相关论文: Geometroneurodynamics
The recent controversy of applicability of quantum formalism to brain dynamics has been critically analysed. The prerequisites for any type of quantum formalism or quantum field theory is to investigate whether the anatomical structure of…
We develop a kind of quantum formalism (Hilbert space probabilistic calculus) for measurements performed over cognitive (in particular, conscious) systems. By using this formalism we could predict averages of cognitive observables.…
At the turn of the 20th century, Henri Poincar{\'e} explained that geometry is a convention and that the properties of space and time are the properties of our measuring instruments. Intriguingly, numerous contemporary authors argue that…
Effective analysis in neuroscience benefits significantly from robust conceptual frameworks. Traditional metrics of interbrain synchrony in social neuroscience typically depend on fixed, correlation-based approaches, restricting their…
Neural computation in biological and artificial networks relies on the nonlinear summation of many inputs. The structural connectivity matrix of synaptic weights between neurons is a critical determinant of overall network function, but…
Starting from the morphological-functional assumption of the fractal brain, a mathematical model is given by activating brain non-differentiable dynamics through the determinism-nondeterminism inference of the responsible mechanisms. The…
The cognitive state of mind concerning a range of choices to be made can effectively be modelled in terms of an element of a high-dimensional Hilbert space. The dynamics of the state of mind resulting form information acquisition is…
Physics explains the laws of motion that govern the time evolution of observable properties and the dynamical response of systems to various interactions. However, quantum theory separates the observable part of physics from the…
Many basis sets for electronic structure calculations evolve with varying external parameters, such as moving atoms in dynamic simulations, giving rise to extra derivative terms in the dynamical equations. Here we revisit these derivatives…
Dynamics play a critical role in computation. The principled evolution of states over time enables both biological and artificial networks to represent and integrate information to make decisions. In the past few decades, significant…
To optimize a neural network one often thinks of optimizing its parameters, but it is ultimately a matter of optimizing the function that maps inputs to outputs. Since a change in the parameters might serve as a poor proxy for the change in…
The idea that the brain functions so as to minimize certain costs pervades theoretical neuroscience. Since a cost function by itself does not predict how the brain finds its minima, additional assumptions about the optimization method need…
Neural activity patterns related to behavior occur at many scales in time and space from the atomic and molecular to the whole brain. Here we explore the feasibility of interpreting neurophysiological data in the context of many-body…
Partial synchronization plays a crucial role in the functioning of neuronal networks: selective, coordinated activation of neurons enables information processing that flexibly adapts to a changing computational context. Since the structure…
Symmetries impose structure on the Hilbert space of a quantum mechanical model. The mathematical units of this structure are the irreducible representations of symmetry groups and I consider how they function as conceptual units of…
State-space models (SSMs) have become a cornerstone for unraveling brain dynamics, revealing how latent neural states evolve over time and give rise to observed signals. By combining the flexibility of deep learning with the principled…
In the mammalian brain, many neuronal ensembles are involved in representing spatial structure of the environment. In particular, there exist cells that encode the animal's location and cells that encode head direction. A number of studies…
The integration and transmission of information in the brain are dependent on the interplay between structural and dynamical properties. Implicit in any pursuit aimed at understanding neural dynamics from appropriate sets of mathematically…
Statistical neurodynamics studies macroscopic behaviors of randomly connected neural networks. We consider a deep layered feedforward network where input signals are processed layer by layer. The manifold of input signals is embedded in a…
The space of possible behaviors complex biological systems may exhibit is unimaginably vast, and these systems often appear to be stochastic, whether due to variable noisy environmental inputs or intrinsically generated chaos. The brain is…