Mixed random walks with a trap in scale-free networks including nearest-neighbor and next-nearest-neighbor jumps

Random walks including non-nearest-neighbor jumps appear in many real situations such as the diffusion of adatoms and have found numerous applications including PageRank search algorithm, however, related theoretical results are much less for this dynamical process. In this paper, we present a study of mixed random walks in a family of fractal scale-free networks, where both nearest-neighbor and next-nearest-neighbor jumps are included. We focus on trapping problem in the network family, which is a particular case of random walks with a perfect trap fixed at the central high-degree node. We derive analytical expressions for the average trapping time (ATT), a quantitative indicator measuring the efficiency of the trapping process, by using two different methods, the results of which are consistent with each other. Furthermore, we analytically determine all the eigenvalues and their multiplicities for the fundamental matrix characterizing the dynamical process. Our results show that although next-nearest-neighbor jumps have no effect on the leading sacling of the trapping efficiency, they can strongly affect the prefactor of ATT, providing insight into better understanding of random-walk process in complex systems.Comment: Definitive version accepted for publication in The Journal of Chemical Physic

Lower Complexity Bounds of Finite-Sum Optimization Problems: The Results and Construction

The contribution of this paper includes two aspects. First, we study the lower bound complexity for the minimax optimization problem whose objective function is the average of $n$ individual smooth component functions. We consider Proximal Incremental First-order (PIFO) algorithms which have access to gradient and proximal oracle for each individual component. We develop a novel approach for constructing adversarial problems, which partitions the tridiagonal matrix of classical examples into $n$ groups. This construction is friendly to the analysis of incremental gradient and proximal oracle. With this approach, we demonstrate the lower bounds of first-order algorithms for finding an $\varepsilon$-suboptimal point and an $\varepsilon$-stationary point in different settings. Second, we also derive the lower bounds of minimization optimization with PIFO algorithms from our approach, which can cover the results in \citep{woodworth2016tight} and improve the results in \citep{zhou2019lower}

Radio AGN jet alignment: Radio and Optical Position Angle of Radio Galaxies

It is well established that AGNs play an important role in the evolution of galaxies. These AGNs can be linked to the accretion processes onto massive black holes and past merger events in their host galaxies, which may lead to different alignments of the jets with respect to the host galaxies. This paper presents a study of the PA differences between radio and optical images of radio AGNs based on the LoTSS DR2, the FIRST, the DESI Legacy Imaging Surveys and the SDSS. We assessed PA measurement biases in the data and classified the radio AGNs based on the radio luminosity and infrared colour from the WISE. This resulted in the largest yet published sample of 3682 radio AGNs with reliable radio and optical PA measurements. The PA difference (dPA) distributions for the radio AGN sample show a prominent minor-axis alignment tendency. Based on some simple assumptions, we simulated the projection effect to estimate the intrinsic jet-galaxy alignment. The observed dPA distribution can be well described by a two-component jet-alignment model in which one component is more aligned with the minor axis of the host galaxy than the other. The fitting results indicate that the jet alignment is dependent on radio luminosity and the shape of the host galaxies, with the jets being more likely to be aligned with the minor axis of the galaxy for lower radio luminosity and for optically more elongated radio AGNs. The minor-axis alignment of the entire sample may suggest a coherent accretion model present in most AGN host galaxies, while a considerable number of luminous radio-AGN with massive host galaxies might have undergone an accretion according to the chaotic model or past merger events.Comment: 23 pages, 18 figures, accepted for publication in A&

Finite Element Analysis of Elastic Behavior of Suction Caisson

As the demand on energy increases rapidly, exploration and production in deep water and facilities in shallow water are in imperative need. Suction caissons are most commonly used as anchoring system for offshore floating structures and are used as foundations for coastal wind turbines in relatively shallow water. For a long time, suction caisson loaded in soft clay such as in Gulf of Mexico are considered rigid due to the stiffness being stronger than soft clay. The objective of this study is to investigate the elastic behavior of suction caissons in soft clay. A new 3-D finite element analysis method using coupled caisson-springs model is introduced. The properties of springs are developed based on a 2-D continuum finite element analysis and scaled to 3-D scenario. Computer program ABAQUS is used for the numerical analysis for the coupled caisson-springs model. Results show that elastic behavior of caissons is quite different with a rigid caisson particularly under small displacement. Taking the advantage of the newly developed model, the structural response of the caisson is also assessed

Stochastic Distributed Optimization under Average Second-order Similarity: Algorithms and Analysis

We study finite-sum distributed optimization problems involving a master node and $n-1$ local nodes under the popular $\delta$-similarity and $\mu$-strong convexity conditions. We propose two new algorithms, SVRS and AccSVRS, motivated by previous works. The non-accelerated SVRS method combines the techniques of gradient sliding and variance reduction and achieves a better communication complexity of $\tilde{\mathcal{O}}(n {+} \sqrt{n}\delta/\mu)$ compared to existing non-accelerated algorithms. Applying the framework proposed in Katyusha X, we also develop a directly accelerated version named AccSVRS with the $\tilde{\mathcal{O}}(n {+} n^{3/4}\sqrt{\delta/\mu})$ communication complexity. In contrast to existing results, our complexity bounds are entirely smoothness-free and exhibit superiority in ill-conditioned cases. Furthermore, we establish a nearly matched lower bound to verify the tightness of our AccSVRS method.Comment: Camera-ready version for NeurIPS 202

China is on the track tackling Enteromorpha spp forming green tide

Green tide management is supposed to be a long term fight rather than an episode during the 29th Olympic Games for China, since it has been gaining in scale and frequency during the past 3 decades in both marine and estuary environment all over the world. A number of rapid-responding studies including oceanographic comprehensive surveys along the coastline have been conducted during the bloom and post-bloom periods in 2008 by Chinese marine scientists. The preliminary results are as below: (1) phylogenetic analysis indicates that the bloom forming alga forms a clade with representatives of the green seaweed Enteromorpha linza, though, the alga has been identified as E. proliera by means of morphological; (2) the present data suggest that the bloom was originated from south of Yellow Sea, but not the severely affected area near Qingdao City; (3) pathways of reproduction for E. prolifera have approved to be multifarious, including sexual, asexual and vegetative propagation; (4) somatic cells may act as a propagule bank, which is supposed to be a very dangerous transmitting way for its marked movability, adaptability and viability; (5) pyrolysis of the alga showed that three stages appeared during the process, which are dehydration (18–20^o^C), main devolatilization (200–450^o^C) and residual decomposition (450–750^o^C), and activation energy of the alga was determined at 237.23 KJ•mol^-1^. Although the scarce knowlegde on E. prolifera not yet allow a fully understanding of the green tide, some of the results suggests possible directions in further green tide research and management

Revealing the Biexciton and Trion-exciton Complexes in BN Encapsulated WSe2

Strong Coulomb interactions in single-layer transition metal dichalcogenides (TMDs) result in the emergence of strongly bound excitons, trions and biexcitons. These excitonic complexes possess the valley degree of freedom, which can be exploited for quantum optoelectronics. However, in contrast to the good understanding of the exciton and trion properties, the binding energy of the biexciton remains elusive, with theoretical calculations and experimental studies reporting discrepant results. In this work, we resolve the conflict by employing low-temperature photoluminescence spectroscopy to identify the biexciton state in BN encapsulated single-layer WSe2. The biexciton state only exists in charge neutral WSe2, which is realized through the control of efficient electrostatic gating. In the lightly electron-doped WSe2, one free electron binds to a biexciton and forms the trion-exciton complex. Improved understanding of the biexciton and trion-exciton complexes paves the way for exploiting the many-body physics in TMDs for novel optoelectronics applications