A unified framework for Simplicial Kuramoto models

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In this thesis, we concentrate on advancing high-level behavioral control policies for robotic systems within the framework of Dynamical Systems (DS). Throughout the course of this research, a unifying thread weaving through diverse fields emerges, and tha ...

Modern optimization is tasked with handling applications of increasingly large scale, chiefly due to the massive amounts of widely available data and the ever-growing reach of Machine Learning. Consequently, this area of research is under steady pressure t ...

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Animals, including humans, exhibit a remarkable variety of complex behaviours. How the nervous system controls all these behaviours ranging from simple, stereotyped movements to flexible, adaptive actions is a central questions of neuroscience. One of the ...

The motor learning process entails plastic changes in the brain, especially in brain network reconfigurations. In the current study, we sought to characterize motor learning by determining changes in the coupling behaviour between the brain functional and ...

Dynamical System (DS)-based closed-loop control is a simple and effective way to generate reactive motion policies that well generalize to the robotic workspace, while retaining stability guarantees. Lately the formalism has been expanded in order to handl ...

The knowledge that brain functional connectomes are unique and reliable has enabled behaviourally relevant inferences at a subject level. However, whether such "fingerprints" persist under altered states of consciousness is unknown. Ayahuasca is a potent s ...

The brain is composed of several anatomically clearly separated structures. This parcellation is often extended into the isocortex, based on anatomical, physiological or functional differences. Here, we derive a parcellation scheme based purely on the spat ...

The brain's functional networks can be assessed using imaging techniques like functional magnetic resonance imaging (fMRI) and electroencephalography (EEG). Recent studies have suggested a link between the dynamic functional connectivity (dFC) captured by ...

Treatment-resistant depression is a severe form of major depressive disorder and deep brain stimulation is currently an investigational treatment. The stimulation's therapeutic effect may be explained through the functional and structural connectivities be ...

Phase synchronizations in models of coupled oscillators such as the Kuramoto model have been widely studied with pairwise couplings on arbitrary topologies, showing many unexpected dynamical behaviors. Here, based on a recent formulation the Kuramoto model ...

The field of computational topology has developed many powerful tools to describe the shape of data, offering an alternative point of view from classical statistics. This results in a variety of complex structures that are not always directly amenable for ...

Background: Functional connectivity quantifies the statistical dependencies between the activity of brain regions, measured using neuroimaging data such as functional magnetic resonance imaging (fMRI) blood-oxygenation-level dependent time series. The netw ...

Collapsing cell complexes was first introduced in the 1930's as a way to deform a space into a topological-equivalent subspace with a sequence of elementary moves. Recently, discrete Morse theory techniques provided an efficient way to construct deformatio ...

The design and construction of doubly-curved structures often reveals to be challenging and can result in complex manufacturing and assembly. A recent strategy to tackle this difficulty consists in exploiting the connection between discrete differential ge ...

Recent developments in network neuroscience have highlighted the importance of developing techniques for analysing and modelling brain networks. A particularly powerful approach for studying complex neural systems is to formulate generative models that use ...

Measuring the temporal complexity of functional MRI (fMRI) time series is one approach to assess how brain activity changes over time. In fact, hemodynamic response of the brain is known to exhibit critical behaviour at the edge between order and disorder. ...

In this letter, we present a method for integrating central pattern generators (CPGs), i.e. systems of coupled oscillators, into the deep reinforcement learning (DRL) framework to produce robust and omnidirectional quadruped locomotion. The agent learns to ...

Systems with low mechanical dissipation are extensively used in precision measurements such as gravitational wave detection, atomic force microscopy, and quantum control of mechanical oscillators via optomechanics and electromechanics. The mechanical quali ...

When learning from data, leveraging the symmetries of the domain the data lies on is a principled way to combat the curse of dimensionality: it constrains the set of functions to learn from. It is more data efficient than augmentation and gives a generaliz ...

A unified framework for Simplicial Kuramoto models

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Scalable constrained optimization

Experimental observation of topological transition in linear and nonlinear parametric oscillators

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Brain connectome correlates of short-term motor learning in healthy older subjects

Hybrid Quadratic Programming - Pullback Bundle Dynamical Systems Control

Shared functional connectome fingerprints following ritualistic ayahuasca intake

A parcellation scheme of mouse isocortex based on reversals in connectivity gradients

Brain's Dynamic Functional Organization with Simultaneous EEG-fMRI Networks

Linking connectivity of deep brain stimulation of nucleus accumbens area with clinical depression improvements: a retrospective longitudinal case series

Connecting Hodge and Sakaguchi-Kuramoto through a mathematical framework for coupled oscillators on simplicial complexes

Reduced representations of complexes, signals, and multifiltrations

Improving Functional Connectome Fingerprinting with Degree-Normalization

Collapse-invariant properties of spaces equipped with signals or directions

Discrete Voss surfaces: Designing geodesic gridshells with planar cladding panels

Investigating cognitive ability using action-based models of structural brain networks

On the Spatial Distribution of Temporal Complexity in Resting State and Task Functional MRI

CPG-RL: Learning Central Pattern Generators for Quadruped Locomotion

Perimeter Modes of Nanomechanical Resonators Exhibit Quality Factors Exceeding 10(9) at Room Temperature

Leveraging topology, geometry, and symmetries for efficient Machine Learning