Efficient calculation of the robustness measure R for complex networks

In a recent work, Schneider et al. (2011) proposed a new measure R for network robustness, where the value of R is calculated within the entire process of malicious node attacks. In this paper, we present an approach to improve the calculation efficiency of R, in which a computationally efficient robustness measure R' is introduced when the fraction of failed nodes reaches to a critical threshold qc. Simulation results on three different types of network models and three real networks show that these networks all exhibit a computationally efficient robustness measure R'. The relationships between R' and the network size N and the network average degree are also explored. It is found that the value of R' decreases with N while increases with . Our results would be useful for improving the calculation efficiency of network robustness measure R for complex networks.Peer ReviewedPostprint (author's final draft

Hinge solitons in three-dimensional second-order topological insulators

A second-order topological insulator in three dimensions refers to a topological insulator with gapless states localized on the hinges, which is a generalization of a traditional topological insulator with gapless states localized on the surfaces. Here we theoretically demonstrate the existence of stable solitons localized on the hinges of a second-order topological insulator in three dimensions when nonlinearity is involved. By means of systematic numerical study, we find that the soliton has strong localization in real space and propagates along the hinge unidirectionally without changing its shape. We further construct an electric network to simulate the second-order topological insulator. When a nonlinear inductor is appropriately involved, we find that the system can support a bright soliton for the voltage distribution demonstrated by stable time evolution of a voltage pulse.Comment: 11 pages, 6 figure

Scale Invariant Privacy Preserving Video via Wavelet Decomposition

Video surveillance has become ubiquitous in the modern world. Mobile devices, surveillance cameras, and IoT devices, all can record video that can violate our privacy. One proposed solution for this is privacy-preserving video, which removes identifying information from the video as it is produced. Several algorithms for this have been proposed, but all of them suffer from scale issues: in order to sufficiently anonymize near-camera objects, distant objects become unidentifiable. In this paper, we propose a scale-invariant method, based on wavelet decomposition

Deep Learning and Inverse Problems

Machine Learning (ML) methods and tools have gained great success in many data, signal, image and video processing tasks, such as classification, clustering, object detection, semantic segmentation, language processing, Human-Machine interface, etc. In computer vision, image and video processing, these methods are mainly based on Neural Networks (NN) and in particular Convolutional NN (CNN), and more generally Deep NN. Inverse problems arise anywhere we have indirect measurement. As, in general, those inverse problems are ill-posed, to obtain satisfactory solutions for them needs prior information. Different regularization methods have been proposed, where the problem becomes the optimization of a criterion with a likelihood term and a regularization term. The main difficulty, however, in great dimensional real applications, remains the computational cost. Using NN, and in particular Deep Learning (DL) surrogate models and approximate computation, can become very helpful. In this work, we focus on NN and DL particularly adapted for inverse problems. We consider two cases: First the case where the forward operator is known and used as physics constraint, the second more general data driven DL methods.Comment: arXiv admin note: text overlap with arXiv:2308.1549

On sumsets involving kkth power residues

In this paper, we study some topics concerning the additive decompostions of the set $D_k$ of all $k$th power residues modulo a prime $p$. For example, we prove that $$\lim_{x\rightarrow+\infty}\frac{B(x)}{\pi(x)}=0,$$ where $\pi(x)$ is the number of primes $\le x$ and $B(x)$ denotes the cardinality of the set $$\{p\le x: p\equiv1\pmod k; D_k\ \text{has a non-trivial 2-additive decomposition}\}.$

On generalized Legendre matrices involving roots of unity over finite fields

In this paper, motivated by the work of Chapman, Vsemirnov and Sun et al., we investigate some arithmetic properties of the generalized Legendre matrices over finite fields. For example, letting $a_1,\cdots,a_{(q-1)/2}$ be all non-zero squares in the finite field $\mathbb{F}_q$ which contains $q$ elements with $2\nmid q$, we give the explicit value of $D_{(q-1)/2}=\det[(a_i+a_j)^{(q-3)/2}]_{1\le i,j\le (q-1)/2}$. In particular, if $q=p$ is a prime greater than $3$, then \left(\frac{\det D_{(p-1)/2}}{p}\right)= \begin{cases} 1 & \mbox{if}\ p\equiv1\pmod4, (-1)^{(h(-p)+1)/2} & \mbox{if}\ p\equiv 3\pmod4\ \text{and}\ p>3, \end{cases} where $(\cdot/p)$ is the Legendre symbol and $h(-p)$ is the class number of $\mathbb{Q}(\sqrt{-p})$.Comment: 12 page

Terrestrial water storage anomalies emphasize interannual variations in global mean sea level during 1997-1998 and 2015-2016 El Nino Events

© The Author(s), 2021. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Kuo, Y.-N., Lo, M.-H., Liang, Y.-C., Tseng, Y.-H., & Hsu, C.-W. Terrestrial water storage anomalies emphasize interannual variations in global mean sea level during 1997-1998 and 2015-2016 El Nino Events. Geophysical Research Letters, 48(18), (2021): e2021GL094104, https://doi.org/10.1029/2021GL094104.Interannual variations in global mean sea level (GMSL) closely correlate with the evolution of El Niño-Southern Oscillation. However, GMSL differences occur in extreme El Niños; for example, in the 2015–2016 and 1997–1998 El Niños, the peak GMSL during the mature stage of the former (9.00 mm) is almost 2.5 times higher than the latter (3.72 mm). Analyses from satellite and reanalysis data sets show that the disparity in GMSL is primarily due to barystatic (ocean mass) changes. We find that the 2015–2016 event developed not purely as an Eastern Pacific El Niño event but with Central Pacific (CP) El Niño forcing. CP El Niños contribute to a stronger negative anomaly of global terrestrial water storage and subsequent higher barystatic heights. Our results suggest that the mechanism of hydrology-related interannual variations of GMSL should be further emphasized, as more CP El Niño events are projected to occur.This study was supported by a grant of MOST 106-2111-M-002-010-MY4 to National Taiwan University

Messenger RNA Design via Expected Partition Function and Continuous Optimization

The tasks of designing RNAs are discrete optimization problems, and several versions of these problems are NP-hard. As an alternative to commonly used local search methods, we formulate these problems as continuous optimization and develop a general framework for this optimization based on a generalization of classical partition function which we call "expected partition function". The basic idea is to start with a distribution over all possible candidate sequences, and extend the objective function from a sequence to a distribution. We then use gradient descent-based optimization methods to improve the extended objective function, and the distribution will gradually shrink towards a one-hot sequence (i.e., a single sequence). As a case study, we consider the important problem of mRNA design with wide applications in vaccines and therapeutics. While the recent work of LinearDesign can efficiently optimize mRNAs for minimum free energy (MFE), optimizing for ensemble free energy is much harder and likely intractable. Our approach can consistently improve over the LinearDesign solution in terms of ensemble free energy, with bigger improvements on longer sequences