Related papers: Kauffman networks with threshold functions
We consider the training process of a neural network as a dynamical system acting on the high-dimensional weight space. Each epoch is an application of the map induced by the optimization algorithm and the loss function. Using this induced…
Multiple dynamic pathways always exist in biological networks, but their robustness against internal fluctuations and relative stability have not been well recognized and carefully analyzed yet. Here we try to address these issues through…
Boolean network models of molecular regulatory networks have been used successfully in computational systems biology. The Boolean functions that appear in published models tend to have special properties, in particular the property of being…
Random Boolean networks (RBNs) are frequently employed for modelling complex systems driven by information processing, e.g. for gene regulatory networks (GRNs). Here we propose a hierarchical adaptive RBN (HARBN) as a system consisting of…
We derive an exact representation of the topological effect on the dynamics of sequence processing neural networks within signal-to-noise analysis. A new network structure parameter, loopiness coefficient, is introduced to quantitatively…
We study the asymptotic behavior for asymmetric neuronal dynamics in a network of linear Hopfield neurons. The interaction between the neurons is modeled by random couplings which are centered i.i.d. random variables with finite moments of…
We explicitly construct the quantum field theory corresponding to a general class of deep neural networks encompassing both recurrent and feedforward architectures. We first consider the mean-field theory (MFT) obtained as the leading…
The co-evolution of network topology and dynamics is studied in an evolutionary Boolean network model that is a simple model of gene regulatory network. We find that a critical state emerges spontaneously resulting from interplay between…
Many natural, complex systems are remarkably stable thanks to an absence of feedback acting on their elements. When described as networks, these exhibit few or no cycles, and associated matrices have small leading eigenvalues. It has been…
A classification of critical behavior is provided in systems for which the renormalization group equations are control-parameter dependent. It describes phase transitions in networks with a recursive, hierarchical structure but appears to…
We study the Boolean dynamics of the "quenched" Kauffman models with a directed scale-free network, comparing with that of the original directed random Kauffman networks and that of the directed exponential-fluctuation networks. We have…
Nowadays, experimental techniques allow scientists to have access to large amounts of data. In order to obtain reliable information from the complex systems which produce these data, appropriate analysis tools are needed}. The Kalman filter…
We examine a hierarchy of equivalence classes of quasi-random properties of Boolean Functions. In particular, we prove an equivalence between a number of properties including balanced influences, spectral discrepancy, local strong…
We try to design a quantum neural network with qubits instead of classical neurons with deterministic states, and also with quantum operators replacing teh classical action potentials. With our choice of gates interconnecting teh neural…
Boolean automata networks (aka Boolean networks) are space-time discrete dynamical systems, studied as a model of computation and as a representative model of natural phenomena. A collection of simple entities (the automata) update their…
The dynamics of complex-valued fractional-order neuronal networks are investigated, focusing on stability, instability and Hopf bifurcations. Sufficient conditions for the asymptotic stability and instability of a steady state of the…
Massively parallel recordings of spiking activity in cortical networks show that covariances vary widely across pairs of neurons. Their low average is well understood, but an explanation for the wide distribution in relation to the static…
We present a characterization of short-term stability of random Boolean networks under \emph{arbitrary} distributions of transfer functions. Given any distribution of transfer functions for a random Boolean network, we present a formula…
Restricted Boltzmann Machines are key tools in Machine Learning and are described by the energy function of bipartite spin-glasses. From a statistical mechanical perspective, they share the same Gibbs measure of Hopfield networks for…
Quantum networks are a new paradigm of complex networks, allowing us to harness networked quantum technologies and to develop a quantum internet. But how robust is a quantum network when its links and nodes start failing? We show that…