Some properties of Ramsey numbers

AbstractIn this paper, some properties of Ramsey numbers are studied, and the following results are presented. 1.(1) For any positive integers k1, k2, …, km l1, l2, …, lm (m > 1), we have r ∏i=1m ki + 1, ∏i=1m li + 1 ≥ ∏i=1m [ r (ki + 1,li + 1) − 1] + 1.2.(2) For any positive integers k1, k2, …, km, l1, l2, …, ln , we have r ∑i=1m ki + 1, ∑j=1n lj + 1 ≥ ∑i=1m∑j=1n r (ki + 1,lj + 1) − mn + 1. Based on the known results of Ramsey numbers, some results of upper bounds and lower bounds of Ramsey numbers can be directly derived by those properties

An Unpaired Cross-modality Segmentation Framework Using Data Augmentation and Hybrid Convolutional Networks for Segmenting Vestibular Schwannoma and Cochlea

The crossMoDA challenge aims to automatically segment the vestibular schwannoma (VS) tumor and cochlea regions of unlabeled high-resolution T2 scans by leveraging labeled contrast-enhanced T1 scans. The 2022 edition extends the segmentation task by including multi-institutional scans. In this work, we proposed an unpaired cross-modality segmentation framework using data augmentation and hybrid convolutional networks. Considering heterogeneous distributions and various image sizes for multi-institutional scans, we apply the min-max normalization for scaling the intensities of all scans between -1 and 1, and use the voxel size resampling and center cropping to obtain fixed-size sub-volumes for training. We adopt two data augmentation methods for effectively learning the semantic information and generating realistic target domain scans: generative and online data augmentation. For generative data augmentation, we use CUT and CycleGAN to generate two groups of realistic T2 volumes with different details and appearances for supervised segmentation training. For online data augmentation, we design a random tumor signal reducing method for simulating the heterogeneity of VS tumor signals. Furthermore, we utilize an advanced hybrid convolutional network with multi-dimensional convolutions to adaptively learn sparse inter-slice information and dense intra-slice information for accurate volumetric segmentation of VS tumor and cochlea regions in anisotropic scans. On the crossMoDA2022 validation dataset, our method produces promising results and achieves the mean DSC values of 72.47% and 76.48% and ASSD values of 3.42 mm and 0.53 mm for VS tumor and cochlea regions, respectively.Comment: Accepted by BrainLes MICCAI proceeding

MLVA distribution characteristics of Yersinia pestis in China and the correlation analysis

<p>Abstract</p> <p>Background</p> <p><it>Yersinia pestis</it>, the aetiological agent of plague, has been well defined genotypically on local and worldwide scales. In November 2005, five cases of severe pneumonia of unknown causes, resulting in two deaths, were reported in Yulong, Yunnan province. In this study, we compared <it>Y. pestis </it>isolated from the Yulong focus to strains from other areas.</p> <p>Results</p> <p>Two hundred and thirteen <it>Y. pestis </it>strains collected from different plague foci in China and a live attenuated vaccine strain of <it>Y. pestis </it>(EV76) were genotyped using multiple-locus variable-number tandem repeat analysis (MLVA) on 14 loci. A total of 214 <it>Y. pestis </it>strains were divided into 85 MLVA types, and Nei's genetic diversity indices of the various loci ranged between 0.02 - 0.76. Minimum spanning tree analysis showed that <it>Y. pestis </it>in China could be divided into six complexes. It was observed that Microtus strains were different from the other three biovar strains. Each plague focus had its own unique MLVA types.</p> <p>Conclusion</p> <p>The strains isolated from Yulong, Yunnan province had a unique MLVA type, indicating a new clone group. Our results suggest that Yulong strains may have a close relationship with strains from the Qinghai-Tibet Plateau plague focus.</p

A Variational Bayesian Superresolution Approach Using Adaptive Image Prior Model

The objective of superresolution is to reconstruct a high-resolution image by using the information of a set of low-resolution images. Recently, the variational Bayesian superresolution approach has been widely used. However, these methods cannot preserve edges well while removing noises. For this reason, we propose a new image prior model and establish a Bayesian superresolution reconstruction algorithm. In the proposed prior model, the degree of interaction between pixels is adjusted adaptively by an adaptive norm, which is derived based on the local image features. Moreover, in this paper, a monotonically decreasing function is used to calculate and update the single parameter, which is used to control the severity of penalizing image gradients in the proposed prior model. Thus, the proposed prior model is adaptive to the local image features thoroughly. With the proposed prior model, the edge details are preserved and noises are reduced simultaneously. A variational Bayesian inference is employed in this paper, and the formulas for calculating all the variables including the HR image, motion parameters, and hyperparameters are derived. These variables are refined progressively in an iterative manner. Experimental results show that the proposed SR approach is very efficient when compared to existing approaches

Quasiperiodic biosequences and modulo incidence matrices

Algorithm development for finding quasiperiodic regions in sequences is at the core of many problems arising in biological sequence analysis. We solve an important problem in this area. Let A be an alphabet of size n and A ’ denote the set of sequences of length 1 over A. Given a sequence S = ~1.52...sl E A’, a positive integer p is called a period of S if s; = s;+ ~ for 1 5 i 5 1- p. S is called p-periodic if it has a minimum period p. Let n,(p) denote the set of p-periodic sequences in A I. A natural measure of “nearness to p-periodicity” for S is the average Hamming distance to the nearest p-periodic sequence: D(S) = minTEal(plD(S,T). If T is a sequence E n,(p) such that D(S,T) = D(S), then T is called a nearest p-periodic sequence of S and S is called p-quasiperiodic associated with the score D(S). This paper develops an efficient algorithm for finding a nearest p-periodic sequence of S by means of its modulo-p incidence matrix. Let c\ / = (crr;..,c\/,) and /? = (q+ l;..,q+l 4 where 1 = CV ~ + CV ~ +... + CV, is a partition of 1 and 4 is the quotientPaLd r is the remainder when 1 is divided by p. This paper shows that there exists a sequence in A ’ whose modulo-p incidence matrix has row sum vector c\ / and column sum vector 0

Multi-Branch Ensemble Learning Architecture Based on 3D CNN for False Positive Reduction in Lung Nodule Detection

It is critical to have accurate detection of lung nodules in CT images for the early diagnosis of lung cancer. In order to achieve this, it is necessary to reduce the false positive rate of detection. Due to the heterogeneity of lung nodules and their similarity to the background, it is difficult to distinguish true lung nodules from numerous candidate nodules. In this paper, in order to solve this challenging problem, we propose a Multi-Branch Ensemble Learning architecture based on the three-dimensional (3D) convolutional neural networks (MBEL-3D-CNN). The method combines three key ideas: 1) constructing a 3D-CNN to make the maximum utilization of spatial information of lung nodules in the 3D space; 2) embedding a multi-branch network architecture in the 3D-CNN that is well adapted to the heterogeneity of lung nodules, and; 3) using ensemble learning to effectively improve the generalization performance of the 3D-CNN model. In addition, we use offline hard mining operations to make the network capable of handling those indistinguishable positive and negative samples. The proposed method was tested on the dataset LUNA16 in our experiments. The experimental results show that MBEL-3D-CNN architecture can achieve better screening results