Jaewook Lee

Convergent regions of the Newton homotopy method for nonlinear systems: theory and computational applications

This paper introduces the concept of the convergent region of a solution of a general nonlinear equation using the Newton homotopy method. The question of whether an initial guess converges to the solution of our interest using the Newton homotopy method is investigated. It is shown that convergent regions of the Newton homotopy method are equal to stability regions of a corresponding Newton dynamic system. A necessary and sufficient condition for the adjacency of two solutions using the Newton homotopy method is derived. An algebraic characterization of a convergent region and its boundary for a large class of nonlinear systems is derived. This characterization is explicit and computationally feasible. A numerical method to determine the convergent region and to establish simple criteria to avoid revisits of the same solutions from different initial guesses is developed. It is shown that for general nonlinear systems or gradient systems, it is computationally infeasible to construct a set of initial guesses which converge to the set of all type-one equilibrium points on the stability boundary of a stable equilibrium point x/sub s/ from a finite number of function values and derivatives near x/sub s/ using the Newton homotopy method. Several examples are applied to illustrate the theoretical developments.

A Fair Listen-Before-Talk Algorithm for Coexistence of LTE-U and WLAN

Recently, there has been an increasing interest in operating long-term evolution (LTE) in unlicensed bands (i.e., LTE-U). However, since LTE and wireless local area networks (WLANs) are designed to operate in different bands, they have no coexistence mechanism, which leads to significant performance degradation. In particular, since LTE does not sense channel vacancy prior to transmissions, the LTE interference severely affects the WLAN operation. To address this problem, we propose a fair listen-before-talk (F-LBT) algorithm for coexistence of LTE-U and WLAN in unlicensed bands. F-LBT jointly considers the total system throughput and the fairness between LTE-U and WLAN and then allocates an appropriate idle period for WLAN. Evaluation results demonstrate that F-LBT can improve the total system throughput while providing the fairness between LTE-U and WLAN.

Calcific Tendinitis of the Rectus Femoris

This article describes calcific tendinitis of the rectus femoris treated with a local injection of a mixture of steroid and local anesthetic under C-arm control. From March 2004 to May 2005, 6 patients were treated for calcific tendinitis of the rectus femoris at our institution and followed for at least 2 years. The male:female ratio was 1:5, and mean patient age was 41 years (range, 33-49 years). Calcifications were located in the direct head in 1 patient and in the reflected head of the rectus femoris in 5. One patient underwent open surgical removal and 5 were treated with a local steroid and anesthetic injection. The patient undergoing surgical removal obtained immediate pain relief but reported discomfort in the wound area for 10 days postoperatively. The 5 patients receiving injections achieved dramatic pain relief within 2 days; follow-up radiographs revealed complete calcification disappearance within 16 weeks of treatment in all 5. No patient had experienced recurrence or complications at >2-year follow-up. Prompt diagnosis and early treatment with a local injection of a mixture of steroid and local anesthetic under C-arm control successfully relieved symptoms and facilitated a return to normality.

Knee Extensor Mechanism Reconstruction with an Extended Gastrocnemius Flap and a Saphenous Neurocutaneous Flap

A 35-year-old woman had multiple fractures due to pedestrian versus motor vehicle accident by a truck. An open comminuted patellar fracture was initially managed with a tension band and cerclage wiring and primary closure of the wound. Other fractures were managed with proper internal fixation. Unfortunately, the fractured patella and overlying soft tissue became totally infected and a wide necrosis occurred. To control the wound, a complete debridement of dead tissue was undertaken and the patella and its tendon were removed, leaving a large bone and soft tissue defect on the knee joint. To reconstruct the extensor mechanism, an extended medial gastrocnemius flap including a tendinous portion of the Achilles was used. A saphenous neurocutaneous flap was simultaneously used for additional soft tissue coverage around the proximal tibia and remaining patellar tendon. At 12 months postoperatively, she showed complete extension, 135 degrees of flexion, and grade IV knee extensor power and was able to ambulate without a walking aid.

Constructive homotopy methods for finding all or multiple DC operating points of nonlinear circuits and systems

A comprehensive analysis of homotopy methods on the computation of all DC operating points of nonlinear circuits and systems is conducted. Several sufficient conditions for the connectivity of all the solutions along a single homotopy path are derived. These conditions offer criteria to determine a starting point from which one can find all the solutions along one homotopy path. For the class of nonlinear circuits and systems in which all the solutions lie on several homotopy paths, a new systematic method to explicitly construct a starting point for each homotopy path is developed, From a practical viewpoint, the constructive method developed does not require the difficult task of finding a good initial guess and is applicable to general nonlinear circuits and systems. From a methodological viewpoint, the constructive method developed is applicable to general homotopy methods with different homotopy functions.

Stability regions of non-hyperbolic dynamical systems: theory and optimal estimation

The concept of a stability region (region of attraction) of nonlinear dynamical systems is widely used in many fields such as engineering and the sciences. In this paper, we study the notion of stability regions for a class of non-hyperbolic dynamical systems. A complete characterization of the stability boundary is presented for a fairly large class of non-hyperbolic dynamical systems. Several necessary and sufficient conditions for an equilibrium manifold (the generalized concept of an equilibrium point) to lie on the stability boundary are derived. It is shown that the stability boundary of this class of systems consists of the union of the stable manifolds of the equilibrium manifolds on the stability boundary. In addition, an effective scheme to estimate stability regions by using an energy function is developed. It is shown that the scheme can optimally estimate stability regions for a class of non-hyperbolic dynamical systems. Two examples are given to illustrate the theoretical prediction.

Improved spinal fusion efficacy by long-term delivery of bone morphogenetic protein-2 in a rabbit model

Background and purpose Various new delivery systems for recombinant human bone morphogenetic protein-2 (rhBMP-2) have been introduced to improve its efficacy in osteogenesis. Of these, we have previously developed heparin-conjugated PLGA nanospheres (HCPN) as a long-term delivery system for BMP-2. In vitro studies have shown that the BMP-2 long-term delivery system enhances the level of bone formation. However, the long-term effects of BMP-2 on spinal fusion have not been assessed. Therefore, we now tested the hypothesis that the long-term delivery of BMP-2 using HCPN improves spinal fusion compared to short-term delivery in a rabbit fusion model. Methods 24 adult New Zealand White rabbits underwent posterolateral fusion (6 animals in 4 groups). The autograft group received an autologous iliac chip bone graft as a positive control. The BMP-2-PN group received rhBMP-2 (20 μg per implant) and PLGA nanospheres (PN) suspended in fibrin gel, and served as a short-term release group. The HCPN group received HCPN suspended in fibrin gel without BMP-2 as a negative control. The BMP-2-HCPN group received rhBMP-2 (20 μg per implant)-bound HCPN suspended in fibrin gel and served as a long-term release group. All animals were killed 12 weeks after surgery. Manual palpation, axial tensile tests, radiography, and histological evaluations were then performed. Results The spinal fusion rate and Youngs modulus of the fusion mass were better in the BMP-2 long-term delivery group than in the short-term delivery group at an equivalent dose. However, the outcome of the long-term delivery was inferior to that of the autograft group. Interpretation The HCPN system showed potential as an effective carrier that might improve the osteogenic efficacy of BMP-2 for spinal fusion.

Quotient gradient methods for solving constraint satisfaction problems

In this paper, we propose a novel systematic method for locating multiple disjoint feasible regions for a general constraint satisfaction problems (or non-linearly constrained systems of equations). A theoretical foundation of the novel method is developed on the basis of the stability theory for a class of non-hyperbolic dynamical systems. The proposed method consists of the following: (i) approach a feasible region and (ii) escape from a feasible region and move toward another feasible region. Two numerical examples are given to illustrate the proposed method.

Opportunistic push scheme for online social networking services in heterogeneous wireless networks

The article synchronization is one of the most fundamental issues in online social networking services. In particular, an efficient synchronization scheme should be devised when users enjoy online social networking services in heterogeneous wireless networks where multiple access networks with different transmission costs are deployed. In this paper, we propose an opportunistic push scheme (OPS) that aggregates the published articles and pushes opportunistically the aggregated articles through low-cost access networks (e.g., open WiFi networks). To balance the reduced transmission cost and the consistency of articles, a Markov decision process (MDP) problem is formulated and the optimal policy is determined. Numerical results demonstrate that OPS with the optimal policy can reduce the number of transmissions in high-cost access networks while satisfying users quality of experience (QoE) in terms of the article consistency.

Computation of multiple type-one equilibrium points on the stability boundary using generalized fixed-point homotopy methods

This paper presents an efficient algorithm for the computation of all or multiple type-one equilibrium points (i.e., equilibrium point where the Jacobian has exactly one negative eigenvalue) for nonlinear systems. This algorithm is based on homotopy-continuation approaches and is devised to reduce the difficulty of choosing a set of proper initial points which converge to the set of all the type-one equilibrium points on the stability boundary (the boundary of the domain of attraction). The computational complexities for this algorithm and other existing algorithms including reflected gradient methods are discussed. The method is shown to be very efficient and reliable from numerical simulations.