human tendons in vivo is not well established. Understanding the details of tendon plasticity in response to mechanical loading applied to the tendon in vivo may help to improve tendon adaptation, reduce tendon injury risks and increases the performance potential of the human system. This paper aimed (a) to present the effects of a controlled modulation of strain magnitude and strain frequency applied to the Achilles tendon on the plasticity of tendon mechanical and morphological properties and (b) to investigate whether an exercise induced increase in tendon-aponeurosis stiffness and contractile strength at the triceps surae muscle-tendon unit affect running economy

The Glasgow-Maastricht foot model, evaluation of a 26 segment kinematic model of the foot

BACKGROUND: Accurately measuring of intrinsic foot kinematics using skin mounted markers is difficult, limited in part by the physical dimensions of the foot. Existing kinematic foot models solve this problem by combining multiple bones into idealized rigid segments. This study presents a novel foot model that allows the motion of the 26 bones to be individually estimated via a combination of partial joint constraints and coupling the motion of separate joints using kinematic rhythms. METHODS: Segmented CT data from one healthy subject was used to create a template Glasgow-Maastricht foot model (GM-model). Following this, the template was scaled to produce subject-specific models for five additional healthy participants using a surface scan of the foot and ankle. Forty-three skin mounted markers, mainly positioned around the foot and ankle, were used to capture the stance phase of the right foot of the six healthy participants during walking. The GM-model was then applied to calculate the intrinsic foot kinematics. RESULTS: Distinct motion patterns where found for all joints. The variability in outcome depended on the location of the joint, with reasonable results for sagittal plane motions and poor results for transverse plane motions. CONCLUSIONS: The results of the GM-model were comparable with existing literature, including bone pin studies, with respect to the range of motion, motion pattern and timing of the motion in the studied joints. This novel model is the most complete kinematic model to date. Further evaluation of the model is warranted