** Name: ** Liron Karpati

** School: ** University of Maryland, College Park

** Majors: ** Mathematics & Computer Science

** Minor: ** Philosophy

** Email: ** liron.karpati@gmail.com

** Project: ** Identifying Motifs in Brain Connectome Data

** Mentor: ** Dr. Jie Gao

** Collaborators: ** Iris Horng

- Presented the research topic to DIMACS REU students (see slides)
- Set up this website

- Read and annoted article titled "Brain network motifs are markers of loss and recovery of consciousness".
- Summary: Although total motif frequency did not differ between conscious and unconscious

states the distribution of where particular motifs were located changed. Also certain global

metrics of the graph's topology were significantly different between conscious and unconscious states. - I learned about different kinds of motif analyses that I could use for my own project.

The distrubition analysis was particularaly interesting. The paper serves as an excellent model for the types of methods

I should consider using and learn more about. - I learned some scientific paper writing hygeine. For example, one should be explicit about what

analysis was done post-hoc (after testing the initial hypotheses). Further, it makes the paper stronger

if you can show how your findings fit into theoeretical predictions to explain why your results make sense. - I identified 13 references that would be potentially interesting to look more into.
- Attempted to set up github for jupyter notebooks but got errors.
- Next Steps:
- Understand the different methodologies and unknown terminology in the paper mentioned above.

For example, I would like to understand the the phase lag index (dPLI) and symbolic transfer entropy methods

for constructing the graph from the EEG data. I will need to see if these methods work for fMRI data too. - Filter and explore some of the referenced papers to see more examples of using motifs for predictions.
- Continue exploring the dataset.
- Set up a github repo before playing with data.

- Understand the different methodologies and unknown terminology in the paper mentioned above.

- Set up github for project and succesfully visualized one of the connectome files as a graph in networkX.
- Read "The role of motifs in understanding behavior in social and engineered networks". Unforunately, the

paper did not go into much specifics because it turned out to be a project proposal wearing a science paper's clothes. - Began learning how connectomes are constructed. In doing so I came accross the book

"Fundamentals of Brain Network Analysis" by Fornito, Zalesky, and Bullmore. I began reading it

to see if it might be a good reference for our project. - Set up a github repo before playing with data.

- Had research meeting in which we discussed 1) The paper I read called "Brain network motifs are

markers of loss and recovery of consciousness" and how it would be a good model for if we get access

to connectome data of patients experiencing seizures and 2) Persistent homology to analyze global structure.

- Determined that a good next step would be to read the "Fundamentals of Brain Network Analysis".

- Read "Fundamentals of Brain Network Analysis" chapters 1 - 2

- Read "Fundamentals of Brain Network Analysis" chapters 3 - 4

- Read "Fundamentals of Brain Network Analysis" chapters 5 - 6

- Read "Fundamentals of Brain Network Analysis" chapters 7 - 8

- Read "Fundamentals of Brain Network Analysis" chapter 9
- Research meeting. Discussed persistent homology, rich club/ small world structure

of the connectome, motif analysis, spectral analysis, and curvature analysis. - My next steps are to do some spectral analysis (look into cheeger constant) and

read about delta-hyperbolicity. There are also a number of papers I have found that

I would like to read.

- Read "Laplacians of graphs and Cheeger inequalities" by Chung.
- Computed eigen value bounds on the Cheeger constant for one of our connectomes.

When I plotted the connectome, it was not connected which is counter intuitive since

since we expect connectomes to be connected. I will inquire about this. I also computed

the Cheeger bounds for the completely connected weighted graph of correlations.

The analysis was done in networkX. From what I have understood, it does not seem like

the Cheeger value will be particular useful because it is a measure of bottle neck behavior.

One place I reason it might be interesting is to look at regional connections across the corpus collosum. - Read "The Large Scale Curvature of Networks" by Narayan and Saniee
- Read "Tree-Like Structure in Large Social and Information Networks" by Adcock, Sullivan, and Mahoney.

- Read "Functional Geometry of Human Connectomes" by TadiÄ‡, AndjelkoviÄ‡, and Melnik
- Read "Curvature-based Methods for Brain Network Analysis" by Weber et al
- Read "Large Scale Curvature of Networks" by Narayan and Saniee

- Had a research meeting in which I presented my results for the Cheeger value and proposed

a new direction for research. Based on the paper "Curvature-based Methods for Brain Network Analysis"

by Weber et al, it seems that curvature can help identify a backbone structure for a network. Given that

it is also said that the rich club is backbone structure, I want to understand what the meaning of the curvature backbone

might be. In particular, is the curvature backbone similar to the ruch club backbone? I plan to do

a path motif analysis of curvature to answer this question. The approach will model the path motif analysis

on rich clubs described in the book "Fundamentals of Brain Network Analysis". My first goal will be to

prototype the analysis by performing the ruch club path motif analysis on open source structural connectome data.

- Read "Rich-Club Organization of the Human Connectome" by van den Heuver and Sporns.
- Read "High cost, high capacity backbone for global brain communicaiton" by van den Heuver, Kahn, Goni, and Sporns.

This was the paper which did the rich club path motif analysis.

- Researched open source connectome data and settled on NeuroData.
- Familiarized myself with NeuroData and the different connectome atlases
- Did preliminary plotting of degree distributions for different parcellations of the same scan.

- Reread paper and chapter on computing the rich club coefficient.
- Began implementing weighted rich club coefficient.
- Had research meeting. Iris presented her preliminary results from her persistent homology analysis.

We discussed ways of improving the efficiency of the persistent homology algorithm. We reviewed the paper

"Topological Data Analysis of Human Brain Network Through Order Statistics" by Das, Vijay, and Chung.

- Continued developing and testing algorithm for generating rich club coefficients (weighted and unweighted).

- Met with Dr. Stamoulis team of researchers who is apart of the larger team working with

our dataset. We discussed papers and briefly presented our research projects. - Finalized code for computing rich club coefficients (weighted and unweighted).
- Began reading about creating null models to compute normalized rich club coefficients.

- Found the "Brain Connectivity Toolbox" online which provides support for connectome analyses.

In particular it can compute null models. I began playing around with the library to try and generate

null models.

- Created normalized weighted and unweighted rich club coefficient plots for different parcellations

of the same structural connectome from OpenNeuro. - Found that there was not a clear rich club structure. The different parcellations led to slightly different

rich club curves.

- Began playing around with ricci curvature library to understand how to compute the ricci curvature of the edges of a graph. Ran into some difficulties.
- Has research meeting.

- Successfully computed the ricci curvature for a graph's edges. Plotted distributions.
- Installed and learned how to use Gephi for graph visualization.
- Began exploring different visualizations of the graph with curvature attribute data for different kinds

of connectomes (structural, fMRI, and C. Elegans connectome).

- 4th of July

- Continued exploring different visualizations of the graph with curvature attribute data for different kinds

of connectomes (structural, fMRI, and C. Elegans connectome). Found that C. Elegans connectome

has a main core of neurons that are highly connected (since the edges between high degree nodes and in that core have

high curvature). That main core is connected with many low curvature edges connecting to what seem like peripheral neurons.

The fMRI connectome showed an interesting structure. There seem to be three clusters of nodes which are

connected by a central cluster. I hope to see if this central cluster is a rich club. This visualization

explains why the curvature based community detection algorithm Prof. Gao helped develop did not work on the

functional connectome data we have. The central cluster which overlaps the other clusters confounds a clear

community structure. I hope to understand what the three clusters of functional activity corresponds to in the brain

.

- I worked on creating an algorithm to count curvature path motifs. For example to count the number of

paths that exhibit the sequence of curvature edges values - + + - . - I looked for a relationship between curvature and other edge properties in the different connectomes.

In the structural dwi connectome, there was a shocking relationship between structural weight (in terms of fibers)

and curvature. The only edges with high (potentially very high) structural weight were those with curvature near one.

There was no relationship between chemical weight and curvature nor between electrical weight and curvature in the C. Elegan

connectome. (We later figured out that the shocking relationship was because OpenNeuro, where the data came from does

not automatically filter out edges with small fiber counts).

- Continued working on algorithm and testing it.
- Had research meeting.

- Solved combinatorial problem of the number of 2-paths and 3-paths in a graph for testing purposes.
- Used solution to test and modify the curvature path motif counting algorithm I wrote.
- Added region labels to fMRI visualization

- Tried to figure out how to compute random graphs that preserve degree distributions

in python to be able to null hypothesis test the algorithm. Eventually found I can use the

networkit library. - Tried running the path motif counting algorithm on fMRI functional connectome but runtime was

too large for it to be feasible.

Also computing the Ollivier curvature was too intensive. I - Had meeting with Dr. Stamoulis' group at Boston Children's Hospital which we collaborate with for

connectome data. One of her students presented papers they had been reading.

- Did path motif counting on C. Elegans and this worked but still took awhile to run. To compute

the number of paths with a given curvature pattern I set up a way for the function to run overnight and

store the information in a file.

- Found surprising result that almost all path patterns were signficant in C. Elegans.

After further examination this proved to be artifical. When we examined the curvature distribution

it turned out that the distribution for the null graphs were similar qualitatively to the

curvature distribution for C. Elegans but with a left shift. It also turns out that most edges have

near 0 curvature in both C. Elegans and the random graphs, but in the C. Elegans the majority are

just above 0 and in the random graphs the majority are just below 0 (since left shifted). This led

to an artificial significance of curvature path motifs since we only classified edges as positive

or negative. - Had research meeting. We tried to find a way to count patterned 3-paths

explicitly rather than using the recursive function I wrote. We were not successful. - Had zoom meeting with a researcher in Dr. Stamoulis' group at Boston Children's hospital

to learn about how to visualize connectome data within the brains actual geo-spatial topology.

- All day DIMACS field trip to Bell Labs.

- Modified algorithm to be able to count paths with edges classified as either

positive, neutral, or negative. Reran computation to find path motifs in sample of 1000

random 'null' graphs. - Discovered that the C. Elegans has relatively few neutral-neutral-neutral paths with

an incredibly significant p-value, even with Bonferroni correction! - Began final presentation

- Worked on presentation
- Had research meeting to discuss presentation and state of research
- Computed the rest of the curvature 3-path motifs for C. Elegans

- Worked on presentation and deeply understanding Ollivier-Ricci curvature.
- Began writing final paper report
- Worked on computing persistent homology with curvature as the filtration

- Had research meeting to practice presentation. Modified and then finalized presentation.

- Did curvature path motif analysis with restricted attention to shortest paths as well
- Listened to group presentations in the morning

- Listened to group presentations and presented.
- Worked on final paper

- Sick with covid

- Sick with covid

- Sick with covid

- Worked on final paper

- Worked and submitted final paper