Hierarchy and Polysynchrony in an adaptive network

We describe a simple adaptive network of coupled chaotic maps. The network reaches a stationary state (frozen topology) for all values of the coupling parameter, although the dynamics of the maps at the nodes of the network can be non-trivial. The structure of the network shows interesting hierarchical properties and in certain parameter regions the dynamics is polysynchronous: nodes can be divided in differently synchronized classes but contrary to cluster synchronization, nodes in the same class need not be connected to each other. These complicated synchrony patterns have been conjectured to play roles in systems biology and circuits. The adaptive system we study describes ways whereby this behaviour can evolve from undifferentiated nodes.Comment: 13 pages, 17 figure

Coexistence of periods in a bisecting bifurcation

The inner structure of the attractor appearing when the Varley-Gradwell-Hassell population model bifurcates from regular to chaotic behaviour is studied. By algebraic and geometric arguments the coexistence of a continuum of neutrally stable limit cycles with different periods in the attractor is explained.Comment: 13 pages, 5 figure

Bifurcations in the Lozi map

We study the presence in the Lozi map of a type of abrupt order-to-order and order-to-chaos transitions which are mediated by an attractor made of a continuum of neutrally stable limit cycles, all with the same period.Comment: 17 pages, 12 figure

Families of piecewise linear maps with constant Lyapunov exponent

We consider families of piecewise linear maps in which the moduli of the two slopes take different values. In some parameter regions, despite the variations in the dynamics, the Lyapunov exponent and the topological entropy remain constant. We provide numerical evidence of this fact and we prove it analytically for some special cases. The mechanism is very different from that of the logistic map and we conjecture that the Lyapunov plateaus reflect arithmetic relations between the slopes.Comment: 26 pages, 13 figure

Emergence of hierarchical networks and polysynchronous behaviour in simple adaptive systems

We describe the dynamics of a simple adaptive network. The network architecture evolves to a number of disconnected components on which the dynamics is characterized by the possibility of differently synchronized nodes within the same network (polysynchronous states). These systems may have implications for the evolutionary emergence of polysynchrony and hierarchical networks in physical or biological systems modeled by adaptive networks.Comment: 4 pages, 4 figure

Jarlskog-like invariants for theories with scalars and fermions

Within the framework of theories where both scalars and fermions are present, we develop a systematic prescription for the construction of CP-violating quantities that are invariant under basis transformations of those matter fields. In theories with Spontaneous Symmetry Breaking, the analysis involves the vevs' transformation properties under a scalar basis change, with a considerable simplification of the study of CP violation in the scalar sector. These techniques are then applied in detail to the two Higgs-doublet model with quarks. It is shown that there are new invariants involving scalar-fermion interactions, besides those already derived in previous analyses for the fermion-gauge and scalar-gauge sectors.Comment: 12 pages, Latex, no figure

Dynamics of a map with power-law tail

We analyze a one-dimensional piecewise continuous discrete model proposed originally in studies on population ecology. The map is composed of a linear part and a power-law decreasing piece, and has three parameters. The system presents both regular and chaotic behavior. We study numerically and, in part, analytically different bifurcation structures. Particularly interesting is the description of the abrupt transition order-to-chaos mediated by an attractor made of an infinite number of limit cycles with only a finite number of different periods. It is shown that the power-law piece in the map is at the origin of this type of bifurcation. The system exhibits interior crises and crisis-induced intermittency.Comment: 28 pages, 17 figure

Bioluminescent-like squamation in the galeomorph shark Apristurus ampliceps (Chondrichthyes: Elasmobranchii)

Galeomorph sharks constitute the most taxonomically and ecologically diverse superorder of living selachians. Despite comprising several typically deep-water taxa, no bioluminescent species have been reported in this group so far. Interestingly, the study of shark squamation has been revealed in recent years to be a good proxy for inferring some ecological aspects of poorly known species. In particular, the high morphological specificity of the dermal denticles and the squamation patterns of all currently-known bioluminescent sharks could constitute a potential tool for predicting bioluminescence in both fossil and living taxa. Following this idea, we provide the first evidence supporting the possible existence of bioluminescence among galeomorph sharks by means of the quantitative study of Apristurus ampliceps squamation pattern. Classical morphometric analysis and multivariate statistical procedures have allowed us to determine that A. ampliceps squamation, composed mainly of bristle-shaped dermal denticles, is highly convergent with that of the bioluminescent shark Etmopterus spinax. The ecology of A. ampliceps, being a species that exclusively inhabits aphotic waters, is in agreement with such a morphofunctional interpretation, but finding photophores is imperative to confirm this prediction

Motivation for Therapy: an important ingredient to change?

We analyse the levels of motivation for therapy, as well as explore if there are significant differences between the group of clients who drop-out from therapy and those who continue. Is there a relation between the different dimensions of motivation and the way the client perceive the therapeutic environment? 39 dyads of therapist and clients from Portugal participated. The Client motivation for therapy scale, adapted from Pelletier, Tucson and Haddad (1997) and the modified HCCQ from Williams, McGregor, King, Nelson and Glasgow (2005) were administered to the clients in 1st, 3rd, 5th and 8th session. Significant differences in the intrinsic motivation and amotivation dimension and no significant differences were found, between those who give up/continue psychotherapy (p>.05). Nevertheless it was found a positive significant correlation (rs=.467) between the level of perception of the therapeutic environment and integrated motivation, as well as a negative correlation with amotivation (rs=.521), that is to say, the better the perception of the therapeutic environment, more motivated they are for therapy.Keywords: motivation, psychotherapy, clients, therapeutic environment

New Sensor Based on Magnetic Fields for Monitoring the Concentration of Organic Fertilisers in Fertigation Systems

[EN] In this paper, we test three prototypes with different characteristics for controlling the quantity of organic fertiliser in the agricultural irrigation system. We use 0.4 mm of copper diameter, distributing in different layers, maintaining the relation of 40 spires for powered coil and 80 for the induced coil. Moreover, we develop sensors with 8, 4, and 2 layers of copper. The coils are powered by a sine wave of 3.3 V peak to peak, and the other part is induced. To verify the functioning of this sensor, we perform several simulations with COMSOL Multiphysics to verify the magnetic field created around the powered coil, as well as the electric field, followed by a series of tests, using six samples between the 0 g/L and 20 g/L of organic fertiliser, and measure their conductivity. First, we find the working frequency doing a sweep for each prototype and four configurations. In this case, for all samples, making a sweep between 10 kHz and 300 kHz. We obtained that in prototype 1 (P1) (coil with 8 layers) the working frequency is around 100 kHz, in P2 (coil with 4 layers) around 110 kHz, and for P3 (coil with 2 layers) around 140 kHz. Then, we calibrate the prototypes measuring the six samples at four different configurations for each sensor to evaluate the possible variances. Likewise, the measures were taken in triplicate to reduce the possible errors. The obtained results show that the maximum difference of induced voltage between the lowest and the highest concentration is for the P2/configuration 4 with 1.84 V. Likewise, we have obtained an optimum correlation of 0.997. Then, we use the other three samples to verify the optimum functioning of the obtained calibrates. Moreover, the ANOVA simple procedure is applied to the data of all prototypes, in the working frequency of each configuration, to verify the significant difference between the values. The obtained results indicate that there is a significate difference between the average of concentration (g/L) and the induced voltage, and another with a level of 5% of significance. Finally, we compare all of the tested prototypes and configurations, and have determined that prototype three with configuration 1 is the best device to be used as a fertiliser sensor in water.This work is partially funded by the Conselleria de Educacion, Cultura y Deporte with the Subvenciones para la contratacion de personal investigador en fase postdoctoral, grant number APOSTD/2019/04, by the European Union, through the ERANETMED (Euromediterranean Cooperation through ERANET joint activities and beyond) project ERANETMED3-227 SMARTWATIR, and by the European Union with the "Fondo Europeo Agricola de Desarrollo Rural (FEADER)-Europa invierte en zonas rurales", the MAPAMA, and Comunidad de Madrid with the IMIDRA, under the mark of the PDR-CM 2014-2020" project number PDR18-XEROCESPED.Basterrechea-Chertudi, DA.; Parra-Boronat, L.; Botella-Campos, M.; Lloret, J.; Mauri, PV. (2020). 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Journal of Soils and Sediments, 14(7), 1235-1241. doi:10.1007/s11368-013-0813-0Comsol Multiphysicshttps://www.comsol.com/Kleinberg, R. L., Chew, W. C., & Griffin, D. D. (1989). Noncontacting electrical conductivity sensor for remote, hostile environments. IEEE Transactions on Instrumentation and Measurement, 38(1), 22-26. doi:10.1109/19.19992Parra, L., Marín, J., Mauri, P. V., Lloret, J., Torices, V., & Massager, A. (2019). Scatternet Formation Protocol for Environmental Monitoring in a Smart Garden. Network Protocols and Algorithms, 10(3), 63. doi:10.5296/npa.v10i3.14122Wood, L. T., Rottmann, R. M., & Barrera, R. (2004). Faraday’s law, Lenz’s law, and conservation of energy. American Journal of Physics, 72(3), 376-380. doi:10.1119/1.1646131Parra, L., Sendra, S., Lloret, J., & Bosch, I. (2015). Development of a Conductivity Sensor for Monitoring Groundwater Resources to Optimize Water Management in Smart City Environments. 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