Research

Neuroimaging data comprises of three major components: spatial, temporal, and populational. Consequently, I aim to address this complexity by bridging mathematical theories and models, and applying them to clinical datasets in my research. To achieve this goal, I employ tools from complex networks, Topological Data Analysis (TDA), dynamical systems and AI/ML toolbox. I delve into these pursuits in my Ph.D. dissertation "Characterizing Dynamics on and of Networks via Higher-Order Interactions: Applications in Computational Neuroscience".

In particular, one of the key areas that excites me the most exploring in my research is temporal network organization and state dynamics, i.e., how populational neuronal activity is integrated into a network state. Moreover, I am also curious to investigate the interplay between wiring architectures of the micro-circuitry and very basic, fundamental biological mechanisms. I am interested in studying how different network topologies arise from biological functions behind different experiences, behaviors and cognitive states.

For a detailed discussion of these topics, please reach out to me for my research statement.

Publications

Kilic, B. Ü. , Muldoon, S. Skeleton coupling: a novel interlayer mapping of community evolution in temporal networks, Journal of Complex Networks, Volume 12, Issue 2, 2024, cnae011, https://doi.org/10.1093/comnet/cnae011.

Kilic, B. Ü. , Taylor, D. Simplicial cascades are orchestrated by the multidimensional geometry of neuronal complexes. Communications Physics 5, 278 (2022), https://doi.org/10.1038/s42005-022-01062-3.

Kilic, B. Ü. , Characterizing Dynamics on and of Networks via Higher-Order Interactions: Applications in Computational Neuroscience, State University of New York at Buffalo, ProQuest Dissertation Publishing, 2023. (PhD Thesis).

Talks

Boston University, Dynamical Systems Seminar, 2022. Thresholding and multi-body interactions orient cascades in spatially embedded networks.

Contagion on Complex Social Systems (CCSS), 2022. A simplicial threshold model for higher-order cascades.

Network Science Society (Netsci), 2022. Simplicial cascades are orchestrated by the multidimensional geometry of neuronal complexes.

Northeastern Regional Conference on Complex Systems (NERCCS), 2022. Simplicial cascades are orchestrated by the multidimensional geometry of neuronal complexes.

Northeastern Regional Conference on Complex Systems (NERCCS), 2021. Characterization of communities in dynamic functional networks.

Northeastern Regional Conference on Complex Systems (NERCCS), 2021. Geometrical and topological data analyses reveal that higher-order flow structures provide flow channels for neuronal avalanches.

Networks2021, A joint Sunbelt and NetSci Conference, 2021. Higher-order flow channels of neuronal avalanches uncovered by topological data analysis of simplicial contagions.

Posters

Northeastern Regional Conference on Complex Systems (NERCCS), 2022. Skeleton coupling: a novel topologically based method for defining interlayer links in dynamic community detection.

Dynamics Days (DD), 2022. Cascades over simplicial complexes preferably follow geometrically reinforced channels.

Society for Neuroscience (SFN), 2019. Cell detection and segmentation via persistent homology.

Teaching

I co-organized a Directed Reading Program (DRP-Turkey).

University at Buffalo, SUNY

• Graduate Teaching Assistant, MTH141, College Calculus I, Fall'18
• Graduate Teaching Assistant, MTH142, College Calculus II, Spring'18/Spring'21/Fall'22
• Graduate Teaching Assistant, MTH241, College Calculus III, Fall'19/Fall'21/Spring'22/Fall'22/Spring'23
• Graduate Teaching Assistant, MTH309, Linear Algebra, Spring'20
• Graduate Teaching Assistant, MTH417, Survey of Multivariable Calculus, Spring'22/Spring'23

• Adjunct Instructor, MTH131, Mathematical Analysis For Management, Summer'19
• Adjunct Instructor, MTH241, College Calculus III, Summer'20

Directed Reading Program (DRP-Turkey)

• Mentor for the project: `Critical Thresholds for Epidemics on Networks', Summer'23
• Mentor for the project: `Mathematics of deep learning', Summer'22
• Mentor for the project: `Graph theoretical analysis of brain networks', Summer'21

Directed Reading Program (DRP-UB)

• Mentor for the project: `Network analysis for real-world applications', Spring'22

Code

I developed several APIs for quantitative research pipelines by writing modular code in Python with accompanied documentations.

Neuronal Cascades

• Neuronal Cascades is a computational framework to simulate spreading processes on networks of coupled systems. Package contains generalizability options for networks (small-world, Erdos-Renyi, Watts-Strogatz etc..), models (higher-order models, monotonic/non-monotonic models etc..) and analysis tools (quantiative measures for the speed and the rate of spreading, topological data analysis, dimensionality reduction etc..).

Temporal Network Analysis

• Temporal Network Analysis is a python wrap-up for applying several dynamic community detection methods to temporal networks. Package contains some helper functions to construct network snapshots (for synthetic and real-world data) from time series data.

DONU-TDA: Donut-like Object segmeNtation Utilizing Topological Data Analysis

• DONUTDA is another python package I coded for applying TDA to biomedical image segmentation. Algorithm takes grayscale images as input and builds cubical complexes. Applying persistent homology yields either connected components or loops in the images. Accordingly, algorithm is suitable for localization/segmentation of different cell types, blob-like or donut-like. For the application oriented faculty and researchers, a graphical user interface (GUI) is available.