Efficiently learning mixture of Gaussians is a fundamental problem in statistics and learning theory. Given samples coming from a random one out of k Gaussian distributions in R n , the learning problem asks to estimate the means and the covariance matrices of these Gaussians. This learning problem arises in many areas ranging from the natural sciences to the social sciences, and has also found many machine learning applications.Unfortunately, learning mixture of Gaussians is an information theoretically hard problem: in order to learn the parameters up to a reasonable accuracy, the number of samples required is exponential in the number of Gaussian components in the worst case. In this work, we show that provided we are in high enough dimensions, the class of Gaussian mixtures is learnable in its most general form under a smoothed analysis framework, where the parameters are randomly perturbed from an adversarial starting point.In particular, given samples from a mixture of Gaussians with randomly perturbed parameters, when n ≥ Ω(k 2 ), we give an algorithm that learns the parameters with polynomial running time and using polynomial number of samples.The central algorithmic ideas consist of new ways to decompose the moment tensor of the Gaussian mixture by exploiting its structural properties. The symmetries of this tensor are derived from the combinatorial structure of higher order moments of Gaussian distributions (sometimes referred to as Isserlis' theorem or Wick's theorem). We also develop new tools for bounding smallest singular values of structured random matrices, which could be useful in other smoothed analysis settings. * Microsoft Research, New England.

Abstract:A satellite image time series (SITS) contains a significant amount of temporal information. By analysing this type of data, the pattern of the changes in the object of concern can be explored. The natural change in the Earth's surface is relatively slow and exhibits a pronounced pattern. Some natural events (for example, fires, floods, plant diseases, and insect pests) and human activities (for example, deforestation and urbanisation) will disturb this pattern and cause a relatively profound change on the Earth's surface. These events are usually referred to as disturbances. However, disturbances in ecosystems are not easy to detect from SITS data, because SITS contain combined information on disturbances, phenological variations and noise in remote sensing data. In this paper, a novel framework is proposed for online disturbance detection from SITS. The framework is based on long short-term memory (LSTM) networks. First, LSTM networks are trained by historical SITS. The trained LSTM networks are then used to predict new time series data. Last, the predicted data are compared with real data, and the noticeable deviations reveal disturbances. Experimental results using 16-day compositions of the moderate resolution imaging spectroradiometer (MOD13Q1) illustrate the effectiveness and stability of the proposed approach for online disturbance detection.

In this paper, we propose a two-timescale delay-optimal dynamic clustering and power allocation design for downlink network MIMO systems. The dynamic clustering control is adaptive to the global queue state information (GQSI) only and computed at the base station controller (BSC) over a longer time scale. On the other hand, the power allocations of all the BSs in one cluster are adaptive to both intra-cluster channel state information (CCSI) and intra-cluster queue state information (CQSI), and computed at the cluster manager (CM) over a shorter time scale. We show that the two-timescale delayoptimal control can be formulated as an infinite-horizon average cost Constrained Partially Observed Markov Decision Process (CPOMDP). By exploiting the special problem structure, we shall derive an equivalent Bellman equation in terms of Pattern Selection Q-factor to solve the CPOMDP. To address the distributive requirement and the issue of exponential memory requirement and computational complexity, we approximate the Pattern Selection Q-factor by the sum of Per-cluster Potential functions and propose a novel distributive online learning algorithm to estimate the Per-cluster Potential functions (at each CM) as well as the Lagrange multipliers (LM) (at each BS). We show that the proposed distributive online learning algorithm converges almost surely (with probability 1). By exploiting the birth-death structure of the queue dynamics, we further decompose the Per-cluster Potential function into sum of Per-cluster Per-user Potential functions and formulate the instantaneous power allocation as a Per-stage QSI-aware Interference Game played among all the CMs. We also propose a QSI-aware Simultaneous Iterative Water-filling Algorithm (QSIWFA) and show that it can achieve the Nash Equilibrium (NE).

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A novel type of multi-stimuli responsive dendrimer with thermo-, pH-, and CO2-responsiveness was developed through facile modification of polyamidoamine dendrimers with various N-dialkylaminoethyl carbamate moieties.

Cancerous inhibitor of protein phosphatase 2A (CIP2A) is a human oncoprotein that is overexpressed in various tumors. A previous study found that CIP2A expression is associated with doxorubicin (Dox) resistance. In the present study, we investigated whether cucurbitacin B (CuB), a natural anticancer compound found in Cucurbitaceae, reversed multidrug resistance (MDR) and downregulated CIP2A expression in MCF-7/Adriamycin (MCF-7/Adr) cells, a human breast multidrug-resistant cancer cell line. CuB treatment significantly suppressed MCF-7/Adr cell proliferation, and reversed Dox resistance. CuB treatment also induced caspase-dependent apoptosis, decreased phosphorylation of Akt (pAkt). The suppression of pAkt was mediated through CuB-induced activation of protein phosphatase 2A (PP2A). Furthermore, CuB activated PP2A through the suppression of CIP2A. Silencing CIP2A enhanced CuB-induced growth inhibition, apoptosis and MDR inhibition in MCF-7/Adr cells. In conclusion, we found that enhancement of PP2A activity by inhibition of CIP2A promotes the reversal of MDR induced by CuB.

Abstract. Gastric cancer is the third most frequent cause of cancer-associated mortality and almost all patients who respond initially to cisplatin (DDP) later develop drug resistance, indicating multi-drug resistance (MDR) is an essential aspect of the failure of treatment. The natural diterpenoid component Oridonin (Ori) has exhibited efficient inhibition in several types of human cancer. However, the effect and potential mechanism of Ori-reversed MDR in human gastric cancer has not been fully elucidated. In the present study, it was found that Ori significantly suppressed DDP-resistant human SGC7901/DDP cell proliferation, growth and colony formation, causing increased caspase-dependent apoptosis, decreased expression of P-glycoprotein (P-gp), encoded by the MDR gene, multi-drug resistance-associated protein (MRP1), and cyclin D1. SGC7901/DDP cells were cultured with different groups of drugs (Ori, DDP alone, or the combination of Ori and DDP). The drug sensitivity, cell apoptosis and effects on MDR were detected by MTT assay and western blot analysis. The results revealed that Ori is able to reverse the DDP resistance and has a clear synergistic effect with DDP in SGC7901/DDP cells by decreasing the levels of P-gp, MRP1, cyclin D1 and cancerous inhibitor of protein phosphatase 2A. Thus, Ori may be a novel effective candidate to treat DDP-resistant human gastric cancer cells. IntroductionGastric cancer is one of the most common cancers in Eastern Asia, including China, Japan and South Korea, and Eastern Europe (1). The incidence and mortality of gastric cancer have declined markedly over the past half-century in the majority of developed countries, but it remains the second most common cause of cancer-associated mortality in the world. An estimated 28,000 incident cases (17,750 in males and 10,250 in females) of gastric cancer will be diagnosed in 2017, and 10,960 mortalities (6,720 in males and 4,240 in females) are estimated to occur from the disease (2). In China, approximately two-thirds of patients develop advanced or metastatic disease, and >50% have recurrent disease following curative surgery (3). Systematic chemotherapy plays a critical role in the treatment of gastric cancer. Cisplatin (DDP) has been commonly used in the treatment of gastric cancer (4). Despite an initial response to surgical debulking and front-line platinum chemotherapy, the majority of tumors eventually develop a drug resistant relapse selected during the course of therapy. The reasons for drug resistance are complicated and several previous studies have aimed to explore the question (1). The development of multidrug resistance (MDR) to cancer chemotherapy is a major obstacle to the effective treatment of advanced gastric cancer (5). Additionally, the mechanism of MDR remains obscure. Mechanisms including increased expression of P-glycoprotein (P-gp) and MDR-associated protein (MRP), cell cycle arrest, increased DNA damage repair and resistance of tumor cells to apoptosis may account for MDR (6). Restoring DDP sensitivity by reve...