相关论文: Obstructions to convexity in neural codes

Networks of neurons in the brain encode preferred patterns of neural activity via their synaptic connections. Despite receiving considerable attention, the precise relationship between network connectivity and encoded patterns is still…

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…

Primary visual cortex (V1) is the first stage of cortical image processing, and a major effort in systems neuroscience is devoted to understanding how it encodes information about visual stimuli. Within V1, many neurons respond selectively…

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…

Learning to read places a strong challenge on the visual system. Years of expertise lead to a remarkable capacity to separate highly similar letters and encode their relative positions, thus distinguishing words such as FORM and FROM,…

Place cells in the hippocampus are active when an animal visits a certain location (referred to as a place field) within an environment. Grid cells in the medial entorhinal cortex (MEC) respond at multiple locations, with firing fields that…

Hippocampal neurons track positions of self, others, and gaze direction. However, it is unclear how their respective neural codes differ enough to avoid confusion while allowing for abstraction. We recorded from populations of hippocampal…

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…

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…

This dissertation explores applications of discrete geometry in mathematical neuroscience. We begin with convex neural codes, which model the activity of hippocampal place cells and other neurons with convex receptive fields. In Chapter 4,…

This note is a brief survey of some results of the recent collaboration of neurobiologists and mathematicians dedicated to stimulus reconstruction from neuronal spiking activity. This collaboration, in particular, led to the consideration…

Hyperplane codes are a class of convex codes that arise as the output of a one layer feed-forward neural network. Here we establish several natural properties of stable hyperplane codes in terms of the {\it polar complex} of the code, a…

Grid cells in the entorhinal cortex encode the position of an animal in its environment using spatially periodic tuning curves of varying periodicity. Recent experiments established that these cells are functionally organized in discrete…

Grid cells in the medial entorhinal cortex (MEC) of the mammalian brain exhibit a strikingly regular hexagonal firing field over space. These cells are learned after birth and are thought to support spatial navigation but also more abstract…

The hippocampal system contains neural populations that encode an animal's position and velocity as it navigates through space. Here, we show that such populations can embed two codes within their spike trains: a firing rate code (R)…

We define a notion of morphism between combinatorial codes, making the class of all combinatorial codes into a category $\mathbf{Code}$. We show that morphisms can be used to remove redundant information from a code, and that morphisms…

The entorhinal-hippocampal circuit plays a critical role in higher brain functions, especially spatial cognition. Grid cells in the medial entorhinal cortex (MEC) periodically fire with different grid spacing and orientation, which makes a…

The brain's spatial orientation system uses different neuron ensembles to aid in environment-based navigation. Two of the ways brains encode spatial information is through head direction cells and grid cells. Brains use head direction cells…

We take the testing perspective to understand what the minimal discrimination time between two stimuli is for different types of rate coding neurons. Our main goal is to describe the testing abilities of two different encoding systems:…

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…