On powers of Hamilton cycles in Ramsey-Tur\'{a}n Theory

We prove that for $r\in \mathbb{N}$ with $r\geq 2$ and $\mu>0$, there exist $\alpha>0$ and $n_{0}$ such that for every $n\geq n_{0}$, every $n$-vertex graph $G$ with $\delta(G)\geq \left(1-\frac{1}{r}+\mu\right)n$ and $\alpha(G)\leq \alpha n$ contains an $r$-th power of a Hamilton cycle. We also show that the minimum degree condition is asymptotically sharp for $r=2, 3$ and the $r=2$ case was recently conjectured by Staden and Treglown.Comment: 19 pages, 4 figure

Microstructural analysis of skeletal muscle force generation during aging.

Human aging results in a progressive decline in the active force generation capability of skeletal muscle. While many factors related to the changes of morphological and structural properties in muscle fibers and the extracellular matrix (ECM) have been considered as possible reasons for causing age-related force reduction, it is still not fully understood why the decrease in force generation under eccentric contraction (lengthening) is much less than that under concentric contraction (shortening). Biomechanically, it was observed that connective tissues (endomysium) stiffen as ages, and the volume ratio of connective tissues exhibits an age-related increase. However, limited skeletal muscle models take into account the microstructural characteristics as well as the volume fraction of tissue material. This study aims to provide a numerical investigation in which the muscle fibers and the ECM are explicitly represented to allow quantitative assessment of the age-related force reduction mechanism. To this end, a fiber-level honeycomb-like microstructure is constructed and modeled by a pixel-based Reproducing Kernel Particle Method (RKPM), which allows modeling of smooth transition in biomaterial properties across material interfaces. The numerical investigation reveals that the increased stiffness of the passive materials of muscle tissue reduces the force generation capability under concentric contraction while maintains the force generation capability under eccentric contraction. The proposed RKPM microscopic model provides effective means for the cellular-scale numerical investigation of skeletal muscle physiology. NOVELTY STATEMENT: A cellular-scale honeycomb-like microstructural muscle model constructed from a histological cross-sectional image of muscle is employed to study the causal relations between age-associated microstructural changes and age-related force loss using Reproducing Kernel Particle Method (RKPM). The employed RKPM offers an effective means for modeling biological materials based on pixel points in the medical images and allow modeling of smooth transition in the material properties across interfaces. The proposed microstructure-informed muscle model enables quantitative evaluation on how cellular-scale compositions contribute to muscle functionality and explain differences in age-related force changes during concentric, isometric and eccentric contractions

The Devil is the Classifier: Investigating Long Tail Relation Classification with Decoupling Analysis

Long-tailed relation classification is a challenging problem as the head classes may dominate the training phase, thereby leading to the deterioration of the tail performance. Existing solutions usually address this issue via class-balancing strategies, e.g., data re-sampling and loss re-weighting, but all these methods adhere to the schema of entangling learning of the representation and classifier. In this study, we conduct an in-depth empirical investigation into the long-tailed problem and found that pre-trained models with instance-balanced sampling already capture the well-learned representations for all classes; moreover, it is possible to achieve better long-tailed classification ability at low cost by only adjusting the classifier. Inspired by this observation, we propose a robust classifier with attentive relation routing, which assigns soft weights by automatically aggregating the relations. Extensive experiments on two datasets demonstrate the effectiveness of our proposed approach. Code and datasets are available in https://github.com/zjunlp/deepke