Node Sampling using Random Centrifugal Walks

Sampling a network with a given probability distribution has been identified as a useful operation. In this paper we propose distributed algorithms for sampling networks, so that nodes are selected by a special node, called the \emph{source}, with a given probability distribution. All these algorithms are based on a new class of random walks, that we call Random Centrifugal Walks (RCW). A RCW is a random walk that starts at the source and always moves away from it. Firstly, an algorithm to sample any connected network using RCW is proposed. The algorithm assumes that each node has a weight, so that the sampling process must select a node with a probability proportional to its weight. This algorithm requires a preprocessing phase before the sampling of nodes. In particular, a minimum diameter spanning tree (MDST) is created in the network, and then nodes' weights are efficiently aggregated using the tree. The good news are that the preprocessing is done only once, regardless of the number of sources and the number of samples taken from the network. After that, every sample is done with a RCW whose length is bounded by the network diameter. Secondly, RCW algorithms that do not require preprocessing are proposed for grids and networks with regular concentric connectivity, for the case when the probability of selecting a node is a function of its distance to the source. The key features of the RCW algorithms (unlike previous Markovian approaches) are that (1) they do not need to warm-up (stabilize), (2) the sampling always finishes in a number of hops bounded by the network diameter, and (3) it selects a node with the exact probability distribution

Brief Announcement: Node Sampling Using Centrifugal Random Walks.

We propose distributed algorithms for sampling networks based on a new class of random walks that we call Centrifugal Random Walks (CRW). A CRW is a random walk that starts at a source and always moves away from it. We propose CRW algorithms for connected networks with arbitrary probability distributions, and for grids and networks with regular concentric connectivity with distance based distributions. All CRW sampling algorithms select a node with the exact probability distribution, do not need warm-up, and end in a number of hops bounded by the network diameter

Comparison of Rotational Energies and Rigidity of OCS-paraH_2 and OCS-4He complexes

We analyze the nature of the rotational energy level structure of the OCS-He and OCS-H_2 complexes with a comparison of exact calculations to several differentdynamical approximations. We compare with the clamped coordinate quasiadiabatic approximation that introduces an effective potential for each asymmetric rotor level, with an effective rotation Hamiltonian constructed from ground state averages of the inverse of the inertial matrix, and investigate the usefulness of the Eckart condition to decouple rotations and vibrations of these weakly bound complexes between linear OCS and 4He or H_2. Comparison with exact results allows an assessment of the accuracies of the different approximate methods and indicates which approaches are suitable for larger clusters of OCS with 4He and with H_2. We find the OCS-H_2 complex is considerably more rigid than the OCS-4He complex, suggesting that semi-rigid models are useful for analysis of larger clusters of H_2 with OCS.Comment: accepted by Chem. Phys., 200

Hybrid and Conventional Mesons in the Flux Tube Model: Numerical Studies and their Phenomenological Implications

We present results from analytical and numerical studies of a flux tube model of hybrid mesons. Our numerical results use a Hamiltonian Monte Carlo algorithm and so improve on previous analytical treatments, which assumed small flux tube oscillations and an adiabatic separation of quark and flux tube motion. We find that the small oscillation approximation is inappropriate for typical hadrons and that the hybrid mass is underestimated by the adiabatic approximation. For physical parameters in the ``one-bead" flux tube model we estimate the lightest hybrid masses (${}_\Lambda L = {}_1 P$ states) to be 1.8-1.9~GeV for $u\bar u$ hybrids, 2.1-2.2~GeV for $s\bar s$ and 4.1-4.2~GeV for $c\bar c$. We also determine masses of conventional $q\bar q$ mesons with $L=0$ to $L=3$ in this model, and confirm good agreement with experimental $J$-averaged multiplet masses. Mass estimates are also given for hybrids with higher orbital and flux-tube excitations. The gap from the lightest hybrid level (${}_1P$) to the first hybrid orbital excitation (${}_1D$) is predicted to be $\approx 0.4$~GeV for light quarks $(q=u,d)$ and $\approx 0.3$~GeV for $q=c$. Both ${}_1P$ and ${}_1D$ hybrid multiplets contain the exotics $1^{-+}$ and $2^{+-}$; in addition the ${}_1P$ has a $0^{+-}$ and the ${}_1D$ contains a $3^{-+}$. Hybrid mesons with doubly-excited flux tubes are also considered. The implications of our results for spectroscopy are discussed, with emphasis on charmonium hybrids, which may be accessible at facilities such as BEPC, KEK, a Tau-Charm Factory, and in $\psi$ production at hadron colliders.Comment: 39 pages of RevTex. Figures available via anonymous ftp at ftp://compsci.cas.vanderbilt.edu/QSM/bcsfig1.ps and /QSM/bcsfig6.p

Efficient Humanoid Contact Planning using Learned Centroidal Dynamics Prediction

Humanoid robots dynamically navigate an environment by interacting with it via contact wrenches exerted at intermittent contact poses. Therefore, it is important to consider dynamics when planning a contact sequence. Traditional contact planning approaches assume a quasi-static balance criterion to reduce the computational challenges of selecting a contact sequence over a rough terrain. This however limits the applicability of the approach when dynamic motions are required, such as when walking down a steep slope or crossing a wide gap. Recent methods overcome this limitation with the help of efficient mixed integer convex programming solvers capable of synthesizing dynamic contact sequences. Nevertheless, its exponential-time complexity limits its applicability to short time horizon contact sequences within small environments. In this paper, we go beyond current approaches by learning a prediction of the dynamic evolution of the robot centroidal momenta, which can then be used for quickly generating dynamically robust contact sequences for robots with arms and legs using a search-based contact planner. We demonstrate the efficiency and quality of the results of the proposed approach in a set of dynamically challenging scenarios

Unified Robust Path Planning and Optimal Trajectory Generation for Efficient 3D Area Coverage of Quadrotor UAVs

Area coverage is an important problem in robotics applications, which has been widely used in search and rescue, offshore industrial inspection, and smart agriculture. This paper demonstrates a novel unified robust path planning, optimal trajectory generation, and control architecture for a quadrotor coverage mission. To achieve safe navigation in uncertain working environments containing obstacles, the proposed algorithm applies a modified probabilistic roadmap to generating a connected search graph considering the risk of collision with the obstacles. Furthermore, a recursive node and link generation scheme determines a more efficient search graph without extra complexity to reduce the computational burden during the planning procedure. An optimal three-dimensional trajectory generation is then suggested to connect the optimal discrete path generated by the planning algorithm, and the robust control policy is designed based on the cascade NLH∞ framework. The integrated framework is capable of compensating for the effects of uncertainties and disturbances while accomplishing the area coverage mission. The feasibility, robustness and performance of the proposed framework are evaluated through Monte Carlo simulations, PX4 Software-In-the-Loop test facility, and real-world experiments

FGO-ILNS: Tightly Coupled Multi-Sensor Integrated Navigation System Based on Factor Graph Optimization for Autonomous Underwater Vehicle

Multi-sensor fusion is an effective way to enhance the positioning performance of autonomous underwater vehicles (AUVs). However, underwater multi-sensor fusion faces challenges such as heterogeneous frequency and dynamic availability of sensors. Traditional filter-based algorithms suffer from low accuracy and robustness when sensors become unavailable. The factor graph optimization (FGO) can enable multi-sensor plug-and-play despite data frequency. Therefore, we present an FGO-based strapdown inertial navigation system (SINS) and long baseline location (LBL) system tightly coupled navigation system (FGO-ILNS). Sensors such as Doppler velocity log (DVL), magnetic compass pilot (MCP), pressure sensor (PS), and global navigation satellite system (GNSS) can be tightly coupled with FGO-ILNS to satisfy different navigation scenarios. In this system, we propose a floating LBL slant range difference factor model tightly coupled with IMU preintegration factor to achieve unification of global position above and below water. Furthermore, to address the issue of sensor measurements not being synchronized with the LBL during fusion, we employ forward-backward IMU preintegration to construct sensor factors such as GNSS and DVL. Moreover, we utilize the marginalization method to reduce the computational load of factor graph optimization. Simulation and public KAIST dataset experiments have verified that, compared to filter-based algorithms like the extended Kalman filter and federal Kalman filter, as well as the state-of-the-art optimization-based algorithm ORB-SLAM3, our proposed FGO-ILNS leads in accuracy and robustness

Dynamic Neuromechanical Sets for Locomotion

Most biological systems employ multiple redundant actuators, which is a complicated problem of controls and analysis. Unless assumptions about how the brain and body work together, and assumptions about how the body prioritizes tasks are applied, it is not possible to find the actuator controls. The purpose of this research is to develop computational tools for the analysis of arbitrary musculoskeletal models that employ redundant actuators. Instead of relying primarily on optimization frameworks and numerical methods or task prioritization schemes used typically in biomechanics to find a singular solution for actuator controls, tools for feasible sets analysis are instead developed to find the bounds of possible actuator controls. Previously in the literature, feasible sets analysis has been used in order analyze models assuming static poses. Here, tools that explore the feasible sets of actuator controls over the course of a dynamic task are developed. The cost-function agnostic methods of analysis developed in this work run parallel and in concert with other methods of analysis such as principle components analysis, muscle synergies theory and task prioritization. Researchers and healthcare professionals can gain greater insights into decision making during behavioral tasks by layering these other tools on top of feasible sets analysis

Fractal Physiology and the Fractional Calculus: A Perspective

This paper presents a restricted overview of Fractal Physiology focusing on the complexity of the human body and the characterization of that complexity through fractal measures and their dynamics, with fractal dynamics being described by the fractional calculus. Not only are anatomical structures (Grizzi and Chiriva-Internati, 2005), such as the convoluted surface of the brain, the lining of the bowel, neural networks and placenta, fractal, but the output of dynamical physiologic networks are fractal as well (Bassingthwaighte et al., 1994). The time series for the inter-beat intervals of the heart, inter-breath intervals and inter-stride intervals have all been shown to be fractal and/or multifractal statistical phenomena. Consequently, the fractal dimension turns out to be a significantly better indicator of organismic functions in health and disease than the traditional average measures, such as heart rate, breathing rate, and stride rate. The observation that human physiology is primarily fractal was first made in the 1980s, based on the analysis of a limited number of datasets. We review some of these phenomena herein by applying an allometric aggregation approach to the processing of physiologic time series. This straight forward method establishes the scaling behavior of complex physiologic networks and some dynamic models capable of generating such scaling are reviewed. These models include simple and fractional random walks, which describe how the scaling of correlation functions and probability densities are related to time series data. Subsequently, it is suggested that a proper methodology for describing the dynamics of fractal time series may well be the fractional calculus, either through the fractional Langevin equation or the fractional diffusion equation. A fractional operator (derivative or integral) acting on a fractal function, yields another fractal function, allowing us to construct a fractional Langevin equation to describe the evolution of a fractal statistical process. Control of physiologic complexity is one of the goals of medicine, in particular, understanding and controlling physiological networks in order to ensure their proper operation. We emphasize the difference between homeostatic and allometric control mechanisms. Homeostatic control has a negative feedback character, which is both local and rapid. Allometric control, on the other hand, is a relatively new concept that takes into account long-time memory, correlations that are inverse power law in time, as well as long-range interactions in complex phenomena as manifest by inverse power-law distributions in the network variable. We hypothesize that allometric control maintains the fractal character of erratic physiologic time series to enhance the robustness of physiological networks. Moreover, allometric control can often be described using the fractional calculus to capture the dynamics of complex physiologic networks

An in-shoe gait analysis device to measure the maximum shear stresses at the first metatarsal head

Bibliography: leaf 107.Recent research indicates that the shear stresses acting on a diabetic's foot are one of the major mechanical contributors to the high incidence of ulceration experienced by these patients. These stresses together with direct pressure are thought to have an effect on blood flow occlusion elsewhere in the body. The reduced blood flow may relate in moderation to reduced tissue tolerance or repair capability or even in more severe cases to cell death. Repeated vascular occlusion in a normal person would produce a minor blister or a swollen area, but with a diabetic patient it has the ability to create large incisions and ulcers. This is because diabetic patients are unable to redistribute the load on their feet due to the lack of sensation in their lower extremities. This results in diabetes being the number one cause of all lower limb amputations and accounting for 50 to 70 % of all non-traumatic amputations in the U.S. In the same country, it accounts for $200 million a year in treatment costs directly related to diabetic foot infections. Quantifying the magnitude and duration of these shear stresses therefore has the potential to play a crucial role in assisting podiatrists and clinicians in their diagnosis and treatment of these patients. However these stresses have not been widely evaluated due to lack of suitable instrumentation for their measurement. A technique which has proven to be the most successful in measuring these stresses involves placing a discrete transducer inside a customised insole and fitting it to a patient's shoe. This report sets out to design a similar technique but with the use of a differently designed transducer. The validity of and confidence in the proposed transducer was established by assessing and comparing the results of the transducer under a series of controlled tests with the results of other transducers presented in the literature. To allow an accurate assessment of the transducer to be made, the tests which were performed on the transducer were controlled and conducted at a fixed walking speed. The computational theory used was based on the assumptions and equations of two dimensional plane strain for linear elastic isotropic homogeneous materials. The transducer is based on the principle that a shear angle is induced on a plane when a shear stress is applied to a plane continuous and orthogonal to it. This principle was adapted into the design of the transducer in the form of a square block of material, whose two orthogonal lateral surfaces were used to measure the shear stress applied to its top surface. The design of the transducer consists of a block of material, two laterally positioned rectangular strain rosettes and a circular base. The first series of tests conducted on the transducer were intended to verify and establish its material properties and characteristics. A model of the transducer was then constructed using the finite element package ABAQUS. Two Shape Factors – one for calibration purposes and the other for in-shoe testing - were generated for the transducer to allow for the effects of the geometrical inconsistencies present in its design to be accounted for. Without these Shape Factors the equations and assumptions of linear elasticity would not have been appropriate. A series of controlled pilot and analysis tests were then performed using the custom designed insole and transducer fitted to a diabetic shoe. The diabetic shoe was worn by a subject who performed the tests on a treadmill at a laboratory in the Sports Institute of South Africa