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Ma.Me.Mo.Bi.A

Revolutionizing healthcare with advanced mathematics in imaging, segmentation, and disease diagnosis

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Mathematical Models

From deciphering biological systems to enhancing medical imaging, our models, rooted in mathematical precision.

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Biomedical Applications

The versatility of mathematical models in decoding biological mysteries, advancing medical imaging, and revolutionizing epidemiological insights.

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About Us

Welcome to 'Mathematical Methods and Models for Biomedical Applications'



Project Overview



Project financed by National Recovery and Resilience Plan PNRR-III-C9-2022-I8
”Mathematical Methods and Models for Biomedical Applications” (Ma.Me.Mo.Bi.A)
(Project code: 125/15.11.2022, Contract no. 760076/23.05.2023)

Main Objectives

The aim of the present project Ma.Me.Mo.Bi.A. is to develop a series of mathematical models that can be used in biomedical applications. Developing a theoretical foundation based on Mathematical Analysis, Fourier Analysis, and Approximation Theory, the project will provide three different and equally important applications in Digital Image Processing in connection with some real-world models in the biomedical field.

The project will develop a procedure for the diagnosis

  • Diagnosis of vascular pathologies (using Computer Tomography images)
  • Diagnosis of retinal pathologies (involving Optical Coherence Tomography images)
  • Evaluation of biomarkers in Alzheimer disease (based on brain Magnetic Resonance images)

by applying a new de-noising and resizing algorithm to existing medical imaging, yielding results that are quite similar in quality to the imaging conducted with the use of contrast medium.

Vascular Pathologies

Diagnosis using Computer Tomography images.

Retinal Pathologies

Diagnosis involving Optical Coherence Tomography images.

Alzheimer Disease Biomarkers

Evaluation based on brain Magnetic Resonance images.

Team

Meet the team

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Gianluca Vinti

Project Director

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Ana Maria Acu

Executive Manager

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Daniela Trocan

Assistant Manager

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Florin Sofonea

Researcher, Faculty of Sciences, Sibiu

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Ioan Rașa

Researcher, UT Cluj

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Augusta Rațiu

Researcher, ULBS

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Miruna-Ştefana Sorea

Postdoctoral Researcher, ULBS

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Cristina Cismaș (Brumar)

Post Ph.D. ULBS

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Pepenar Alin

Doctoral Researcher, ULBS

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Sergiu-Vlad Paşca

Doctoral Researcher, ULBS

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Arianna Travaglini

Doctoral Researcher, University of Florence

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Mihai Ilina

Doctoral Researcher, ULBS

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Chivu Georgian-Cristian

Doctoral Researcher, ULBS

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Ovio Olaru

Researcher, ULBS

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Martin Anca Simina

Researcher, ULBS

Results & Publications

  • [1] Ana-Maria Acu, Ioan Rasa, Ancuta Emilia Steopoaie, Bernstein-Kantorovich operators, approximation and shape preserving properties, Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 118, 107 (2024). Link
  • [2] A.M. Acu, Ioan Rasa, G. Motronea, Bernstein polynomials and dual functionals, Bulletin of the Transilvania University of Brasov, Series III: Mathematics and Computer Science, 65(2), 2023. Link
  • [3] Gabriela Motronea, Alin Pepenar, Variance and information potential of some random variables, General Mathematics, Vol. 31, No. 2 (2023), 80–84. Link
  • [4] S.V. Pasca, A. Seserman, A. Steopoaie, Iterates of positive linear operators and linear systems of equations, Dolomites Research Notes on Approximation, 17(2), 52-58, (2024). Link
  • [5] Bodin, Arnaud, Evelia Rosa García Barroso, Patrick Popescu-Pampu, Miruna-Stefana Sorea, Combinatorial study of morsifications of real univariate singularities, Mathematische Nachrichten, 2024. Link
  • [6] L. Rinelli, A. Travaglini, N. Vescera, G. Vinti: An approximation-based approach versus an AI one for the study of CT images of abdominal aorta aneurysms, submitted to ArXiv– arXiv. 2406.01764 and ready to be submitted in a scientific journal (2024). Link
  • [7] D. Costarelli, M. Piconi, G. Vinti: On the regularization by Durrmeyer-sampling type operators in Lp-spaces via a distributional approach, J Fourier Anal Appl 31, 11 (2025). Link
  • [8] A.M. Acu, H. Gonska, Overiteration of d-variate tensor product Bernstein operators: A quantitative result, Stud. Univ. Babes-Bolyai Math. 69(2024), No. 4, 895-903. Link
  • [9] Acu, A.M., Ilina, M., Sofonea, F., Travaglini, A., Vinti, G. (2026). A Comparison Between Neural Network and Sampling Kantorovich Operators in Terms of Image denoising. In: Gervasi, O., et al. Computational Science and Its Applications – ICCSA 2025 Workshops. ICCSA 2025. Lecture Notes in Computer Science, vol 15892. Springer, Cham. Link
  • [10] Gheorghe Craciun, Jiaxin Jin, Miruna-Stefana Sorea, The structure of the toric locus of a reaction network, NONLINEARITY, 38(1), 2025. Link
  • [11] K. Kohn, R. Piene, K. Ranestad, F. Rydell, B. Shapiro, R. Sinn, MS Sorea, S. Telen, Adjoints and canonical forms of polypols, DOCUMENTA MATHEMATICA, 30P, 275-346, 2025. Link

Conference Talks

  • [1] First Annual FORTHEM Conference FORTHEM - For the Future (Section: Natural Sciences – Be innovative) - Event Link
    • Miruna-Stefana Sorea, How to measure the non-convexity
    • Georgian-Cristian Chivu, Generative Image Algorithms based on AI approach with comparative results
    • Ilina Mihai, Otsu's Method for Image Segmentation
  • [2] Approximation: Theory, Methods and Applications, Lecce, Italy, June 11-14, 2024 - Event Link
    • Ana-Maria Acu, Ioan Rasa, Positive linear operators, convexity and approximation-online
  • [3] 60th International Symposium on Functional Equations June 9-15, 2024, Kościelisko, Poland - Event Link
    • Ana-Maria Acu, Ioan Rasa, Functional inequalities and convex stochastic orders (II)-onsite
  • [4] International Conference on Approximation Theory and its Applications, 17-20 Iulie, 2024, Sibiu, Romania - Event Link
    • Ioan Rasa, Cauchy problems and positive linear operators (prelegere invitata)
    • Alin Pepenar, Rates of convergence for iterates of positive linear operators
    • Sergiu-Vlad Pașca, The eigenstructure of certain operators
    • Georgian-Cristian Chivu, Introduction into Image Segmentation Techniques based on AI approach, exploring advanced Techniques and Architectures
    • Miruna-Ștefana Sorea, Morsifications of univariate real singularities – a combinatorial study
  • [5] Approximation Theory and Special Functions – ATSF Conference – 8th Series, 4-7 septembrie 2024, Ankara, Turcia - Event Link
    • Ana Maria Acu, Multivariate Aldaz-Kounchev-Render Operators and Their Approximation Properties (prelegere invitata)
    • Ioan Rasa, Positive Linear Operators and Convex Stochastic Orders
    • Augusta Ratiu, Some Bounds for Several Statistical Indicators
  • [6] The 14th AIMS Conference 2024, 16-20 December 2024, Abu Dhabi, UAE - Event Link
    • Gianluca Vinti, Discrete and semi-discrete sampling type operators and applications to image segmentation
    • Augusta Ratiu, A Cauchy problem and a semigroup of positive operators
    • Ana Maria Acu, Weakly convex and generalized subharmonic functions related to a $C_0$-semigroup
  • [7] 2nd FORTHEM Annual Conference - Connecting Worlds of Science and Society, Jan 29–31, 2025, ONLINE - Event Link
    • Georgian-Cristian Chivu, Usage of Neural Networks U-Net & GANs in image segmentation, a study case with application
    • Miruna-Stefana Sorea, The structure of the toric locus of a reaction network
    • Ilina Mihai, Linear operators applied in image processing
  • [8] International Scientific Conference-Aczél 100, Hajdúszoboszló, Hungary, February 2-7, 2025 - Event Link
    • Ana-Maria Acu, Types of convexity related to a C0-semigroup
    • Ioan Rasa, Functional equations related to Appell polynomials and Heun functions (II)
  • [9] Documentare: 28 Feb – 6 Mar 2025, Universitatea din Perugia, Italia
    • Ana-Maria Acu, Participant
  • [10] Documentare: 2 – 16 Aprilie 2025, Technische Hochschule Mittelhessen, Friedberg, Germania
    • Ana-Maria Acu, Ioan Rasa, Participanti
  • [11] Sesiunea de Comunicări Științifice ale Studenților – Matematică, Universitatea Babeș-Bolyai, Cluj-Napoca, 24 Mai 2025 - Event Link
    • Mihai Ilina, Aplicarea operatorilor liniari de tip retea neuronala in procesarea imaginilor
    • Georgian-Cristian Chivu, Integrarea inteligentei artificiale in procesarea si segmentarea imaginilor: arhitecturi si modele
  • [12] 61st International Symposium on Functional Equations, June 15-21, 2025, Cluj-Napoca, Romania - Event Link
    • Ioan Rasa, Characterizations of the limits of certain sequences of positive linear operators
    • Alexandra Maduta, Probability distributions and their entropies
  • [13] The 25th International Conference on Computational Science and Its Applications, June 30 - July 3, 2025, Istanbul, Türkiye - Event Link
    • Ana Maria Acu, Mihai Ilina, Daniel Florin Sofonea, Arianna Travaglini, Gianluca Vinti, A comparison between Neural Network and sampling Kantorovich operators in terms of image denoising
    • Martina Longaroni, Lucrezia Rinelli, Arianna Travaglini, Gianluca Vinti, Mathematical models and algorithms for processing retinal OCTA images
  • [14] 3rd International Conference: Constructive Mathematical Analysis, 02-05 July 2025, Konya, Turkey - Event Link
    • Ioan Rasa, Sequences of Positive Linear Operators and their limits
    • Arianna Travaglini, Approximation Properties of Neural Network and Sampling Kantorovich Operators in terms of Image Reconstruction
  • [15] International Mathematical Summer Center - Modern Perspectives in Approximation Theory: Graphs, Networks, quasi-interpolation and Sampling Theory, Cetraro, Italy - July 21-24, 2025 - Event Link
    • Participanti: Arianna Travaglini, Mihai Ilina, Georgian Chivu, Alin Pepenar, Vlad Pasca, Ana-Maria Acu, Ioan Rasa

News

We have great pleasure to invite you to attend the “International Conference on Approximation Theory and its Applications” (ICATA 2024), which will take place on July 17-20, 2024 in Sibiu, Romania. Please find the on-line registration form and all further necessary details on the web-site https://conferences.ulbsibiu.ro/icata/

All Works

Here are the main works we done until now,
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