Recurrence spectrum in smooth dynamical systems

We prove that for conformal expanding maps the return time does have constant multifractal spectrum. This is the counterpart of the result by Feng and Wu in the symbolic setting

Social diversity and promotion of cooperation in the spatial prisoner's dilemma game

The diversity in wealth and social status is present not only among humans, but throughout the animal world. We account for this observation by generating random variables that determ ine the social diversity of players engaging in the prisoner's dilemma game. Here the term social diversity is used to address extrinsic factors that determine the mapping of game pay offs to individual fitness. These factors may increase or decrease the fitness of a player depending on its location on the spatial grid. We consider different distributions of extrin sic factors that determine the social diversity of players, and find that the power-law distribution enables the best promotion of cooperation. The facilitation of the cooperative str ategy relies mostly on the inhomogeneous social state of players, resulting in the formation of cooperative clusters which are ruled by socially high-ranking players that are able to prevail against the defectors even when there is a large temptation to defect. To confirm this, we also study the impact of spatially correlated social diversity and find that coopera tion deteriorates as the spatial correlation length increases. Our results suggest that the distribution of wealth and social status might have played a crucial role by the evolution of cooperation amongst egoistic individuals.Comment: 5 two-column pages, 5 figure

Equilibrium states for potentials with \sup\phi - \inf\phi < \htop(f)

In the context of smooth interval maps, we study an inducing scheme approach to prove existence and uniqueness of equilibrium states for potentials $\phi$ with he `bounded range' condition \sup \phi - \inf \phi < \htop, first used by Hofbauer and Keller. We compare our results to Hofbauer and Keller's use of Perron-Frobenius operators. We demonstrate that this `bounded range' condition on the potential is important even if the potential is H\"older continuous. We also prove analyticity of the pressure in this context.Comment: Added Lemma 6 to deal with the disparity between leading eigenvalues and operator norms. Added extra references and corrected some typo

Comparison of personality traits among patients with psoriasis, atopic dermatitis, and stress: a pilot study

Background: Psoriasis and atopic dermatitis are chronic skin diseases that greatly affect the quality of life. Both diseases can be triggered or exacerbated by stress. Objective: We aimed to differentiate personality traits between patients with chronic skin conditions and people treated for stress in a pilot study. Methods: Patients participating voluntarily in educational programs in Belgium and Switzerland were recruited to complete personality trait questionnaires, including the Temperament and Character Inventory (TCI) and the Tridimensional Personality Questionnaire (TPQ). A comparison was made with patients treated for work-related stress. Results: A total of 48 and 91 patients suffering from skin diseases and work-related stress, respectively, were included in the study. Based on the questionnaires, we found that dermatology patients were less persistent and impulsive than those with work-related stress. Dermatology patients also exhibited more rigidness and less focus on performance. Finally, patients with work-related stress seem more likely to change in response to health-promoting programs than patients with chronic dermatoses. Conclusion: Patients with chronic skin diseases may perceive and cope with stress differently in comparison to patients with work-related stress due to inherent personality traits. Therefore, stress coping mechanisms may differ among different diseases. More research is needed into the design of educational interventions and the impact of personality traits in disease-specific groups

State Differentiation by Transient Truncation in Coupled Threshold Dynamics

Dynamics with a threshold input--output relation commonly exist in gene, signal-transduction, and neural networks. Coupled dynamical systems of such threshold elements are investigated, in an effort to find differentiation of elements induced by the interaction. Through global diffusive coupling, novel states are found to be generated that are not the original attractor of single-element threshold dynamics, but are sustained through the interaction with the elements located at the original attractor. This stabilization of the novel state(s) is not related to symmetry breaking, but is explained as the truncation of transient trajectories to the original attractor due to the coupling. Single-element dynamics with winding transient trajectories located at a low-dimensional manifold and having turning points are shown to be essential to the generation of such novel state(s) in a coupled system. Universality of this mechanism for the novel state generation and its relevance to biological cell differentiation are briefly discussed.Comment: 8 pages. Phys. Rev. E. in pres

Dephasing of quantum dot exciton polaritons in electrically tunable nanocavities

We experimentally and theoretically investigate dephasing of zero dimensional microcavity polaritons in electrically tunable single dot photonic crystal nanocavities. Such devices allow us to alter the dot-cavity detuning in-situ and to directly probe the influence on the emission spectrum of varying the incoherent excitation level and the lattice temperature. By comparing our results with theory we obtain the polariton dephasing rate and clarify its dependence on optical excitation power and lattice temperature. For low excitation levels we observe a linear temperature dependence, indicative of phonon mediated polariton dephasing. At higher excitation levels, excitation induced dephasing is observed due to coupling to the solid-state environment. The results provide new information on coherence properties of quantum dot microcavity polaritons.Comment: Figure 2, panel (b) changed to logarithmic + linear scal

Complementarity and diversity in a soluble model ecosystem

Complementarity among species with different traits is one of the basic processes affecting biodiversity, defined as the number of species in the ecosystem. We present here a soluble model ecosystem in which the species are characterized by binary traits and their pairwise interactions follow a complementarity principle. Manipulation of the species composition, and so the study of its effects on the species diversity is achieved through the introduction of a bias parameter favoring one of the traits. Using statistical mechanics tools we find explicit expressions for the allowed values of the equilibrium species concentrations in terms of the control parameters of the model

Metastability and anomalous fixation in evolutionary games on scale-free networks

We study the influence of complex graphs on the metastability and fixation properties of a set of evolutionary processes. In the framework of evolutionary game theory, where the fitness and selection are frequency-dependent and vary with the population composition, we analyze the dynamics of snowdrift games (characterized by a metastable coexistence state) on scale-free networks. Using an effective diffusion theory in the weak selection limit, we demonstrate how the scale-free structure affects the system's metastable state and leads to anomalous fixation. In particular, we analytically and numerically show that the probability and mean time of fixation are characterized by stretched exponential behaviors with exponents depending on the network's degree distribution.Comment: 5 pages, 4 figures, to appear in Physical Review Letter