Introduction to complexity science

Speaker: Malbor Asllani

This organizational meeting will introduce the new Complexity Seminar and provide a brief overview of complexity science and its applications. Topics will include network science, nonlinear and stochastic dynamics, collective behavior, pattern formation, evolutionary game theory, mathematical biology, and neuroscience. I will also explain the seminar’s format and discuss the schedule of talks by local and international researchers, postdoctoral scholars, and senior graduate students.

Canceled (Faculty meeting)

Speaker:

Topological Descriptors in Graph Representation Learning: From Persistent Homology to Scalable Embeddings

Speaker: Astrit Tola (FSU)

The intersection of algebraic topology and machine learning has opened new avenues for understanding the multi-scale structural properties of complex data. While Graph Neural Networks (GNNs) excel at capturing local neighborhood information, they often fail to account for higher-order topological features, such as cycles and voids, which are critical for structural robustness. In this talk, I will discuss how to mathematically formalize these features using Topological Data Analysis (TDA) and integrate them into modern learning architectures.First, I will introduce TopoFormer (ICLR 2026), a scalable framework that integrates topological structure into attention-based architectures. TopoFormer uses a novel Topo-Scan module to convert graphs into ordered sequences of topological tokens, enabling the use of Transformers for graph-level representation learning. This approach preserves multi-scale structural information, provides theoretical stability guarantees, and achieves state-of-the-art results in graph classification and molecular property prediction, while remaining computationally efficient and parallelizable.Next, I will present TopER – Topological Evolution Rate (NeurIPS 2025), which introduces a low-dimensional, interpretable graph embedding derived from a simplified persistent homology pipeline. By quantifying the evolution rate of graph substructures across filtrations, TopER produces intuitive representations that enable visualization and interpretability while achieving competitive or state-of-the-art performance on molecular, biological, and social network benchmarks. The method is also available as an open-source Python package on PyPI.Together, these works illustrate a broader research direction: embedding topological inductive biases into modern deep learning architectures to achieve interpretability, scalability, and strong predictive performance.

Entropic Collapse: How Combinatorial Geometry Alters Extreme First-Passage Times

Speaker: Bhargav Karamched (FSU)

Extreme first passage times are a rich area of study in physics, mathematics, chemistry, and biology. But how their statistics look in discrete time and space geometries is not as well understood as in continuum processes. In this talk, I will discuss extreme first passage times in discrete time and space geometries and show how their statistics are fundamentally different from the continuum counterparts. I will discuss a mechanism known as ‘Entropic Collapse’ which is a crucial phenomenon in discrete geometries. Thereafter, I will discuss how the theory pertains to foraging ants and ant colonies competing for a common resource.

Habitat fragmentation promotes spatial scale separation under resource competition

Speaker: Austin Orgeron (FSU)

Habitat fragmentation, often driven by human activities, alters ecological landscapes by disrupting connectivity and reshaping species interactions. In such fragmented environments, habitats can be modeled as networks, where individuals disperse across interconnected patches. We consider an intraspecific competition model, where individuals compete for space while dispersing according to a nonlinear random walk, capturing the heterogeneity of the network. The interplay between asymmetric competition, dispersal dynamics, and spatial heterogeneity leads to nonuniform species distribution: individuals with stronger competitive traits accumulate in central (hub) habitat patches, while those with weaker traits are displaced toward the periphery. We provide analytical insights into this mechanism, supported by numerical simulations, demonstrating how competition and spatial structure jointly influence species segregation. In the large-network limit, this effect becomes extreme, with dominant individuals disappearing from peripheral patches and subordinate ones from central regions, establishing spatial segregation. This pattern may act as a potential precursor to both speciation and diversity, as physical separation can reinforce divergence within the population over time and potentially support coexistence at the landscape scale.

Predicting the response of structurally altered and asymmetrical networks

Speaker: Melvin Tyloo (University of Exeter (UK))

The response of networked system essentially depends on the structure of the coupling. It is therefore interesting to assess how the response is impacted when the structure is altered or has specific properties. Here, we consider the challenging problem of multiplicative structural alterations and asymmetrical interaction coupling. We introduce a framework to approximate the averaged response at each network node for general structural alterations, including non-normal and asymmetrical ones. Our findings indicate that both the asymmetry and non-normality of the structural alterations impact the global and local responses at different orders in time. We propose a set of matrices to identify the nodes whose response is affected the most by the structural alteration.