Continuity estimates for doubly degenerate parabolic equations with lower order terms via nonlinear potentials

This article studies the continuity of bounded nonnegative weak solutions to inhomogeneous doubly nonlinear parabolic equations. A model equation is \begin{equation*}\partial_t u-\operatorname{div}(u^{m-1}|Du|^{p-2}Du)=f\qquad \text{in}\quad\Omega\times(-T,0)\subset \mathbb{R}^{n+1}.\end{equation*} Here, we consider the case $m>1$ and $2<p<n$. We establish a continuity estimate for $u$ in terms of elliptic Riesz potentials of the right-hand side of the equation

AN INDUCTIVE POWER TRANSFER SYSTEM WITH A HIGH-Q RESONANT TANK FOR PORTABLE DEVICE CHARGING

Master'sMASTER OF ENGINEERIN

Personalized Federated X -armed Bandit

In this work, we study the personalized federated $\mathcal{X}$-armed bandit problem, where the heterogeneous local objectives of the clients are optimized simultaneously in the federated learning paradigm. We propose the \texttt{PF-PNE} algorithm with a unique double elimination strategy, which safely eliminates the non-optimal regions while encouraging federated collaboration through biased but effective evaluations of the local objectives. The proposed \texttt{PF-PNE} algorithm is able to optimize local objectives with arbitrary levels of heterogeneity, and its limited communications protects the confidentiality of the client-wise reward data. Our theoretical analysis shows the benefit of the proposed algorithm over single-client algorithms. Experimentally, \texttt{PF-PNE} outperforms multiple baselines on both synthetic and real life datasets

Improving Selfie Aesthetics with Interactive Guidance based on Empirical Models

We introduce RealSelfie, a smartphone camera application providing interactive guid- ance to help people take better self-portrait photos (commonly called “selfies”). The appli- cation uses empirical models to estimate aesthetic quality built from data gathered by 2,700 Amazon Mechanical Turk (AMT) aesthetic quality assessments of synthetic photographs. The synthetic photographs are generated from 3D models of realistic human models by manipulating a virtual camera and virtual lighting to precisely explore the space of three photographic principle parameters: face size, face position, and light direction. The Re- alSelfie application calculates the current value for each parameter using computer vision techniques and then compares those values with each model’s aesthetic estimates to display directional hints overlaid on the live camera preview. As part of this system, we contribute an algorithm to estimate lighting direction using the pattern of light and shade near the nose. We conduct a study to evaluate the RealSelfie application with 20 participants in a controlled environment to eliminate background and lighting confounds. AMT ratings of the photos show that RealSelfie provides a 26% increase in aesthetics over providing no guidance