Epidemic spreading on heterogeneous networks with identical infectivity

In this paper, we propose a modified susceptible-infected-recovered (SIR) model, in which each node is assigned with an identical capability of active contacts, $A$, at each time step. In contrast to the previous studies, we find that on scale-free networks, the density of the recovered individuals in the present model shows a threshold behavior. We obtain the analytical results using the mean-field theory and find that the threshold value equals 1/A, indicating that the threshold value is independent of the topology of the underlying network. The simulations agree well with the analytic results. Furthermore, we study the time behavior of the epidemic propagation and find a hierarchical dynamics with three plateaus. Once the highly connected hubs are reached, the infection pervades almost the whole network in a progressive cascade across smaller degree classes. Then, after the previously infected hubs are recovered, the disease can only propagate to the class of smallest degree till the infected individuals are all recovered. The present results could be of practical importance in the setup of dynamic control strategies.Comment: 5 pages, 3 figure

UniPC: A Unified Predictor-Corrector Framework for Fast Sampling of Diffusion Models

Diffusion probabilistic models (DPMs) have demonstrated a very promising ability in high-resolution image synthesis. However, sampling from a pre-trained DPM is time-consuming due to the multiple evaluations of the denoising network, making it more and more important to accelerate the sampling of DPMs. Despite recent progress in designing fast samplers, existing methods still cannot generate satisfying images in many applications where fewer steps (e.g., $<$10) are favored. In this paper, we develop a unified corrector (UniC) that can be applied after any existing DPM sampler to increase the order of accuracy without extra model evaluations, and derive a unified predictor (UniP) that supports arbitrary order as a byproduct. Combining UniP and UniC, we propose a unified predictor-corrector framework called UniPC for the fast sampling of DPMs, which has a unified analytical form for any order and can significantly improve the sampling quality over previous methods, especially in extremely few steps. We evaluate our methods through extensive experiments including both unconditional and conditional sampling using pixel-space and latent-space DPMs. Our UniPC can achieve 3.87 FID on CIFAR10 (unconditional) and 7.51 FID on ImageNet 256$\times$256 (conditional) with only 10 function evaluations. Code is available at https://github.com/wl-zhao/UniPC.Comment: Accepted by NeurIPS 2023. Project page: https://unipc.ivg-research.xy

2-[3-(2-Chloro­phen­yl)-5-oxo-1,5-diphenyl­pentyl­idene]malononitrile

In the title compound, C26H19ClN2O, the 2-chloro­phenyl group forms dihedral angles of 59.6 (1) and 31.9 (1)° with the phenyl rings. The two phenyl rings are inclined at a dihedral angle of 32.9 (1)° with respect to each other. In the crystal, an inter­molecular C—H⋯N hydrogen bond links the mol­ecules into a polymeric chain running along the c axis

Immunization of Susceptible-Infected Model on Scale-Free networks

In this paper, we investigate two major immunization strategies, random immunization and targeted immunization, of the susceptible-infected (SI) Model on the Barab\'{a}si-Albert (BA) networks. For the heterogenous structure, the random strategy is quite ineffective if the vaccinated proportion is quite small, while the targeted one which prefers to vaccinate the individuals with the largest degree can sharply depress the epidemic spreading even only a small amount of population are vaccinated. The analytical solution is also obtained,which can capture the trend of velocity change versus the amount of vaccinated population.Comment: 5 pages, 4 figure

5-Phenyl-3,4,4a,5,6,12c-hexa­hydro-2H-benzo[f]pyrano[3,2-c]quinoline

In the title compound, C22H21N, the pyridine ring adopts a distorted boat conformation, while the adjacent pyran ring adopts a chair conformation; the heterocyclic rings make a dihedral angle of 40.1 (2)° with each other

Deep Supervised Hashing using Symmetric Relative Entropy

By virtue of their simplicity and efficiency, hashing algorithms have achieved significant success on large-scale approximate nearest neighbor search. Recently, many deep neural network based hashing methods have been proposed to improve the search accuracy by simultaneously learning both the feature representation and the binary hash functions. Most deep hashing methods depend on supervised semantic label information for preserving the distance or similarity between local structures, which unfortunately ignores the global distribution of the learned hash codes. We propose a novel deep supervised hashing method that aims to minimize the information loss generated during the embedding process. Specifically, the information loss is measured by the Jensen-Shannon divergence to ensure that compact hash codes have a similar distribution with those from the original images. Experimental results show that our method outperforms current state-of-the-art approaches on two benchmark datasets

Behaviors of susceptible-infected epidemics on scale-free networks with identical infectivity

In this article, we proposed a susceptible-infected model with identical infectivity, in which, at every time step, each node can only contact a constant number of neighbors. We implemented this model on scale-free networks, and found that the infected population grows in an exponential form with the time scale proportional to the spreading rate. Further more, by numerical simulation, we demonstrated that the targeted immunization of the present model is much less efficient than that of the standard susceptible-infected model. Finally, we investigated a fast spreading strategy when only local information is available. Different from the extensively studied path finding strategy, the strategy preferring small-degree nodes is more efficient than that preferring large-degree nodes. Our results indicate the existence of an essential relationship between network traffic and network epidemic on scale-free networks.Comment: 5 figures and 7 page

A new species of karst-dwelling freshwater crab of the genus Chinapotamon Dai & Naiyanetr, 1994 (Crustacea: Decapoda: Brachyura: Potamidae), from Guizhou, southwest China

Chinapotamon maolanense sp. n. from Maolan National Nature Reserve, Guizhou, southwest China, is described. C. maolanense sp. n. has diagnostic features of Chinapotamon, such as a slender and sinuous male first gonopod, prominently convex carapace, and one-third ratio of frons to carapace width. This new species can be distinguished from congeners by the combination of the following characters: relatively slender subterminal segment of the first gonopods, nearly oval-shaped carapace, anterolateral margin cristate of carapace and an oval-shaped gap between the fingers of the male major chela. In addition, we used a 16S rRNA gene fragment to explore the relationship between C. maolanense sp. n. and C. glabrum, C. depressum and other freshwater crabs distributed in Guizhou; the results support the new species being assigned to Chinapotamon and clearly different from other species used in the analysis