Pointwise wave behavior of the Navier-Stokes equations in half space

In this paper, we investigate the pointwise behavior of the solution for the compressible Navier-Stokes equations with mixed boundary condition in half space. Our results show that the leading order of Green's function for the linear system in half space are heat kernels propagating with sound speed in two opposite directions and reflected heat kernel (due to the boundary effect) propagating with positive sound speed. With the strong wave interactions, the nonlinear analysis exhibits the rich wave structure: the diffusion waves interact with each other and consequently, the solution decays with algebraic rate.Comment: Comments and references are added and some typos are corrected. Accepted by DCDS-

Pointwise wave behavior of the Navier-Stokes equations in half space

In this paper, we investigate the pointwise behavior of the solution for the compressible Navier-Stokes equations with mixed boundary condition in half space. Our results show that the leading order of Green's function for the linear system in half space are heat kernels propagating with sound speed in two opposite directions and reflected heat kernel (due to the boundary effect) propagating with positive sound speed. With the strong wave interactions, the nonlinear analysis exhibits the rich wave structure: the diffusion waves interact with each other and consequently, the solution decays with algebraic rate.Comment: Comments and references are added and some typos are corrected. Accepted by DCDS-

Probabilistic Modeling and Inference for Obfuscated Network Attack Sequences

Prevalent computing devices with networking capabilities have become critical network infrastructure for government, industry, academia and every-day life. As their value rises, the motivation driving network attacks on this infrastructure has shifted from the pursuit of notoriety to the pursuit of profit or political gains, leading to network attack on various scales. Facing diverse network attack strategies and overwhelming alters, much work has been devoted to correlate observed malicious events to pre-defined scenarios, attempting to deduce the attack plans based on expert models of how network attacks may transpire. We started the exploration of characterizing network attacks by investigating how temporal and spatial features of attack sequence can be used to describe different types of attack sources in real data set. Attack sequence models were built from real data set to describe different attack strategies. Based on the probabilistic attack sequence model, attack predictions were made to actively predict next possible actions. Experiments through attack predictions have revealed that sophisticated attackers can employ a number of obfuscation techniques to confuse the alert correlation engine or classifier. Unfortunately, most exiting work treats attack obfuscations by developing ad-hoc fixes to specific obfuscation technique. To this end, we developed an attack modeling framework that enables a systematical analysis of obfuscations. The proposed framework represents network attack strategies as general finite order Markov models and integrates it with different attack obfuscation models to form probabilistic graphical model models. A set of algorithms is developed to inference the network attack strategies given the models and the observed sequences, which are likely to be obfuscated. The algorithms enable an efficient analysis of the impact of different obfuscation techniques and attack strategies, by determining the expected classification accuracy of the obfuscated sequences. The algorithms are developed by integrating the recursion concept in dynamic programming and the Monte-Carlo method. The primary contributions of this work include the development of the formal framework and the algorithms to evaluate the impact of attack obfuscations. Several knowledge-driven attack obfuscation models are developed and analyzed to demonstrate the impact of different types of commonly used obfuscation techniques. The framework and algorithms developed in this work can also be applied to other contexts beyond network security. Any behavior sequences that might suffer from noise and require matching to pre-defined models can use this work to recover the most likely original sequence or evaluate quantitatively the expected classification accuracy one can achieve to separate the sequences

THE EFFECTS OF STATIC STRETCHING AFTER STRENUOUS TRAINING ON ULTRASTRUCTURE AND FLEXIBILITY OF RATS' GASTROCNEMIUS

The purpose of the present study was to investigate effects of static stretching after strenuous training on the ultrastructure and flexibility of rats' gastrocnemius. 24 male Sprague-Dawley rats were randomly divided into three groups: normal control (NC), training control(TC) and stretching group(ST). The results were as follows: 1) The myofilaments became supercontracted and Z discs were obscure in TC. On the contrary, the myofilaments arranged orderly and the Z lines were clear and the mitochondrial cristas were manifolded in ST. 2) Compared with NC, the ultimate tensile strength of gastrocnemius was increased in TC, while the Max. deformation of gastorcnemius was decreased. However, the Max. deformation in ST was increased than that of NC. The conclusion was that the ultrastructure of muscle was resumed and the ability of distortion and flexibility was improved by static stretching, which decreased the risk of injury

A self-supported, flexible, binder-free pseudo-supercapacitor electrode material with high capacitance and cycling stability from hollow, capsular polypyrrole fibers

Flexible energy devices with high performance and long-term stability are highly promising for applications in portable electronics, but remain challenging to develop. As an electrode material for pseudo-supercapacitors, conducting polymers typically show higher energy storage ability over carbon materials and larger conductivity than transition-metal oxides. However, conducting polymer-based supercapacitors often have poor cycling stability, attributable to the structural rupture caused by the large volume contrast between doping and de-doping states, which has been the main obstacle to their practical applications. Herein, we report a simple method to prepare a flexible, binder-free, self-supported polypyrrole (PPy) supercapacitor electrode with high cycling stability through using novel, hollow PPy nanofibers with porous capsular walls as a film-forming material. The unique fiber structure and capsular walls provide the PPy film with enough free-space to adapt to volume variation during doping/de-doping, leading to super-high cycling stability (capacitance retention > 90% after 11000 charge-discharge cycles at a high current density of 10 A g-1) and high rate capability (capacitance retention ∼ 82.1% at a current density in the range of 0.25-10 A g-1)

Neuron with Steady Response Leads to Better Generalization

Regularization can mitigate the generalization gap between training and inference by introducing inductive bias. Existing works have already proposed various inductive biases from diverse perspectives. However, none of them explores inductive bias from the perspective of class-dependent response distribution of individual neurons. In this paper, we conduct a substantial analysis of the characteristics of such distribution. Based on the analysis results, we articulate the Neuron Steadiness Hypothesis: the neuron with similar responses to instances of the same class leads to better generalization. Accordingly, we propose a new regularization method called Neuron Steadiness Regularization (NSR) to reduce neuron intra-class response variance. Based on the Complexity Measure, we theoretically guarantee the effectiveness of NSR for improving generalization. We conduct extensive experiments on Multilayer Perceptron, Convolutional Neural Networks, and Graph Neural Networks with popular benchmark datasets of diverse domains, which show that our Neuron Steadiness Regularization consistently outperforms the vanilla version of models with significant gain and low additional computational overhead.Comment: Accepted by NeurIPS'2