arXiv subjects
Publications and source records attributed to Fateme Movahedi.
Let $G=(V, E)$ be a simple graph with vertex set $V$ and edge set $E$. The Sombor index of the graph $G$ is a degree-based topological index, defined as $$SO(G)=\sum_{uv \in E}\sqrt{d(u)^2+d(v)^2},$$ in which $d(x)$ is the degree of the vertex $x \in V$ for $x=u, v$. In this paper, we characterize the extremal trees with a given degree sequence that maximizes the Sombor index.
The nuclear protein Ki-67 and Tumor infiltrating lymphocytes (TILs) have been introduced as prognostic factors in predicting tumor progression and its treatment response. The value of the Ki-67 index and TILs in approach to heterogeneous tumors such as Breast cancer (BC), known as the most common cancer in women worldwide, has been highlighted in the literature. Due to the indeterminable and subjective nature of Ki-67 as well as TILs scoring, automated methods using machine learning, specifically approaches based on deep learning, have attracted attention. Yet, deep learning methods need considerable annotated data. In the absence of publicly available benchmarks for BC Ki-67 stained cell detection and further annotated classification of cells, we propose SHIDC-BC-Ki-67 as a dataset for the aforementioned purpose. We also introduce a novel pipeline and a backend, namely PathoNet for Ki-67 immunostained cell detection and classification and simultaneous determination of intratumoral TILs score. Further, we show that despite facing challenges, our proposed backend, PathoNet, outperforms the state of the art methods proposed to date in the harmonic mean measure.