Related papers: When are correlations strong?
For three decades statistical mechanics has been providing a framework to analyse neural networks. However, the theoretically tractable models, e.g., perceptrons, random features models and kernel machines, or multi-index models and…
We present atomistic molecular dynamics simulations of two Polyethylene systems where all entanglements are trapped: a perfect network, and a melt with grafted chain ends. We examine microscopically at what level topological constraints can…
Collaboration networks are studied as an example of growing bipartite networks. These have been previously observed to have structure such as positive correlations between nearest-neighbour degrees. However, a detailed understanding of the…
This work deals with the asymptotic distribution of both potentials and couplings of entropic regularized optimal transport for compactly supported probabilities in $\R^d$. We first provide the central limit theorem of the Sinkhorn…
Many social, technological and biological interactions involve network relationships whose outcome intimately depends on the structure of the network and on the strengths of the connections. Yet, although much information is now available…
In the past decades, weak convergence theory for stochastic processes has become a standard tool for analyzing the asymptotic properties of various statistics. Routinely, weak convergence is considered in the space of bounded functions…
Understanding the structural complexity and predictability of complex networks is a central challenge in network science. Although recent studies have revealed a relationship between compression-based entropy and link prediction…
Sampling considerations limit the experimental conditions under which information theoretic analyses of neurophysiological data yield reliable results. We develop a procedure for computing the full temporal entropy and information of…
Spin chains with open boundaries, such as the transverse field Ising model, can display coherence times for edge spins that diverge with the system size as a consequence of almost conserved operators, the so-called strong zero modes. Here,…
Many real world systems can be expressed as complex networks of interconnected nodes. It is frequently important to be able to quantify the relative importance of the various nodes in the network, a task accomplished by defining some…
We study expanding circle maps interacting in a heterogeneous random network. Heterogeneity means that some nodes in the network are massively connected, while the remaining nodes are only poorly connected. We provide a probabilistic…
When real networks are considered, coupled networks with connectivity and feedback-dependency links are not rare but more general. Here we develop a mathematical framework and study numerically and analytically percolation of interacting…
Across scientific disciplines, thresholded pairwise measures of statistical dependence between time series are taken as proxies for the interactions between the dynamical units of a network. Yet such correlation measures often fail to…
Inhibitory neurons play a crucial role in maintaining persistent neuronal activity. Although connected extensively through electrical synapses (gap-junctions), these neurons also exhibit interactions through chemical synapses in certain…
Complex networks have recently attracted much interest due to their prevalence in nature and our daily lives [1, 2]. A critical property of a network is its resilience to random breakdown and failure [3-6], typically studied as a…
The characterisation of neuronal connectivity is one of the most important matters in neuroscience. In this work, we show that a recently proposed informational quantity, the causal mutual information, employed with an appropriate…
The pairwise maximum entropy model, also known as the Ising model, has been widely used to analyze the collective activity of neurons. However, controversy persists in the literature about seemingly inconsistent findings, whose significance…
The inverse Ising model is used in computational neuroscience to infer probability distributions of the synchronous activity of large neuronal populations. This method allows for finding the Boltzmann distribution with single neuron biases…
Yang, Wang, and Motter [Phys. Rev. Lett. 109, 258701 (2012)] analyzed a model for network observability transitions in which a sensor placed on a node makes the node and the adjacent nodes observable. The size of the connected components…
It is commonly accepted that some phenomena are social: for example, individuals' smoking habits often correlate with those of their peers. Such correlations can have a variety of explanations, such as direct contagion or shared…