Convergence of Online Mirror Descent

In this paper we consider online mirror descent (OMD) algorithms, a class of scalable online learning algorithms exploiting data geometric structures through mirror maps. Necessary and sufficient conditions are presented in terms of the step size sequence $\{\eta_t\}_{t}$ for the convergence of an OMD algorithm with respect to the expected Bregman distance induced by the mirror map. The condition is $\lim_{t\to\infty}\eta_t=0, \sum_{t=1}^{\infty}\eta_t=\infty$ in the case of positive variances. It is reduced to $\sum_{t=1}^{\infty}\eta_t=\infty$ in the case of zero variances for which the linear convergence may be achieved by taking a constant step size sequence. A sufficient condition on the almost sure convergence is also given. We establish tight error bounds under mild conditions on the mirror map, the loss function, and the regularizer. Our results are achieved by some novel analysis on the one-step progress of the OMD algorithm using smoothness and strong convexity of the mirror map and the loss function.Comment: Published in Applied and Computational Harmonic Analysis, 202

Enhancing web marketing by using ontology

The existence of the Web has a major impact on people\u27s life styles. Online shopping, online banking, email, instant messenger services, search engines and bulletin boards have gradually become parts of our daily life. All kinds of information can be found on the Web. Web marketing is one of the ways to make use of online information. By extracting demographic information and interest information from the Web, marketing knowledge can be augmented by applying data mining algorithms. Therefore, this knowledge which connects customers to products can be used for marketing purposes and for targeting existing and potential customers. The Web Marketing Project with Ontology Support has the purpose to find and improve marketing knowledge. In the Web Marketing Project, association rules about marketing knowledge have been derived by applying data mining algorithms to existing Web users\u27 data. An ontology was used as a knowledge backbone to enhance data mining for marketing. The Raising Method was developed by taking advantage of the ontology. Data are preprocessed by Raising before being fed into data mining algorithms. Raising improves the quality of the set of mined association rules by increasing the average support value. Also, new rules have been discovered after applying Raising. This dissertation thoroughly describes the development and analysis of the Raising method. Moreover, a new structure, called Intersection Ontology, is introduced to represent customer groups on demand. Only needed customer nodes are created. Such an ontology is used to simplify the marketing knowledge representation. Finally, some additional ontology usages are mentioned. By integrating an ontology into Web marketing, the marketing process support has been greatly improved

Wildfire impact on permafrost : changes in microbial community and soil decomposition

Permafrost is prone to thawing under disturbances resulting from frequent wildfires in boreal forests due to climate change, increasing the risk of the release of carbon (C) from it. Although the decomposition of organic C is mainly determined by the activity of soil microorganisms, productions of pyrogenic material after fire may offset this process. To evaluate the C dynamics related to wildfire disturbance in permafrost regions, this study examined the postfire changes in soil organic matter (SOM) decomposition, and the microbial community composition and its potential functions during a > 100-year chronosequence of burnt boreal forests. Based on the kinetic theory, the temperature sensitivity of slowly decomposing SOM tends to be higher than that of easily decomposing SOM. Consistently, we found the decomposition of SOM in burnt surface soils containing less-decomposable SOM generated by fire, was more sensitive to temperature than that in old-growth forests. Fire also decreased the microbial biomass and the fungal-to-bacterial ratio of the surface soils. Despite this, soil heterotrophic respiration and the microbial C:N:P ratio in burnt forests remained similar level to that in old-growth forests regardless of the changing SOM quality and quantity. This suggests the notion of a lower microbial C use efficiency following a fire. Unexpectedly, permafrost thaw did not alter the microbial biomass and the fungal-to-bacterial ratio, but increased the microbial metabolic quotient. Illumina Miseq sequencing of bacterial 16S rDNA revealed that the bacterial community composition in recently burnt surface soils differed from it in old-growth forest soils. Permafrost thaw, however, showed little effect on the bacterial community composition. Bacterial communities of burnt surface-soil exhibited higher abundance of Ktedonobacteria (Chloroflexi) but lower abundance of Betaproteobacteria. Functional gene compositions (DNA-based) of the burnt surface soil differed from those of the unburnt ones; particularly for genes coding for C degradation and the nitrogen cycle. Yet, the difference in the frequency of genes responsible for C degradation between thawed and frozen permafrost was not statistically significant. This thesis provides further evidence for effects of wildfire on the microbial biomass, microbial community composition, and its potential functions on the C and N cycles in boreal permafrost regions. To estimate the real pattern of soil C cycles following a fire, we must understand how fire affects the metabolic processes of soil microorganisms.Permafrost is prone to thawing under disturbances resulting from frequent wildfires in boreal forests due to climate change, increasing the risk of the release of carbon (C) from it. Although the decomposition of organic C is mainly determined by the activity of soil microorganisms, productions of pyrogenic material after fire may offset this process. To evaluate the C dynamics related to wildfire disturbance in permafrost regions, this study examined the postfire changes in soil organic matter (SOM) decomposition, and the microbial community composition and its potential functions during a > 100-year chronosequence of burnt boreal forests. Based on the kinetic theory, the temperature sensitivity of slowly decomposing SOM tends to be higher than that of easily decomposing SOM. Consistently, we found the decomposition of SOM in burnt surface soils containing less-decomposable SOM generated by fire, was more sensitive to temperature than that in old-growth forests. Fire also decreased the microbial biomass and the fungal-to-bacterial ratio of the surface soils. Despite this, soil heterotrophic respiration and the microbial C:N:P ratio in burnt forests remained similar level to that in old-growth forests regardless of the changing SOM quality and quantity. This suggests the notion of a lower microbial C use efficiency following a fire. Unexpectedly, permafrost thaw did not alter the microbial biomass and the fungal-to-bacterial ratio, but increased the microbial metabolic quotient. Illumina Miseq sequencing of bacterial 16S rDNA revealed that the bacterial community composition in recently burnt surface soils differed from it in old-growth forest soils. Permafrost thaw, however, showed little effect on the bacterial community composition. Bacterial communities of burnt surface-soil exhibited higher abundance of Ktedonobacteria (Chloroflexi) but lower abundance of Betaproteobacteria. Functional gene compositions (DNA-based) of the burnt surface soil differed from those of the unburnt ones; particularly for genes coding for C degradation and the nitrogen cycle. Yet, the difference in the frequency of genes responsible for C degradation between thawed and frozen permafrost was not statistically significant. This thesis provides further evidence for effects of wildfire on the microbial biomass, microbial community composition, and its potential functions on the C and N cycles in boreal permafrost regions. To estimate the real pattern of soil C cycles following a fire, we must understand how fire affects the metabolic processes of soil microorganisms

Issues with the Development of Professional Preschool Teaching Staff in China and Developmental Strategies

Teaching in preschool institutions is a specialized profession that requires professional expertise and techniques. Currently, certain issues with the professionalization of early childhood education practitioners have negatively impacted the quality of Chinese preschool education. This article analyzed the necessity of professionalizing pre-primary teachers and pinpointed the challenges faced by China’s educational community in building professional preschool education staff. Relevant strategies were also proposed for strengthening China’s pre-primary teaching force