Prior-free and prior-dependent regret bounds for Thompson Sampling

We consider the stochastic multi-armed bandit problem with a prior distribution on the reward distributions. We are interested in studying prior-free and prior-dependent regret bounds, very much in the same spirit as the usual distribution-free and distribution-dependent bounds for the non-Bayesian stochastic bandit. Building on the techniques of Audibert and Bubeck [2009] and Russo and Roy [2013] we first show that Thompson Sampling attains an optimal prior-free bound in the sense that for any prior distribution its Bayesian regret is bounded from above by $14 \sqrt{n K}$. This result is unimprovable in the sense that there exists a prior distribution such that any algorithm has a Bayesian regret bounded from below by $\frac{1}{20} \sqrt{n K}$. We also study the case of priors for the setting of Bubeck et al. [2013] (where the optimal mean is known as well as a lower bound on the smallest gap) and we show that in this case the regret of Thompson Sampling is in fact uniformly bounded over time, thus showing that Thompson Sampling can greatly take advantage of the nice properties of these priors.Comment: A previous version appeared under the title 'A note on the Bayesian regret of Thompson Sampling with an arbitrary prior

RETRACTED ARTICLE: STMN-1 is a potential marker of lymph node metastasis in distal esophageal adenocarcinomas and silencing its expression can reverse malignant phenotype of tumor cells

BACKGROUND: Distal esophageal adenocarcinoma is a highly aggressive neoplasm. Despite advances in diagnosis and therapy, the prognosis is still poor. Stathmin (STMN-1) is a ubiquitously expressed microtubule destabilizing phosphoprotein. It promotes the disassembly of microtubules and prevents assembly. STMN-1 can cause uncontrolled cell proliferation when mutated and not functioning properly. Recently, found to be overexpressed in many types of human cancers. However, its clinical significance remains elusive in distal esophageal adenocarcinoma. Here, we reported for the first time that STMN-1 is highly overexpressed in adenocarcinomas of the distal esophagus and strongly associated with lymph node metastasis. METHODS: STMN-1 expression in 63 cases of distal esophageal adenocarcinoma was analyzed by immunoblotting, while expression in esophageal adenocarcinoma cells was determined by immunocytochemistry, immunofluorescence, qRT-PCR and western blotting. Lentivirus-mediated RNAi was employed to knock-down STMN-1 expression in Human esophageal adenocarcinoma cells. The relationship between STMN-1 expression and lymph node metastasis in distal esophageal adenocarcinoma was determined by univariate and multivariate analyses. RESULTS: STMN-1 was detected in 31 (49.21%) of the 63 cases. STMN-1 was highly overexpressed in specimens with lymph node metastasis pN (+), but its expression was almost undetected in pN (−) status. Multivarian regression analysis demonstrated that STMN-1 overexpression is an independent factor for lymph node metastasis in distal esophageal adenocarcinoma. STMN-1 shRNA effectively reduced STMN-1 expression in esophageal adenocarcinoma cells (P < 0.05), which significantly suppressed proliferation (P < 0.05), increased migration (P < 0.05) and invasion ability (P < 0.05) and G1 phase arrest (P < 0.05) which lead to induction of apoptosis in esophageal adenocarcinoma cells in vitro. To verify the in vitro data, we conducted in vivo tumor xenograft studies. Esophageal adenocarcinoma cells stably transfected with STMN-1 shRNA significantly reduced tumor xenografts volume in vivo. CONCLUSIONS: STMN-1 overexpression is associated with lymph node metastasis and increase malignancy in distal esophageal adenocarcinoma. In vivo and in vitro laboratory findings, suggests that STMN-1 may be a suitable target for future therapeutic strategies in distal esophageal adenocarcinoma

Potential Osteoporosis Recovery by Deep Sea Water through Bone Regeneration in SAMP8 Mice

The aim of this study is to examine the therapeutic potential of deep sea water (DSW) on osteoporosis. Previously, we have established the ovariectomized senescence-accelerated mice (OVX-SAMP8) and demonstrated strong recovery of osteoporosis by stem cell and platelet-rich plasma (PRP). Deep sea water at hardness (HD) 1000 showed significant increase in proliferation of osteoblastic cell (MC3T3) by MTT assay. For in vivo animal study, bone mineral density (BMD) was strongly enhanced followed by the significantly increased trabecular numbers through micro-CT examination after a 4-month deep sea water treatment, and biochemistry analysis showed that serum alkaline phosphatase (ALP) activity was decreased. For stage-specific osteogenesis, bone marrow-derived stromal cells (BMSCs) were harvested and examined. Deep sea water-treated BMSCs showed stronger osteogenic differentiation such as BMP2, RUNX2, OPN, and OCN, and enhanced colony forming abilities, compared to the control group. Interestingly, most untreated OVX-SAMP8 mice died around 10 months; however, approximately 57% of DSW-treated groups lived up to 16.6 months, a life expectancy similar to the previously reported life expectancy for SAMR1 24 months. The results demonstrated the regenerative potentials of deep sea water on osteogenesis, showing that deep sea water could potentially be applied in osteoporosis therapy as a complementary and alternative medicine (CAM)