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Yongtao Li

Publications and source records attributed to Yongtao Li.

63 records · Page 4Linked to original sources
arXiv2021

The Weighted Arithmetic Mean-Geometric Mean Inequality is Equivalent to the Hölder Inequality

In the current note, we investigate the mathematical relations among the weighted arithmetic mean-geometric mean (AM-GM) inequality, the Hölder inequality and the weighted power-mean inequality. Meanwhile, the proofs of mathematical equivalence among the weighted AM-GM inequality, the weighted power-mean inequality and the Hölder inequality are fully achieved. The new results are more generalized than those of previous studies.

math.FA↗
arXiv2020

An Oppenheim type determinantal inequality for the Khatri-Rao product

We first give an Oppenheim type determinantal inequality for the Khatri-Rao product of two block positive semidefinite matrices, and then we extend our result to multiple block matrices. As products, the extensions of Oppenheim type inequalities for the Hadamard product are also included.

math.FA↗
arXiv2020

Another determinantal inequality involving partial traces

Let $A$ be a positive semidefinite $m\times m$ block matrix with each block $n$-square, then the following determinantal inequality for partial traces holds \[ (\mathrm{tr} A)^{mn} - \det(\mathrm{tr}_2 A)^n \ge \bigl| \det A - \det(\mathrm{tr}_1 A)^m \bigr|, \] where $\mathrm{tr}_1$ and $\mathrm{tr}_2$ stand for the first and second partial trace, respectively. This result improves a recent result of Lin [14].

math.FA↗
arXiv2020

Deep Learning System to Screen Coronavirus Disease 2019 Pneumonia

We found that the real time reverse transcription-polymerase chain reaction (RT-PCR) detection of viral RNA from sputum or nasopharyngeal swab has a relatively low positive rate in the early stage to determine COVID-19 (named by the World Health Organization). The manifestations of computed tomography (CT) imaging of COVID-19 had their own characteristics, which are different from other types of viral pneumonia, such as Influenza-A viral pneumonia. Therefore, clinical doctors call for another early diagnostic criteria for this new type of pneumonia as soon as possible.This study aimed to establish an early screening model to distinguish COVID-19 pneumonia from Influenza-A viral pneumonia and healthy cases with pulmonary CT images using deep learning techniques. The candidate infection regions were first segmented out using a 3-dimensional deep learning model from pulmonary CT image set. These separated images were then categorized into COVID-19, Influenza-A viral pneumonia and irrelevant to infection groups, together with the corresponding confidence scores using a location-attention classification model. Finally the infection type and total confidence score of this CT case were calculated with Noisy-or Bayesian function.The experiments result of benchmark dataset showed that the overall accuracy was 86.7 % from the perspective of CT cases as a whole.The deep learning models established in this study were effective for the early screening of COVID-19 patients and demonstrated to be a promising supplementary diagnostic method for frontline clinical doctors.

physics.med-ph↗
arXiv2020

Some applications of two completely copositive maps

A linear map $Φ:\mathbb{M}_n \to \mathbb{M}_k$ is called completely copositive if the resulting matrix $[Φ(A_{j,i})]_{i,j=1}^m$ is positive semidefinite for any integer $m$ and positive semidefinite matrix $[A_{i,j}]_{i,j=1}^m$. In this paper, we present some applications of the completely copositive maps $Φ(X)=(\mathrm{tr} X)I+X$ and $Ψ(X)= (\mathrm{tr} X)I-X$. Some new extensions about traces inequalities of positive semidefinite $3\times 3$ block matrices are included.

math.FA↗
arXiv2019

Some properties for morphism of representations

Let $ψ: G\to GL(V)$ and $φ:G \to GL (W)$ be representations of finite group $G$. A linear map $T: V\to W$ is called a morphism from $ψ$ to $φ$ if it satisfys $Tψ_g= φ_g T$ for each $g\in G$ and let $\mathrm{Hom}_G (ψ,φ)$ denote the set of all morphisms. In this paper, we make full stufy of the subspace $\mathrm{Hom}_G(ψ, φ)$. As byproducts, we include the proof of the first orthogonality relation and Schur's orthogonality relation.

math.RT↗
arXiv2016

A note on the proofs of generalized radon inequality

In this paper, we introduce and prove the generalizations of Radon inequality. The proofs in the paper unify and are simpler than those in former work. Meanwhile, we also find mathematical equivalences among the Bernoulli inequality, the weighted AM-GM inequality, the Hölder inequality, the weighted power mean inequality and the Minkowski inequality. Finally, a series of the applications are shown in this note.

math.CA↗