On the long-term correlations and multifractal properties of electric arc furnace time series

In this paper, we study long-term correlations and multifractal properties elaborated from time series of three-phase current signals coming from an industrial electric arc furnace plant. Implicit sinusoidal trends are suitably detected by considering the scaling of the fluctuation functions. Time series are then filtered via a Fourier-based analysis, removing hence such strong periodicities. In the filtered time series we detected long-term, positive correlations. The presence of positive correlations is in agreement with the typical V--I characteristic (hysteresis) of the electric arc furnace, providing thus a sound physical justification for the memory effects found in the current time series. The multifractal signature is strong enough in the filtered time series to be effectively classified as multifractal

A generative model for protein contact networks

In this paper we present a generative model for protein contact networks. The soundness of the proposed model is investigated by focusing primarily on mesoscopic properties elaborated from the spectra of the graph Laplacian. To complement the analysis, we study also classical topological descriptors, such as statistics of the shortest paths and the important feature of modularity. Our experiments show that the proposed model results in a considerable improvement with respect to two suitably chosen generative mechanisms, mimicking with better approximation real protein contact networks in terms of diffusion properties elaborated from the Laplacian spectra. However, as well as the other considered models, it does not reproduce with sufficient accuracy the shortest paths structure. To compensate this drawback, we designed a second step involving a targeted edge reconfiguration process. The ensemble of reconfigured networks denotes improvements that are statistically significant. As a byproduct of our study, we demonstrate that modularity, a well-known property of proteins, does not entirely explain the actual network architecture characterizing protein contact networks. In fact, we conclude that modularity, intended as a quantification of an underlying community structure, should be considered as an emergent property of the structural organization of proteins. Interestingly, such a property is suitably optimized in protein contact networks together with the feature of path efficiency.Comment: 18 pages, 67 reference

Multifractal Characterization of Protein Contact Networks

The multifractal detrended fluctuation analysis of time series is able to reveal the presence of long-range correlations and, at the same time, to characterize the self-similarity of the series. The rich information derivable from the characteristic exponents and the multifractal spectrum can be further analyzed to discover important insights about the underlying dynamical process. In this paper, we employ multifractal analysis techniques in the study of protein contact networks. To this end, initially a network is mapped to three different time series, each of which is generated by a stationary unbiased random walk. To capture the peculiarities of the networks at different levels, we accordingly consider three observables at each vertex: the degree, the clustering coefficient, and the closeness centrality. To compare the results with suitable references, we consider also instances of three well-known network models and two typical time series with pure monofractal and multifractal properties. The first result of notable interest is that time series associated to proteins contact networks exhibit long-range correlations (strong persistence), which are consistent with signals in-between the typical monofractal and multifractal behavior. Successively, a suitable embedding of the multifractal spectra allows to focus on ensemble properties, which in turn gives us the possibility to make further observations regarding the considered networks. In particular, we highlight the different role that small and large fluctuations of the considered observables play in the characterization of the network topology

An Agent-Based Algorithm exploiting Multiple Local Dissimilarities for Clusters Mining and Knowledge Discovery

We propose a multi-agent algorithm able to automatically discover relevant regularities in a given dataset, determining at the same time the set of configurations of the adopted parametric dissimilarity measure yielding compact and separated clusters. Each agent operates independently by performing a Markovian random walk on a suitable weighted graph representation of the input dataset. Such a weighted graph representation is induced by the specific parameter configuration of the dissimilarity measure adopted by the agent, which searches and takes decisions autonomously for one cluster at a time. Results show that the algorithm is able to discover parameter configurations that yield a consistent and interpretable collection of clusters. Moreover, we demonstrate that our algorithm shows comparable performances with other similar state-of-the-art algorithms when facing specific clustering problems

Analysis of heat kernel highlights the strongly modular and heat-preserving structure of proteins

In this paper, we study the structure and dynamical properties of protein contact networks with respect to other biological networks, together with simulated archetypal models acting as probes. We consider both classical topological descriptors, such as the modularity and statistics of the shortest paths, and different interpretations in terms of diffusion provided by the discrete heat kernel, which is elaborated from the normalized graph Laplacians. A principal component analysis shows high discrimination among the network types, either by considering the topological and heat kernel based vector characterizations. Furthermore, a canonical correlation analysis demonstrates the strong agreement among those two characterizations, providing thus an important justification in terms of interpretability for the heat kernel. Finally, and most importantly, the focused analysis of the heat kernel provides a way to yield insights on the fact that proteins have to satisfy specific structural design constraints that the other considered networks do not need to obey. Notably, the heat trace decay of an ensemble of varying-size proteins denotes subdiffusion, a peculiar property of proteins

Temporal overdrive recurrent neural network

In this work we present a novel recurrent neural network architecture designed to model systems characterized by multiple characteristic timescales in their dynamics. The proposed network is composed by several recurrent groups of neurons that are trained to separately adapt to each timescale, in order to improve the system identification process. We test our framework on time series prediction tasks and we show some promising, preliminary results achieved on synthetic data. To evaluate the capabilities of our network, we compare the performance with several state-of-the-art recurrent architectures

Learning an unknown transformation via a genetic approach

Recent developments in integrated photonics technology are opening the way to the fabrication of complex linear optical interferometers. The application of this platform is ubiquitous in quantum information science, from quantum simulation to quantum metrology, including the quest for quantum supremacy via the boson sampling problem. Within these contexts, the capability to learn efficiently the unitary operation of the implemented interferometers becomes a crucial requirement. In this letter we develop a reconstruction algorithm based on a genetic approach, which can be adopted as a tool to characterize an unknown linear optical network. We report an experimental test of the described method by performing the reconstruction of a 7-mode interferometer implemented via the femtosecond laser writing technique. Further applications of genetic approaches can be found in other contexts, such as quantum metrology or learning unknown general Hamiltonian evolutions

Analysis and modeling of complex networks by means of computational intelligence techniques

In this thesis I explore the organizing principles between protein structure by means of their network representation, with the aid of machine learning and computational intelligence methodologies. The study is structured in two main parts. In the first part I investigate the structural properties of Protein Contact Networks (PCN) and compare them with several other biological and synthetic networks. I characterize PCNs by their heat diffusion properties, obtained with heat kernel analysis, and highlight critical differences with respect to the other analyzed networks. In particular, I observe heat subdiffusion on the PCNs topology. This peculiar character is also confirmed by the study of the correlation properties of random walks performed on the networks, analyzed via Multifractal Detrended Fluctuation Analysis. The second part of the thesis is mainly concerned with the problem of generating new networks that show similar spectral properties with respect to PCNs. A generative model is defined as a variant of the model proposed by Bartoli et al. in 2007, obtaining closer spectral properties. The samples generated through this generative model are subsequently improved by means of an evolutionary optimization scheme. As a result, the spectral distribution of the generated samples is nearly identical to the reference distribution calculated from the set of PCNs