WeakIdent: Weak formulation for Identifying Differential Equations using Narrow-fit and Trimming

Data-driven identification of differential equations is an interesting but challenging problem, especially when the given data are corrupted by noise. When the governing differential equation is a linear combination of various differential terms, the identification problem can be formulated as solving a linear system, with the feature matrix consisting of linear and nonlinear terms multiplied by a coefficient vector. This product is equal to the time derivative term, and thus generates dynamical behaviors. The goal is to identify the correct terms that form the equation to capture the dynamics of the given data. We propose a general and robust framework to recover differential equations using a weak formulation, for both ordinary and partial differential equations (ODEs and PDEs). The weak formulation facilitates an efficient and robust way to handle noise. For a robust recovery against noise and the choice of hyper-parameters, we introduce two new mechanisms, narrow-fit and trimming, for the coefficient support and value recovery, respectively. For each sparsity level, Subspace Pursuit is utilized to find an initial set of support from the large dictionary. Then, we focus on highly dynamic regions (rows of the feature matrix), and error normalize the feature matrix in the narrow-fit step. The support is further updated via trimming of the terms that contribute the least. Finally, the support set of features with the smallest Cross-Validation error is chosen as the result. A comprehensive set of numerical experiments are presented for both systems of ODEs and PDEs with various noise levels. The proposed method gives a robust recovery of the coefficients, and a significant denoising effect which can handle up to $100\%$ noise-to-signal ratio for some equations. We compare the proposed method with several state-of-the-art algorithms for the recovery of differential equations

Fourier Features for Identifying Differential Equations (FourierIdent)

We investigate the benefits and challenges of utilizing the frequency information in differential equation identification. Solving differential equations and Fourier analysis are closely related, yet there is limited work in exploring this connection in the identification of differential equations. Given a single realization of the differential equation perturbed by noise, we aim to identify the underlying differential equation governed by a linear combination of linear and nonlinear differential and polynomial terms in the frequency domain. This is challenging due to large magnitudes and sensitivity to noise. We introduce a Fourier feature denoising, and define the meaningful data region and the core regions of features to reduce the effect of noise in the frequency domain. We use Subspace Pursuit on the core region of the time derivative feature, and introduce a group trimming step to refine the support. We further introduce a new energy based on the core regions of features for coefficient identification. Utilizing the core regions of features serves two critical purposes: eliminating the low-response regions dominated by noise, and enhancing the accuracy in coefficient identification. The proposed method is tested on various differential equations with linear, nonlinear, and high-order derivative feature terms. Our results demonstrate the advantages of the proposed method, particularly on complex and highly corrupted datasets

Research on Warnings with New Thought of Neuro-IE

AbstractSafety production is a seriously stubborn problem in modern industry engineering. Warnings, as the most fundamental and important measure used in safety management, especially in Mine Exploitation, have played a vital role in risk cognition, behaviors guide and accidents prevention. However, traditional researches are so subjective that it's hard to deeply explore the inner mechanism and process, which has been hidden behind the outer behaviors. As a result, the effectiveness of Warnings is much discounted. In this paper, we make use of neuroscience methods to study Warnings from the basically cognitive levels and have acquired preliminary achievements, which provide new evidence, discussion and introductions for former researches

Inherent P2X7 Receptors Regulate Macrophage Functions during Inflammatory Diseases

Macrophages are mononuclear phagocytes which derive either from blood-borne monocytes or reside as resident macrophages in peripheral (Kupffer cells of the liver, marginal zone macrophages of the spleen, alveolar macrophages of the lung) and central tissue (microglia). They occur as M1 (pro-inflammatory; classic) or M2 (anti-inflammatory; alternatively activated) phenotypes. Macrophages possess P2X7 receptors (Rs) which respond to high concentrations of extracellular ATP under pathological conditions by allowing the non-selective fluxes of cations (Na+, Ca2+, K+). Activation of P2X7Rs by still higher concentrations of ATP, especially after repetitive agonist application, leads to the opening of membrane pores permeable to ~900 Da molecules. For this effect an interaction of the P2X7R with a range of other membrane channels (e.g., P2X4R, transient receptor potential A1 [TRPA1], pannexin-1 hemichannel, ANO6 chloride channel) is required. Macrophagelocalized P2X7Rs have to be co-activated with the lipopolysaccharide-sensitive toll-like receptor 4 (TLR4) in order to induce the formation of the inflammasome 3 (NLRP3), which then activates the pro-interleukin-1 (pro-IL-1)-degrading caspase-1 to lead to IL-1 release. Moreover, inflammatory diseases (e.g., rheumatoid arthritis, Crohn’s disease, sepsis, etc.) are generated downstream of the P2X7R-induced upregulation of intracellular second messengers (e.g., phospholipase A2, p38 mitogen-activated kinase, and rho G proteins). In conclusion, P2X7Rs at macrophages appear to be important targets to preserve immune homeostasis with possible therapeutic consequences

System-on-Chip Packet Processor for an Experimental Network Services Platform

As the focus of networking research shifts from raw performance to the delivery of advanced network services, there is a growing need for open-platform systems for extensible networking research. The Applied Research Laboratory at Washington University in Saint Louis has developed a flexible Network Services Platform (NSP) to meet this need. The NSP provides an extensible platform for prototyping next-generation network services and applications. This paper describes the design of a system-on-chip Packet Processor for the NSP which performs all core packet processing functions including segmentation and reassembly, packet classification, route lookup, and queue management. Targeted to a commercial configurable logic device, the system is designed to support gigabit links and switch fabrics with a 2:1 speed advantage. We provide resource consumption results for each component of the Packet Processor design

Long Non-Coding RNA TUG1 Attenuates Insulin Resistance in Mice with Gestational Diabetes Mellitus via Regulation of the MicroRNA-328-3p/SREBP-2/ERK Axis

Background Long non-coding RNAs (lncRNAs) have been illustrated to contribute to the development of gestational diabetes mellitus (GDM). In the present study, we aimed to elucidate how lncRNA taurine upregulated gene 1 (TUG1) influences insulin resistance (IR) in a high-fat diet (HFD)-induced mouse model of GDM. Methods We initially developed a mouse model of HFD-induced GDM, from which islet tissues were collected for RNA and protein extraction. Interactions among lncRNA TUG1/microRNA (miR)-328-3p/sterol regulatory element binding protein 2 (SREBP-2) were assessed by dual-luciferase reporter assay. Fasting blood glucose (FBG), fasting insulin (FINS), homeostasis model assessment of insulin resistance (HOMA-IR), HOMA pancreatic β-cell function (HOMA-β), insulin sensitivity index for oral glucose tolerance tests (ISOGTT) and insulinogenic index (IGI) levels in mouse serum were measured through conducting gain- and loss-of-function experiments. Results Abundant expression of miR-328 and deficient expression of lncRNA TUG1 and SREBP-2 were characterized in the islet tissues of mice with HFD-induced GDM. LncRNA TUG1 competitively bound to miR-328-3p, which specifically targeted SREBP-2. Either depletion of miR-328-3p or restoration of lncRNA TUG1 and SREBP-2 reduced the FBG, FINS, HOMA-β, and HOMA-IR levels while increasing ISOGTT and IGI levels, promoting the expression of the extracellular signal-regulated kinase (ERK) signaling pathway-related genes, and inhibiting apoptosis of islet cells in GDM mice. Upregulation miR-328-3p reversed the alleviative effects of SREBP-2 and lncRNA TUG1 on IR. Conclusion Our study provides evidence that the lncRNA TUG1 may prevent IR following GDM through competitively binding to miR-328-3p and promoting the SREBP-2-mediated ERK signaling pathway inactivation

Novel Parameterized Utility Function on Dual Hesitant Fuzzy Rough Sets and Its Application in Pattern Recognition

Based on comparative studies on correlation coefficient theory and utility theory, a series of rules that utility functions on dual hesitant fuzzy rough sets (DHFRSs) should satisfy, and a kind of novel utility function on DHFRSs are proposed. The characteristic of the introduced utility function is a parameter, which is determined by decision-makers according to their experiences. By using the proposed utility function on DHFRSs, a novel dual hesitant fuzzy rough pattern recognition method is also proposed. Furthermore, this study also points out that the classical dual tool is suitable to cope with dynamic data in exploratory data analysis situations, while the newly proposed one is suitable to cope with static data in confirmatory data analysis situations. Finally, a medical diagnosis and a traffic engineering example are introduced to reveal the effectiveness of the newly proposed utility functions on DHFRSs. Document type: Articl

New Algorithms for Secure Outsourcing of Modular Exponentiations

With the rapid development in availability of cloud services, the techniques for securely outsourcing the prohibitively expensive computations to untrusted servers are getting more and more attentions in the scientific community. Exponentiations modulo a large prime have been considered the most expensive operation in discrete-logarithm based cryptographic protocols, and the computationally limited devices such as RFID tags or smartcard may be incapable to accomplish these operations. Therefore, it is meaningful to present an efficient method to securely outsource most of this work-load to (untrusted) cloud servers. In this paper, we propose a new secure outsourcing algorithm for (variable-exponent, variable-base) exponentiation modular a prime in the two untrusted program model. Compared with the state-of-the-art algorithm \cite{HL05}, the proposed algorithm is superior in both efficiency and checkability. We then utilize this algorithm as a subroutine to achieve outsource-secure Cramer-Shoup encryptions and Schnorr signatures. Besides, we propose the first outsource-secure and efficient algorithm for simultaneous modular exponentiations. Moreover, we formally prove that both the algorithms can achieve the desired security notions. We also provide the experimental evaluation that demonstrates the efficiency and effectiveness of the proposed outsourcing algorithms and schemes