A note on additive complements of the squares

Let $\mathcal{S}=\{1^2,2^2,3^2,...\}$ be the set of squares and $\mathcal{W}=\{w_n\}_{n=1}^{\infty} \subset \mathbb{N}$ be an additive complement of $\mathcal{S}$ so that $\mathcal{S} + \mathcal{W} \supset \{n \in \mathbb{N}: n \geq N_0\}$ for some $N_0$. Let $\mathcal{R}_{\mathcal{S},\mathcal{W}}(n) = \#\{(s,w):n=s+w, s\in \mathcal{S}, w\in \mathcal{W}\}$. In 2017, Chen-Fang \cite{C-F} studied the lower bound of $\sum_{n=1}^NR_{\mathcal{S},\mathcal{W}}(n)$. In this note, we improve Cheng-Fang's result and get that $$\sum_{n=1}^NR_{\mathcal{S},\mathcal{W}}(n)-N\gg N^{1/2}.$$ As an application, we make some progress on a problem of Ben Green problem by showing that $$\limsup_{n\rightarrow\infty}\frac{\frac{\pi^2}{16}n^2-w_n}{n}\ge \frac{\pi}{4}+\frac{0.193\pi^2}{8}.$$Comment: The new version significantly improves the result of the former on

Cyber-physical system based optimization framework for intelligent powertrain control

The interactions between automatic controls, physics, and driver is an important step towards highly automated driving. This study investigates the dynamical interactions between human-selected driving modes, vehicle controller and physical plant parameters, to determine how to optimally adapt powertrain control to different human-like driving requirements. A cyber-physical system (CPS) based framework is proposed for co-design optimization of the physical plant parameters and controller variables for an electric powertrain, in view of vehicle’s dynamic performance, ride comfort, and energy efficiency under different driving modes. System structure, performance requirements and constraints, optimization goals and methodology are investigated. Intelligent powertrain control algorithms are synthesized for three driving modes, namely sport, eco, and normal modes, with appropriate protocol selections. The performance exploration methodology is presented. Simulation-based parameter optimizations are carried out according to the objective functions. Simulation results show that an electric powertrain with intelligent controller can perform its tasks well under sport, eco, and normal driving modes. The vehicle further improves overall performance in vehicle dynamics, ride comfort, and energy efficiency. The results validate the feasibility and effectiveness of the proposed CPS-based optimization framework, and demonstrate its advantages over a baseline benchmark

PrivateDroid: Private Browsing Mode for Android

Abstract—Private browsing mode is a privacy feature adopted by many modern computer browsers. With the increased use of mobile devices and escalating privacy concerns for mobile users, browser applications on mobile devices have also started incorporating private browsing mode. Even so, the use of private browsing mode is limited to the browser applications and cannot be applied directly on other third-party mobile applications. In this paper, we propose PrivateDroid, which provides a private browsing mode for third-party applications on the Android plat-form. First, we discuss three possible approaches of implementing mobile private browsing mode: code instrumentation, an extra sandbox, and a Linux container approach. Then, we implement PrivateDroid, which creates a new sandbox for every application in private mode and destroys the sandbox once the application is closed. After that, we evaluate usability, efficiency and security of the system with 25 popular Android applications. Our design considerations, implementation details, evaluation results, and challenges lay a foundation of private browsing mode on mobile platforms. Index Terms—Mobile Privacy, Private Browsing Mode I

A two-dimensional angular-resolved proton spectrometer

We present a novel design of two-dimensional (2D) angular-resolved spectrometer for full beam characterization of ultrashort intense laser driven proton sources. A rotated 2D pinhole array was employed, as selective entrance before a pair of parallel permanent magnets, to sample the full proton beam into discrete beamlets. The proton beamlets are subsequently dispersed without overlapping onto a planar detector. Representative experimental result of protons generated from femtosecond intense laser interaction with thin foil target is presented

A facial depression recognition method based on hybrid multi-head cross attention network

IntroductionDeep-learn methods based on convolutional neural networks (CNNs) have demonstrated impressive performance in depression analysis. Nevertheless, some critical challenges need to be resolved in these methods: (1) It is still difficult for CNNs to learn long-range inductive biases in the low-level feature extraction of different facial regions because of the spatial locality. (2) It is difficult for a model with only a single attention head to concentrate on various parts of the face simultaneously, leading to less sensitivity to other important facial regions associated with depression. In the case of facial depression recognition, many of the clues come from a few areas of the face simultaneously, e.g., the mouth and eyes.MethodsTo address these issues, we present an end-to-end integrated framework called Hybrid Multi-head Cross Attention Network (HMHN), which includes two stages. The first stage consists of the Grid-Wise Attention block (GWA) and Deep Feature Fusion block (DFF) for the low-level visual depression feature learning. In the second stage, we obtain the global representation by encoding high-order interactions among local features with Multi-head Cross Attention block (MAB) and Attention Fusion block (AFB).ResultsWe experimented on AVEC2013 and AVEC2014 depression datasets. The results of AVEC 2013 (RMSE = 7.38, MAE = 6.05) and AVEC 2014 (RMSE = 7.60, MAE = 6.01) demonstrated the efficacy of our method and outperformed most of the state-of-the-art video-based depression recognition approaches.DiscussionWe proposed a deep learning hybrid model for depression recognition by capturing the higher-order interactions between the depression features of multiple facial regions, which can effectively reduce the error in depression recognition and gives great potential for clinical experiments