A Galerkin boundary node method and its convergence analysis

AbstractThe boundary node method (BNM) exploits the dimensionality of the boundary integral equation (BIE) and the meshless attribute of the moving least-square (MLS) approximations. However, since MLS shape functions lack the property of a delta function, it is difficult to exactly satisfy boundary conditions in BNM. Besides, the system matrices of BNM are non-symmetric.A Galerkin boundary node method (GBNM) is proposed in this paper for solving boundary value problems. In this approach, an equivalent variational form of a BIE is used for representing the governing equation, and the trial and test functions of the variational formulation are generated by the MLS approximation. As a result, boundary conditions can be implemented accurately and the system matrices are symmetric. Total details of numerical implementation and error analysis are given for a general BIE. Taking the Dirichlet problem of Laplace equation as an example, we set up a framework for error estimates of GBNM. Some numerical examples are also given to demonstrate the efficacity of the method

Defense against Adversarial Attacks Using High-Level Representation Guided Denoiser

Neural networks are vulnerable to adversarial examples, which poses a threat to their application in security sensitive systems. We propose high-level representation guided denoiser (HGD) as a defense for image classification. Standard denoiser suffers from the error amplification effect, in which small residual adversarial noise is progressively amplified and leads to wrong classifications. HGD overcomes this problem by using a loss function defined as the difference between the target model's outputs activated by the clean image and denoised image. Compared with ensemble adversarial training which is the state-of-the-art defending method on large images, HGD has three advantages. First, with HGD as a defense, the target model is more robust to either white-box or black-box adversarial attacks. Second, HGD can be trained on a small subset of the images and generalizes well to other images and unseen classes. Third, HGD can be transferred to defend models other than the one guiding it. In NIPS competition on defense against adversarial attacks, our HGD solution won the first place and outperformed other models by a large margin

Excursion theory and local times for Bessel and Brownian diffusions: with applications to credit risk

By means of excursion theory, the evolution of a continuous Markov process satisfying regularity assumptions is analysed in terms of its behaviour between visits to a recurrent point, for instance the point zero in the state space of Brownian and Bessel diffusions of type reflecting at the origin. As a preliminary conclusion, a sample path of the process can be reconstructed by the excursions away from zero of random finite lengths and the time spent at visits to zero. These two together constitute the core of the work in this thesis. With respect to the zero-free intervals, we study the duration of the excursion in process away from zero by time t, namely the age process, of a Bessel process instantaneously reflected at the origin. The main contribution of our work is the development of a hybrid structural-reduced form model with an endogenous intensity defined by the age process. This model provides a framework for assessing default probabilities within a circumstance of very limited information, assuming that some statistics about a firm are not observable but the time points when they reach certain level are. Results presented include distributional properties for the default time and level as a joint stopping process, by which we discover a decomposition theorem that contributes to exact schemes for simulating the default process. A counting process for monitoring consecutive arrivals of some event driven by the same intensity is also established. Main aspects to be addressed are the properties and the derivations of distributional quantities concerning the interarrival times, the arrival of the nth event and the associated counting process. With respect to the zero set, we construct a continuous family of functionals for the part of time spent at the origin by the age process, namely the local time at zero. It is a well known fact that there is no unified representation for the local time of Markov process, as it can be approximated as a limit of various processes describing the behaviour of trajectories of the underlying process. That being so, the focus and efforts are put on the certain properties of the limit processes served as the approximations, and on the first and second order limit theorems for the convergences to the local time

Learning Fast and Slow: PROPEDEUTICA for Real-time Malware Detection

In this paper, we introduce and evaluate PROPEDEUTICA, a novel methodology and framework for efficient and effective real-time malware detection, leveraging the best of conventional machine learning (ML) and deep learning (DL) algorithms. In PROPEDEUTICA, all software processes in the system start execution subjected to a conventional ML detector for fast classification. If a piece of software receives a borderline classification, it is subjected to further analysis via more performance expensive and more accurate DL methods, via our newly proposed DL algorithm DEEPMALWARE. Further, we introduce delays to the execution of software subjected to deep learning analysis as a way to "buy time" for DL analysis and to rate-limit the impact of possible malware in the system. We evaluated PROPEDEUTICA with a set of 9,115 malware samples and 877 commonly used benign software samples from various categories for the Windows OS. Our results show that the false positive rate for conventional ML methods can reach 20%, and for modern DL methods it is usually below 6%. However, the classification time for DL can be 100X longer than conventional ML methods. PROPEDEUTICA improved the detection F1-score from 77.54% (conventional ML method) to 90.25%, and reduced the detection time by 54.86%. Further, the percentage of software subjected to DL analysis was approximately 40% on average. Further, the application of delays in software subjected to ML reduced the detection time by approximately 10%. Finally, we found and discussed a discrepancy between the detection accuracy offline (analysis after all traces are collected) and on-the-fly (analysis in tandem with trace collection). Our insights show that conventional ML and modern DL-based malware detectors in isolation cannot meet the needs of efficient and effective malware detection: high accuracy, low false positive rate, and short classification time.Comment: 17 pages, 7 figure

Anodic Nanostructures for Solar Cell Applications

As a versatile, straightforward, and cost-effective strategy for the synthesis of self-organized nanomaterials, electrochemical anodization is nowadays frequently used to synthesize anodic metal oxide nanostructures for various solar cell applications. This chapter mainly discusses the synthesis of various anodic TiO2 nanostructures on foils and as membranes or powders, and their potential use as the photoanode materials based on foils, transparent conductive oxide substrates, and flexible substrates in dye-sensitized solar cell applications, acting as dye-loading frames, light-harvesting enhancement assembly, and electron transport medium. Through the control and modulation of the electrical and chemical parameters of electrochemical anodization process, such as applied voltages, currents, bath temperatures, electrolyte composition, or post-treatments, anodic nanostructures with controllable structures and geometries and unique optical, electronic, and photoelectric properties in solar cell applications can be obtained. Compared with other types of nanostructures, there are several major advantages for anodic nanostructures to be used in solar cells. They are (1) optimized solar cell configuration to achieve efficient light utilization; (2) easy fabrication of large size nanostructures to enhance light scattering; (3) precise modulation of the electrochemical processes to realize periodic nanostructured geometry with excellent optical properties; (4) unidirectional electron transport pathways with suppressed charge recombination; and (5) large surface areas by modification of nanostructures. Due to the simple fabrication processes and unique properties, the anodic nanostructures will have a fascinating future to boost the solar cell performances

Amplification trojan network: Attack deep neural networks by amplifying their inherent weakness

Recent works found that deep neural networks (DNNs) can be fooled by adversarial examples, which are crafted by adding adversarial noise on clean inputs. The accuracy of DNNs on adversarial examples will decrease as the magnitude of the adversarial noise increase. In this study, we show that DNNs can be also fooled when the noise is very small under certain circumstances. This new type of attack is called Amplification Trojan Attack (ATAttack). Specifically, we use a trojan network to transform the inputs before sending them to the target DNN. This trojan network serves as an amplifier to amplify the inherent weakness of the target DNN. The target DNN, which is infected by the trojan network, performs normally on clean data while being more vulnerable to adversarial examples. Since it only transforms the inputs, the trojan network can hide in DNN-based pipelines, e.g. by infecting the pre-processing procedure of the inputs before sending them to the DNNs. This new type of threat should be considered in developing safe DNNs.Comment: Published Sep 2022 in Neurocomputin