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This article discusses how the individual morphological properties of basic objects (e.g. neurons, molecules and aggregates), jointly with their particular spatial distribution, can determine the connectivity and dynamics of systems…
In the last decade, network science has shed new light both on the structural (anatomical) and on the functional (correlations in the activity) connectivity among the different areas of the human brain. The analysis of brain networks has…
Some geometric properties of the wavelet analysis performed by visual neurons are discussed and compared with experimental data. In particular, several relationships between the cortical morphologies and the parametric dependencies of…
Understanding how brain structure and function interact is key to explaining intelligence yet modeling them jointly is challenging as the structural and functional connectome capture complementary aspects of organization. We introduced…
This article is concerned with finite rank stability theory, and more precisely two classical ways to decompose a type using minimal types. The first is its domination equivalence to a Morley power of minimal types, and the second its…
The interactions play one of the central roles in the brain mediating various processes and functions. They are particularly important for the brain as a complex system that has many different functions from the same structural…
Alzheimer's disease and Frontotemporal dementia are common forms of neurodegenerative dementia. Behavioral alterations and cognitive impairments are found in the clinical courses of both diseases and their differential diagnosis is…
Minkowski functionals provide a novel tool to characterize the large-scale galaxy distribution in the Universe. Here we give a brief tutorial on the basic features of these morphological measures and indicate their practical application for…
Since gyri and sulci, two basic anatomical building blocks of cortical folding patterns, were suggested to bear different functional roles, a precise mapping from brain function to gyro-sulcal patterns can provide profound insights into…
Equivalences between conformal foliations on Euclidean $3$-space, Hermitian structures on Euclidean $4$-space, shear-free ray congruences on Minkowski $4$-space, and holomorphic foliations on complex $4$-space are explained geometrically…
Neuroscience has long informed the development of artificial neural networks, but the success of modern architectures invites, in turn, the converse: can modern networks teach us lessons about brain function? Here, we examine the structure…
Decoupling multivariate polynomials is useful for obtaining an insight into the workings of a nonlinear mapping, performing parameter reduction, or approximating nonlinear functions. Several different tensor-based approaches have been…
Neuronal function requires precise spatial organization of mitochondria to meet localized energetic demand. However, the physical constraints governing mitochondrial transport in axons remain poorly defined. Bidirectional motor-driven…
The cortical array is a structure consisting of highly aligned microtubules which plays a crucial role in the characteristic uniaxial expansion of all growing plant cells. Recent experiments have shown polymerization-driven collisions…
One major challenge of neuroscience is finding interesting structures in a seemingly disorganized neural activity. Often these structures have computational implications that help to understand the functional role of a particular brain…
The brain may be thought of as a many-body architecture with a spatio-temporal dynamics described by neuronal structures. The oscillatory nature of brain activity allows these structures (nodes) to be described as a set of coupled…
Recent studies have shown how spiking networks can learn complex functionality through error-correcting plasticity, but the resulting structures and dynamics remain poorly studied. To elucidate how these models may link to observed dynamics…
We already saw in [A1] that the space of dynamically marked rational maps can be identified to a subspace of the space of covers between trees of spheres on which there is a notion of convergence that makes it sequentially compact. In the…
Layered monoidal theories provide a categorical framework for studying scientific theories at different levels of abstraction, via string diagrammatic algebra. We introduce models for three closely related classes of layered monoidal…
Bio-inspired computing has focused on neuron and synapses with great success. However, the connections between these, the dendrites, also play an important role. In this paper, we investigate the motivation for replicating dendritic…