**7** Publications

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Entropy (Basel) 2020 Nov 19;22(11). Epub 2020 Nov 19.

Faculty of Modern Languages and Literature, Adam Mickiewicz University in Poznań, 61-874 Poznań, Poland.

Using simulated annealing, we examine a bipartitioning of small worlds obtained by adding a fraction of randomly chosen links to a one-dimensional chain or a square lattice. Models defined on small worlds typically exhibit a mean-field behavior, regardless of the underlying lattice. Our work demonstrates that the bipartitioning of small worlds does depend on the underlying lattice. Simulations show that for one-dimensional small worlds, optimal partitions are finite size clusters for any fraction of additional links. In the two-dimensional case, we observe two regimes: when the fraction of additional links is sufficiently small, the optimal partitions have a stripe-like shape, which is lost for a larger number of additional links as optimal partitions become disordered. Some arguments, which interpret additional links as thermal excitations and refer to the thermodynamics of Ising models, suggest a qualitative explanation of such a behavior. The histogram of overlaps suggests that a replica symmetry is broken in a one-dimensional small world. In the two-dimensional case, the replica symmetry seems to hold, but with some additional degeneracy of stripe-like partitions.

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http://dx.doi.org/10.3390/e22111319 | DOI Listing |

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7712369 | PMC |

November 2020

Sci Rep 2019 09 11;9(1):13162. Epub 2019 Sep 11.

Departamento de Física & I3N, Universidade de Aveiro, 3810-193, Aveiro, Portugal.

Many social, technological, and biological systems with asymmetric interactions display a variety of collective phenomena, such as opinion formation and synchronization. This has motivated much research on the dynamical impact of local and mesoscopic structure in directed networks. However, the unique constraints imposed by the global organization of directed networks remain largely undiscussed. Here, we control the global organization of directed Erdős-Rényi networks, and study its impact on the emergence of synchronization and ferromagnetic ordering, using Kuramoto and Ising dynamics. In doing so, we demonstrate that source nodes - peripheral nodes without incoming links - can disrupt or entirely suppress the emergence of collective states in directed networks. This effect is imposed by the bow-tie organization of directed networks, where a large connected core does not uniquely ensure the emergence of collective states, as it does for undirected networks.

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http://dx.doi.org/10.1038/s41598-019-49537-8 | DOI Listing |

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6739311 | PMC |

September 2019

Int J Artif Organs 2012 Apr 11;35(4):263-71. Epub 2012 Apr 11.

Department of Biomedical Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania - USA and Department of Mathematics, Federal University of Maranhão, Maranhão - Brazil.

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http://dx.doi.org/10.5301/ijao.5000066 | DOI Listing |

April 2012

Annu Int Conf IEEE Eng Med Biol Soc 2011 ;2011:223-6

Department of Mathematics, Federal University of Maranhao, Sao Luis, MA 65080-040, Brazil.

A new index to assess left ventricular (LV) function in patients implanted with continuous flow left-ventricular assist devices (LVADs) is proposed. Derived from the pump flow signal, this index is defined as the coefficient (k) of the semilogarithmic relationship between "pseudo-ejection" fraction (pEF) and the volume discharged by the pump in diastole, (V d). pEF is defined as the ratio of the "pseudo-stroke volume" (pSV) to V d. The pseudo-stroke volume is the difference between V d and the volume discharged by the pump in systole (V s), both obtained by integrating pump flow with respect to time in a cardiac cycle. k was compared in-vivo with others two indices: the LV pressure-based index, M(TP), and the pump flow-based index, I(Q). M(TP) is the slope of the linear regression between the "triple-product" and end-diastolic pressure, EDP. The triple-product, TP = LV SP.dP/dt(max). HR, is the product of LV systolic pressure, maximum time-derivative of LV pressure, and heart rate. I(Q) is the slope of the linear regression between maximum time-derivative of pump flow, dQ/dt(max), and pump flow peak-to-peak amplitude variation, Q(P2P). To test the response of k to contractile state changes, contractility was altered through pharmacological interventions. The absolute value of k decreased from 1.354 ± 0.25 (baseline) to 0.685 ± 0.21 after esmolol infusion. The proposed index is sensitive to changes in inotropic state, and has the potential to be used clinically to assess contractile function of patients implanted with VAD.

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http://dx.doi.org/10.1109/IEMBS.2011.6090041 | DOI Listing |

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3265331 | PMC |

June 2012

Phys Rev E Stat Nonlin Soft Matter Phys 2006 Mar 31;73(3 Pt 1):032102. Epub 2006 Mar 31.

Faculty of Physics, Adam Mickiewicz University, 61-614 Poznań, Poland.

Using event-driven molecular dynamics we study one- and two-dimensional ballistic annihilation. We estimate exponents xi and gamma, which describe the long-time decay of the number of particles [n(t) approximately t-xi] and of their typical velocity [v(t) approximately t-gamma]. To a good accuracy our results confirm the scaling relation xi+gamma=1. In the two-dimensional case our results are in good agreement with those obtained from Boltzmann kinetic theory.

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http://dx.doi.org/10.1103/PhysRevE.73.032102 | DOI Listing |

March 2006

Phys Rev E Stat Nonlin Soft Matter Phys 2003 May 13;67(5 Pt 2):056108. Epub 2003 May 13.

Department of Physics, University of Geneva, CH 1211 Geneva 4, Switzerland.

Recently some two-dimensional models with double symmetric absorbing states were shown to share the same critical behavior that was called the voter universality class. We show that, for an absorbing-states Potts model with finite but further than nearest-neighbor range of interactions, the critical point is split into two critical points: one of the Ising type and the other of the directed percolation universality class. Similar splitting takes place in the three-dimensional nearest-neighbor model.

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http://dx.doi.org/10.1103/PhysRevE.67.056108 | DOI Listing |

May 2003

Phys Rev E Stat Nonlin Soft Matter Phys 2002 Dec 9;66(6 Pt 2):066107. Epub 2002 Dec 9.

Department of Physics, A. Mickiewicz University, 61-614 Poznań, Poland.

Using Monte Carlo simulations we study two-dimensional prey-predator systems. Measuring the variance of densities of prey and predators on the triangular lattice and on the lattice with eight neighbors, we conclude that temporal oscillations of these densities vanish in the thermodynamic limit. This result suggests that such oscillations do not exist in two-dimensional models, at least when driven by local dynamics. Depending on the control parameter, the model could be either in an active or in an absorbing phase, which are separated by the critical point. The critical behavior of this model is studied using the dynamical Monte Carlo method. This model has two dynamically nonsymmetric absorbing states. In principle both absorbing states can be used for the analysis of the critical point. However, dynamical simulations which start from the unstable absorbing state suffer from metastablelike effects, which sometimes renders the method inefficient.

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http://dx.doi.org/10.1103/PhysRevE.66.066107 | DOI Listing |

December 2002