From synchronization to multistability in two coupled quadratic maps

The phenomenology of a system of two coupled quadratic maps is studied both analytically and numerically. Conditions for synchronization are given and the bifurcations of periodic orbits from this regime are identified. In addition, we show that an arbitrarily large number of distinct stable periodic orbits may be obtained when the maps parameter is at the Feigenbaum period-doubling accumulation point. An estimate is given for the coupling strength needed to obtain any given number of stable orbits.Comment: 13 pages Latex, 9 figure

PROTOCOLO DE AVALIAÇÃO E CONTROLO DA DOR AGUDA NO DOENTE PEDIÁTRICO

INTRODUÇÃO: a prevenção, avaliação e controlo da dor em pediatria, pelas caraterísticas próprias dos seus utentes, constitui um desafio para os profissionais de saúde, pelo que constituímos uma equipa com a missão de elaborar um Protocolo de Orientação Clínica (POC) para a avaliação e controlo da dor aguda no doente pediátrico. OBJETIVOS: apresentar o percurso para elaboração e implementação do POC na instituição;divulgar alguns conteúdos do POC; apresentar resultados da última monitorização. MATERIAIS E MÉTODOS: constituiu-se uma equipa com médicos e enfermeiros, com representação de pediatria, anestesiologia, cirurgia e cuidados intensivos; foi elaborado e implementado o POC da dor aguda no doente pediátrico e efetuada monitorização dos registos. RESULTADOS: o POC apresenta as escalas de avaliação da dor, define critérios de seleção, metodologia de avaliação, registo de intensidade, intervenções farmacológicas e não farmacológicas e define estratégias de atuação em procedimentos dolorosos. Efetuada formação às diversas equipas médicas e de enfermagem e várias monitorizações pontuais. O início do registo informático aconteceu no dia 01/06/2013. O POC foi revisto em 2015. Efetuamos um levantamento retrospetivo dos registos da dor dos dias 4, 12, 20 e 28/01/2016 no Serviço de Cuidados Intensivos Pediátricos (SCIP) a um total de 29 crianças e no Serviço de Cuidados Intensivos Neonatais (SCIN) a um total de 79 recém-nascidos. Definimos 3 indicadores: (i) intervenção avaliar dor - no SCIP 93.3% das crianças tinham a intervenção programada e no SCIN 96.2%; (ii) avaliação da dor em 3 turnos nas 24h - no SCIP foi avaliada a dor a 66.8% das crianças e no SCIN a 90%; (iii) intensidade da dor - no SCIP 29.6% das crianças tiveram dor ligeira, 22.2% moderada e 11.1% intensa, no SCIN 78.9% tiveram dor ligeira e 12.7% moderada. Relativamente às escalas utilizadas verificamos que no SCIP a FLACC-R foi aplicada a 38.4% das crianças, a EDIN a 30.8%, a FLACC a 15.4% e Escalas de Autoavaliação a 15.4%. No SCIN, a 95.9% das crianças foi aplicada a escala de EDIN e a 4.1% a N-PASS. CONCLUSÃO: A avaliação e controlo da dor aguda é uma mais valia para a instituição e para as crianças/família a quem disponibiliza cuidados de saúde. Embora não tenhamos crianças com dor muito intensa, os resultados encontram-se aquém das expectativas, contudo, resultam do percurso efetuado e revelam potencial para desenvolver este projeto de melhoria da qualidadeinfo:eu-repo/semantics/draf

Stability Analysis of a Hybrid Cellular Automaton Model of Cell Colony Growth

Cell colonies of bacteria, tumour cells and fungi, under nutrient limited growth conditions, exhibit complex branched growth patterns. In order to investigate this phenomenon we present a simple hybrid cellular automaton model of cell colony growth. In the model the growth of the colony is limited by a nutrient that is consumed by the cells and which inhibits cell division if it falls below a certain threshold. Using this model we have investigated how the nutrient consumption rate of the cells affects the growth dynamics of the colony. We found that for low consumption rates the colony takes on a Eden-like morphology, while for higher consumption rates the morphology of the colony is branched with a fractal geometry. These findings are in agreement with previous results, but the simplicity of the model presented here allows for a linear stability analysis of the system. By observing that the local growth of the colony is proportional to the flux of the nutrient we derive an approximate dispersion relation for the growth of the colony interface. This dispersion relation shows that the stability of the growth depends on how far the nutrient penetrates into the colony. For low nutrient consumption rates the penetration distance is large, which stabilises the growth, while for high consumption rates the penetration distance is small, which leads to unstable branched growth. When the penetration distance vanishes the dispersion relation is reduced to the one describing Laplacian growth without ultra-violet regularisation. The dispersion relation was verified by measuring how the average branch width depends on the consumption rate of the cells and shows good agreement between theory and simulations.Comment: 8 pages, 6 figure

Stratification of the orbit space in gauge theories. The role of nongeneric strata

Gauge theory is a theory with constraints and, for that reason, the space of physical states is not a manifold but a stratified space (orbifold) with singularities. The classification of strata for smooth (and generalized) connections is reviewed as well as the formulation of the physical space as the zero set of a momentum map. Several important features of nongeneric strata are discussed and new results are presented suggesting an important role for these strata as concentrators of the measure in ground state functionals and as a source of multiple structures in low-lying excitations.Comment: 22 pages Latex, 1 figur

Dynamical complexity of discrete time regulatory networks

Genetic regulatory networks are usually modeled by systems of coupled differential equations and by finite state models, better known as logical networks, are also used. In this paper we consider a class of models of regulatory networks which present both discrete and continuous aspects. Our models consist of a network of units, whose states are quantified by a continuous real variable. The state of each unit in the network evolves according to a contractive transformation chosen from a finite collection of possible transformations, according to a rule which depends on the state of the neighboring units. As a first approximation to the complete description of the dynamics of this networks we focus on a global characteristic, the dynamical complexity, related to the proliferation of distinguishable temporal behaviors. In this work we give explicit conditions under which explicit relations between the topological structure of the regulatory network, and the growth rate of the dynamical complexity can be established. We illustrate our results by means of some biologically motivated examples.Comment: 28 pages, 4 figure

On the regular-geometric-figure solution to the N-body problem

The regular-geometric-figure solution to the $N$-body problem is presented in a very simple way. The Newtonian formalism is used without resorting to a more involved rotating coordinate system. Those configurations occur for other kinds of interactions beyond the gravitational ones for some special values of the parameters of the forces. For the harmonic oscillator, in particular, it is shown that the $N$-body problem is reduced to $N$ one-body problems.Comment: To appear in Eur. J. Phys. (5 pages

Experimental polarization encoded quantum key distribution over optical fibres with real-time continuous birefringence compensation

In this paper we demonstrate an active polarization drift compensation scheme for optical fibres employed in a quantum key distribution experiment with polarization encoded qubits. The quantum signals are wavelength multiplexed in one fibre along with two classical optical side channels that provide the control information for the polarization compensation scheme. This set-up allows us to continuously track any polarization change without the need to interrupt the key exchange. The results obtained show that fast polarization rotations of the order of 40*pi rad/s are effectively compensated for. We demonstrate that our set-up allows continuous quantum key distribution even in a fibre stressed by random polarization fluctuations. Our results pave the way for Bell-state measurements using only linear optics with parties separated by long-distance optical fibres