Related papers: Canonical Cortical Field Theories
The study of neural computation aims to understand the function of a neural system as an information processing machine. Neural systems are undoubtedly complex, necessitating principled and automated tools to abstract away details to…
Cortical activity in-vivo displays relaxational time scales much longer than the membrane time constant of the neurons or the deactivation time of ionotropic synaptic conductances. The mechanisms responsible for such slow dynamics are not…
We consider the problem of sampling lattice field configurations on a lattice from the Boltzmann distribution corresponding to some action. Since such densities arise as approximationw of an underlying functional density, we frame the task…
We propose a mechanism enabling the appearance of border cells -- neurons firing at the boundaries of the navigated enclosures. The approach is based on the recent discovery of discrete complex analysis on a triangular lattice, which allows…
Patterns of microcircuitry suggest that the brain has an array of repeated canonical computational units. Yet neural representations are distributed, so the relevant computations may only be related indirectly to single-neuron…
Non-equilibrium dynamics are present in many aspects of our lives, ranging from microscopic physical systems to the functioning of the brain. What characterizes stochastic models of non-equilibrium processes is the breaking of the…
Neural mass models have been actively used since the 1970s to model the coarse grained activity of large populations of neurons and synapses. They have proven especially useful in understanding brain rhythms. However, although motivated by…
The paper examines the discrete-time dynamics of neuron models (of excitatory and inhibitory types) with piecewise linear activation functions, which are connected in a network. The properties of a pair of neurons (one excitatory and the…
The neural dynamics generating sensory, motor, and cognitive functions are commonly understood through field theories for neural population activity. Classic neural field theories are derived from highly simplified models of individual…
We consider a ring network of quadratic integrate-and-fire neurons with nonlocal synaptic and gap junction coupling. The corresponding neural field model supports solutions such as standing and travelling waves, and also lurching waves. We…
Robust information representation and its persistent maintenance are fundamental for higher cognitive functions. Existing models employ distinct neural mechanisms to separately address noise-resistant processing or information maintenance,…
The LCDM model has been presented with a number of cosmic tensions in the face of precision cosmological data, suggesting the presence of a dynamical dark energy component. In this context, we investigate the cosmology arising from a…
The brain did not develop a dedicated device for reasoning. This fact bears dramatic consequences. While for perceptuo-motor functions neural activity is shaped by the input's statistical properties, and processing is carried out at high…
In the wake of recent advances in experimental methods in neuroscience, the ability to record in-vivo neuronal activity from awake animals has become feasible. The availability of such rich and detailed physiological measurements calls for…
This paper describes how realistic neuromorphic networks can have their connectivity fully characterized in analytical fashion. By assuming that all neurons have the same shape and are regularly distributed along the two-dimensional…
We develop the theory of canonical-dissipative systems, based on the assumption that both the conservative and the dissipative elements of the dynamics are determined by invariants of motion. In this case, known solutions for conservative…
Dynamic functional connectivity is an effective measure for the brain's responses to continuous stimuli. We propose an inferential method to detect the dynamic changes of brain networks based on time-varying graphical models. Whereas most…
With the covariant formulation in hand from the first paper of this series (physics/9801019), we begin in this second paper to study the canonical (or ``instantaneous'') formulation of classical field theories. The canonical formluation…
The cerebral cortex spontaneously displays different patterns of activity that evolve over time according to the brain state. Sleep, wakefulness, resting states, and attention are examples of a wide spectrum of physiological states that can…
In the fields of computation and neuroscience, much is still unknown about the underlying computations that enable key cognitive functions including learning, memory, abstraction and behavior. This paper proposes a mathematical and…