Large Steklov eigenvalues on hyperbolic surfaces

In this paper, we first construct a sequence of hyperbolic surfaces with connected geodesic boundary such that the first normalized Steklov eigenvalue $\tilde{\sigma}_1$ tends to infinity. We then prove that as $g\rightarrow \infty$, a generic $\Sigma\in \mathcal{M}_{g,n}(L_g)$ satisfies $\tilde{\sigma}_1(\Sigma)>C\cdot \|L_g\|_1$ where $C$ is a positive universal constant. Here $\mathcal{M}_{g,n}(L_g)$ is the moduli space of hyperbolic surfaces of genus $g$ and $n$ boundary components of length $L_g=(L_g^1,\cdots, L_g^n)$ endowed with the Weil-Petersson metric where $\|L_g\|_1\rightarrow\infty$ satisfies certain conditions.Comment: 20pages, new results added, second theorem is improve

Understanding the Generalization Ability of Deep Learning Algorithms: A Kernelized Renyi's Entropy Perspective

Recently, information theoretic analysis has become a popular framework for understanding the generalization behavior of deep neural networks. It allows a direct analysis for stochastic gradient/Langevin descent (SGD/SGLD) learning algorithms without strong assumptions such as Lipschitz or convexity conditions. However, the current generalization error bounds within this framework are still far from optimal, while substantial improvements on these bounds are quite challenging due to the intractability of high-dimensional information quantities. To address this issue, we first propose a novel information theoretical measure: kernelized Renyi's entropy, by utilizing operator representation in Hilbert space. It inherits the properties of Shannon's entropy and can be effectively calculated via simple random sampling, while remaining independent of the input dimension. We then establish the generalization error bounds for SGD/SGLD under kernelized Renyi's entropy, where the mutual information quantities can be directly calculated, enabling evaluation of the tightness of each intermediate step. We show that our information-theoretical bounds depend on the statistics of the stochastic gradients evaluated along with the iterates, and are rigorously tighter than the current state-of-the-art (SOTA) results. The theoretical findings are also supported by large-scale empirical studies1

Seasonal variation of thermal sensations in residential buildings in the hot summer and cold winter zone of China

The seasonal differences of neutral or acceptable temperatures between summer and winter were revealed by previous researchers, but the studies on the difference of human thermal adaption in transitional seasons are insufficient. To clarify this, this paper analyzes the data from a nationwide field study database, including a year-long survey which was carried out in 505 residential buildings in six cities located in the Hot Summer and Cold Winter (HSCW) zone of China involving 11,524 subjects. Results show a significant difference of adaptive responses in different seasons. Air temperature is found to be the most significant driver for behavioral responses, and a lag of behavioral responses behind climate change in transitional seasons is observed. Occupants not only adjust clothing insulation according to air temperature in different seasons, but also actively control indoor air movement, including closing/opening windows and using fans. The seasonal, monthly and daily neutral temperatures are studied, implying that occupants’ thermal experience history has significant effect on their thermal comfort by behavioral, physiological and psychological paths. Thus, the running mean air temperature method and aPMV model are recommended for thermal comfort evaluation in free-running space. The research results provide comprehensive understanding of the thermal comfort demand which directly affects the energy needs for heating and cooling purpose. The findings provide scientific evidence to the concept that dynamic thermal comfort temperature range should be considered in the evaluation of indoor thermal environment

Automated Testing of Web Services Based on Algebraic Specifications

The testing of web services must be done in a completely automated manner when it takes place on-the-fly due to third-party services are dynamically composed to. We present an approach that uses algebraic specification to make this possible. Test data is generated from a formal specification and then used to construct and submit service requests. Test results are then extracted and checked against the specification. All these are done automatically, as required. We present ASSAT (Algebraic Specification-Based Service Automated Testing), a prototype tool that performs these tasks and demonstrate its utility by applying it to Amazon Web Services, a real-life industrial example

Redox-responsive inorganic fluorescent nanoprobes for serodiagnosis and bioimaging

Redox reactions play fundamental roles in life and are at the core of metabolism. Thus, observing and quantifying these reactions is crucial for diagnostics and therapy. Recent advances in inorganic fluorescent nanoprobes have revolutionized the field, enabling in vitro diagnostics by providing reliable tools for real-time, quantitative determination of redox biomolecule levels in biological samples and cells. Due to their high stability, these probes are also widely used in bioimaging, providing real-time information for in vivo diagnostics and guiding treatment of diseases associated with redox biomolecules. This review explores the diverse landscape of inorganic fluorescent nanoprobes designed for the detection of biologically relevant reactive oxygen and nitrogen species. The discussion is divided into several sections, each focusing on nanoprobes tailored for specific oxidative species. The impact of tailored nanoprobes in diagnostics and imaging-guided treatment depends on their chemical composition, surface property, and fluorescence mechanism. The discussions highlight the current strengths and weaknesses, which will help to design more efficient redox-responsive inorganic fluorescent nanoprobes in the future

De novo assembly and transcriptome characterization: novel insights into the natural resistance mechanisms of Microtus fortis against Schistosoma japonicum

BACKGROUND: Microtus fortis is a non-permissive host of Schistosoma japonicum. It has natural resistance against schistosomes, although the precise resistance mechanisms remain unclear. The paucity of genetic information for M. fortis limits the use of available immunological methods. Thus, studies based on high-throughput sequencing technologies are required to obtain information about resistance mechanisms against S. japonicum. RESULTS: Using Illumina single-end technology, a de novo assembly of the M. fortis transcriptome produced 67,751 unigenes with an average length of 868 nucleotides. Comparisons were made between M. fortis before and after infection with S. japonicum using RNA-seq quantification analysis. The highest number of differentially expressed genes (DEGs) occurred two weeks after infection, and the highest number of down-regulated DEGs occurred three weeks after infection. Simultaneously, the strongest pathological changes in the liver were observed at week two. Gene ontology terms and pathways related to the DEGs revealed that up-regulated transcripts were involved in metabolism, immunity and inflammatory responses. Quantitative real-time PCR analysis showed that patterns of gene expression were consistent with RNA-seq results. CONCLUSIONS: After infection with S. japonicum, a defensive reaction in M. fortis commenced rapidly, increasing dramatically in the second week, and gradually decreasing three weeks after infection. The obtained M. fortis transcriptome and DEGs profile data demonstrated that natural and adaptive immune responses, play an important role in M. fortis immunity to S. japonicum. These findings provide a better understanding of the natural resistance mechanisms of M. fortis against schistosomes. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi: 10.1186/1471-2164-15-417) contains supplementary material, which is available to authorized users