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A little bit about me

• Recently completed my doctoral research at Stanford University.
• Will be transitioning to industry Jan 2023.

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• Was a part of math club in high school (Mu Alpha Theta).

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• Love high-fantasy and sci-fi.

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• I still play video games and am on my fourth play through of Witcher 3.

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• I like to code for fun!

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What is graduate school like, you ask?

“When action grows unprofitable, gather information; when information grows unprofitable, sleep.”

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What is graduate school like, you ask?

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• You will learn a range of hard and soft skills
• Hard skills: Knowledge essential to your subject, coding, math, etc…
• Soft skills: Communication skills, time management, problem-solving

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• Talking to people is how most projects start!

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• You are expected to be both independent and a team-player
• Choose your PI (i.e., advisor) wisely!

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• Written and oral communication are fundamental skills for promulgating knowledge
• Conference posters, oral presentations, fellowships, manuscripts.

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• Resilience, resilience, resilience
• Validation is at a minimal.
• Your work will be criticized.
• You will never forget the moment you made your key discovery.

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Understanding neural function with math

Farrell, Nguyen, & Soltesz. Neuron (2019).

Generative modeling, dynamical systems, numerical estimation,

optimization, graph theory, linear algebra, software engineering (time-complexity analysis, etc)

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Wide variety of applications in health and pathology

Utah electrode array

Neural spike data

Brain computer interfaces (BCIs) can help individuals with quadriplegia interact with the world again!

Hidden Markov Model

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Wide variety of applications in health and pathology

Transcranial magnetic stimulation (TMS) for treating depression (rave reviews)

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Wide variety of applications in health and pathology

• Previous studies looked at either single cells over small brain regions OR bulk activity over the entire brain.

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• What if we could do both? Single-cells across the whole brain. What could we learn about how the brain communicates in health and disease?

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• How does this change how we treat the brain?

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Step 1: In vivo Ca²⁺ imaging

Step 2: Network inference

dentate gyrus

granule

cells

data | model

whole-brain

single-cells

Step 3: Network mining

GCaMP

GCaMP

infer effective connections

GCaMP

GCaMP

control + chemoconvulsant

control +

chronically epileptic

Computational pipeline predicts superhubs as a maximally selective single-cell target for seizure control

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Whole-brain cellular resolution imaging of the epileptic brain

Fraser Sparks

Columbia

Matt Lovett-Barron

UCSD

Karl Deisseroth

Stanford

Scott Baraban

UCSF

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Chaotic recurrent neural networks

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Network inference through dynamical systems optimization

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The problem of time

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for all epochs [1..M]:

for all time steps [1..T]:

1. Integration

1a. get dx/dt

1b. get z(t)

1c. get e²(t)

2. Update weight

2a. Get c

2b. Get P(t)

2c. Get dJ

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1. A = Pφ yields an Nx1 vector takes O(N²) time
2. φ^TA is a dot product and takes O(N) time
3. Therefore c(t) is O(N²) + O(N) time

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• For P(t), we already have A = Pφ, so we don’t need to do that operation again.
• B = φ^TP yields an 1xN vector and takes O(N²) time.
• A*B takes O(N²) time and yields an NxN matrix.
• Therefore, calculating P(t) takes O(N²) time.

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• dJ is O(N²) time but note we already have A = Pφ.

Optimization takes O(M*T*N²) time on a single cpu, O(p*M*T*N²) time on supercomputers [0 < p < 1]

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synaptic current

noise

PreSz

Model was not driven by noise

Reduced inhibition during presz state

Mode sanity checks

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Graph theoretical analysis provides new insight on the organization of epileptic circuits

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Happy to take questions!

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Motif-based approximate PageRank algorithm [MAPPR] (Yin, 2017)

Key concepts: (1) Local cluster; (2) conductance

Higher-order analysis using MAPPR algorithm

Jure Leskovec

Stanford