Related papers: Evolution of recursive trees with limited memory

We make the first steps towards generalizing the theory of stochastic block models, in the sparse regime, towards a model where the discrete community structure is replaced by an underlying geometry. We consider a geometric random graph…

This paper is a review dealing with the study of large size random recurrent neural networks. The connection weights are selected according to a probability law and it is possible to predict the network dynamics at a macroscopic scale using…

We consider a model for the formation of a river network in which erosion process plays a role only at the initial stage. Once a global connectivity is achieved, no further evolution takes place. In spite of this, the network reproduces…

We study a random fragmentation process and its associated random tree. The process has earlier been studied by Dean and Majumdar (J. Phys. A: Math. Gen., vol. 35, L501--L507), who found a phase transition: the number of fragmentations is…

In specific motifs of three recurrently connected neurons with probabilistic response, the spontaneous information flux, defined as the mutual information between subsequent states, has been shown to increase by adding ongoing white noise…

Dynamic tree data structures maintain a forest while supporting insertion and deletion of edges and a broad set of queries in $O(\log n)$ time per operation. Such data structures are at the core of many modern algorithms. Recent work has…

Motivated by applications to COVID dynamics, we describe a branching process in random environments model $\{Z_n\}$ whose characteristics change when crossing upper and lower thresholds. This introduces a cyclical path behavior involving…

We present a model for growing information networks where the ageing of a node depends on the time at which it entered the network and on the last time it was cited. The model is shown to undergo a transition from a small-world to…

Inside the discipline of graph theory exists an extension known as the hypergraph. This generalization of graphs includes vertices along with hyperedges consisting of collections of two or more vertices. One well-studied application of this…

Leaves, i.e., vertices of degree one, can play a significant role in graph structure, especially in sparsely connected settings in which leaves often constitute the largest fraction of vertices. We consider a leaf-based counterpart of the…

Due to the dynamic nature of biological systems, biological networks underlying temporal process such as the development of {\it Drosophila melanogaster} can exhibit significant topological changes to facilitate dynamic regulatory…

Decision trees are widely used for classification and regression tasks in a variety of application fields due to their interpretability and good accuracy. During the past decade, growing attention has been devoted to globally optimized…

In this paper, we propose DeepTree, a novel method for modeling trees based on learning developmental rules for branching structures instead of manually defining them. We call our deep neural model situated latent because its behavior is…

Tackling simulation optimization problems with non-convex objective functions remains a fundamental challenge in operations research. In this paper, we propose a class of random search algorithms, called Regular Tree Search, which…

Reservoir computing (RC), first applied to temporal signal processing, is a recurrent neural network in which neurons are randomly connected. Once initialized, the connection strengths remain unchanged. Such a simple structure turns RC into…

We discuss methods for visualizing neural network decision boundaries and decision regions. We use these visualizations to investigate issues related to reproducibility and generalization in neural network training. We observe that changes…

Tree-structured LSTM is promising way to consider long-distance interaction over hierarchies. However, there have been few research efforts on the hyperparameter tuning of the construction and traversal of tree-structured LSTM. To name a…

Many biological phenomena or social events critically depend on how information evolves in complex networks. However, a general theory to characterize information evolution is yet absent. Consequently, numerous unknowns remain about the…

We consider the transmission of a state from the root of a tree towards its leaves, assuming that each transmission occurs through a noisy channel. The states at the leaves are observed, while at deeper nodes we can compute the likelihood…

We study the training dynamics of shallow neural networks, in a two-timescale regime in which the stepsizes for the inner layer are much smaller than those for the outer layer. In this regime, we prove convergence of the gradient flow to a…