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In this paper we prove gradient estimates of both elliptic and parabolic types, specifically, of Souplet-Zhang, Hamilton and Li-Yau types for positive smooth solutions to a class of nonlinear parabolic equations involving the Witten or drifting Laplacian on smooth metric measure spaces. These estimates are established under various curvature conditions and lower bounds on the generalised Bakry-\'Emery Ricci tensor and find utility in proving elliptic and parabolic Harnack-type inequalities as well as general elliptic and parabolic Liouville-type and other global constancy results. Several applications and consequences are presented and discussed., Comment: 44 pages

In this article we present new gradient estimates for positive solutions to a class of nonlinear elliptic equations involving the f-Laplacian on a smooth metric measure space. The gradient estimates of interest are of Souplet-Zhang and Hamilton types respectively and are established under natural lower bounds on the generalised Bakry-\'Emery Ricci curvature tensor. From these estimates we derive amongst other things Harnack inequalities and general global constancy and Liouville-type theorems. The results and approach undertaken here provide a unified treatment and extend and improve various existing results in the literature. Some implications and applications are presented and discussed., Comment: 27 pages

This article presents new parabolic and elliptic type gradient estimates for positive smooth solutions to a nonlinear parabolic equation involving the Witten Laplacian in the context of smooth metric measure spaces. The metric and potential here are time dependent and evolve under a super Perelman-Ricci flow. The estimates are derived under natural lower bounds on the associated generalised Bakry-\'Emery Ricci curvature tensors and are utilised in establishing fairly general local and global bounds, Harnack-type inequalities and Liouville-type global constancy theorems to mention a few. Other implications and consequences of the results are also discussed., Comment: 41 pages

This article presents new local and global gradient estimates of Li-Yau type for positive solutions to a class of nonlinear elliptic equations on smooth metric measure spaces involving the Witten Laplacian. The estimates are derived under natural lower bounds on the associated Bakry-\'Emery Ricci curvature tensor and find utility in proving general Harnack inequalities and Liouville-type theorems to mention a few. The results here unify, extend and improve various existing results in the literature for special nonlinearities already of huge interest and applications. Some important consequences are presented and discussed., Comment: 20 pages

The aim of this paper is to prove the existence of multiple solutions for a family of nonlinear elliptic systems in divergence form coupled with a pointwise gradient constraint: \begin{align*} \left\{ \begin{array}{ll} \dive\{\A(|x|,|u|^2,|\nabla u|^2) \nabla u\} + \B(|x|,|u|^2,|\nabla u|^2) u = \dive \{ \mcP(x) [{\rm cof}\,\nabla u] \} \quad &\text{ in} \ \Omega , \\ \text{det}\, \nabla u = 1 \ &\text{ in} \ \Omega , \\ u =\varphi \ &\text{ on} \ \partial \Omega, \end{array} \right. \end{align*} where $\Omega \subset \mathbb{R}^n$ ($n \ge 2$) is a bounded domain, $u=(u_1, \dots, u_n)$ is a vector-map and $\varphi$ is a prescribed boundary condition. Moreover $\mathscr{P}$ is a hydrostatic pressure associated with the constraint $\det \nabla u \equiv 1$ and $\A = \A(|x|,|u|^2,|\nabla u|^2)$, $\B = \B(|x|,|u|^2,|\nabla u|^2)$ are sufficiently regular scalar-valued functions satisfying suitable growths at infinity. The system arises in diverse areas, e.g., in continuum mechanics and nonlinear elasticity, as well as geometric function theory to name a few and a clear understanding of the form and structure of the solutions set is of great significance. The geometric type of solutions constructed here draws upon intimate links with the Lie group ${\bf SO}(n)$, its Lie exponential and the multi-dimensional curl operator acting on certain vector fields. Most notably a discriminant type quantity $\Delta=\Delta(\A,\B)$, prompting from the PDE, will be shown to have a decisive role on the structure and multiplicity of these solutions., Comment: 24 pages

Solid-State Drives (SSDs) have significant performance advantages over traditional Hard Disk Drives (HDDs) such as lower latency and higher throughput. Significantly higher price per capacity and limited lifetime, however, prevents designers to completely substitute HDDs by SSDs in enterprise storage systems. SSD-based caching has recently been suggested for storage systems to benefit from higher performance of SSDs while minimizing the overall cost. While conventional caching algorithms such as Least Recently Used (LRU) provide high hit ratio in processors, due to the highly random behavior of Input/Output (I/O) workloads, they hardly provide the required performance level for storage systems. In addition to poor performance, inefficient algorithms also shorten SSD lifetime with unnecessary cache replacements. Such shortcomings motivate us to benefit from more complex non-linear algorithms to achieve higher cache performance and extend SSD lifetime. In this paper, we propose RC-RNN, the first reconfigurable SSD-based cache architecture for storage systems that utilizes machine learning to identify performance-critical data pages for I/O caching. The proposed architecture uses Recurrent Neural Networks (RNN) to characterize ongoing workloads and optimize itself towards higher cache performance while improving SSD lifetime. RC-RNN attempts to learn characteristics of the running workload to predict its behavior and then uses the collected information to identify performance-critical data pages to fetch into the cache. Experimental results show that RC-RNN characterizes workloads with an accuracy up to 94.6% for SNIA I/O workloads. RC-RNN can perform similarly to the optimal cache algorithm by an accuracy of 95% on average, and outperforms previous SSD caching architectures by providing up to 7x higher hit ratio and decreasing cache replacements by up to 2x., Comment: Date of Publication: 09 August 2021

Protecting users' privacy over the Internet is of great importance; however, it becomes harder and harder to maintain due to the increasing complexity of network protocols and components. Therefore, investigating and understanding how data is leaked from the information transmission platforms and protocols can lead us to a more secure environment. In this paper, we propose a framework to systematically find the most vulnerable information fields in a network protocol. To this end, focusing on the transport layer security (TLS) protocol, we perform different machine-learning-based fingerprinting attacks on the collected data from more than 70 domains (websites) to understand how and where this information leakage occurs in the TLS protocol. Then, by employing the interpretation techniques developed in the machine learning community and applying our framework, we find the most vulnerable information fields in the TLS protocol. Our findings demonstrate that the TLS handshake (which is mainly unencrypted), the TLS record length appearing in the TLS application data header, and the initialization vector (IV) field are among the most critical leaker parts in this protocol, respectively.

Coiled Carbon Nanotubes (CCNTs) are increasingly set to become a vital factor in the new generation of nanodevices and energy-absorbing materials due to their outstanding properties. In the following work, the multi-objective optimization of CCNTs is applied regarding their mechanical performances. Apart from finding the best trade-off between conflicting mechanical properties (e.g. yield stress and yield strain), the optimization enables us to find the astonishing CCNTs concerning their stretchability. To the best of our knowledge, these structures have not been recognized before, both experimentally and computationally. Several highly accurate analytical equations are derived by insights from the findings of multi-objective optimization and fitting a theoretical model to the results of Molecular Dynamics (MD) simulations. The structures resulted from optimizations are highly resilient because of two distinct deformation mechanisms depending on the dimensions of CCNTs. For small CCNTs, extraordinary extensibility is mainly contributed by buckling and nanohinge-like deformation with maintaining the inner coil diameter, whereas for large CCNTs this is accomplished by the creation of a straight CNT-like structure in the inner-edge of the CCNT with a helical graphene ribbon twisted around it. These findings would shed light on the design of CCNT based mechanical nanodevices., Comment: 31 pages, 13 figures, 2 tables

We present and evaluate Deep Private-Feature Extractor (DPFE), a deep model which is trained and evaluated based on information theoretic constraints. Using the selective exchange of information between a user's device and a service provider, DPFE enables the user to prevent certain sensitive information from being shared with a service provider, while allowing them to extract approved information using their model. We introduce and utilize the log-rank privacy, a novel measure to assess the effectiveness of DPFE in removing sensitive information and compare different models based on their accuracy-privacy tradeoff. We then implement and evaluate the performance of DPFE on smartphones to understand its complexity, resource demands, and efficiency tradeoffs. Our results on benchmark image datasets demonstrate that under moderate resource utilization, DPFE can achieve high accuracy for primary tasks while preserving the privacy of sensitive features.

Deep neural networks are increasingly being used in a variety of machine learning applications applied to rich user data on the cloud. However, this approach introduces a number of privacy and efficiency challenges, as the cloud operator can perform secondary inferences on the available data. Recently, advances in edge processing have paved the way for more efficient, and private, data processing at the source for simple tasks and lighter models, though they remain a challenge for larger, and more complicated models. In this paper, we present a hybrid approach for breaking down large, complex deep models for cooperative, privacy-preserving analytics. We do this by breaking down the popular deep architectures and fine-tune them in a particular way. We then evaluate the privacy benefits of this approach based on the information exposed to the cloud service. We also asses the local inference cost of different layers on a modern handset for mobile applications. Our evaluations show that by using certain kind of fine-tuning and embedding techniques and at a small processing costs, we can greatly reduce the level of information available to unintended tasks applied to the data feature on the cloud, and hence achieving the desired tradeoff between privacy and performance., Comment: arXiv admin note: substantial text overlap with arXiv:1703.02952

Internet of Things (IoT) devices and applications are being deployed in our homes and workplaces. These devices often rely on continuous data collection to feed machine learning models. However, this approach introduces several privacy and efficiency challenges, as the service operator can perform unwanted inferences on the available data. Recently, advances in edge processing have paved the way for more efficient, and private, data processing at the source for simple tasks and lighter models, though they remain a challenge for larger, and more complicated models. In this paper, we present a hybrid approach for breaking down large, complex deep neural networks for cooperative, privacy-preserving analytics. To this end, instead of performing the whole operation on the cloud, we let an IoT device to run the initial layers of the neural network, and then send the output to the cloud to feed the remaining layers and produce the final result. In order to ensure that the user's device contains no extra information except what is necessary for the main task and preventing any secondary inference on the data, we introduce Siamese fine-tuning. We evaluate the privacy benefits of this approach based on the information exposed to the cloud service. We also assess the local inference cost of different layers on a modern handset. Our evaluations show that by using Siamese fine-tuning and at a small processing cost, we can greatly reduce the level of unnecessary, potentially sensitive information in the personal data, and thus achieving the desired trade-off between utility, privacy, and performance., Comment: To appear in IEEE Internet of Things Journal

We examine the asymptotics of the spectral counting function of a compact Riemannian manifold by V.G.~Avakumovic \cite{Avakumovic} and L.~H\"ormander \cite{Hormander-eigen} and show that for the scale of orthogonal and unitary groups ${\bf SO}(N)$, ${\bf SU}(N)$, ${\bf U}(N)$ and ${\bf Spin}(N)$ it is not sharp. While for negative sectional curvature improvements are possible and known, {\it cf.} e.g., J.J.~Duistermaat $\&$ V.~Guillemin \cite{Duist-Guill}, here, we give sharp and contrasting examples in the positive Ricci curvature case [non-negative for ${\bf U}(N)$]. Furthermore here the improvements are sharp and quantitative relating to the dimension and {\it rank} of the group. We discuss the implications of these results on the closely related problem of closed geodesics and the length spectrum.

Let $\X = \X[a, b] = \{x: a<|x|

We carry out molecular dynamics simulations of nanoindentation to investigate the effect of cementite size and temperature on the deformation behavior of nanocomposite pearlite composed of alternating ferrite and cementite layers. We find that, instead of the coherent transmission, dislocation propagates by forming a widespread plastic deformation in cementite layer. We also show that increasing temperature enhances the distribution of plastic strain in the ferrite layer, which reduces the stress acting on the cementite layer. Hence, thickening cementite layer or increasing temperature reduces the likelihood of dislocation propagation through the cementite layer. Our finding sheds a light on the mechanism of dislocation blocking by cementite layer in the pearlite.