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The uncontrolled and unstructured growth of brain cells is known as brain tumor, which has one of the highest mortality rates among diseases from all types of cancers. Due to limited diagnostic and treatment capabilities, they pose…

Evoked EMG M-responses obtained from the thenar muscle in the palm by electrical stimulation of the median nerve demonstrate a well-established smooth bipolar shape for normal healthy subjects while kinks are observed in certain…

This paper presents a static electrical impedance tomography (EIT) technique that evaluates abdominal obesity by estimating the thickness of subcutaneous fat. EIT has a fundamental drawback for absolute admittivity imaging because of its…

Reconstructing visual stimuli from EEG signals is a crucial step in realizing brain-computer interfaces. In this paper, we propose a transformer-based EEG signal encoder integrating the Discrete Wavelet Transform (DWT) and the gating…

We introduce the effectual topological complexity (ETC) of a $G$-space $X$. This is a $G$-equivariant homotopy invariant sitting in between the effective topological complexity of the pair $(X,G)$ and the (regular) topological complexity of…

Accurate and efficient brain tumor segmentation remains a critical challenge in neuroimaging due to the heterogeneous nature of tumor subregions and the high computational cost of volumetric inference. In this paper, we propose…

The computer vision task of reconstructing 3D images, i.e., shapes, from their single 2D image slices is extremely challenging, more so in the regime of limited data. Deep learning models typically optimize geometric loss functions, which…

The histopathology analysis is of great significance for the diagnosis and prognosis of cancers, however, it has great challenges due to the enormous heterogeneity of gigapixel whole slide images (WSIs) and the intricate representation of…

We pursue a computational analysis of the biomedical problem on the identification of the cancerous tumor at an early stage of development based on the Electrical Impedance Tomography (EIT) and optimal control of elliptic partial…

We write the Euler characteristic X(G) of a four dimensional finite simple geometric graph G=(V,E) in terms of the Euler characteristic X(G(w)) of two-dimensional geometric subgraphs G(w). The Euler curvature K(x) of a four dimensional…

Electrical impedance tomography (EIT) is a non-invasive imaging method with diverse applications, including medical imaging and non-destructive testing. The inverse problem of reconstructing internal electrical conductivity from boundary…

Equivariant Graph Neural Networks (GNNs) have significantly advanced the modeling of 3D molecular structure by leveraging group representations. However, their message passing, heavily relying on Clebsch-Gordan tensor product convolutions,…

The Wirtinger integral is one of the integral representations of the Gauss hypergeometric function. Its integrand is given by a product of complex powers of theta functions. We study the structure of the twisted homology and cohomology…

The principle of translation equivariance (if an input image is translated an output image should be translated by the same amount), led to the development of convolutional neural networks that revolutionized machine vision. Other…

This research presents an enhanced approach for precise segmentation of brain tumor masses in magnetic resonance imaging (MRI) using an advanced 3D-UNet model combined with a Context Transformer (CoT). By architectural expansion CoT, the…

Euler diagrams are an intuitive and popular method to visualize set-based data. In a Euler diagram, each set is represented as a closed curve, and set intersections are shown by curve overlaps. However, Euler diagrams are not visually…

Accurate prediction of cancer type and primary tumor site is critical for effective diagnosis, personalized treatment, and improved outcomes. Traditional models struggle with the complexity of genomic and clinical data, but quantum…

This paper proposes a nonlinear weighted anisotropic total variation (NWATV) regularization technique for electrical impedance tomography (EIT). The key idea is to incorporate the internal inhomogeneity information (e.g., edges of the…

The multi-scale information among the whole slide images (WSIs) is essential for cancer diagnosis. Although the existing multi-scale vision Transformer has shown its effectiveness for learning multi-scale image representation, it still…

Objective: Transformers, born to remedy the inadequate receptive fields of CNNs, have drawn explosive attention recently. However, the daunting computational complexity of global representation learning, together with rigid window…