Learning mixtures of structured distributions over discrete domains

Let $\mathfrak{C}$ be a class of probability distributions over the discrete domain $[n] = \{1,...,n\}.$ We show that if $\mathfrak{C}$ satisfies a rather general condition -- essentially, that each distribution in $\mathfrak{C}$ can be well-approximated by a variable-width histogram with few bins -- then there is a highly efficient (both in terms of running time and sample complexity) algorithm that can learn any mixture of $k$ unknown distributions from $\mathfrak{C}.$ We analyze several natural types of distributions over $[n]$, including log-concave, monotone hazard rate and unimodal distributions, and show that they have the required structural property of being well-approximated by a histogram with few bins. Applying our general algorithm, we obtain near-optimally efficient algorithms for all these mixture learning problems.Comment: preliminary full version of soda'13 pape

Symmetry Detection and Analysis of Chinese Paifang Using 3D Point Clouds

The Chinese paifang is an essential constituent element for Chinese or many other oriental architectures. In this paper, a new method for detection and analysis of the reflection symmetry of the paifang based on 3D point clouds is proposed. The method invokes a new model to simultaneously fit two vertical planes of symmetry to the 3D point cloud of a paifang to support further symmetry analysis. Several simulated datasets were used to verify the proposed method. The results indicated that the proposed method was able to quantity the symmetry of a paifang in terms of the RMSE obtained from the ICP algorithm, with resistance to the presence of some random noise added to the simulated measurements. For real datasets, three old Chinese paifangs (with ages from 90 to 500 years) were scanned as point clouds to input into the proposed method. The method quantified the degree of symmetry for the three Chinese paifangs in terms of the RMSE, which ranged from 20 to 61 mm. One of the paifangs with apparent asymmetry had the highest RMSE (61 mm). Other than the quantification of the symmetry of the paifangs, the proposed method could also locate which portion of the paifang was relatively more symmetric. The proposed method can potentially be used for structural health inspection and cultural studies of the Chinese paifangs and some other similar architecture

Near-Optimal Density Estimation in Near-Linear Time Using Variable-Width Histograms

Let $p$ be an unknown and arbitrary probability distribution over $[0,1)$. We consider the problem of {\em density estimation}, in which a learning algorithm is given i.i.d. draws from $p$ and must (with high probability) output a hypothesis distribution that is close to $p$. The main contribution of this paper is a highly efficient density estimation algorithm for learning using a variable-width histogram, i.e., a hypothesis distribution with a piecewise constant probability density function. In more detail, for any $k$ and $\epsilon$, we give an algorithm that makes $\tilde{O}(k/\epsilon^2)$ draws from $p$, runs in $\tilde{O}(k/\epsilon^2)$ time, and outputs a hypothesis distribution $h$ that is piecewise constant with $O(k \log^2(1/\epsilon))$ pieces. With high probability the hypothesis $h$ satisfies $d_{\mathrm{TV}}(p,h) \leq C \cdot \mathrm{opt}_k(p) + \epsilon$, where $d_{\mathrm{TV}}$ denotes the total variation distance (statistical distance), $C$ is a universal constant, and $\mathrm{opt}_k(p)$ is the smallest total variation distance between $p$ and any $k$-piecewise constant distribution. The sample size and running time of our algorithm are optimal up to logarithmic factors. The "approximation factor" $C$ in our result is inherent in the problem, as we prove that no algorithm with sample size bounded in terms of $k$ and $\epsilon$ can achieve $C<2$ regardless of what kind of hypothesis distribution it uses.Comment: conference version appears in NIPS 201

rad21 Is Involved in Corneal Stroma Development by Regulating Neural Crest Migration

Previously, we identified RAD21(R450C) from a peripheral sclerocornea pedigree. Injection of this rad21 variant mRNA into Xenopus laevis embryos disrupted the organization of corneal stroma fibrils. To understand the mechanisms of RAD21-mediated corneal stroma defects, gene expression and chromosome conformation analysis were performed using cells from family members affected by peripheral sclerocornea. Both gene expression and chromosome conformation of cell adhesion genes were affected in cells carrying the heterozygous rad21 variant. Since cell migration is essential in early embryonic development and sclerocornea is a congenital disease, we studied neural crest migration during cornea development in X. laevis embryos. In X. laevis embryos injected with rad21 mutant mRNA, neural crest migration was disrupted, and the number of neural crest-derived periocular mesenchymes decreased significantly in the corneal stroma region. Our data indicate that the RAD21(R450C) variant contributes to peripheral sclerocornea by modifying chromosome conformation and gene expression, therefore disturbing neural crest cell migration, which suggests RAD21 plays a key role in corneal stroma development

Long Isoforms of NRF1 Contribute to Arsenic-Induced Antioxidant Response in Human Keratinocytes

BACKGROUND: Human exposure to inorganic arsenic (iAs), a potent oxidative stressor, causes various dermal disorders, including hyperkeratosis and skin cancer. Nuclear factor-erythroid 2-related factor 1 (NRF1, also called NFE2L1) plays a critical role in regulating the expression of many antioxidant response element (ARE)-dependent genes. OBJECTIVES: We investigated the role of NRF1 in arsenic-induced antioxidant response and cytotoxicity in human keratinocytes. RESULTS: In cultured human keratinocyte HaCaT cells, inorganic arsenite (iAs(3+)) enhanced the protein accumulation of long isoforms (120-140 kDa) of NRF1 in a dose-and time-dependent fashion. These isoforms accumulated mainly in the nuclei of HaCaT cells. Selective deficiency of NRF1 by lentiviral short-hairpin RNAs in HaCaT cells [NRF1-knockdown (KD)] led to decreased expression of gamma-glutamate cysteine ligase catalytic subunit (GCLC) and regulatory subunit (GCLM) and a reduced level of intra-cellular glutathione. In response to acute iAs(3+) exposure, induction of some ARE-dependent genes, including NAD(P)H:quinone oxidoreductase 1 (NQO1), GCLC, and GCLM, was significantly attenuated in NRF1-KD cells. However, the iAs(3)-induced expression of heme oxygenase 1 (HMOX-1) was unaltered by silencing NRF1, suggesting that HMOX-1 is not regulated by NRF1. In addition, the lack of NRF1 in HaCaT cells did not disturb iAs(3+)-induced NRF2 accumulation but noticeably decreased Kelch-like ECH-associated protein 1 (KEAP1) levels under basal and iAs(3+)-exposed conditions, suggesting a potential interaction between NRF1 and KEAP1. Consistent with the critical role of NRF1 in the transcriptional regulation of some ARE-bearing genes, knockdown of NRF1 significantly increased iAs(3+)-induced cytotoxicity and apoptosis. CONCLUSIONS: Here, we demonstrate for the first time that long isoforms of NRF1 contribute to arsenic-induced antioxidant response in human keratinocytes and protect the cells from acute arsenic cytotoxicity

Carboxyl-terminal truncated HBx regulates a distinct microRNA transcription program in Hepatocellular carcinoma development

Background: The biological pathways and functional properties by which misexpressed microRNAs (miRNAs) contribute to liver carcinogenesis have been intensively investigated. However, little is known about the upstream mechanisms that deregulate miRNA expressions in this process. In hepatocellular carcinoma (HCC), hepatitis B virus (HBV) X protein (HBx), a transcriptional trans-activator, is frequently expressed in truncated form without carboxyl-terminus but its role in miRNA expression and HCC development is unclear. Methods: Human non-tumorigenic hepatocytes were infected with lentivirus-expressing full-length and carboxyl-terminal truncated HBx (Ct-HBx) for cell growth assay and miRNA profiling. Chromatin immunoprecipitation microarray was performed to identify the miRNA promoters directly associated with HBx. Direct transcriptional control was verified by luciferase reporter assay. The differential miRNA expressions were further validated in a cohort of HBV-associated HCC tissues using real-time PCR. Results: Hepatocytes expressing Ct-HBx grew significantly faster than the full-length HBx counterparts. Ct-HBx decreased while full-length HBx increased the expression of a set of miRNAs with growth-suppressive functions. Interestingly, Ct-HBx bound to and inhibited the transcriptional activity of some of these miRNA promoters. Notably, some of the examined repressed-miRNAs (miR-26a, -29c, -146a and -190) were also significantly down-regulated in a subset of HCC tissues with carboxyl-terminal HBx truncation compared to their matching non-tumor tissues, highlighting the clinical relevance of our data. Conclusion: Our results suggest that Ct-HBx directly regulates miRNA transcription and in turn promotes hepatocellular proliferation, thus revealing a viral contribution of miRNA deregulation during hepatocarcinogenesis. © 2011 Yip et al.published_or_final_versio

The Dark Side of Transfer Pricing: Its Role in Tax Avoidance and Wealth Retentiveness

In conventional accounting literature, ?transfer pricing? is portrayed as a technique for optimal allocation of costs and revenues amongst divisions, subsidiaries and joint ventures within a group of related entities. Such representations of transfer pricing simultaneously acknowledge and occlude how it is deeply implicated in processes of wealth retentiveness that enable companies to avoid taxes and facilitate the flight of capital. A purely technical conception of transfer pricing calculations abstracts them from the politico-economic contexts of their development and use. The context is the modern corporation in an era of globalized trade and its relationship to state tax authorities, shareholders and other possible stakeholders. Transfer pricing practices are responsive to opportunities for determining values in ways that are consequential for enhancing private gains, and thereby contributing to relative social impoverishment, by avoiding the payment of public taxes. Evidence is provided by examining some of the transfer prices practices used by corporations to avoid taxes in developing and developed economies

Long-acting inhaled therapy (beta-agonists, anticholinergics and steroids) for COPD: a network meta-analysis.

BACKGROUND: Pharmacological therapy for chronic obstructive pulmonary disease (COPD) is aimed at relieving symptoms, improving quality of life and preventing or treating exacerbations.Treatment tends to begin with one inhaler, and additional therapies are introduced as necessary. For persistent or worsening symptoms, long-acting inhaled therapies taken once or twice daily are preferred over short-acting inhalers. Several Cochrane reviews have looked at the risks and benefits of specific long-acting inhaled therapies compared with placebo or other treatments. However for patients and clinicians, it is important to understand the merits of these treatments relative to each other, and whether a particular class of inhaled therapies is more beneficial than the others. OBJECTIVES: To assess the efficacy of treatment options for patients whose chronic obstructive pulmonary disease cannot be controlled by short-acting therapies alone. The review will not look at combination therapies usually considered later in the course of the disease.As part of this network meta-analysis, we will address the following issues.1. How does long-term efficacy compare between different pharmacological treatments for COPD?2. Are there limitations in the current evidence base that may compromise the conclusions drawn by this network meta-analysis? If so, what are the implications for future research? SEARCH METHODS: We identified randomised controlled trials (RCTs) in existing Cochrane reviews by searching the Cochrane Database of Systematic Reviews (CDSR). In addition, we ran a comprehensive citation search on the Cochrane Airways Group Register of trials (CAGR) and checked manufacturer websites and reference lists of other reviews. The most recent searches were conducted in September 2013. SELECTION CRITERIA: We included parallel-group RCTs of at least 6 months' duration recruiting people with COPD. Studies were included if they compared any of the following treatments versus any other: long-acting beta2-agonists (LABAs; formoterol, indacaterol, salmeterol); long-acting muscarinic antagonists (LAMAs; aclidinium, glycopyrronium, tiotropium); inhaled corticosteroids (ICSs; budesonide, fluticasone, mometasone); combination long-acting beta2-agonist (LABA) and inhaled corticosteroid (LABA/ICS) (formoterol/budesonide, formoterol/mometasone, salmeterol/fluticasone); and placebo. DATA COLLECTION AND ANALYSIS: We conducted a network meta-analysis using Markov chain Monte Carlo methods for two efficacy outcomes: St George's Respiratory Questionnaire (SGRQ) total score and trough forced expiratory volume in one second (FEV1). We modelled the relative effectiveness of any two treatments as a function of each treatment relative to the reference treatment (placebo). We assumed that treatment effects were similar within treatment classes (LAMA, LABA, ICS, LABA/ICS). We present estimates of class effects, variability between treatments within each class and individual treatment effects compared with every other.To justify the analyses, we assessed the trials for clinical and methodological transitivity across comparisons. We tested the robustness of our analyses by performing sensitivity analyses for lack of blinding and by considering six- and 12-month data separately. MAIN RESULTS: We identified 71 RCTs randomly assigning 73,062 people with COPD to 184 treatment arms of interest. Trials were similar with regards to methodology, inclusion and exclusion criteria and key baseline characteristics. Participants were more often male, aged in their mid sixties, with FEV1 predicted normal between 40% and 50% and with substantial smoking histories (40+ pack-years). The risk of bias was generally low, although missing information made it hard to judge risk of selection bias and selective outcome reporting. Fixed effects were used for SGRQ analyses, and random effects for Trough FEV1 analyses, based on model fit statistics and deviance information criteria (DIC). SGRQ SGRQ data were available in 42 studies (n = 54,613). At six months, 39 pairwise comparisons were made between 18 treatments in 25 studies (n = 27,024). Combination LABA/ICS was the highest ranked intervention, with a mean improvement over placebo of -3.89 units at six months (95% credible interval (CrI) -4.70 to -2.97) and -3.60 at 12 months (95% CrI -4.63 to -2.34). LAMAs and LABAs were ranked second and third at six months, with mean differences of -2.63 (95% CrI -3.53 to -1.97) and -2.29 (95% CrI -3.18 to -1.53), respectively. Inhaled corticosteroids were ranked fourth (MD -2.00, 95% CrI -3.06 to -0.87). Class differences between LABA, LAMA and ICS were less prominent at 12 months. Indacaterol and aclidinium were ranked somewhat higher than other members of their classes, and formoterol 12 mcg, budesonide 400 mcg and formoterol/mometasone combination were ranked lower within their classes. There was considerable overlap in credible intervals and rankings for both classes and individual treatments. Trough FEV1 Trough FEV1 data were available in 46 studies (n = 47,409). At six months, 41 pairwise comparisons were made between 20 treatments in 31 studies (n = 29,271). As for SGRQ, combination LABA/ICS was the highest ranked class, with a mean improvement over placebo of 133.3 mL at six months (95% CrI 100.6 to 164.0) and slightly less at 12 months (mean difference (MD) 100, 95% CrI 55.5 to 140.1). LAMAs (MD 103.5, 95% CrI 81.8 to 124.9) and LABAs (MD 99.4, 95% CrI 72.0 to 127.8) showed roughly equivalent results at six months, and ICSs were the fourth ranked class (MD 65.4, 95% CrI 33.1 to 96.9). As with SGRQ, initial differences between classes were not so prominent at 12 months. Indacaterol and salmeterol/fluticasone were ranked slightly better than others in their class, and formoterol 12, aclidinium, budesonide and formoterol/budesonide combination were ranked lower within their classes. All credible intervals for individual rankings were wide. AUTHORS' CONCLUSIONS: This network meta-analysis compares four different classes of long-acting inhalers for people with COPD who need more than short-acting bronchodilators. Quality of life and lung function were improved most on combination inhalers (LABA and ICS) and least on ICS alone at 6 and at 12 months. Overall LAMA and LABA inhalers had similar effects, particularly at 12 months. The network has demonstrated the benefit of ICS when added to LABA for these outcomes in participants who largely had an FEV1 that was less than 50% predicted, but the additional expense of combination inhalers and any potential for increased adverse events (which has been established by other reviews) require consideration. Our findings are in keeping with current National Institute for Health and Care Excellence (NICE) guidelines