Abstract. A capture-convergence rate theorem is proved for variable metric gradient projection processes near nonsingular local minimizers in convex feasible sets defined by nonlinear inequalities in a real Hilbert space X. The minimizers in question satisfy standard Kuhn-Tucker second-order sufficient conditions for local optimality.
Background: Osteoporotic compression fractures often progress to neurological impairment and severe pain, which results in restriction of mobility in elderly patients. Conventional open spinal decompression and stabilization in these patients have significant morbidities related to age, surgical approach, and blood loss. This case series evaluates the treatment of osteoporotic compression fractures at the thoracolumbar junction with short-segment stabilization with cement-augmented fenestrated pedicle screws and vertebroplasty using a minimally invasive percutaneous technique.Methods: Eleven patients aged 75 years or older who had osteoporotic vertebral fractures with worsening back pain and neurologic impairment were included in this study. Plain radiographs, magnetic resonance imaging, and computed tomography images of these patients were assessed. These patients underwent minimally invasive percutaneous stabilization with cementaugmented fenestrated pedicle screws and vertebroplasty with or without decompression. Preoperative and postoperative American Spinal Cord Injury Association score, visual analog scale (VAS) score, and Charlson Comorbidity Index were recorded. Cobb angle, spinal alignment, spinal canal encroachment, and anterior vertebral body height were recorded preoperatively and during each follow-up.Results: All patients neurologically recovered, and the VAS score significantly improved from an average of 9 before surgery to 2 immediately after surgery and 1 at final follow-up (P < 0.001). An average, local angle of kyphosis was 15° preoperatively, which decreased to 7° postoperatively (P < 0.01). The average anterior vertebral body height was 11 mm, which increased to 22 mm postoperatively (P < 0.001). No revision was required due to screw loosening or failure of construct.
Conclusion:We concluded that patients with osteoporotic vertebral fractures treated with short-segment stabilization with cement-augmented fenestrated pedicle screws and vertebroplasty by minimally invasive percutaneous technique are associated with good clinical outcomes during an average follow-up of 18 months after spinal surgery.
Developments in synchronous (SDHISONET) transmission products has let to increased use of ring structures in telecommunications networks, on account of their "self-healing" properties. Often, a set of nodes is interconnected by a fami1y" of such rings, which all follow the same fiber route. In this situation, each node is served by a subset of the rings in the family. For a given set of nodes and a given matrix of point-to-point traffic, we describe a design methodology that determines which rings should serve each node, and how traffic should be routed on the rings. The objective is to minimize the amount of equipment required. Whereas earlier work has addressed this problem for the case of uni-directional rings, the methodology described here can be applied to bi-directional rings as well.
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