Exploiting Higher Order Smoothness in Derivative-free Optimization and Continuous Bandits

We study the problem of zero-order optimization of a strongly convex function. The goal is to find the minimizer of the function by a sequential exploration of its values, under measurement noise. We study the impact of higher order smoothness properties of the function on the optimization error and on the cumulative regret. To solve this problem we consider a randomized approximation of the projected gradient descent algorithm. The gradient is estimated by a randomized procedure involving two function evaluations and a smoothing kernel. We derive upper bounds for this algorithm both in the constrained and unconstrained settings and prove minimax lower bounds for any sequential search method. Our results imply that the zero-order algorithm is nearly optimal in terms of sample complexity and the problem parameters. Based on this algorithm, we also propose an estimator of the minimum value of the function achieving almost sharp oracle behavior. We compare our results with the state-of-the-art, highlighting a number of key improvements

Estimating the minimizer and the minimum value of a regression function under passive design

We propose a new method for estimating the minimizer $\boldsymbol{x}^*$ and the minimum value $f^*$ of a smooth and strongly convex regression function $f$ from the observations contaminated by random noise. Our estimator $\boldsymbol{z}_n$ of the minimizer $\boldsymbol{x}^*$ is based on a version of the projected gradient descent with the gradient estimated by a regularized local polynomial algorithm. Next, we propose a two-stage procedure for estimation of the minimum value $f^*$ of regression function $f$. At the first stage, we construct an accurate enough estimator of $\boldsymbol{x}^*$, which can be, for example, $\boldsymbol{z}_n$. At the second stage, we estimate the function value at the point obtained in the first stage using a rate optimal nonparametric procedure. We derive non-asymptotic upper bounds for the quadratic risk and optimization error of $\boldsymbol{z}_n$, and for the risk of estimating $f^*$. We establish minimax lower bounds showing that, under certain choice of parameters, the proposed algorithms achieve the minimax optimal rates of convergence on the class of smooth and strongly convex functions.Comment: 35 page

Diagnostic values of serum levels of pepsinogens and gastrin-17 for screening gastritis and gastric cancer in a high risk area in Northern Iran

Background: Gastric cancer (GC) is the second cause of cancer related death in the world. It may develop by progression from its precancerous condition, called gastric atrophy (GA) due to gastritis. The aim of this study was to evaluate the accuracy of serum levels of pepsinogens (Pg) and gastrin-17 (G17) as non-invasive methods to discriminate GA or GC (GA/GC) patients. Materials and Methods: Subjects referred to gastrointestinal clinics of Golestan province of Iran during 2010 and 2011 were invited to participate. Serum levels of PgI, PgII and G17 were measured using a GastroPanel kit. Based on the pathological examination of endoscopic biopsy samples, subjects were classified into four groups: normal, non-atrophic gastritis, GA, and GC. Receiver operating curve (ROC) analysis was used to determine cut-off values. Indices of validity were calculated for serum markers. Results: Study groups were normal individuals (n=74), non-atrophic gastritis (n=90), GA (n=31) and GC patients (n=30). The best cut-off points for PgI, PgI/II ratio, G17 and HP were 80 μg/L, 10, 6 pmol/L, and 20 EIU, respectively. PgI could differentiate GA/GC with high accuracy (AUC=0.83; 95%CI: 0.76-0.89). The accuracy of a combination of PgI and PgI/II ratio for detecting GA/GC was also relatively high (AUC=0.78; 95%CI: 0.70-0.86). Conclusions: Our findings suggested PgI alone as well as a combination of PgI and PgI/II ratio are valid markers to differentiate GA/GC. Therefore, Pgs may be considered in conducting GC screening programs in high-risk areas

Gradient-free optimization of highly smooth functions: improved analysis and a new algorithm

This work studies minimization problems with zero-order noisy oracle information under the assumption that the objective function is highly smooth and possibly satisfies additional properties. We consider two kinds of zero-order projected gradient descent algorithms, which differ in the form of the gradient estimator. The first algorithm uses a gradient estimator based on randomization over the $\ell_2$ sphere due to Bach and Perchet (2016). We present an improved analysis of this algorithm on the class of highly smooth and strongly convex functions studied in the prior work, and we derive rates of convergence for two more general classes of non-convex functions. Namely, we consider highly smooth functions satisfying the Polyak-{\L}ojasiewicz condition and the class of highly smooth functions with no additional property. The second algorithm is based on randomization over the $\ell_1$ sphere, and it extends to the highly smooth setting the algorithm that was recently proposed for Lipschitz convex functions in Akhavan et al. (2022). We show that, in the case of noiseless oracle, this novel algorithm enjoys better bounds on bias and variance than the $\ell_2$ randomization and the commonly used Gaussian randomization algorithms, while in the noisy case both $\ell_1$ and $\ell_2$ algorithms benefit from similar improved theoretical guarantees. The improvements are achieved thanks to a new proof techniques based on Poincar\'e type inequalities for uniform distributions on the $\ell_1$ or $\ell_2$ spheres. The results are established under weak (almost adversarial) assumptions on the noise. Moreover, we provide minimax lower bounds proving optimality or near optimality of the obtained upper bounds in several cases

Large-area semi-transparent light-sensitive nanocrystal skins

Cataloged from PDF version of article.We report a large-area, semi-transparent, light-sensitive nanocrystal skin (LS-NS) platform consisting of single monolayer colloidal nanocrystals. LS-NS devices, which were fabricated over areas up to 48 cm(2) using spray-coating and several cm-squares using dip-coating, are operated on the principle of photogenerated potential buildup, unlike the conventional charge collection. Implementing proof-of-concept devices using CdTe nanocrystals with ligand removal, we observed a substantial sensitivity enhancement factor of similar to 73%, accompanied with a 3-fold faster response time (<100 ms). With fully sealed nanocrystal monolayers, LS-NS is found to be highly stable under ambient conditions, promising for low-cost large-area UV/visible sensing in windows and facades of smart buildings. (C) 2012 Optical Society of Americ

Fabrication and microfluidic analysis of graphene-based molecular communication receiver for Internet of Nano Things (IoNT).

Bio-inspired molecular communications (MC), where molecules are used to transfer information, is the most promising technique to realise the Internet of Nano Things (IoNT), thanks to its inherent biocompatibility, energy-efficiency, and reliability in physiologically-relevant environments. Despite a substantial body of theoretical work concerning MC, the lack of practical micro/nanoscale MC devices and MC testbeds has led researchers to make overly simplifying assumptions about the implications of the channel conditions and the physical architectures of the practical transceivers in developing theoretical models and devising communication methods for MC. On the other hand, MC imposes unique challenges resulting from the highly complex, nonlinear, time-varying channel properties that cannot be always tackled by conventional information and communication tools and technologies (ICT). As a result, the reliability of the existing MC methods, which are mostly adopted from electromagnetic communications and not validated with practical testbeds, is highly questionable. As the first step to remove this discrepancy, in this study, we report on the fabrication of a nanoscale MC receiver based on graphene field-effect transistor biosensors. We perform its ICT characterisation in a custom-designed microfluidic MC system with the information encoded into the concentration of single-stranded DNA molecules. This experimental platform is the first practical implementation of a micro/nanoscale MC system with nanoscale MC receivers, and can serve as a testbed for developing realistic MC methods and IoNT applications.Tis work was supported in part by the ERC (Project MINERVA, ERC-2013-CoG #616922) and by the AXA Research Fund (AXA Chair for Internet of Everything at Koc University)

Dry Surface Treatments of Silk Biomaterials and Their Utility in Biomedical Applications

Silk-based materials are widely used in biomaterial and tissue engineering applications due to their cytocompatibility and tunable mechanical and biodegradation properties. Aqueous-based processing techniques have enabled the fabrication of silk into a broad range of material formats, making it a highly versatile material platform across multiple industries. Utilizing the full potential of silk in biomedical applications frequently requires modification of silk's surface properties. Dry surface modification techniques, including irradiation and plasma treatment, offer an alternative to the conventional wet chemistry strategies to modify the physical and chemical properties of silk materials without compromising their bulk properties. While dry surface modification techniques are more prevalent in textiles and sterilization applications, the range of modifications available and resultant changes to silk materials all point to the utility of dry surface modification for the development of new, functional silk biomaterials. Dry surface treatment affects the surface chemistry, secondary structure, molecular weight, topography, surface energy, and mechanical properties of silk materials. This Review describes and critically evaluates the effect of physical dry surface modification techniques, including irradiation and plasma processes, on silk materials and discusses their utility in biomedical applications, including recent examples of modulation of cell/protein interactions on silk biomaterials, in vivo performance of implanted biomaterials, and applications in material biofunctionalization and lithographic surface patterning approaches

Excitonic enhancement of nonradiative energy transfer to bulk silicon with the hybridization of cascaded quantum dots

Cataloged from PDF version of article.We report enhanced sensitization of silicon through nonradiative energy transfer (NRET) of the excitons in an energy-gradient structure composed of a cascaded bilayer of green-and red-emitting CdTe quantum dots (QDs) on bulk silicon. Here NRET dynamics were systematically investigated comparatively for the cascaded energy-gradient and mono-dispersed QD structures at room temperature. We show experimentally that NRET from the QD layer into silicon is enhanced by 40% in the case of an energy-gradient cascaded structure as compared to the mono-dispersed structures, which is in agreement with the theoretical analysis based on the excited state population-depopulation dynamics of the QDs. (C) 2013 AIP Publishing LLC

Risk Stratification and Early Oncologic Outcomes Following Robotic Prostatectomy

Results of this study suggest that robotic prostatectomy provides good cancer outcomes for clinically localized disease