Noisy population recovery in polynomial time

In the noisy population recovery problem of Dvir et al., the goal is to learn an unknown distribution $f$ on binary strings of length $n$ from noisy samples. For some parameter $\mu \in [0,1]$, a noisy sample is generated by flipping each coordinate of a sample from $f$ independently with probability $(1-\mu)/2$. We assume an upper bound $k$ on the size of the support of the distribution, and the goal is to estimate the probability of any string to within some given error $\varepsilon$. It is known that the algorithmic complexity and sample complexity of this problem are polynomially related to each other. We show that for $\mu > 0$, the sample complexity (and hence the algorithmic complexity) is bounded by a polynomial in $k$, $n$ and $1/\varepsilon$ improving upon the previous best result of $\mathsf{poly}(k^{\log\log k},n,1/\varepsilon)$ due to Lovett and Zhang. Our proof combines ideas from Lovett and Zhang with a \emph{noise attenuated} version of M\"{o}bius inversion. In turn, the latter crucially uses the construction of \emph{robust local inverse} due to Moitra and Saks

The Role of Microenvironment Reagent Solubility on Reaction Kinetics of 4-Nitrophenol Reduction

The Role of Microenvironment Reagent Solubility on Reaction Kinetics of 4-Nitrophenol Reduction Michael Zeevi1 with Andrew Harrison1 and Christina Tang, PhD1 1Department of Chemical and Life Science Engineering, VCU School of Engineering Introduction: Nanoparticles are of increasing interest due to their high surface area to volume ratio, as well as that they enable fine-tuning of the reaction microenvironment. Through flash nanoprecipitation, core-shell polymer nanoreactors were formed by directed self-assembly. Using the reduction of 4-nitrophenol as a model reduction reaction, we investigated the effect of reagent solubility in the nanoreactor microenvironment’s on nanoreactor kinetics. Methods: The standard reaction was conducted at room temperature, with a 1000-fold excess of sodium borohydride in a quartz cuvette for real-time in situ­ UV-Vis analysis. Reagent concentrations were varied to examine the resulting effect on the calculated reaction rate constant. Reagent solubility limits in the nanoreactor microenvironment were estimated from solubility measurements in solvents with similar Hansen solubility parameters. Ethanol was chosen to represent the hydrophilic poly(ethylene) glycol phase and chloroform was chosen to represent the hydrophobic polystyrene phase. The hydrophilic phase had a visual absorbance at nm, and thus UV-Vis spectrometry was used to determine the saturation concentration. 1H NMR analysis with chloroform-D containing an internal standard (v/v TMS 0.03%) was used to measure the reagent solubility in the hydrophobic phase. Results: 4-nitrophenol solubility in ethanol was determined by UV-Vis spectrometry to be . The solubility in chloroform-D was determined by 1H NMR to be . When 4-nitrophenol concentration is varied independently of sodium borohydride, an inverse relationship is observed with respect to the rate constant. However, when 4-nitrophenol and sodium borohydride concentrations are varied concurrently, no change is witnessed in the rate constant above the standard reaction concentration. Conclusions: This experiment demonstrated that the rate of reaction in polystyrene core nanoreactors is not dependent on the reagent concentrations above the standard concentration. Solubility in each phase was measured in an effort to explain this behavior. The differences in solubility observed between the hydrophobic and hydrophilic phases may serve to explain this behavior if the interior, hydrophobic phase is saturated by 4-nitrophenol at the standard concentration. Future work should include study of concentrations at lower values than the standard concentration to determine when a change in the observed rate constant occurs.https://scholarscompass.vcu.edu/uresposters/1287/thumbnail.jp

Likelihood based inference for current status data on a grid: A boundary phenomenon and an adaptive inference procedure

In this paper, we study the nonparametric maximum likelihood estimator for an event time distribution function at a point in the current status model with observation times supported on a grid of potentially unknown sparsity and with multiple subjects sharing the same observation time. This is of interest since observation time ties occur frequently with current status data. The grid resolution is specified as $cn^{-\gamma}$ with $c>0$ being a scaling constant and $\gamma>0$ regulating the sparsity of the grid relative to $n$, the number of subjects. The asymptotic behavior falls into three cases depending on $\gamma$: regular Gaussian-type asymptotics obtain for $\gamma<1/3$, nonstandard cube-root asymptotics prevail when $\gamma>1/3$ and $\gamma=1/3$ serves as a boundary at which the transition happens. The limit distribution at the boundary is different from either of the previous cases and converges weakly to those obtained with $\gamma\in(0,1/3)$ and $\gamma\in(1/3,\infty)$ as $c$ goes to $\infty$ and 0, respectively. This weak convergence allows us to develop an adaptive procedure to construct confidence intervals for the value of the event time distribution at a point of interest without needing to know or estimate $\gamma$, which is of enormous advantage from the perspective of inference. A simulation study of the adaptive procedure is presented.Comment: Published in at http://dx.doi.org/10.1214/11-AOS942 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Ranking News-Quality Multimedia

News editors need to find the photos that best illustrate a news piece and fulfill news-media quality standards, while being pressed to also find the most recent photos of live events. Recently, it became common to use social-media content in the context of news media for its unique value in terms of immediacy and quality. Consequently, the amount of images to be considered and filtered through is now too much to be handled by a person. To aid the news editor in this process, we propose a framework designed to deliver high-quality, news-press type photos to the user. The framework, composed of two parts, is based on a ranking algorithm tuned to rank professional media highly and a visual SPAM detection module designed to filter-out low-quality media. The core ranking algorithm is leveraged by aesthetic, social and deep-learning semantic features. Evaluation showed that the proposed framework is effective at finding high-quality photos (true-positive rate) achieving a retrieval MAP of 64.5% and a classification precision of 70%.Comment: To appear in ICMR'1

Temperature rise in shear bands in a simulated metallic glass

Temperature rise ($\Delta T$) associated with shear-banding of metallic glasses is of great importance for their performance. However, experimental measurement of $\Delta T$ is difficult due to temporal and spatial localization of shear bands and, as a result, our understanding of the mechanism of $\Delta T$ is limited. Here, based on molecular dynamics simulations we observe a spectrum of $\Delta T$, which depends on both sample size and strain rate, in the shear bands of CuZr metallic glass under tension. More importantly, we find that the maximum sliding velocity of the shear bands correlates linearly with the corresponding $\Delta T$, ranging from $\sim$25 K up to near the melting point for the samples studied. Taking heat diffusion into account, we expect $\Delta T$ to be lower than 25 K for the lower end of sliding velocity. At high temperature, shear band bifurcation and/or multiplication can occur as a negative feedback mechanism that prevents temperature rising well above the melting point