Brain oscillation (spatiotemporal)
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Marker of life
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conflicts
- Product or source?
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Well-defined and classified signal is detected
- EEG from head skin = dendrite potential
- Since axons are myelinated ⇒ high-frequency & small signals
- Can be analyzed by Fourier transform (power spectrum)
- A single pattern is made from the superposition of multiple waves
- Complexity itself highly correlates with brain states
- Brain seizure prediction problem
- Traditionally: seizure onset is random?
- NO! Complexity diminished 20min before seizure.
- Hypo: seizure = complexity reset procedure?
- Brain seizure prediction problem
- EEG from head skin = dendrite potential
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Chaotic nature
- Nonlinear dynamical system
- Fractal structure & self-similarity?
- Synchronization: cannot be understood considering axonal delay
- Not stochastic process, there exist some governing rules that determine the dynamics?
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Determinism vs Randomize Experiment
→ More random than fully deterministic system, but not fully random
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Stationary ↔ Non-stationary
- Stationarity-assuming methodologies may not be useful
- Dynamical non-stationarity?
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Bottom-up vs top-down
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Retracting governing DE from x(t) data ← Physics research
- Takens’ Embedding theorem (1981)
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Phase space analysis
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pendulum → displacement, velocity
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Dynamics to d, v phase space
(spiral form in damped oscillatory pendulum system)
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If we measure any single variable with sufficient accuracy for a long period of time, it is possible to reconstruct the underlying dynamic structure of the entire system form the behavior of that single variable using delay coordinates and the embedding procedure.
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One of the most cited paper in late 20C (unusual for mathematical papers)
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Stochastic factor가 있어도 성립하는가?
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Let’s use topologically invariant analyses, then analyze with dynamical measures!
- E.g. Substantia Nigra single cell → D2, ISI analyses
- Dimension of a certain dynamics = Required number of dimension to represent = Before the dynamics’ properties are ‘shrinked’
- Bursting data = 4-dimensional (1 < 2 < 3 < 4 = 5 = 6 = …)
- Vascular dementia — Alzheimer’s disease
- Conflicts around Schizophrenia
- Now: hypo-frontality → Schizophrenia
- E.g. Substantia Nigra single cell → D2, ISI analyses
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- Takens’ Embedding theorem (1981)
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Brain: Complex Network
- Mutual information of Alzheimer’s disease
- Nonlinear coupling
- Small-world network
- Watts, Strogats. 1998. Collective Dynamics of ‘small-world’ networks.
- Randomness is high → Fast synchronization
- Measures clustring(randomness low), path length(randomness high)
- Just a few interconnectional wires (=small-world) can make both high clustering and good path length
- AD = disconnection syndrome?
- Scale-free network: no dominant scale
- P(k) follows a power-free distribution
- Preferential attachment ← Albert-Lazlo Barabasi
- The rich get richer
- Hub의 hierarchy는 어느 connection에서도 유지되는가?
- e.g. Bullmore and Sporns 2009
- Watts, Strogats. 1998. Collective Dynamics of ‘small-world’ networks.
- Dynamic network
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Functional Segregation and Integration
- Both shows local and global behaviors via different resolution
어떤 시스템을 수학적으로 표현한다는 것은 곧 그 시스템을 정확히 이해하고 있다는 것이다. Computational Neuroscience의 이해 수준이 곧 neural system에 대한 이해 수준이다.---