Selected Work

Selected work. For more, check my profiles on Google Scholar and ORCID or contact me.


Gradient Porous Structures of Mycelium: A Quantitative Structure-Mechanical Property Analysis
E Oliverio, E Gawronska, P Manimuda, D Jivani, F Zullfikar Chaggan, Z Corey, T Stona De Almeida, J Kaplan-Bie, G McIntyre, O Wodo, P C Nalam
Scientific Reports 13, 19285 (2023):
Abstract: Gradient porous structures (GPS) are characterized by structural variations along a specific direction, leading to enhanced mechanical and functional properties compared to homogeneous structures. This study explores the potential of mycelium, the root part of fungus, as a biomaterial for generating GPS. During intentional growth of mycelium, the filamentous network undergoes structural changes as the hyphae grow away from the feed substrate. Through microstructural analysis of sections obtained from the mycelium tissue, systematic variations in fiber characteristics (such as fiber radii distribution, crosslink density, network density, segment length) and pore characteristics (including pore size, number, porosity) are observed. Furthermore, the mesoscale mechanical moduli of the mycelium networks exhibit a gradual variation in local elastic modulus, with a significant change of approximately 50% across a 1.2-inch-thick mycelium tissue. The structure-property analysis reveals a direct correlation between the local mechanical moduli and the network density of the mycelium. This study presents the potential of controlling growth conditions to generate mycelium-based GPS with desired functional properties. This approach, which is both sustainable and economically viable, expands the applications of mycelium-based GPS to include filtration membranes, bio-scaffolds, tissue regeneration platforms, and more.
Keywords: Gradient Porous Structures; Fibrous Networks; Mycelium; Micromechanics; Microstructure Informatics.

Mining Artifacts in Mycelium SEM Micrographs
T Stona de Almeida
Preprint v.1 (v.2 to be submitted soon): arXiv:2103.07573
Abstract: Mycelium is a promising biomaterial based on fungal mycelium, a highly porous, nanofibrous structure. Scanning electron micrographs are used to characterize its network, but the currently available tools for nanofibrous microstructures do not contemplate the particularities of biomaterials. The adoption of a software for artificial nanofibrous microstructure for mycelium characterization adds the uncertainty of imaging artifact formation to the analysis. The reported work combines supervised and unsupervised machine learning methods to automate the identification of artifacts in the mapped pores of mycelium microstructure.
Keywords: Machine Learning; Unsupervised Learning; Image Processing; Mycelium; Microstructure Informatics.

ZIP Code versus Georeference
JL Bazán Guzmán, TS de Almeida, MM Ferreira, DCF Guzmán, F Louzada, M Miranda, AL Mota, S Rangel, CM Russo, LA Santos, MO Santos, F Toledo
Mathematics in Industry Reports (2021), Cambridge Open Engage, doi:10.33774/miir-2021-4lgsp-v3
Abstract: When dealing with predictive modeling of credit-granting, different types of attributes are used: Cadastral, Behavioral, Business / Proposal, Credit Bureaux, in addition to Public, Private or Subsidiaries Sources. The Postal Address Code (Código de Endereçamento Postal CEP in Portuguese) in Brazil, in particular, has a unique contribution capacity (uncorrelated with most other attributes in general) and reasonably good predictive power. CEP is frequently used by truncating its numeric representation, considering the first d digits, for example. In this report, a preliminary methodology is proposed, aiming to elaborate clustering sets of CEPs by considering the information of clients' defaults over a period of time. Additionally, we tested the number of clusters obtained using the Information Value criterion. Promising solutions are obtained using statistical and optimizing approaches. Other methodologies are suggested and could be complementary with the principal methodology proposed.
Keywords: Classification; Clustering; Geospatial Data; Optimization; Credit Risk; Machine Learning; Computational Geometry; Information Value.


Convex Geometric Reasoning for Crystalline Energies
T Stona de Almeida
Caspian Journal of Computational & Mathematical Engineering, 2016, 51-62 (arXiv:2102.12683)
Abstract: The present work revisits the classical Wulff problem restricted to crystalline integrands, a class of surface energies that gives rise to finitely faceted crystals. The general proof of the Wulff theorem was given by J.E. Taylor (1978) by methods of Geometric Measure Theory. This work follows a simpler and direct way through Minkowski Theory by taking advantage of the convex properties of the considered Wulff shapes.
Keywords: Wulff Shape; Energy Minimization; Anisotropy; Surface Energy; Geometric Inequality.
MSC: 35A15-Variational methods; 49J40-Variational inequalities; 49K20-Problems involving PDEs; 49Q10-Shape optimization other than minimal surfaces; 52B60-Isoperimetric problems for polytopes; 82D25-Crystals

A mathematician's questions about the Hirshfeld surface
T Stona de Almeida
Talk; Abstract in Book of abstracts of İzmir Mathematics Days V, 2023, Türki̇ye; p. 28. ISBN: 978-625-00-8356-7. Conference website
Abstract: The Hirshfeld surface is, at first sight, an intuitive object: the geometric locus that equally splits the electronic density contribution of a subset of atoms - the promolecule - within a larger molecule or crystal cell - the procrystal. The result is a closed surface that is not necessarily convex but still easy to imagine. Or is it? The application of the Hirshfeld surface is often qualitative and visual, being used as a supporting argument or to gather intuitive clues to guide a more analytical approach in chemical characterization. For this, the surface is computationally estimated and plotted in 3D, where a color-coded scalar property can be added to represent a 4th dimension e.g. curvature. Finally, the Hirshfeld surface fingerprint is calculated, a color-coded 2-dimensional bivariate histogram of internal and external distances between the surface and the internal and external atomic nuclei relative to the promolecule. Questions arise regarding the numerical method employed to compute the surface mesh, which often contains multiple vertices where only one should be present; the accuracy of the fingerprint choice of bin size and its consequences; the loss of information that could be preserved by other methods. Are there other more appropriate scalar properties of the surface to be explored? This work is an exercise of critical thinking about the Hirshfeld surface method, a dissection of its geometry, its interpretation, and applications.
Keywords: Hirshfeld surface analysis; molecular geometry; mathematical chemistry.

The Mathematics of Equilibrium Shapes: From Geometric Inequalities to the Crystalline Variational Problem
T Stona de Almeida
Poster in Current Trends in Analysis and Partial Differential Equations, 2015, IMPA, Brazil. Conference website
Abstract: This work explores the anisotropic version of the Isoperimetric Inequality for anisotropic surface energies γ, the Crystalline Variational Problem, also known as the Wulff Problem. Our starting point is Taylor’s geometric measure approach of the Wulff problem, Crystalline Variational Problems (1978). This project was developed at the Fields Institute thematic program on Variational Problems, Fall 2014.


Transcript of Dissecting the Hirshfeld Surface
T Stona de Almeida
Cambridge Open Engage (2023), doi:10.33774/coe-2023-7nqjm (Preferred source)
Zenodo, 11 Nov. 2023, doi:10.5281/zenodo.10112561
Link to the talk at Ronin Institute's channel on YouTube: Ronin Institute Lightning Talks, October 2023
Abstract of talk:
The Hirshfeld surface was introduced by Spackman and Byrom in 1997, based on the Hirshfeld partitioning scheme for electronic contribution in molecular crystals. The Hirshfeld surface analysis and its fingerprint have become since then popular tools for visualization of intermolecular interactions and crystal packing. In this talk, I would like to go over some aspects of the Hirshfeld surface protocol and raise some questions about the method.

Structure-Bonding Relationships in Perovskites: Statistics of Hirshfeld Surfaces
T Stona de Almeida
ProQuest (2021)
Abstract: A computational quantum chemistry framework is coupled with traditional approaches, presenting a new protocol to assess perovskite stability both visually and statistically. A ranking of these metrics is defined and contextualized. The thesis provides new contributions to the understanding of the chemical bonding interpretation to the role of the tolerance/octahedral factor in perovskite systems. Results also include a database of circa 20k perovskites, containing ionic radii and tolerance factors, plus chemical features - eg: bandgap, volume, thermodynamic properties; the first large scale Hirshfeld surface quantum library for perovskite structures, consisting of circa 1500 perovskite compounds; a protocol for unsupervised classification of Hirshfeld statistics and their employment as a predictive feature in perovskite design; a dimensionality reduction analysis of the large database, and other insights.
Keywords: Machine Learning; Hirshfeld Surfaces; QSPR; Perovskites; Materials Informatics.