相关论文: Algebraic signatures of convex and non-convex code…
Neural codes allow the brain to represent, process, and store information about the world. Combinatorial codes, comprised of binary patterns of neural activity, encode information via the collective behavior of populations of neurons. A…
Neural codes serve as a language for neurons in the brain. Convex codes, which arise from the pattern of intersections of convex sets in Euclidean space, are of particular relevance to neuroscience. Not every code is convex, however, and…
Neural codes, represented as collections of binary strings, encode neural activity and show relationships among stimuli. Certain neurons, called place cells, have been shown experimentally to fire in convex regions in space. A natural…
Much work has been done to identify which binary codes can be represented by collections of open convex or closed convex sets. While not all binary codes can be realized by such sets, here we prove that every binary code can be realized by…
Neural codes, represented as collections of binary strings called codewords, are used to encode neural activity. A code is called convex if its codewords are represented as an arrangement of convex open sets in Euclidean space. Previous…
Convex neural codes are subsets of the Boolean lattice that record the intersection patterns of convex sets in Euclidean space. Much work in recent years has focused on finding combinatorial criteria on codes that can be used to classify…
Previous work on convexity of neural codes has produced codes that are open-convex but not closed-convex -- or vice-versa. However, why a code is one but not the other, and how to detect such discrepancies are open questions. We tackle…
Neurons in the brain represent external stimuli via neural codes. These codes often arise from stereotyped stimulus-response maps, associating to each neuron a convex receptive field. An important problem confronted by the brain is to infer…
We introduce new geometric and combinatorial criteria that preclude a neural code from being convex, and use them to tackle the classification problem for codes on six neurons. Along the way, we give the first example of a code that is…
Neurons in the brain represent external stimuli via neural codes. These codes often arise from stimulus-response maps, associating to each neuron a convex receptive field. An important problem confronted by the brain is to infer properties…
Neural codes are collections of binary strings motivated by patterns of neural activity. In this paper, we study algorithmic and enumerative aspects of convex neural codes in dimension 1 (i.e. on a line or a circle). We use the theory of…
The brain encodes spacial structure through a combinatorial code of neural activity. Experiments suggest such codes correspond to convex areas of the subject's environment. We present an intrinsic condition that implies a neural code may…
Convex neural codes are combinatorial structures describing the intersection pattern of a collection of convex sets. Inductively pierced codes are a particularly nice subclass of neural codes introduced in the information visualization…
A neural code $\mathcal{C}$ is a collection of binary vectors of a given length n that record the co-firing patterns of a set of neurons. Our focus is on neural codes arising from place cells, neurons that respond to geographic stimulus. In…
How does the brain encode spatial structure? One way is through hippocampal neurons called place cells, which become associated to convex regions of space known as their receptive fields: each place cell fires at a high rate precisely when…
Given an intersection pattern of arbitrary sets in Euclidean space, is there an arrangement of convex open sets in Euclidean space that exhibits the same intersections? This question is combinatorial and topological in nature, but is…
Neural codes are lists of subsets of neurons that fire together. Of particular interest are neurons called place cells, which fire when an animal is in specific, usually convex regions in space. A fundamental question, therefore, is to…
Determining how the brain stores information is one of the most pressing problems in neuroscience. In many instances, the collection of stimuli for a given neuron can be modeled by a convex set in $\mathbb{R}^d$. Combinatorial objects known…
Place cells are neurons that act as biological position sensors, associated with and firing in response to regions of an environment to situate an organism in space. These associations are recorded in (combinatorial) neural codes,…
Neural codes are binary codes in $\{0,1\}^n$; here we focus on the ones which represent the firing patterns of a type of neurons called place cells. There is much interest in determining which neural codes can be realized by a collection of…