Critical values of Gaussian SU(2) random polynomials

In this note, we will get the estimate of the expected distribution of critical values of Gaussian SU(2) random polynomials as the degree large enough. The result is a direct application of the Kac-Rice formula. The critical values will accumulate at infinity, we further study the rate of this convergence and its rescaling limit as $n\to\infty$.Comment: the growth of critical values is further studied, the rescaling limit of the density is added, some typos are fixed, to appear in Proceeding of AM

Detail-revealing Deep Video Super-resolution

Previous CNN-based video super-resolution approaches need to align multiple frames to the reference. In this paper, we show that proper frame alignment and motion compensation is crucial for achieving high quality results. We accordingly propose a `sub-pixel motion compensation' (SPMC) layer in a CNN framework. Analysis and experiments show the suitability of this layer in video SR. The final end-to-end, scalable CNN framework effectively incorporates the SPMC layer and fuses multiple frames to reveal image details. Our implementation can generate visually and quantitatively high-quality results, superior to current state-of-the-arts, without the need of parameter tuning.Comment: 9 pages, submitted to conferenc

Aesthetic Psychological Change on Fine Art Creation in the New Period

This paper mainly discusses the aesthetic psychology on fine art creation in the new period of China. This paper considers aesthetic psychology to contain both historic aesthetic heritage and present aesthetic practices. The main logic lies in that: based on the historic heritage after the “Cultural Revolution”, new aesthetic psychology has been generated and developed to trigger present confrontations; secondly, consequences caused directly by the aesthetic change make aesthetics no longer a political game. Aesthetic subjects began to abandon the pervious political point of view, and reflect on their aesthetic attitudes and aesthetic positions by aesthetic practices

Prognostic nomogram for bladder cancer with brain metastases: a National Cancer Database analysis.

BACKGROUND: This study aimed to establish and validate a nomogram for predicting brain metastasis in patients with bladder cancer (BCa) and assess various treatment modalities using a primary cohort comprising 234 patients with clinicopathologically-confirmed BCa from 2004 to 2015 in the National Cancer Database. METHODS: Machine learning method and Cox model were used for nomogram construction. For BCa patients with brain metastasis, surgery of the primary site, chemotherapy, radiation therapy, palliative care, brain confinement of metastatic sites, and the Charlson/Deyo Score were predictive features identified for building the nomogram. RESULTS: For the original 169 patients considered in the model, the areas under the receiver operating characteristic curve (AUC) were 0.823 (95% CI 0.758-0.889, P \u3c 0.001) and 0.854 (95% CI 0.785-0.924, P \u3c 0.001) for 0.5- and 1-year overall survival respectively. In the validation cohort, the nomogram displayed similar AUCs of 0.838 (95% CI 0.738-0.937, P \u3c 0.001) and 0.809 (95% CI 0.680-0.939, P \u3c 0.001), respectively. The high and low risk groups had median survivals of 1.91 and 5.09 months for the training cohort and 1.68 and 8.05 months for the validation set, respectively (both P \u3c 0.0001). CONCLUSIONS: Our prognostic nomogram provides a useful tool for overall survival prediction as well as assessing the risk and optimal treatment for BCa patients with brain metastasis

Nonlinear focal modulation microscopy

Here we report nonlinear focal modulation microscopy (NFOMM) to achieve super-resolution imaging. Abandoning the previous persistence on minimizing the size of Gaussian emission pattern by directly narrowing (e.g. Minimizing the detection pinhole in Airyscan, Zeiss) or by indirectly peeling its outer profiles (e.g., Depleting the outer emission region in STED, stimulated emission microscopy) in pointwise scanning scenarios, we stick to a more general basis------ maximizing the system frequency shifting ability. In NFOMM, we implement a nonlinear focal modulation by applying phase modulations with high-intensity illumination, thereby extending the effective spatial-frequency bandwidth of the imaging system for reconstructing super-resolved images. NFOMM employs a spatial light modulator (SLM) for assisting pattern-modulated pointwise scanning, making the system single beam path while achieving a transverse resolution of 60 nm on imaging fluorescent nanoparticles. While exploring a relatively simple and flexible system, the imagingperformance of NFOMM is comparable with STED as evidenced in imaging nuclear pore complexes, demonstrating NFOMM is a suitable observation tool for fundamental studies in biology. Since NFOMM is implemented as an add-on module to an existing laser scanning microscope and easy to be aligned, we anticipate it will be adopted rapidly by the biological community.Comment: 5 Figures, under review in PR