Analyze the Trend of Post Replies Based on Linear Regression Model-----take Tianyawebsiteas examples

In recent years, users spend more time on surfing the social networking than ever before. How to make the information spread rapidlywhen facing vast amounts of information?Scholars have conducted information dissemination in social networking. On the basis of previous research, the authors divide posts into popular posts and ordinary posts and then use the linear regression model to predict the replies at specified time. After comparing the difference between two types of posts, the authors concludethat ordinary posts could become popular posts if the posts could maintain a large number of replies within former five hours and increase replies by making use of community mechanism. This conclusion provides a reasonable proposal for enterprises and administrators to identify andrecommendpopular posts

Description of the newly observed Ωc∗\Omega^{*}_c states as molecular states

In this work, we study the strong decays of the newly observed $\Omega^{*}_c(3185)$ and $\Omega^{*}_c(3327)$ assuming that $\Omega^{*}_c(3185)$ and $\Omega^{*}_c(3327)$ as $S$-wave $D\Xi$ and $D^{*}\Xi$ molecular state, respectively. Since the $\Omega_c^{*}$ was observed in the $\Xi_c^{+}K^{-}$ invariant mass distributions, the partial decay width of $\Omega^{*}_c(3185)$ and $\Omega^{*}_c(3327)$ into $\Xi_c^{+}K^{-}$ through hadronic loops are evaluated with the help of the effective Lagrangians. Moreover, the decay channel of $\Xi_c^{'}\bar{K}$ is also included. The decay process is described by the $t$-channel $\Lambda$, $\Sigma$ baryons and $D_s$, $D_s^{*}$ mesons exchanges, respectively. By comparison with the LHCb observation, the current results support the $\Omega^{*}_c(3327)$ with$J^P=3/2^{-}$ as pure $D^{*}\Xi$ molecule while the $\Omega^{*}_c(3327)$ with $J^P=1/2^{-}$ can not be well reproduced in the molecular state picture. In addition, the spin-parity $J^P=1/2^{-}$ $D\Xi$ molecular assumptions for the $\Omega^{*}_c(3185)$ can't be conclusively determined. It may be a meson-baryon molecule with a big $D\Xi$ component. Although the decay width of the $\Omega_c^{*}\to{}\bar{K}\Xi_c^{'}$ is of the order several MeV, it can be well employed to test the molecule interpretations of $\Omega^{*}_c(3185)$ and $\Omega^{*}_c(3327)$

Uniqueness of the critical points of solutions to two kinds of semilinear elliptic equations in higher dimensional domains

In this paper, we provide an affirmative answer to the conjecture A for bounded simple rotationally symmetric domains $\Omega\subset \mathbb{R}^n(n\geq 3)$ along $x_n$ axis. Precisely, we use a new simple argument to study the symmetry of positive solutions for two kinds of semilinear elliptic equations. To do this, when $f(\cdot,s)$ is strictly convex with respect to $s$, we show that the nonnegativity of the first eigenvalue of the corresponding linearized operator in somehow symmetric domains is a sufficient condition for the symmetry of $u$. Moreover, we prove the uniqueness of critical points of a positive solution to semilinear elliptic equation $-\triangle u=f(\cdot,u)$ with zero Dirichlet boundary condition for simple rotationally symmetric domains in $\mathbb{R}^n$ by continuity method and a variety of maximum principles.Comment: 18 page

Learning Trajectories are Generalization Indicators

This paper explores the connection between learning trajectories of Deep Neural Networks (DNNs) and their generalization capabilities when optimized using (stochastic) gradient descent algorithms. Instead of concentrating solely on the generalization error of the DNN post-training, we present a novel perspective for analyzing generalization error by investigating the contribution of each update step to the change in generalization error. This perspective allows for a more direct comprehension of how the learning trajectory influences generalization error. Building upon this analysis, we propose a new generalization bound that incorporates more extensive trajectory information. Our proposed generalization bound depends on the complexity of learning trajectory and the ratio between the bias and diversity of training set. Experimental findings reveal that our method effectively captures the generalization error throughout the training process. Furthermore, our approach can also track changes in generalization error when adjustments are made to learning rates and label noise levels. These results demonstrate that learning trajectory information is a valuable indicator of a model's generalization capabilities

Is the Age Structure of the Population One of the Determinants of the Household Saving Rate in China? A Spatial Panel Analysis of Provincial Data

In this paper, we use provincial panel data on China for the 2002-19 period to conduct a spatial autocorrelation analysis of household saving rates as well as a dynamic panel analysis of the determinants of household saving rates using a spatial Durbin model. To summarize our main findings, we find that, in China, the household saving rate shows significant positive spatial autocorrelation with an overall “high-high” and “low-low”clustering pattern, that, as predicted by the life-cycle hypothesis, the youth dependency ratio and the old-age dependency ratio have a negative and significant impact on the household saving rate, and that the logarithm of per capita household disposable income, the regional economic growth rate, the share of the urban population, the industrialization rate, and the income disparity between urban and rural areas also have a significant impact on the household saving rate