Related papers: An uncertainty principle underlying the pinwheel s…
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 brain can be considered as a system that dynamically optimizes the structure of anatomical connections based on the efficiency requirements of functional connectivity. To illustrate the power of this principle in organizing the…
The paper surveys topological problems relevant to the motion planning problem of robotics and includes some new results and constructions. First we analyse the notion of topological complexity of configuration spaces which is responsible…
An arrangement of pseudocircles is a finite set of oriented closed Jordan curves each two of which cross each other in exactly two points. To describe the combinatorial structure of arrangements on closed orientable surfaces, in (Linhart,…
A pressing scientific challenge is to understand how brains work. Of particular interest is the neocortex,the part of the brain that is especially large in humans, capable of handling a wide variety of tasks including visual, auditory,…
A prominent formulation of the uncertainty principle identifies the fundamental quantum feature that no particle may be prepared with certain outcomes for both position and momentum measurements. Often the statistical uncertainties are…
Sequences of neuronal activation have long been implicated in a variety of brain functions. In particular, these sequences have been tied to memory formation and spatial navigation in the hippocampus, a region of mammalian brains.…
Generally, the normal displacement-based formation control has a sensing mode that requires the agent not only to have certain knowledge of its direction, but also to gather its local information characterized by nonnegative coupling…
Topological techniques have become a popular tool for studying information flows in neural networks. In particular, simplicial homology theory is used to analyze how cognitive representations of space emerge from large conglomerates of…
Since their discovery in 1927, the Heisenberg Inequalities have become an icon of quantum mechanics. Often inappropriately referred to as the Uncertainty Principle, these inequalities relating the standard deviations of the position and…
Predictive coding is a unifying framework for understanding perception, action and neocortical organization. In predictive coding, different areas of the neocortex implement a hierarchical generative model of the world that is learned from…
We investigate the structural and spectral properties of deterministic aperiodic arrays designed from the statistically isotropic pinwheel tiling. By studying the scaling of the cumulative integral of its structure factor in combination…
Although Hubel and Wiesel established decades ago how individual V1 neurons transform retinal inputs, functions of V1 as a whole are being discovered only recently. First, V1 acts as a motor cortex for exogenously guiding saccades by…
A proof-of-concept framework for identifying molecules of unknown elemental composition and structure using experimental rotational data and probabilistic deep learning is presented. Using a minimal set of input data determined…
Scope of this paper is to consider a mean field neural model which takes into account the functional neurogeometry of the visual cortex modelled as a group of rotations and translations. The model generalizes well known results of Bressloff…
We propose an exact iterative algorithm for minimization of a class of continuous cell-wise linear convex functions on a hyperplane arrangement. Our particular setup is motivated by evaluation of so-called rank estimators used in robust…
A mathematical model of figure-ground articulation is presented, taking into account both local and global gestalt laws. The model is compatible with the functional architecture of the primary visual cortex (V1). Particularly the local…
The Lindblad generators of the master equation define which kind of decoherence happens in an open quantum system. We are working with a two qubit system and choose the generators to be projection operators on the eigenstates of the system…
We have carried out a Monte Carlo simulation of a modified version of Vicsek model for the motion of self-propelled particles in two dimensions. In this model the neighborhood of interaction of a particle is a sector of the circle with the…
The neural manifold hypothesis postulates that the activity of a neural population forms a low-dimensional manifold whose structure reflects that of the encoded task variables. In this work, we combine topological deep generative models and…