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• An accelerated growth model to generate complex networks with connectivity distribution slope that varies with time

  P. Castillo Castillo, P.D. Arjona-Villicaña, and J. Acosta-Elias

  128-132

  2019-03-26

  Abstract:

  Many real-life complex networks have in-degree and out-degree distributions that decay as a
  power-law. However, the few models that have been able to reproduce both of these properties,
  cannot reproduce the wide range of values found in real systems. Another limitation of these
  models is that they add links from nodes which are created into the network, as well as between
  nodes already present in this network. However, adding links between existing nodes is not a
  characteristic available in all systems. This paper introduces a new complex network growth
  model that, without adding links between existing nodes is able to generate complex topologies
  with in-degree and out-degree distributions that decay as a power-law. Moreover, in this growth
  model, the ratio at which links are created is greater than the ratio at which nodes are born, which
  produces an accelerated growth phenomenon that can be found in some real systems, like the
  Internet at the Autonomous System level.

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  DOI: https://doi.org/10.31349/RevMexFis.65.128

• On the Lagrangians and potentials of a two coupled damped Duffing oscillators system and their application on three-node motif networks

  J. J. Barba-Franco,, P. B. Espinoza,, A. Gallegos,, R. Jaimes-Reategui, J.E. Macias-Diaz

  440-445

  2020-07-01

  Abstract:

  In this work, we investigate the Lagrangians and potentials for two coupled damped Duffing oscillators both directionally and bi-directionally. We show that, although it is not always possible to define a potential in dissipative systems, the potential of our model can be defined if the damping coefficient has a logarithmic derivative form. It is possible to apply these results to the analysis of the dynamics of complex networks based on three-node motif configurations. As an example, we study numerically the dynamics for one of the thirteen different possible configurations. Here, the phenomenon of synchronization is observed in terms of the coupling parameter.

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  DOI: https://doi.org/10.31349/RevMexFis.66.440

• Information-theoretical analysis of gene expression data to infer transcriptional interactions

  K. Baca-López, E. Hernández-Lemus, M. Ma, orga.

  456-0

  2009-01-01

  Abstract:

  The majority of human diseases are related with the dynamic interaction of many genes and their products as well as environmental constraints. Cancer (and breast cancer in particular) is a paradigmatic example of such complex behavior. Since gene regulation is a non-equilibrium process, the inference and analysis of such phenomena could be done following the tenets of non-equilibrium physics. The traditional \emph{programme} in statistical mechanics consists in inferring the joint probability distribution for either microscopic states (equilibrium) or mesoscopic-states (non-equilibrium), given a model for the particle interactions (e.g. the potentials). An \emph{inverse problem} in statistical mechanics, in the other hand, is based on considering a \emph{realization} of the probability distribution of micro- or meso-states and used it to infer the interaction potentials between particles. This is the approach taken in what follows. We analyzed 261 whole-genome gene expression experiments in breast cancer patients, and by means of an information-theoretical analysis, we deconvolute the associated set of transcriptional interactions, i.e. we discover a set of fundamental biochemical reactions related to this pathology. By doing this, we showed how to apply the tools of non-linear statistical physics to generate hypothesis to be tested on clinical and biochemical settings in relation to cancer phenomenology.

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• EEG motor imagery classification using machine learning techniques

  R. T. Páez-Amaro, E. Moreno-Barbosa, J. M. Hernández-López, C. H. Zepeda-Fernández, L. F. Rebolledo-Herrera, Benito de Celis Alonso

  041102 1–12

  2022-06-07

  Abstract:

  A brain-machine interface (BMI), is a device or experimental setup that receives a brain signal, classifies it, and then uses it as a computer command. Even if large amounts of work exist in the field, there is not a consensus on which kind of learning methodology (deep learning, convolutional networks, AI, etc.) and/or type of algorithms in each methodology, are best to run BMIs. The aim of this work was to build a low-cost, portable, easy-to-use and a reliable BMI based on Motor Imagery Electro-encephalography. To this end, different algorithms were compared to find the one that best satisfied such conditions. In this study, motor imagery EEG signals, from both PhysioNet public data and from our own laboratory obtained using an Emotiv headset, were classified with four machine learning algorithms. These algorithms were: Common spatial patterns combined with linear discriminant analysis, Deep neural network, convolutional neural network and finally Riemannian minimum distance to mean. The mean accuracy for each method was 78%, 66%, 60% and 80% respectively. The best results were obtained for the baseline vs Motor Imagery comparison. With global-training public data, an accuracy between 86.4% and 99.9% was achieved. With global-training lab data, the accuracy was above 99% for Common Spatial Patterns and Riemannian cases. For lab data, the classification/prediction computing time per event were 8.3 ms, 18.1 ms, 62 ms and 9.9 ms, respectively. In the discussion a comparison between the results presented here and state-of-the-art of methodologies and algorithms for BMIs can be found. We concluded that Common spatial patterns and Riemannian minimum distance to mean, algorithms resulted in fast (computing time) and effective (success rate) tools for their implementation as deep learning algorithms in BMIs.

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  DOI: https://doi.org/10.31349/RevMexFis.68.041102

• Scale-free growing networks and gravity

  J. A

  201-0

  2013-01-01

  Abstract:

  We propose a possible relation between complex networks and gravity. Our guide in our proposal is the power-law distribution of the node degree in network theory and the information approach to gravity. The established bridge may allow us to carry geometric mathematical structures, which are considered in gravitational theories, to probabilistic aspects studied in the framework of complex networks and vice versa.

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• The impact of time delay in the connectivity distribution of complex networks generated using the Barabási-Albert model

  J. Acosta-Elías, P. D, L. Moldes-Navarro

  145-0

  2014-01-01

  Abstract:

  In the Barabási-Albert growth model for complex networks new nodes added to the network, obtain instant information from the entire network and employ preferential connectivity to select a node to establish a connection. In practice, information takes time to propagate from a sender to a receiver. We modify the Barabási-Albert model to include the time information takes to propagate between nodes. In the modified model a time delay is associated to the transmission of information and each new node must wait for a period of time to receive the network connectivity information. By adjusting this waiting time, different functional forms of the connectivity distribution are obtained. These connectivity distributions form a spectrum of functional forms which lie between two limiting cases: a power law distribution for large waiting times and an exponential distribution for short waiting times.

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• Magneto-transport behavior of disordered three dimensional NixCo1−x inverse opal networks

  Hiram Eli Torres Soto, Flavio Abreu Araujo, Joaquín de la Torre Medina

  041603 1–7

  2023-07-04

  Abstract:

  Herein we report on the magneto-transport properties of disordered three dimensional inverse opals (3D-IOs) fabricated by a standard three-probe electrodeposition technique into the interstices of porous membranes made of 150 nm diameter self assembled poly(methyl methacrylate) spheres. This approach has allowed the synthesis of large scale nanocomposites with exact ferromagnetic NixCo1−x alloy compositions and complex interconnected structure. Particularly, the microstructure of Co-rich 3D-IOs is consistent with the hexagonal close packed hcp texture and its corresponding magnetoresistance is explained in terms of the hcp Co magnetocrystalline anisotropy contribution. Conversely, the magnetoresistive behavior of Ni-rich 3D-IO networks is explained in terms of only their magnetostatic field. The control of these features is made possible by the reduced dimensions of necks and walls, in the 40 nm to 60 nm range, of the 3D-IO structure. Despite the disordered morphology of these 3D-IO nanoarchitectures, their microstructural and magneto-transport properties can be fine tuned due to the reduced nanoscale dimensions of the electrical interconnections. These properties have been found to be comparable to those obtained in other 3D networks, making them interesting systems for their potential use for magnetic sensing and spintronic applications.

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  DOI: https://doi.org/10.31349/RevMexFis.69.041603

• Identifying the complex underlying transmission network of COVID-19 in México from 2020 to 2024

  J. Esquivel-Gomez, E. E. Rodríguez Martínez, J. G. Barajas Ramírez

  021701 1–7

  2026-03-09

  Abstract:

  Has been demonstrated that the interaction of individuals in a social network can be modeled using the complex networks theory. In this sense, we believe that knowing at least approximately the underlying network of interaction among the individuals in a society could help to understand the dynamic of diseases transmission among the individuals and elucidate the most effective mechanisms to contain the spread and minimize negative effects like the over-saturation of health systems, such as hospitals and medical clinics. In this work, we study the spread of COVID-19 in Mexico from 2020 to 2024 using the statistical data available in the public health departments of Mexico. Through stochastic simulations we found a complex network that could represent a simplification of the real underlying network of interaction among the Mexican population, in particular we found that the network has degree distribution following a power law P(k) ∼ k −γ with exponent close to γ ≈ 2.5. As mentioned before it could help to understand the spread of future diseases through stochastic simulations using a network structure closer to reality and consequently implement best healthy policies.

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  DOI: https://doi.org/10.31349/RevMexFis.72.021701

• Chaotic synchronization of irregular complex network with hysteretic circuit-like oscillators in hamiltonian form and its application in private communications

  E. Garza-González, C. Posadas-Castillo, A. Rodríguez-Liñan, C. Cruz-Hernández

  51-59

  2016-01-01

  Abstract:

  In this paper, a study on chaotic synchronization of an irregular network is made. Synchronization is achieved by using a modified Hamiltonian approach in a bidirectional irregular arrayed network made of 20 chaotic oscillators. The chaotic oscillator used as example is the Hysteretic circuit. Afterwards the concept is used in chaotic encryption to send secured confidential analog information. As a result, an image is encrypted using additive chaotic encrytion with two channels.

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  DOI: https://doi.org/10.31349/RevMexFis.62.1.51

• Encrypted audio transmission via synchronized chaotic Nd:YAG lasers

  L. Cardoza-Avendaño, R.M. López-Gutiérrez, C. Cruz-Hernández, V.V. Spirin, R.A. Chávez-Pérez, A. Arellano-Delgado

  472-480

  2012-01-01

  Abstract:

  In this paper, encrypted audio transmission via synchronization of coupled chaotic Nd:YAG lasers in master-slave configuration is numerically studied. In particular, we resort to recent results from complex systems theory to achieve chaos synchronization. So that, enconding, transmission, and decoding of confidential audio messeges in chaotic optical communications are presented. In addition, we show transmission of encrypted audio messages when parameter mismatch and channel noise are considered. In order to illustrate this robustness synchronization property, we present the encrypted transmission of audio messages via an improved chaotic transmitted signal, and we obtain at the receiver that, the original audio message is appropriatelly recovered.

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