418 research outputs found
Computational techniques to interpret the neural code underlying complex cognitive processes
Advances in large-scale neural recording technology have significantly improved the
capacity to further elucidate the neural code underlying complex cognitive processes.
This thesis aimed to investigate two research questions in rodent models. First, what
is the role of the hippocampus in memory and specifically what is the underlying
neural code that contributes to spatial memory and navigational decision-making.
Second, how is social cognition represented in the medial prefrontal cortex at the
level of individual neurons. To start, the thesis begins by investigating memory and
social cognition in the context of healthy and diseased states that use non-invasive
methods (i.e. fMRI and animal behavioural studies). The main body of the thesis
then shifts to developing our fundamental understanding of the neural mechanisms
underpinning these cognitive processes by applying computational techniques to ana lyse stable large-scale neural recordings. To achieve this, tailored calcium imaging
and behaviour preprocessing computational pipelines were developed and optimised
for use in social interaction and spatial navigation experimental analysis. In parallel,
a review was conducted on methods for multivariate/neural population analysis. A
comparison of multiple neural manifold learning (NML) algorithms identified that non linear algorithms such as UMAP are more adaptable across datasets of varying noise
and behavioural complexity. Furthermore, the review visualises how NML can be
applied to disease states in the brain and introduces the secondary analyses that
can be used to enhance or characterise a neural manifold. Lastly, the preprocessing
and analytical pipelines were combined to investigate the neural mechanisms in volved in social cognition and spatial memory. The social cognition study explored
how neural firing in the medial Prefrontal cortex changed as a function of the social
dominance paradigm, the "Tube Test". The univariate analysis identified an ensemble
of behavioural-tuned neurons that fire preferentially during specific behaviours such
as "pushing" or "retreating" for the animal’s own behaviour and/or the competitor’s
behaviour. Furthermore, in dominant animals, the neural population exhibited greater
average firing than that of subordinate animals. Next, to investigate spatial memory,
a spatial recency task was used, where rats learnt to navigate towards one of three
reward locations and then recall the rewarded location of the session. During the
task, over 1000 neurons were recorded from the hippocampal CA1 region for five rats
over multiple sessions. Multivariate analysis revealed that the sequence of neurons encoding an animal’s spatial position leading up to a rewarded location was also active
in the decision period before the animal navigates to the rewarded location. The result
posits that prospective replay of neural sequences in the hippocampal CA1 region
could provide a mechanism by which decision-making is supported
Data-assisted modeling of complex chemical and biological systems
Complex systems are abundant in chemistry and biology; they can be multiscale, possibly high-dimensional or stochastic, with nonlinear dynamics and interacting components. It is often nontrivial (and sometimes impossible), to determine and study the macroscopic quantities of interest and the equations they obey. One can only (judiciously or randomly) probe the system, gather observations and study trends. In this thesis, Machine Learning is used as a complement to traditional modeling and numerical methods to enable data-assisted (or data-driven) dynamical systems. As case studies, three complex systems are sourced from diverse fields: The first one is a high-dimensional computational neuroscience model of the Suprachiasmatic Nucleus of the human brain, where bifurcation analysis is performed by simply probing the system. Then, manifold learning is employed to discover a latent space of neuronal heterogeneity. Second, Machine Learning surrogate models are used to optimize dynamically operated catalytic reactors. An algorithmic pipeline is presented through which it is possible to program catalysts with active learning. Third, Machine Learning is employed to extract laws of Partial Differential Equations describing bacterial Chemotaxis. It is demonstrated how Machine Learning manages to capture the rules of bacterial motility in the macroscopic level, starting from diverse data sources (including real-world experimental data). More importantly, a framework is constructed though which already existing, partial knowledge of the system can be exploited. These applications showcase how Machine Learning can be used synergistically with traditional simulations in different scenarios: (i) Equations are available but the overall system is so high-dimensional that efficiency and explainability suffer, (ii) Equations are available but lead to highly nonlinear black-box responses, (iii) Only data are available (of varying source and quality) and equations need to be discovered. For such data-assisted dynamical systems, we can perform fundamental tasks, such as integration, steady-state location, continuation and optimization. This work aims to unify traditional scientific computing and Machine Learning, in an efficient, data-economical, generalizable way, where both the physical system and the algorithm matter
Riemannian statistical techniques with applications in fMRI
Over the past 30 years functional magnetic resonance imaging (fMRI) has become a fundamental
tool in cognitive neuroimaging studies. In particular, the emergence of restingstate
fMRI has gained popularity in determining biomarkers of mental health disorders
(Woodward & Cascio, 2015). Resting-state fMRI can be analysed using the functional
connectivity matrix, an object that encodes the temporal correlation of blood activity
within the brain. Functional connectivity matrices are symmetric positive definite (SPD)
matrices, but common analysis methods either reduce the functional connectivity matrices
to summary statistics or fail to account for the positive definite criteria. However,
through the lens of Riemannian geometry functional connectivity matrices have an intrinsic
non-linear shape that respects the positive definite criteria (the affine-invariant
geometry (Pennec, Fillard, & Ayache, 2006)). With methods from Riemannian geometric
statistics, we can begin to explore the shape of the functional brain to understand this
non-linear structure and reduce data-loss in our analyses.
This thesis o↵ers two novel methodological developments to the field of Riemannian geometric
statistics inspired by methods used in fMRI research. First we propose geometric-
MDMR, a generalisation of multivariate distance matrix regression (MDMR) (McArdle &
Anderson, 2001) to Riemannian manifolds. Our second development is Riemannian partial
least squares (R-PLS), the generalisation of the predictive modelling technique partial least squares (PLS) (H. Wold, 1975) to Riemannian manifolds. R-PLS extends geodesic
regression (Fletcher, 2013) to manifold-valued response and predictor variables, similar to
how PLS extends multiple linear regression. We also generalise the NIPALS algorithm to
Riemannian manifolds and suggest a tangent space approximation as a proposed method
to fit R-PLS.
In addition to our methodological developments, this thesis o↵ers three more contributions
to the literature. Firstly, we develop a novel simulation procedure to simulate
realistic functional connectivity matrices through a combination of bootstrapping and the
Wishart distribution. Second, we propose the R2S
statistic for measuring subspace similarity
using the theory of principal angles between subspaces. Finally, we propose an
extension of the VIP statistic from PLS (S. Wold, Johansson, & Cocchi, 1993) to describe
the relationship between individual predictors and response variables when predicting a
multivariate response with PLS.
All methods in this thesis are applied to two fMRI datasets: the COBRE dataset
relating to schizophrenia, and the ABIDE dataset relating to Autism Spectrum Disorder
(ASD). We show that geometric-MDMR can detect group-based di↵erences between ASD
and neurotypical controls (NTC), unlike its Euclidean counterparts. We also demonstrate
the efficacy of R-PLS through the detection of functional connections related to
schizophrenia and ASD. These results are encouraging for the role of Riemannian geometric
statistics in the future of neuroscientific research.Thesis (Ph.D.) -- University of Adelaide, School of Mathematical Sciences, 202
Geometric Data Analysis: Advancements of the Statistical Methodology and Applications
Data analysis has become fundamental to our society and comes in multiple facets and approaches. Nevertheless, in research and applications, the focus was primarily on data from Euclidean vector spaces. Consequently, the majority of methods that are applied today are not suited for more general data types. Driven by needs from fields like image processing, (medical) shape analysis, and network analysis, more and more attention has recently been given to data from non-Euclidean spaces–particularly (curved) manifolds. It has led to the field of geometric data analysis whose methods explicitly take the structure (for example, the topology and geometry) of the underlying space into account.
This thesis contributes to the methodology of geometric data analysis by generalizing several fundamental notions from multivariate statistics to manifolds. We thereby focus on two different viewpoints.
First, we use Riemannian structures to derive a novel regression scheme for general manifolds that relies on splines of generalized Bézier curves. It can accurately model non-geodesic relationships, for example, time-dependent trends with saturation effects or cyclic trends. Since Bézier curves can be evaluated with the constructive de Casteljau algorithm, working with data from manifolds of high dimensions (for example, a hundred thousand or more) is feasible. Relying on the regression, we further develop
a hierarchical statistical model for an adequate analysis of longitudinal data in manifolds, and a method to control for confounding variables.
We secondly focus on data that is not only manifold- but even Lie group-valued, which is frequently the case in applications. We can only achieve this by endowing the group with an affine connection structure that is generally not Riemannian. Utilizing it, we derive generalizations of several well-known dissimilarity measures between data distributions that can be used for various tasks, including hypothesis testing. Invariance under data translations is proven, and a connection to continuous distributions is given for one measure.
A further central contribution of this thesis is that it shows use cases for all notions in real-world applications, particularly in problems from shape analysis in medical imaging and archaeology. We can replicate or further quantify several known findings for shape changes of the femur and the right hippocampus under osteoarthritis and Alzheimer's, respectively. Furthermore, in an archaeological application, we obtain new insights into the construction principles of ancient sundials. Last but not least, we use the geometric structure underlying human brain connectomes to predict cognitive scores. Utilizing a sample selection procedure, we obtain state-of-the-art results
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