Jose Mejia | Searcharxiv

arXiv2020

Segmentation of brain tumor on magnetic resonance imaging using a convolutional architecture

The brain is a complex organ controlling cognitive process and physical functions. Tumors in the brain are accelerated cell growths affecting the normal function and processes in the brain. MRI scans provides detailed images of the body being one of the most common tests to diagnose brain tumors. The process of segmentation of brain tumors from magnetic resonance imaging can provide a valuable guide for diagnosis, treatment planning and prediction of results. Here we consider the problem brain tumor segmentation using a Deep learning architecture for use in tumor segmentation. Although the proposed architecture is simple and computationally easy to train, it is capable of reaching $IoU$ levels of 0.95.

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arXiv2016

Entanglement distillation using Schur-Weyl decomposition for three qubits

The aim of this work is to examine the exponential rates at which entanglement distillation occur in three-qubits systems. The approach we will follow to elucidate the entanglement concentration is based on the Schur-Weyl decomposition and the Keyl-Werner theorem. In order to clearly state the main results of this work we will have to introduce the notion of SLOCC equivalence and the covariant algebra which will allow us to classify states in different \emph{entanglement classes}. Our main results comprehend the asymptotic rates for the probability of being in an invariant subspace in the Wedderburn decomposition of the state with effective Kronecker coefficient $g_{αβγ}=1$. We will also present a combinatorial formula for the effective Kronecker coefficient for two-row Young diagrams. With this work we hope to shed some light in the way a multipartite system is entangled and at which rate can we convey entanglement for further applications.

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