Related papers: On the conversion of multivalued to Boolean dynami…
The abundance of data affords researchers to pursue more powerful computational tools to learn the dynamics of complex system, such as neural networks, engineered systems and social networks. Traditional machine learning approaches capture…
We study Boolean networks which are simple spatial models of the highly conserved Delta-Notch system. The models assume the inhibition of Delta in each cell by Notch in the same cell, and the activation of Notch in presence of Delta in…
We investigate the expressive power of neural networks from the point of view of descriptive complexity. We study neural networks that use floating-point numbers and piecewise polynomial activation functions from two perspectives: 1) the…
A Boolean network is a function $f:\{0,1\}^n\to\{0,1\}^n$ from which several dynamics can be derived, depending on the context. The most classical ones are the synchronous and asynchronous dynamics. Both are digraphs on $\{0,1\}^n$, but the…
We already know a great deal about dynamical systems with uniqueness in forward time. Indeed, flows, semiflows, and maps (both invertible and not) have been studied at length. A view that has proven particularly fruitful is topological:…
We analyze the macroscopic behavior of multi-populations randomly connected neural networks with interaction delays. Similar to cases occurring in spin glasses, we show that the sequences of empirical measures satisfy a large deviation…
Discrete models have a long tradition in engineering, including finite state machines, Boolean networks, Petri nets, and agent-based models. Of particular importance is the question of how the model structure constrains its dynamics. This…
In human perception and cognition, a fundamental operation that brains perform is interpretation: constructing coherent neural states from noisy, incomplete, and intrinsically ambiguous evidence. The problem of interpretation is well…
The behavior of heterogeneous multi-agent systems is studied when the coupling matrices are possibly all different and/or singular, that is, its rank is less than the system dimension. Rank-deficient coupling allows exchange of limited…
This work studies the operation of multi-agent networks engaged in binary decision tasks, and derives performance expressions and performance operating curves under challenging conditions with some revealing insights. One of the main…
A complex-valued convolutional network (convnet) implements the repeated application of the following composition of three operations, recursively applying the composition to an input vector of nonnegative real numbers: (1) convolution with…
Usually, opinion formation models assume that individuals have an opinion about a given topic which can change due to interactions with others. However, individuals can have different opinions in different topics and therefore n-dimensional…
When a posterior distribution has multiple modes, unconditional expectations, such as the posterior mean, may not offer informative summaries of the distribution. Motivated by this problem, we propose to decompose the sample space of a…
The dynamics of coupled intermittent maps is used to model the correlated structure of genomic sequences. The use of intermittent maps, as opposed to other simple chaotic maps, is particularly suited for the production of long range…
We describe a simple adaptive network of coupled chaotic maps. The network reaches a stationary state (frozen topology) for all values of the coupling parameter, although the dynamics of the maps at the nodes of the network can be…
Elements composing complex systems usually interact in several different ways and as such the interaction architecture is well modelled by a multiplex network. However often this architecture is hidden, as one usually only has experimental…
Finding a succinct representation to describe the ground state of a disordered interacting system could be very helpful in understanding the interplay between the interactions that is manifested in a quantum phase transition. In this work…
We construct and investigate Boolean networks that follow a given reliable trajectory in state space, which is insensitive to fluctuations in the updating schedule, and which is also robust against noise. Robustness is quantified as the…
The paper presents a novel approach for the analysis and control of a multi-agent system with non-identical agents and a path-graph topology. With the help of irrational wave transfer functions, the approach describes the interaction among…
In the landscape of contemporary recommender systems, user-item interactions are inherently dynamic and sequential, often characterized by various behaviors. Prior research has explored the modeling of user preferences through sequential…