arXiv subjects

Lida Kanari

Publications and source records attributed to Lida Kanari.

5 recordsLinked to original sources

arXiv2026

Contextual Cellular Growth (ConCeG) of neural cells for realistic grey matter tissue generation for diffusion MRI simulations

Accurate interpretation of diffusion magnetic resonance imaging (dMRI) signals in grey matter (GM) remains challenging due to the complex, heterogeneous, and densely packed cellular environment. Numerical phantoms provide a controlled framework for investigating the relationship between microstructure and diffusion signals, yet existing approaches often lack the morphological realism and multi-cellular organisation required to faithfully represent GM tissue. In this work, we introduce Contextual Cellular Growth (ConCeG), a generative framework for creating individual cells or constructing dense, three-dimensional, multi-cellular GM substrates informed by real neuronal and glial morphologies. The method combines topological neuron synthesis with a spatially constrained growth network, allowing for the controlled generation of heterogeneous cellular environments with realistic intra- and extracellular compartments. Synthetic cells are generated using morphological and topological characteristics derived from biological reconstructions. We validate the framework through comparisons of structural features with real cellular data, demonstrating strong agreement in branch order, length, angle, and tortuosity distributions. Power spectrum analysis further shows that both intracellular compartments reproduce the spatial correlations observed in biological tissue. Together, these results show ConCeG provides a biologically grounded framework for generating grey matter substrates suitable for large scale diffusion MRI simulation.

physics.med-ph↗

arXiv2024

Decomposing the Persistent Homology Transform of Star-Shaped Objects

In this paper, we study the geometric decomposition of the degree-$0$ Persistent Homology Transform (PHT) as viewed as a persistence diagram bundle. We focus on star-shaped objects as they can be segmented into smaller, simpler regions known as ``sectors". Algebraically, we demonstrate that the degree-$0$ persistence diagram of a star-shaped object in $\R^2$ can be derived from the degree-$0$ persistence diagrams of its sectors. Using this, we then establish sufficient conditions for star-shaped objects in $\R^2$ so that they have ``trivial geometric monodromy''. Consequently, the PHT of such a shape can be decomposed as a union of curves parameterized by $\bS^1$, where the curves are given by the continuous movement of each point in the persistence diagrams that are parameterized by $\bS^{1}$. Finally, we discuss the current challenges of generalizing these results to higher dimensions.

math.AT↗

arXiv2021

From Trees to Barcodes and Back Again II: Combinatorial and Probabilistic Aspects of a Topological Inverse Problem

In this paper we consider two aspects of the inverse problem of how to construct merge trees realizing a given barcode. Much of our investigation exploits a recently discovered connection between the symmetric group and barcodes in general position, based on the simple observation that death order is a permutation of birth order. The first important outcome of our study is a clear combinatorial distinction between the space of phylogenetic trees (as defined by Billera, Holmes and Vogtmann) and the space of merge trees. Generic BHV trees on $n+1$ leaf nodes fall into $(2n-1)!!$ distinct strata, but the analogous number for merge trees is equal to the number of maximal chains in the lattice of partitions, i.e., $(n+1)!n!2^{-n}$. The second aspect of our study is the derivation of precise formulas for the distribution of tree realization numbers (the number of merge trees realizing a given barcode) when we assume that barcodes are sampled using a uniform distribution on the symmetric group. We are able to characterize some of the higher moments of this distribution, thanks in part to a reformulation in terms of Dirichlet convolution. This characterization provides a type of null hypothesis, apparently different from the distributions observed in real neuron data and opens the door to doing more precise science.

math.AT↗

arXiv2020

From trees to barcodes and back again: theoretical and statistical perspectives

Methods of topological data analysis have been successfully applied in a wide range of fields to provide useful summaries of the structure of complex data sets in terms of topological descriptors, such as persistence diagrams. While there are many powerful techniques for computing topological descriptors, the inverse problem, i.e., recovering the input data from topological descriptors, has proved to be challenging. In this article we study in detail the Topological Morphology Descriptor (TMD), which assigns a persistence diagram to any tree embedded in Euclidean space, and a sort of stochastic inverse to the TMD, the Topological Neuron Synthesis (TNS) algorithm, gaining both theoretical and computational insights into the relation between the two. We propose a new approach to classify barcodes using symmetric groups, which provides a concrete language to formulate our results. We investigate to what extent the TNS recovers a geometric tree from its TMD and describe the effect of different types of noise on the process of tree generation from persistence diagrams. We prove moreover that the TNS algorithm is stable with respect to specific types of noise.

math.AT↗

arXiv2016

Quantifying topological invariants of neuronal morphologies

Nervous systems are characterized by neurons displaying a diversity of morphological shapes. Traditionally, different shapes have been qualitatively described based on visual inspection and quantitatively described based on morphometric parameters. Neither process provides a solid foundation for categorizing the various morphologies, a problem that is important in many fields. We propose a stable topological measure as a standardized descriptor for any tree-like morphology, which encodes its skeletal branching anatomy. More specifically it is a barcode of the branching tree as determined by a spherical filtration centered at the root or neuronal soma. This Topological Morphology Descriptor (TMD) allows for the discrimination of groups of random and neuronal trees at linear computational cost.

q-bio.NC↗