Related papers: Comparing dendritic trees with actual trees
Overparameterized neural networks often contain many removable neurons, yet what makes a neuron redundant remains poorly understood. Existing pruning criteria commonly rely on local quantities such as weight magnitude, activation strength,…
The brain is formed by cortical regions that are associated with different cognitive functions. Neurons within the same region are more likely to connect than neurons in distinct regions, making the brain network to have characteristics of…
Deep learning has excelled in image recognition tasks through neural networks inspired by the human brain. However, the necessity for large models to improve prediction accuracy introduces significant computational demands and extended…
Some geometric properties of the wavelet analysis performed by visual neurons are discussed and compared with experimental data. In particular, several relationships between the cortical morphologies and the parametric dependencies of…
In this paper, we introduce two families of planar and self-similar graphs which have small-world properties. The constructed models are based on an iterative process where each step of a certain formulation of modules results in a final…
One of the most challenging problems in polymer physics is providing a theoretical description for the behaviour of rings in dense solutions and melts. Although it is nowadays well established that the overall size of a ring in these…
Recently proposed budding tree is a decision tree algorithm in which every node is part internal node and part leaf. This allows representing every decision tree in a continuous parameter space, and therefore a budding tree can be jointly…
With the recent explosion of publicly available biological data, the analysis of networks has gained significant interest. In particular, recent promising results in Neuroscience show that the way neurons and areas of the brain are…
What is the relationship between brain and behavior? The answer to this question necessitates characterizing the mapping between structure and function. The aim of this paper is to discuss broad issues surrounding the link between structure…
Various structures in human physiology follow a treelike morphology, which often expresses complexity at very fine scales. Examples of such structures are intrathoracic airways, retinal blood vessels, and hepatic blood vessels. Large…
Given a graph, we can form a spanning forest by first sorting the edges in some order, and then only keep edges incident to a vertex which is not incident to any previous edge. The resulting forest is dependent on the ordering of the edges,…
The theory of complex trees is introduced as a new approach to study a broad class of self-similar sets. Systems of equations encoded by complex trees tip-to-tip equivalence relations are used to obtain one-parameter families of connected…
We consider certain groups of tree automorphisms as so-called diffeological groups. The notion of diffeology, due to Souriau, allows to endow non-manifold topological spaces, such as regular trees that we look at, with a kind of a…
The brain is likely the most complex organ, given the variety of functions it controls, the number of cells it comprises, and their corresponding diversity. Studying and identifying neurons, the brain's primary building blocks, is a crucial…
We analyze the structure of two dimensional disordered cellular systems generated by extensive computer simulations. These cellular structures are studied as topological trees rooted on a central cell or as closed shells arranged…
Recent success in training deep neural networks have prompted active investigation into the features learned on their intermediate layers. Such research is difficult because it requires making sense of non-linear computations performed by…
Deep neural network architectures often consist of repetitive structural elements. We introduce an approach that reveals these patterns and can be broadly applied to the study of deep learning. Similarly to how a power strip helps untangle…
Self-similar Markov trees constitute a remarkable family of random compact real trees carrying a decoration function that is positive on the skeleton. As the terminology suggests, they are self-similar objects that further satisfy a Markov…
We discuss a notion of convergence for binary trees that is based on subtree sizes. In analogy to recent developments in the theory of graphs, posets and permutations we investigate some general aspects of the topology, such as a…
The use of machine learning algorithms in finance, medicine, and criminal justice can deeply impact human lives. As a consequence, research into interpretable machine learning has rapidly grown in an attempt to better control and fix…