On the Convergence of (Stochastic) Gradient Descent with Extrapolation for Non-Convex Optimization

Extrapolation is a well-known technique for solving convex optimization and variational inequalities and recently attracts some attention for non-convex optimization. Several recent works have empirically shown its success in some machine learning tasks. However, it has not been analyzed for non-convex minimization and there still remains a gap between the theory and the practice. In this paper, we analyze gradient descent and stochastic gradient descent with extrapolation for finding an approximate first-order stationary point in smooth non-convex optimization problems. Our convergence upper bounds show that the algorithms with extrapolation can be accelerated than without extrapolation

Thyroid Carcinoma with Bone Metastases: A Prognostic Factor Study

Objective Occult clinical presentations usually hinder the early detection and management of patients with bone metastases from thyroid carcinoma. We retrospectively investigated the clinical outcomes of such patients from 1993 to 2004 and analyzed the prognostic parameters. Design The basic demographic data and manifestations of 44 patients who had thyroid carcinoma with bone metastases were reviewed. We studied the gender, age, locations of metastases, histological types, treatment methods, hypercalcemic episodes and results of treatments. We used Kaplan-Meier survival analysis and log-rank tests to access the statistical significance. Main Outcome The incidence of bone metastasis from thyroid carcinomas in this series was 5.0%. Twenty patients (45.4%) had follicular, 16 (36.3%) had papillary, 3 (6.8%) had anaplastic, 3 (6.8%) had medullary, and 2 (4.5%) had Hurthel cell carcinomas. Twelve patients had hypercalcemic episodes, ranging from 2.6 to 2.9 mmolL −1 (mean ± SD: 2.68 ± 0.15 mmolL −1 ). Survival time after bone metastases ranged from 2 months to 8 years (mean ± SD: 5.3 ± 1.3 years). The 5-year survival rate was 79.4% and the 10-year survival rate was 52.9%. Regarding the histological cancer type, patients with papillary and follicular cancers survived significantly longer than those with anaplastic and medullary cancers (p < 0.05). In addition, the patients presenting with hypercalcemia had the worst survival (p < 0.05). Conclusions Thyroid carcinoma can present with bone metastases in its early stage. We found that both tumor type and hypercalcemia were significant prognostic factors for survival time

The Metastasectomy and Timing of Pulmonary Metastases on the Outcome of Osteosarcoma Patients

Background The author intended to clarify the therapeutic effect and prognostic factors of metastasectomy and timing of pulmonary metastases in osteosarcoma patents. Methods Data was obtained retrospectively on all consecutive osteosarcoma patients from 1985 to 2005 in author's institute. Fifty-two patients with pulmonary nodules were identified, including 24 patients undergoing pulmonary metastasectomy treatment. These patients were categorized into four groups: group 1, patients with lung metastases at the initial presentation; group 2, lung metastases identified during the period of pre-operative chemotherapy; group 3, lung metastases identified during period of the post-operative chemotherapy; group 4, lung metastases identified after therapy for the primary osteosarcoma completed. Results In our study, the 2-, 3-, and 5-year overall survival rates for 52 patients were 49%, 39% and 20%. The 2-year overall survival rates were 18% for group 1, 32% for group 3, and 70% for group 4 (p < 0.001). The 5-year overall survival rate was 34% for group 4. Patients who underwent metastesectomy showed a better survival outcome as compared with the patients not undergoing metastasectomy (p = 0.003). The 2-year and 5-year overall survival rates of only one lung metastatic nodule were 62% and 50%, and for initially multiple lung metastatic nodules, 45% and 5%, respectively. In addition, the patients presented with lung metastases had a worse prognosis as compared with those without initial lung metastases (p = 0.0001). Conclusions The patients having single metastatic nodule showed a better prognosis than those with multiple lung nodules. Furthermore, those patients who underwent metastasectomy survived longer than those not undergoing metastasectomy. Patients who had late metastases after complete chemotherapy had a better prognosis; whereas those who had metastases identified at the initial presentation predicted a poor prognosis

Advanced Glycation End Products Induce PeroxisomeProliferator-Activated Receptor c Down-Regulation-Related Inflammatory Signals in Human Chondrocytesvia Toll-Like Receptor-4 and Receptor for AdvancedGlycation End Products

Accumulation of advanced glycation end products (AGEs) in joints is important in the development of cartilage destruction and damage in age-related osteoarthritis (OA). The aim of this study was to investigate the roles of peroxisome proliferator-activated receptor γ (PPARγ), toll-like receptor 4 (TLR4), and receptor for AGEs (RAGE) in AGEs-induced inflammatory signalings in human OA chondrocytes. Human articular chondrocytes were isolated and cultured. The productions of metalloproteinase-13 and interleukin-6 were quantified using the specific ELISA kits. The expressions of related signaling proteins were determined by Western blotting. Our results showed that AGEs enhanced the productions of interleukin-6 and metalloproteinase-13 and the expressions of cyclooxygenase-2 and high-mobility group protein B1 and resulted in the reduction of collagen II expression in human OA chondrocytes. AGEs could also activate nuclear factor (NF)-κB activation. Stimulation of human OA chondrocytes with AGEs significantly induced the up-regulation of TLR4 and RAGE expressions and the down-regulation of PPARγ expression in a time- and concentration-dependent manner. Neutralizing antibodies of TLR4 and RAGE effectively reversed the AGEs-induced inflammatory signalings and PPARγ down-regulation. PPARγ agonist pioglitazone could also reverse the AGEs-increased inflammatory signalings. Specific inhibitors for p38 mitogen-activated protein kinases, c-Jun N-terminal kinase and NF-κB suppressed AGEs-induced PPARγ down-regulation and reduction of collagen II expression. Taken together, these findings suggest that AGEs induce PPARγ down-regulation-mediated inflammatory signalings and reduction of collagen II expression in human OA chondrocytes via TLR4 and RAGE, which may play a crucial role in the development of osteoarthritis pathogenesis induced by AGEs accumulation

A simplified guide ruler from numeric table method in doing rotational osteotomy

<p>Abstract</p> <p>Background</p> <p>Čobeljić et al. recently reported a numeric table method to provide precise rotational osteotomy which is a well established orthopaedic procedure. The numeric table requires four pages in length that is rather inconvenient during performing an osteotomy operation. </p> <p>Methods</p> <p>We thus develop our own method by summarizing the data of the four-page table into a small ruler, which is easy to carry and use in operation room. An electrical version of this ruler is also available. We also build a computer model to verify Čobeljić et al. method.</p> <p>Results</p> <p>The error of Čobeljić et al. is between -37% to 16% (mean ± SD = -6% ± 9%). We verify our ruler by calculating the absolute difference between our method and that of Čobeljić et al. The difference is less than 0.1 mm.</p> <p>Conclusion</p> <p>Our ruler is convenient for practical use for the rotational osteotomy procedure with equal precision. Further clinical verification is needed to justify its real significance.</p

The Effects of Endurance Running Training on Young Adult Bone: Densitometry vs. Biomaterial Properties

Densitometric measurement of bone mineral parameters has been developed in recent decades. Since bone strength is associated with bone mineral density (BMD) and/or bone mineral content (BMC), densitometric measurement is widely accepted and used as one golden standard in clinical settings to determine bone health. Based on this concept, some human studies have suggested that endurance training, such as long distance running, provides no benefit and may even be harmful to bone health or bone mineral accretion during development, since long distance runners often have low BMD and/or BMC and may even exhibit conditions associated with bone loss or osteopenia.1, 2 Conversely, serum bone marker assays in healthy distance runners show normal or positive bone metabolism status.3, 4 Therefore, the definite role of endurance running training (ERT) on bone health remains a controversial issue. It would be valuable to further clarify whether ERT benefits bone health through a pathway other than absolutely increasing BMD or BMC. Clinical observations of human subjects require further basic studies to investigate possible mechanisms. Animal studies can provide unique ways not feasible in studies using human subjects of assessing the effects of endurance running on bone. Generally, previous animal studies further verified benefits of ERT to bone health. However, the limitations of animal studies must be clarified before applying their findings to human beings. The present article reviews the phenomena shown in bone of adolescent or young adult distance runners. Moreover, previous animal studies which adopted growing and young adult rats as subjects are reviewed, and the applicability of the findings to humans is also discussed

Pelvic skeletal metastasis of hepatocellular carcinoma with sarcomatous change: a case report

Sarcomatoid hepatocellular carcinoma (HCC) is a very rare histologic variant of HCC. The characteristic of skeletal metastatic sarcomatoid hepatocellular carcinoma has never been reported. We reported a patient with sarcomatoid hepatocellular carcinoma pelvic metastasis who presented with huge pelvic metastasis that had relatively small osteolytic lesion centrally located accompanied by huge bipeduncular invasive expansile lesions into surrounding soft tissue. The lesion showed almost non-isotope uptake in 99mTc-methylene diphosphonate bone scintigraphy study. He underwent radiotherapy and tumor excision but the tumor rapidly recurred. In addition, serum α-fetoprotein level was never elevated beyond normal limit (< 20 ng/mL) through the whole course of treatment. We considered sarcomatoid hepatocellular carcinoma bone metastasis a highly aggressive lesion with unusual metastatic pattern. Surgical treatment with adequate safe margin in such a huge tumor with hypervascularity and extensive invasion in the pelvis was difficult; and radiotherapy maybe refractory regarding the sarcomatous nature. Therefore, debulking operation with local symptoms control may provide a better quality of life. And the clinical course suggests sarcomatoid hepatocellular carcinoma is derived from the transition of an ordinary hepatocellular carcinoma