Finite-time ruin probability of a perturbed risk model with dependent main and delayed claims

This paper considers a delayed claim risk model with stochastic return and Brownian perturbation in which each main claim may be accompanied with a delayed claim occurring after a stochastic period of time, and the price process of the investment portfolio is described as a geometric Lévy process. By means of the asymptotic results for randomly weighted sum of dependent subexponential random variables we obtain some asymptotics for finite-time ruin probability. A simulation study is also performed to check the accuracy of the obtained theoretical result via the crude Monte Carlo method

Nanofiber-Based Scaffold for Integrative Rotator Cuff Repair

Functional integration of bone with soft tissues such as tendon is essential for joint motion and musculoskeletal function. This is evident in the rotator cuff of the shoulder, which consists of four muscles and their associated tendons that connect the humerus and scapula. The cuff functions to stabilize the shoulder joint, and actively controls shoulder kinematics. Rotator cuff injuries often occur as a result of tendon avulsion at the tendon-bone interface, with more than 250,000 cuff repair surgeries performed annually in the United States. However, these procedures are associated with a high failure rate, as re-tears often occur due to the lack of biological fixation of the tendon to bone post-surgery. Instead of regenerating the tendon-bone interface, current repair techniques and augmentation grafts focus on improving the load bearing capability of the repaired rotator cuff. Biologically, the supraspinatus tendon inserts into bone via a biphasic fibrocartilaginous transition, exhibiting region-dependent changes in its compositional, structural and mechanical properties, which enables efficient load transfer from tendon to bone as well as multi-tissue homeostasis. Inspired by the native tendon-bone interface, we have designed and evaluated a biomimetic bilayer scaffold, comprised of electrospun poly (lactide-co-glycolide) (PLGA) nanofibers seamlessly integrated with PLGA-hydroxyapatite (HA) fibers, in order to engineer tendon-bone integration. The objective of this thesis is to explore the key design parameters that are critical for integrative tendon-bone repair using this biphasic scaffold as a model. Specifically, intrinsic to the scaffold, effects of fiber alignment, fiber diameter, mineral distribution, and polymer composition on integrative rotator cuff tendon-bone healing were evaluated in vivo using a rat model. Results indicated that an aligned, nanofiber-based scaffold with a distinct order of non-mineralized and mineralized regions will lead to insertion regeneration and integrative tendon-bone repair. Additional tissue engineering design parameters such as healing time and animal model were also tested. It was observed that the biphasic scaffold exhibited a stable long term response, as the mechanical properties of rat shoulders repaired by this scaffold remained comparable to that of the control at 20 weeks post-surgery. This scaffold was also evaluated in a large animal model (sheep), in which a clinically-relevant rotator cuff repair procedure was implemented with the biphasic scaffold. Results demonstrated the scaffold lead to integrative rotator cuff repair through the regeneration of the enthesis in both small and large animal models. In summary, through a series of in vivo studies, the work of this thesis has identified the critical tissue engineering parameters for integrative and functional rotator cuff tendon repair. More importantly, the design principles elucidated here are anticipated to have a broader impact in the field of tissue engineering, as they can be readily applied towards the regeneration of other soft-hard tissue interfaces

Upper and Lower Bounds on the Smoothed Complexity of the Simplex Method

The simplex method for linear programming is known to be highly efficient in practice, and understanding its performance from a theoretical perspective is an active research topic. The framework of smoothed analysis, first introduced by Spielman and Teng (JACM '04) for this purpose, defines the smoothed complexity of solving a linear program with $d$ variables and $n$ constraints as the expected running time when Gaussian noise of variance $\sigma^2$ is added to the LP data. We prove that the smoothed complexity of the simplex method is $O(\sigma^{-3/2} d^{13/4}\log^{7/4} n)$, improving the dependence on $1/\sigma$ compared to the previous bound of $O(\sigma^{-2} d^2\sqrt{\log n})$. We accomplish this through a new analysis of the \emph{shadow bound}, key to earlier analyses as well. Illustrating the power of our new method, we use our method to prove a nearly tight upper bound on the smoothed complexity of two-dimensional polygons. We also establish the first non-trivial lower bound on the smoothed complexity of the simplex method, proving that the \emph{shadow vertex simplex method} requires at least $\Omega \Big(\min \big(\sigma^{-1/2} d^{-1/2}\log^{-1/4} d,2^d \big) \Big)$ pivot steps with high probability. A key part of our analysis is a new variation on the extended formulation for the regular $2^k$-gon. We end with a numerical experiment that suggests this analysis could be further improved.Comment: 41 pages, 5 figure

Therapeutic potential of co-enzyme Q10 in retinal diseases

Coenzyme Q10 (CoQ10) plays a critical role in mitochondrial oxidative phosphorylation by serving as an electron carrier in the respiratory electron transport chain. CoQ10 also functions as a lipid-soluble antioxidant by protecting lipids, proteins and DNA damaged by oxidative stress. CoQ10 deficiency has been associated with a number of human diseases including mitochondrial diseases, neurodegenerative disorders, cardiovascular diseases, diabetes, cancer, and with the ageing process. In many of these conditions CoQ10 supplementation therapy has been effective in slowing or reversing pathological changes. Oxidative stress is a major contributory factor in the process of retinal degeneration. In this brief review, we summarize the functions of CoQ10 and highlight its use in the treatment of age-related macular degeneration and glaucoma. In light of these data we propose that CoQ10 could have therapeutic potential for other retinal diseases

Access tunnel engineering to optimize the catalytic cycle of carbohydrate hydrolases with buried active site

The active site of many enzymes is buried inside the protein core and is connected with the surrounding solvent by access tunnels. An emerging approach to optimize these enzymes properties is the engineering of structural features governing the exchange of ligands between the active sites and bulk solvent. However, it is still challenging to redesign the access tunnels of enzymes catalyzing biopolymers like carbohydrate hydrolases because of the extremely complicated substrate structure. In this study, structure-guided saturated mutagenesis was performed to reconstruct all three access tunnels of xylanase S7-xyl from Bacillus halodurans S7, which results in a mutant 254-RL1 with 3.4-fold increase in specific activity. Structural comparison and kinetic analysis revealed that products egress is the rate-limiting step in the catalytic cycle of S7-xyl. The products release tunnel in S7-xyl was experimentally validated, and not the tunnel radius but the length determining the products release efficiency. Application assessment showed that relieving the inhibition of reducing sugars on mutant 254-RL1 could accelerate the hydrolysis efficiency of cellulase on different pretreated lignocellulose materials, representing a good candidate in enzyme cocktails for lignocellulose biodegradation. In addition, the same strategy was successfully utilized to improve the specific activities of three other xylanases with buried active site, suggesting the general application of tunnel engineering to optimize carbohydrate hydrolases with buried active site

Stability in Terms of Two Measures for Nonlinear Impulsive Systems on Time Scales

We investigate some stability problems in terms of two measures for nonlinear dynamic systems on time scales with fixed moments of impulsive effects. Sufficient conditions for (uniform) stability, (uniform) asymptotic stability, and instability in terms of two measures are derived by using the method of Lyapunov functions. Our results include the existing results as special cases when the time scale reduces to the set of real numbers. Particularly, our results provide stability criteria for impulsive discrete systems in terms of two measures, which have not been investigated extensively. Two examples are presented to illustrate the efficiency of the proposed results

Stability in Terms of Two Measures for Nonlinear Impulsive Systems on Time Scales

We investigate some stability problems in terms of two measures for nonlinear dynamic systems on time scales with fixed moments of impulsive effects. Sufficient conditions for (uniform) stability, (uniform) asymptotic stability, and instability in terms of two measures are derived by using the method of Lyapunov functions. Our results include the existing results as special cases when the time scale reduces to the set of real numbers. Particularly, our results provide stability criteria for impulsive discrete systems in terms of two measures, which have not been investigated extensively. Two examples are presented to illustrate the efficiency of the proposed results