Revisiting Lq(0≤q<1)L_q(0\leq q<1) Norm Regularized Optimization

Sparse optimization has seen its advances in recent decades. For scenarios where the true sparsity is unknown, regularization turns out to be a promising solution. Two popular non-convex regularizations are the so-called $L_0$ norm and $L_q$ norm with $0<q<1$, giving rise to extensive research on their induced optimization. This paper explores $L_q$ norm regularized optimization in a unified way for any $0\leq q<1$. In particular, based on the proximal operator of the $L_q$ norm, we establish the first-order and second-order optimality conditions under mild assumptions. Then we integrate the proximal operator and Newton method to develop a proximal Newton pursuit algorithm, followed by the achievements of its global sequence convergence. Moreover, this is the first paper maintaining the locally quadratic convergence rate for an algorithm solving the $L_q$ norm regularization problem for any $0<q<1$. The assumptions to guarantee these results are relatively mild, In particular, there does not necessarily need the strong smoothness. Finally, some numerical experiments have demonstrated its high performance in comparison with several existing leading solvers

Quantifying the Effect of Mobile Channel Visits on Firm Revenue

The explosive penetration of mobile devices is one of the most prominent trends in e-business. Although the importance of mobile channel has prompted growing literature, little is known about the revenue implications of customer visit toward mobile channel. This study examines (1) the differential effect of mobile visits in affecting firm revenue (i.e. mobile vs. desktop visits), and (2) which type of mobile visits are more effective (i.e., direct vs. search engine and referral traffic; visits for high vs. low involvement products). We collect an unique objective daily data from a leading online travel agency in China. With a vector autoregressive (VAR) method, we find that, compared with desktop channel, mobile channel visits have shorter carryover effect, but larger short-term effect on firm revenues. Further, mobile channel has larger short-term effect on firm revenues for search engine traffic and lower involvement products. Our findings provide important theoretical contributions and notable implications for mobile commerce strategy

Synchronous MDADT-Based Fuzzy Adaptive Tracking Control for Switched Multiagent Systems via Modified Self-Triggered Mechanism

In this paper, a self-triggered fuzzy adaptive switched control strategy is proposed to address the synchronous tracking issue in switched stochastic multiagent systems (MASs) based on mode-dependent average dwell-time (MDADT) method. Firstly, a synchronous slow switching mechanism is considered in switched stochastic MASs and realized through a class of designed switching signals under MDADT property. By utilizing the information of both specific agents under switching dynamics and observers with switching features, the synchronous switching signals are designed, which reduces the design complexity. Then, a switched state observer via a switching-related output mask is proposed. The information of agents and their preserved neighbors is utilized to construct the observer and the observation performance of states is improved. Moreover, a modified self- triggered mechanism is designed to improve control performance via proposing auxiliary function. Finally, by analysing the re- lationship between the synchronous switching problem and the different switching features of the followers, the synchronous slow switching mechanism based on MDADT is obtained. Meanwhile, the designed self-triggered controller can guarantee that all signals of the closed-loop system are ultimately bounded under the switching signals. The effectiveness of the designed control method can be verified by some simulation results

Protecting public’s wellbeing against COVID-19 infodemic: The role of trust in information sources and rapid dissemination and transparency of information over time

ObjectivesThis study examined how trust in the information about COVID-19 from social media and official media as well as how the information was disseminated affect public’s wellbeing directly and indirectly through perceived safety over time.MethodsTwo online surveys were conducted in China, with the first survey (Time1, N = 22,718) being at the early stage of the pandemic outbreak and the second one (Time 2, N = 2,901) two and a half years later during the zero-COVID policy lockdown period. Key measured variables include trust in official media and social media, perceived rapid dissemination and transparency of COVID-19-related information, perceived safety, and emotional responses toward the pandemic. Data analysis includes descriptive statistical analysis, independent samples t-test, Pearson correlations, and structural equation modeling.ResultsTrust in official media, perceived rapid dissemination and transparency of COVID-19-related information, perceived safety, as well as positive emotional response toward COVID-19 increased over time, while trust in social media and depressive response decreased over time. Trust in social media and official media played different roles in affecting public’s wellbeing over time. Trust in social media was positively associated with depressive emotions and negatively associated with positive emotion directly and indirectly through decreased perceived safety at Time 1. However, the negative effect of trust in social media on public’s wellbeing was largely decreased at Time 2. In contrast, trust in official media was linked to reduced depressive response and increased positive response directly and indirectly through perceived safety at both times. Rapid dissemination and transparency of COVID-19 information contributed to enhanced trust in official media at both times.ConclusionThe findings highlight the important role of fostering public trust in official media through rapid dissemination and transparency of information in mitigating the negative impact of COVID-19 infodemic on public’s wellbeing over time

Phylogeny more than plant height and leaf area explains variance in seed mass

Although variation in seed mass can be attributed to other plant functional traits such as plant height, leaf size, genome size, growth form, leaf N and phylogeny, until now, there has been little information on the relative contributions of these factors to variation in seed mass. We compiled data consisting of 1071 vascular plant species from the literature to quantify the relationships between seed mass, explanatory variables and phylogeny. Strong phylogenetic signals of these explanatory variables reflected inherited ancestral traits of the plant species. Without controlling phylogeny, growth form and leaf N are associated with seed mass. However, this association disappeared when accounting for phylogeny. Plant height, leaf area, and genome size showed consistent positive relationship with seed mass irrespective of phylogeny. Using phylogenetic partial R2s model, phylogeny explained 50.89% of the variance in seed mass, much more than plant height, leaf area, genome size, leaf N, and growth form explaining only 7.39%, 0.58%, 1.85%, 0.06% and 0.09%, respectively. Therefore, future ecological work investigating the evolution of seed size should be cautious given that phylogeny is the best overall predictor for seed mass. Our study provides a novel avenue for clarifying variation in functional traits across plant species, improving our better understanding of global patterns in plant traits