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State-of-the-art neural networks are getting deeper and wider. While their performance increases with the increasing number of layers and neurons, it is crucial to design an efficient deep architecture in order to reduce computational and…

Projection-based model reduction has become a popular approach to reduce the cost associated with integrating large-scale dynamical systems so they can be used in many-query settings such as optimization and uncertainty quantification. For…

Recurrent Neural Networks (RNN) are widely used to solve a variety of problems and as the quantity of data and the amount of available compute have increased, so have model sizes. The number of parameters in recent state-of-the-art networks…

The life of the modern world essentially depends on the work of the large artificial homogeneous networks, such as wired and wireless communication systems, networks of roads and pipelines. The support of their effective continuous…

In studying network growth, the conventional approach is to devise a growth mechanism, quantify the evolution of a statistic or distribution (such as the degree distribution), and then solve the equations in the steady state (the…

Network backbones provide useful sparse representations of weighted networks by keeping only their most important links, permitting a range of computational speedups and simplifying network visualizations. A key limitation of existing…

Random Boolean networks, the Kauffman model, are revisited by means of a novel decimation algorithm, which reduces the networks to their dynamical cores. The average size of the removed part, the stable core, grows approximately linearly…

Observing the internal state of the whole system using a small number of sensor nodes is important in analysis of complex networks. Here, we study the problem of determining the minimum number of sensor nodes to discriminate attractors…

Probabilistic Boolean Networks have been proposed for estimating the behaviour of dynamical systems as they combine rule-based modelling with uncertainty principles. Inferring PBNs directly from gene data is challenging however, especially…

Network datasets appear across a wide range of scientific fields, including biology, physics, and the social sciences. To enable data-driven discoveries from these networks, statistical inference techniques like estimation and hypothesis…

In this paper, we analyse large random Boolean networks in terms of a constraint satisfaction problem. We first develop an algorithmic scheme which allows to prune simple logical cascades and under-determined variables, returning thereby…

Networks are powerful instruments to study complex phenomena, but they become hard to analyze in data that contain noise. Network backbones provide a tool to extract the latent structure from noisy networks by pruning non-salient edges. We…

This paper introduces a new methodology to analyse bipartite and unipartite networks with nonnegative edge values. The proposed approach combines and adapts a number of ideas from the literature on latent variable network models. The…

We present a novel, domain-agnostic, model-independent, unsupervised, and universally applicable Machine Learning approach for dimensionality reduction based on the principles of algorithmic complexity. Specifically, but without loss of…

We present STAT: a simple algorithm to prune transformer models without any fine-tuning. STAT eliminates both attention heads and neurons from the network, while preserving accuracy by calculating a correction to the weights of the next…

In analyzing and assessing the condition of dynamical systems, it is necessary to account for nonlinearity. Recent advances in computation have rendered previously computationally infeasible analyses readily executable on common computer…

A useful approach to the mathematical analysis of large-scale biological networks is based upon their decompositions into monotone dynamical systems. This paper deals with two computational problems associated to finding decompositions…

The regulation of the cell state is a complex process involving several components. These complex dynamics can be modeled using Boolean networks, allowing us to explain the existence of different cell states and the transition between them.…

We present and discuss the results of an experimental analysis in the design of Boolean networks by means of genetic algorithms. A population of networks is evolved with the aim of finding a network such that the attractor it reaches is of…

Model pruning seeks to induce sparsity in a deep neural network's various connection matrices, thereby reducing the number of nonzero-valued parameters in the model. Recent reports (Han et al., 2015; Narang et al., 2017) prune deep networks…