Classification of solutions for the planar isotropic LpL_p dual Minkowski problem

In his beautiful paper [1], Ben Andrews obtained the complete classification of the solutions of the planar isotropic $L_p$ Minkowski problem. In this paper, by generalizing Ben Andrews's result we obtain the complete classification of the solutions of the planar isotropic $L_p$ dual Minkowski problem, that is, for any $p,q\in\mathbb{R}$ we obtain the complete classification of the solutions of the following equation: \begin{equation*} u^{1-p}(u_{\theta}^2+u^2)^{\frac{q-2}{2}}(u_{\theta\theta}+u)=1\quad\text{on}\ \mathbb{S}^1. \end{equation*} To establish the classification, we convert the ODE for the solution into an integral and study its asymptotic behavior, duality and monotonicity.Comment: 30 pages, 2 figures. All comments are welcome. We add a reference by Liu-Lu who studied the case $p=0$ (or $q=0$

Asymptotic sign free in interacting fermion models

As an intrinsically-unbiased approach, quantum Monte Carlo (QMC) is of vital importance in understanding correlated phases of matter. Unfortunately, it often suffers notorious sign problem when simulating interacting fermion models. Here, we show for the first time that there exist interacting fermion models whose sign problem becomes less severe for larger system sizes and eventually disappears in the thermodynamic limit, which we dub as "asymptotic sign free". We demonstrate asymptotically-free sign in determinant QMC for various interacting models. Moreover, based on renormalization-group-like ideas we propose a heuristic understanding of the feature of asymptotic sign free. We believe that asymptotic sign free behavior could shed new lights to deepening our understanding of sign problem. More importantly, it can provide a promising way to decipher intriguing physics in correlated models which were conventionally thought not accessible by QMC.Comment: 4.5 pages plus supplemental material, 5 figure

Compared Insights on Machine-Learning Anomaly Detection for Process Control Feature

Anomaly detection is becoming increasingly significant in industrial cyber security, and different machine-learning algorithms have been generally acknowledged as various effective intrusion detection engines to successfully identify cyber attacks. However, different machine-learning algorithms may exhibit their own detection effects even if they analyze the same feature samples. As a sequence, after developing one feature generation approach, the most effective and applicable detection engines should be desperately selected by comparing distinct properties of each machine-learning algorithm. Based on process control features generated by directed function transition diagrams, this paper introduces five different machine-learning algorithms as alternative detection engines to discuss their matching abilities. Furthermore, this paper not only describes some qualitative properties to compare their advantages and disadvantages, but also gives an in-depth and meticulous research on their detection accuracies and consuming time. In the verified experiments, two attack models and four different attack intensities are defined to facilitate all quantitative comparisons, and the impacts of detection accuracy caused by the feature parameter are also comparatively analyzed. All experimental results can clearly explain that SVM (Support Vector Machine) and WNN (Wavelet Neural Network) are suggested as two applicable detection engines under differing cases

3,3-Dichloro-1-(chloro­meth­yl)indolin-2-one

In the title compound, C9H6Cl3NO, the pyrrole ring is almost coplanar with the benzene ring [dihedral angle = 1.90 (9)°], while the Cl—C—N—C torsion angle is 98.78 (17)°. In the crystal, pairs of mol­ecules are inter­connected by pairs of Cl⋯Cl inter­actions [3.564 (5) Å], forming dimers, which are further peripherally connected through inter­molecular C—H⋯O=C and π–π inter­actions [centroid–centroid distances = 4.134 (7), 4.134 (6) and 4.238 (7) Å], forming a two-dimensional network