Weierstrass Bridges

We introduce a new class of stochastic processes called fractional Wiener-Weierstrass bridges. They arise by applying the convolution from the construction of the classical, fractal Weierstrass functions to an underlying fractional Brownian bridge. By analyzing the $p$-th variation of the fractional Wiener-Weierstrass bridge along the sequence of $b$-adic partitions, we identify two regimes in which the processes exhibit distinct sample path properties. We also analyze the critical case between those two regimes for Wiener-Weierstrass bridges that are based on standard Brownian bridge. We furthermore prove that fractional Wiener-Weierstrass bridges are never semimartingales, and we show that their covariance functions are typically fractal functions. Some of our results are extended to Weierstrass bridges based on bridges derived from a general continuous Gaussian martingale.Comment: 40 pages, 2 figure

Impact on Travelers Hedonic and Utilitarian Shopping Behavior by Adoption of Mobile Application: Results from a Quasi-experiment

The continuing development of mobile technology has led to an explosion of mobile applications, which have exposed a broader consumer base to mobile consumption. It is currently unclear how mobile apps using will affect travelers’ shopping behavior, particularly from the perspective of the hedonic and utilitarian shopping behavior of travelers. Using a special quasi-experiment launching by an airline, we collected the datasets of more than 10000 travelers and to investigate the impact of mobile app on the travelers’ shopping behavior. The results suggested that mobile apps adoption improved travelers’ hedonic shopping behavior (e.g., ancillary services purchasing), while the utilitarian shopping conduct (e.g. booking tickets in advance) decreased. It was also found that the mobile app adoption increased hedonic shopping in males but decreased hedonic and utilitarian shopping in frequent flyers and members. This investigation can help with the management of travelers’ purchasing habits and provide guidance for industrial decision makers

On the Optimal Lower and Upper Complexity Bounds for a Class of Composite Optimization Problems

We study the optimal lower and upper complexity bounds for finding approximate solutions to the composite problem $\min_x\ f(x)+h(Ax-b)$, where $f$ is smooth and $h$ is convex. Given access to the proximal operator of $h$, for strongly convex, convex, and nonconvex $f$, we design efficient first order algorithms with complexities $\tilde{O}\left(\kappa_A\sqrt{\kappa_f}\log\left(1/{\epsilon}\right)\right)$, $\tilde{O}\left(\kappa_A\sqrt{L_f}D/\sqrt{\epsilon}\right)$, and $\tilde{O}\left(\kappa_A L_f\Delta/\epsilon^2\right)$, respectively. Here, $\kappa_A$ is the condition number of the matrix $A$ in the composition, $L_f$ is the smoothness constant of $f$, and $\kappa_f$ is the condition number of $f$ in the strongly convex case. $D$ is the initial point distance and $\Delta$ is the initial function value gap. Tight lower complexity bounds for the three cases are also derived and they match the upper bounds up to logarithmic factors, thereby demonstrating the optimality of both the upper and lower bounds proposed in this paper

Composite Sorting

We propose a new sorting framework: composite sorting. Composite sorting comprises of (1) distinct worker types assigned to the same occupation, and (2) a given worker type simultaneously being part of both positive and negative sorting. Composite sorting arises when fixed investments mitigate variable costs of mismatch. We completely characterize optimal sorting and additionally show it is more positive when mismatch costs are less concave. We then characterize equilibrium wages. Wages have a regional hierarchical structure - relative wages depend solely on sorting within skill groups. Quantitatively, composite sorting can generate a sizable portion of within-occupations wage dispersion in the US.Comment: 81 pages, 26 figure

A simple HPLC method for determination tobramycin in plasma and Iis application in the study of pharmacokinetics in rats

A simple HPLC method was developed to study the pharmacokinetics of tobramycin in rat after intravenous administration. The plasma samples were deproteinized with acetonitrile after addition of the internal standard, netilmicin. The separation was achieved on a reversed-phase C18 column after derivatization with 9-fluorenylmethyl chloroformate (FMOC-Cl) in borate buffer (0.2 M, pH 6.5) for 15 min at 25 ºC. The mobile phase was water-acetonitrile (6:94, v/v) at a flow rate of 1.0 mL/min. The fluorescence excitation and emission wavelengths were 265 and 315 nm, respectively. The method was linear over the range of 0.12-10.48 μg/mL for tobramycin in plasma. The limit of detection was 0.074 μg/mL. The intra-day and inter-day precisions of tobramycin were both less than 6%. Both derivatives were stable in the reaction solution for 24 h at room temperature. This assay had been successfully applied to the in vivo kinetic study of tobramycin in rats.Colegio de Farmacéuticos de la Provincia de Buenos Aire