Bilinear Spherical Maximal Functions of Product Type

In this paper we introduce and study a bilinear spherical maximal function of product type in the spirit of bilinear Calderón–Zygmund theory. This operator is different from the bilinear spherical maximal function considered by Geba et al. in (Math Res Lett20(4):675–694, 2013). We deal with lacunary and full versions of this operator, and prove weighted estimates with respect to genuine bilinear weights beyond the Banach range. Our results are implied by sharp sparse domination for both the operators,following ideas by Lacey (J Anal Math 139(2):613–635, 2019). In the case of the lacunary maximal operator we also use interpolation of analytic families of operators to address the weighted boundedness for the whole range of tuplesRYC2018-025477-I Ikerbasqu

Bilinear Bochner-Riesz square function and applications

In this paper we introduce Stein's square function associated with bilinear Bochner-Riesz means and develop a systematic study of its $L^p$ boundedness properties. We also discuss applications of bilinear Bochner-Riesz square function in the context of bilinear fractional Schr\"{o}dinger multipliers, generalized bilinear spherical maximal function and more general bilinear multipliers defined on $\mathbb{R}^{2n}$ of the form $(\xi,\eta)\rightarrow m\left(|(\xi,\eta)|^2\right)$.Comment: Comments are welcom

Sharp endpoint Lp−L^p-estimates for Bilinear spherical maximal functions

In this article, we address endpoint issues for the bilinear spherical maximal functions. We obtain borderline restricted weak type estimates for the well studied bilinear spherical maximal function $$\mathfrak{M}(f,g)(x):=\sup_{t>0}\left|\int_{\mathbb S^{2d-1}}f(x-ty_1)g(x-ty_2)\;d\sigma(y_1,y_2)\right|,$$ in dimensions $d=1,2$ and as an application, we deduce sharp endpoint estimates for the multilinear spherical maximal function. We also prove sharp $L^p-$estimates for the local spherical maximal function in all dimensions $d\geq 2$, thus resolving a question left open in the work of Jeong and Lee (https://doi.org/10.1016/j.jfa.2020.108629). We further study necessary conditions for the bilinear maximal function, $$\mathcal M (f,g)(x)=\sup_{t>0}\left|\int_{\mathbb S^{1}}f(x-ty)g(x+ty)\;d\sigma(y)\right|$$ to be bounded from $L^{p_1}(\mathbb R^2)\times L^{p_2}(\mathbb R^2)$ to $L^p(\mathbb R^2)$ and prove sharp results for a linearized version of $\mathcal M$.Comment: 24 pages, 3 figures and 2 tables. Added new results for full and local bilinear spherical maximal functions. Improved the presentation and changed the title of the pape

Retinoblastoma gene mutations in primary human bladder cancer.

Inactivation of the retinoblastoma (RB) gene is known to be implicated in the pathogenesis of several types of human cancers. Since structural alterations of the RB gene have not been well examined in human bladder cancer, we looked for mutations in the entire coding region of this gene using polymerase chain reaction (PCR) and single-strand conformational polymorphism analysis of RNA. We also examined allelic loss of the RB gene using PCR-based restriction fragment length polymorphism analysis. Of 30 samples obtained from patients with bladder cancer, eight (27%) were found to have RB gene mutations. DNA sequencing of the PCR products revealed five cases with single point mutations and three cases with small deletions. These mutations included one (10%) of ten low-grade (grade 1) tumours, four (50%) of eight intermediate-grade (grade 2) tumours and three (25%) of 12 high-grade (grade 3) tumours. Likewise, mutations were found in four (21%) of 19 superficial (pTa and pT1) tumours and four (36%) of 11 invasive (pT2 or greater) tumours. In 15 informative cases, loss of heterozygosity at the RB locus was shown in five cases (33%), three cases with RB mutations and two without them. These results suggest that RB gene mutations are involved in low-grade and superficial bladder cancers as well as in high-grade and invasive cancers

Study of Automatic Forest Road Design Model Considering Shallow Landslides with LiDAR Data of Funyu Experimental Forest

In this study, a model to automatically design a forest road considering shallow landslides using LiDAR data was examined. First, in order to develop a shallow landslide risk map of the Funyu Experimental Forest, a slope stability analysis was carried out using the infinite slope stability analysis formula. The soil depth was surveyed at 167 points using simple penetration tests, and the frequency distributions of the soil depth were estimated as logarithmic normal distributions. A soil depth map of the experimental forest was made using the mode values of the lognormal distributions. Then, shallow landslide risk maps were also made for the experimental forest by a slope stability analysis using these soil depth distributions. Finally, an automatic forest road design model was developed with a LiDAR based highly accurate Digital Terrain Model (DTM) and shallow landslide risk map using cubic spline interpolation and dynamic programming. The program has capability of minimizing the earthwork costs while avoiding shallow landslide risk areas. The program can be effectively used to design an environmentally sound low volume road automatically

A Study of Machine Learning Models in Epidemic Surveillance: Using the Query Logs of Search Engines

Epidemics inevitably result in a large number of deaths and always cause considerable social and economic damage. Epidemic surveillance has thus become an important healthcare research issue. In 2009, Ginsberg et al. observed that the query logs of search engines can be used to estimate the status of epidemics in a timely manner. In this paper, we model epidemic surveillance as a classification problem and employ query statistics from Google to classify the status of a dengue fever epidemic. The query logs of twenty-three dengue-related keywords serve as observations for machine learning and testing, and a number of machine learning models are investigated to evaluate their surveillance performance. Evaluations based on a 5-year real world dataset demonstrate that search engine query logs can be used to construct accurate epidemic status classifiers. Moreover, the learned classifiers generally outperform conventional regression approaches. We also apply various machine learning models, including generative, discriminative, sequential, and non-sequential classification models, to demonstrate their applicability to epidemic surveillance