Better running economy (i.e. a lower rate of energy consumption at a given speed) is correlated with superior distance running performance. There is substantial variation in running economy, even among elite runners. This variation might be due to variation in the storage and reutilization of elastic energy in tendons. Using a simple musculoskeletal model, it was predicted that the amount of en...

Downside deviation, semivariance, or the second lower partial moment are different names for the same risk measure, proposed in the literature for capturing the downside risk of investment decisions. This paper analyzes multiperiod decision making under such a risk measure, and finds that a V-shaped decision rule in wealth is prevalent for the most common assumptions on the distribution of unce...

This paper investigates the problem of sparse covariance matrix estimation while sampling set contains sensitive information, and both differentially private algorithm locally are adopted to preserve privacy. It is worth noting that requirement distribution assumption in our work only existing bounded 4+ε(ε>0) moment. Meanwhile, we reduce error bounds by modifying threshold algorithms. Final...

We present PDE (partial differential equation) model hierarchies for the chemotactically driven motion of biological cells. Starting from stochastic differential models we derive a kinetic formulation of cell motion coupled to diffusion equations for the chemoattractants. Also we derive a fluid dynamic (macroscopic) Keller-Segel type chemotaxis model by scaling limit procedures. We review rigor...

Using recent progress on moment problems, and their connections with semidefinite optimization, we present in this thesis a new methodology based on semidefinite optimization, to obtain a hierarchy of upper and lower bounds on both linear and nonlinear functionals defined on solutions of linear partial differential equations. We apply the proposed methods to examples of PDEs in one and two dime...

1 Neuromusculoskeletal disorders affecting walking ability are often difficult to manage, in part due to 2 limited understanding of how a patient’s lower extremity muscle excitations contribute to the patient’s 3 lower extremity joint moments. To assist in the study of these disorders, researchers have developed 4 electromyography (EMG) driven neuromusculoskeletal models utilizing scaled generi...