Functional organization · predictive dynamics

Brain networks
in motion

The brain’s functional organization is more than a single connectivity map. Networks are expressed in changing combinations as activity unfolds, even in the absence of an imposed task.

This project uses spectral learning to describe those changing combinations, relate them to familiar cortical systems, and examine how they vary across people and experimental conditions.

Two oblique views of cortical atlas surfaces colored by the seven reference functional systems — Seven reference systems provide an anatomical vocabulary for interpreting the learned networks.

Explore the evidence

Two views of network dynamics

Spontaneous organization

Resting state

Which familiar networks emerge without an imposed task, and how consistently are they represented across people?

Default-mode and visual associations are prominent. Network 5 also links dorsal-attention and somatomotor organization on opposing poles, illustrating how one dynamical pattern can span several reference systems.

96 NYU control participants · ABIDE I · 100 cortical parcels

Explore resting state →

Experimentally timed expression

Visual task

How does expression of the learned networks change between visual stimulation and inter-block fixation?

Network 2 pairs visual and default-mode organization. Its average coefficient shifts upward during stimulation in all 15 participants, connecting an anatomical pattern with a consistent condition-related change.

15 participants · 60 localizer runs · Studyforrest · 100 cortical parcels

Explore visual task →

The illustrated associations use the resting-state rank-12 fit and visual-task rank-7 fit. Each study has its own fitted networks; network numbers are local to that fit.

Exploratory pilot · cohort comparison

Resting state-ASD

Do similar network patterns emerge independently in autistic and typical participants? A small pilot compares 72 autistic participants with the 96 NYU controls using the same atlas and model settings.

Several early networks closely resemble their counterparts across cohorts, while others match with reversed orientation or different numbering. Explore the ASD functional anatomy and a network-by-network comparison of the independently learned matrices.

Spatial resemblance is the current result; the cohorts are not matched for age, sex or motion, and this is not a test of diagnostic differences.

Explore the ASD pilot → Compare cohort networks

The method

From regional signals to changing network expression

A connectivity matrix averaged over a recording summarizes overall relationships between regions. Spectral learning instead uses relationships between recent signals and subsequent observations to construct a compact description of their dynamics. The approach revisits the dissertation’s predictive framework and applies it to contemporary cortical parcellations.

Related approaches build network graphs from regional signals, estimate connectivity measures, and use clustering or community detection to summarize their organization. These offer complementary descriptions to the predictive components studied here. Functional interpretation also draws on research into intrinsic activity at rest and the organization of visual systems; those ideas motivate hypotheses rather than determine a component’s function from its atlas match alone.

Regional signals carry the observationsEach cortical parcel supplies a continuous fMRI time series. Anatomical alignment and consistent ROI ordering allow regional relationships to be compared across recordings.
Past–future structure defines the representationRelationships across short temporal windows are compressed into a lower-dimensional predictive space. A shared basis within each study gives participants and runs a common frame of comparison.
Networks combine through timeEach learned spatial matrix describes a pattern of ROI-pair weights. Several patterns can contribute simultaneously, with time-varying coefficients describing their orientation and size.
Opposing poles give spatial contextPositive and negative weights can emphasize different functional systems. One coefficient scales both poles together; changing its sign reverses their contribution. The signs alone do not establish neural excitation or inhibition.
Anatomy and timing answer complementary questionsReference-system matching identifies where a pattern is concentrated. Subject comparisons and task timing reveal when it is expressed and how consistently it appears across recordings.

Mathematical interpretation and scope

The modeled ROI second-moment matrix has the form M(t) = W₀ + Σₖ xₖ(t)Wₖ. Wₖ is a spatial coefficient matrix and xₖ(t) its signed predictive coordinate. Average coefficient describes prevailing orientation; contribution magnitude describes size regardless of orientation. Strong contributions can cancel in a signed average.

Min–max-scaled inputs retain mean structure, so these matrices are not ordinary centered covariance matrices. Learned Network 1 behaves as a mean/bias-like component and is set aside in routine figures while retained in the fit; it is distinct from the explicit constant coordinate. Separate ranks are separate models. The current analyses are exploratory and in-sample; independent prediction and stability require further evaluation.

Follow the scientific questions

Functional systemsWhere do familiar cortical systems appear, and which systems occupy opposing poles?

Network matchesHow closely does each pole resemble a reference system, and how much weight lies there?

Expression over timeWhen do the patterns contribute, and how do they change with stimulation and fixation?

ConsistencyWhich patterns and trajectories recur across participants or repeated runs?

Each study’s Study & Methods section explains the design, preparation and quality checks. Resting recordings have no task labels; inter-block fixation in the visual study is an experimental comparison rather than a separate resting-state acquisition. Differences between the studies’ sampling and processing histories matter when interpreting their results.