DualApp: Tight Over-Approximation for Neural Network Robustness Verification via Under-Approximation

The robustness of neural networks is fundamental to the hosting system's reliability and security. Formal verification has been proven to be effective in providing provable robustness guarantees. To improve the verification scalability, over-approximating the non-linear activation functions in neural networks by linear constraints is widely adopted, which transforms the verification problem into an efficiently solvable linear programming problem. As over-approximations inevitably introduce overestimation, many efforts have been dedicated to defining the tightest possible approximations. Recent studies have however showed that the existing so-called tightest approximations are superior to each other. In this paper we identify and report an crucial factor in defining tight approximations, namely the approximation domains of activation functions. We observe that existing approaches only rely on overestimated domains, while the corresponding tight approximation may not necessarily be tight on its actual domain. We propose a novel under-approximation-guided approach, called dual-approximation, to define tight over-approximations and two complementary under-approximation algorithms based on sampling and gradient descent. The overestimated domain guarantees the soundness while the underestimated one guides the tightness. We implement our approach into a tool called DualApp and extensively evaluate it on a comprehensive benchmark of 84 collected and trained neural networks with different architectures. The experimental results show that DualApp outperforms the state-of-the-art approximation-based approaches, with up to 71.22% improvement to the verification result.Comment: 13 pages, 9 fugures, 3 table

BBReach: Tight and Scalable Black-Box Reachability Analysis of Deep Reinforcement Learning Systems

Reachability analysis is a promising technique to automatically prove or disprove the reliability and safety of AI-empowered software systems that are developed by using Deep Reinforcement Learning (DRL). Existing approaches suffer however from limited scalability and large overestimation as they must over-approximate the complex and almost inexplicable system components, namely deep neural networks (DNNs). In this paper we propose a novel, tight and scalable reachability analysis approach for DRL systems. By training on abstract states, our approach treats the embedded DNNs as black boxes to avoid the over-approximation for neural networks in computing reachable sets. To tackle the state explosion problem inherent to abstraction-based approaches, we devise a novel adjacent interval aggregation algorithm which balances the growth of abstract states and the overestimation caused by the abstraction. We implement a tool, called BBReach, and assess it on an extensive benchmark of control systems to demonstrate its tightness, scalability, and efficiency

Kerr-Sen Black Hole as Accelerator for Spinning Particles

It has been proved that arbitrarily high-energy collision between two particles can occur near the horizon of an extremal Kerr black hole as long as the energy $E$ and angular momentum $L$ of one particle satisfies a critical relation, which is called the BSW mechanism. Previous researchers mainly concentrate on geodesic motion of particles. In this paper, we will take spinning particle which won't move along a timelike geodesic into our consideration, hence, another parameter $s$ describing the particle's spin angular momentum was introduced. By employing the Mathisson-Papapetrou-Dixon equation describing the movement of spinning particle, we will explore whether a Kerr-Sen black hole which is slightly different from Kerr black hole can be used to accelerate a spinning particle to arbitrarily high energy. We found that when one of the two colliding particles satisfies a critical relation between the energy $E$ and the total angular momentum $J$, or has a critical spinning angular momentum $s_c$, a divergence of the center-of-mass energy $E_{cm}$ will be obtained.Comment: Latex,17 pages,1 figure,minor revision,accepted by PR

1-Methyl-1H-indazole-3-carboxylic acid

The asymmetric unit of the title compound, C9H8N2O2, contains two mol­ecules. In the crystal structure, both mol­ecules form inversion dimers via pairs of O—H⋯O hydrogen bonds, and a C—H⋯O inter­ation is also seen

Identification of the chemical components of ethanol extract of Chenopodium ambrosioides and evaluation of their in vitro antioxidant and anti tumor activities

Purpose: To determine the characteristic chemical components of the ethanol extract of Chenopodium ambrosioides and evaluate their antioxidant and anti-tumor effects in vitro. Methods: The plant powder (5 g) was extracted with 1 L of 80 % ethanol at room temperature for 45 min, and then placed at 60 oC at varying microwave power and duration to obtain optimal extraction conditions. Characteristic chemical components were detected using ultra-high performance liquid chromatography quadrupole time of flight mass spectrometry (UPLC-Q-TOF-MS/MS). Kaempferitrin was isolated from the 80 % ethanol extract using a D101 macroporous resin column, and its content was assessed by high performance liquid chromatography (HPLC). The antioxidant effect of kaempferitrin was evaluated by its ability to scavenge 2,2-diphenyl-1-picrylhydrazyl (DPPH) and 2,2'-azinobis-(3-ethylbenzthiazoline-6-sulphonate) (ABTS) radicals, while its anti-proliferation activity in human liver cancer cells SMMC-7721 was determined using cell counting kit-8 (CCK-8) reagent. Results: Three characteristic components of ethanol extract of C. ambrosioides were obtained, namely, kaempferitrin, kaempferol-3-O-apigenin-7-O-rhamnoside and kaempferol-3-O-acetylapigenin-7-O-rhamnoside. Kaempferitrin was shown to possess strong DPPH radical and moderate ABTS radical scavenging activities. Kaempferitrin significantly inhibited the proliferation of SMMC-7721 cells at doses of 4 and 8 μg/mL, with half-maximal concentration (IC50) of 0.38 μM (p < 0.05). Conclusion: Kaempferitrin extracted from C. ambrosioides has antioxidant and anti-tumor activities. The results reported here indicate that C. ambrosioides may have potential use in herbal medicine practice

Enhancement of thermophilic anaerobic sludge digestion by 70ºC pre-treatment : energy considerations

The objective of this work was to investigate the effect of a low temperature pre-treatment (70°C) on the thermophilic anaerobic digestion of sewage sludge. Experimental results were used for the calculation of theoretical energy balances of full-scale digesters with and without pre-treatment step. The 70°C sludge pre-treatment increased sludge solubilization by 10 times and enhanced volatile fatty acids generation. Biogas production increased up to 30-40% and methane content in biogas from 64 to 68-70%. Theoretical calculations showed that additional surplus energy production would be expected by incorporating a 70°C pre-treatment step to a thermophilic reactor