Related papers: Neural ideals and stimulus space visualization
The ability of the organism to distinguish between various stimuli is limited by the structure and noise in the population code of its sensory neurons. Here we infer a distance measure on the stimulus space directly from the recorded…
We investigate the structure of ideals generated by binomials (polynomials with at most two terms) and the schemes and varieties associated to them. The class of binomial ideals contains many classical examples from algebraic geometry, and…
We describe and present a new construction method for codes using encodings from group rings. They consist primarily of two types: zero-divisor and unit-derived codes. Previous codes from group rings focused on ideals; for example cyclic…
With the recent success of deep neural networks in computer vision, it is important to understand the internal working of these networks. What does a given neuron represent? The concepts captured by a neuron may be hard to understand or…
Visual representations can be defined as the activations of neuronal populations in response to images. The activation of a neuron as a function over all image space has been described as a "tuning landscape". As a function over a…
We propose to use bifurcation theory and pattern formation as theoretical probes for various hypotheses about the neural organization of the brain. This allows us to make predictions about the kinds of patterns that should be observed in…
Decoding visual stimuli from neural activity is essential for understanding the human brain. While fMRI methods have successfully reconstructed static images, fMRI-to-video reconstruction faces challenges due to the need for capturing…
The v-number of a graded ideal is an invariant recently introduced in the context of coding theory, particularly in the study of Reed--Muller-type codes. In this work, we study the localized v-numbers of a binomial edge ideal $J_G$…
Neural decoding may be formulated as dynamic state estimation (filtering) based on point process observations, a generally intractable problem. Numerical sampling techniques are often practically useful for the decoding of real neural data.…
Conceptual spaces are geometric representations of conceptual knowledge, in which entities correspond to points, natural properties correspond to convex regions, and the dimensions of the space correspond to salient features. While…
In this paper, we will study the following pattern recognition problem: Every pattern is a 3-dimensional graph, its surface can be split up into some regions, every region is composed of the pixels with the approximately same colour value…
We introduce a novel representation of structured polynomial ideals, which we refer to as chordal networks. The sparsity structure of a polynomial system is often described by a graph that captures the interactions among the variables.…
A cluster graph is a graph whose every connected component is a complete graph. Given a simple undirected graph $G$, a subset of vertices inducing a cluster graph is called an independent union of cliques (IUC), and the IUC polytope…
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.…
Neuroscientists classify neurons into different types that perform similar computations at different locations in the visual field. Traditional methods for neural system identification do not capitalize on this separation of 'what' and…
Area V4 is a mid-level stage of the macaque ventral visual stream, known to encode intermediate visual features such as color, curvature, corners, texture, three-dimensional (3D) solids, and local form. Classical neurophysiological studies…
Cell complexes are topological spaces constructed from simple blocks called cells. They generalize graphs, simplicial complexes, and polyhedral complexes that form important domains for practical applications. They also provide a…
The coding mechanism of sensory memory on the neuron scale is one of the most important questions in neuroscience. We have put forward a quantitative neural network model, which is self organized, self similar, and self adaptive, just like…
In the field of information visualisation, Euler diagrams are an important tool used in various application areas such as engineering, medicine and social analysis. To effectively use Euler diagrams, some of the wellformedness properties…
Neural representations of visual perception are affected by mental imagery and attention. Although attention is known to modulate neural representations, it is unknown how imagery changes neural representations when imagined and perceived…