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Research

 

Matrix Theory & Linear Algebra: matrix means, optimization on manifolds, and applications in medical data
Interdisciplinary Focus: spectral graph theory and its application in Artificial Intelligence, and studying human brain networks

Current research:

I am a matrix theorist. Matrix theory is an interdisciplinary field of study and is a branch
of linear algebra that focuses on the study of matrices and their properties, particularly their
behavior under various operations. Positive-definite matrices, a key topic within this field,
are square matrices where all eigenvalues are positive, implying that for any non-zero vector
x, the quadratic form of the matrix, xTA x > 0. These matrices are fundamental in optimization, statistics,
and machine learning, where they ensure convexity in optimization problems and stability
in numerical algorithms. In applications such as data science, positive definite matrices
appear in covariance matrices, enabling the modeling of correlations between variables, and
in structural and functional connectivity in neuroscience, where they help analyze complex
brain networks.

  • I am a reviewer of Concrete Operators (a peer-reviewed open-access journal publishing articles devoted to all special classes of linear operators acting on function spaces).

Writings:

 

In-process

  1. Structural Connectivity Analysis of the Human Brain in the Early-Stage Schizophrenia Outcome Study.
  2. Using machine learning to identify focused status in confocal images of breast tumor cells’ lab growth.
  3. Application of Matrix Manifolds in Data Science and Data Classification. (in-process).

Published

  1. Sima Ahsani, Geometric Means Inequalities and Their Extensions to Lie Groups,
    Electronic Theses and Dissertations, (2018).
  2. Trung Hoa Dinh, Sima Ahsani, and Tin-Yau Tam, Geometry and Inequalities of
    Geometric Mean, Czechoslovak Mathematical Journal, 66 (2016) 777-792.
  3. Yousef Zamani, Sima Ahsani, On the Decomposable Numerical Range of Operators,
    Bulletin of the Iranian Mathematical Society, 40 (2014) 387-398.
  4. Sima Ahsani, On the Numerical Range of Derivative of an Induced Operator,
    Master’s Thesis, Persian, Iranian Research Institute for Information Science and
    Technology, IranDoc (2008).