860 resultados para Interactive maps


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Magdeburg, Univ., Fak. für Informatik, Diss., 2015

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Report for the scientific sojourn at the Research Institute for Applied Mathematics and Cybernetics, Nizhny Novgorod, Russia, from July to September 2006. Within the project, bifurcations of orbit behavior in area-preserving and reversible maps with a homoclinic tangency were studied. Finitely smooth normal forms for such maps near saddle fixed points were constructed and it was shown that they coincide in the main order with the analytical Birkhoff-Moser normal form. Bifurcations of single-round periodic orbits for two-dimensional symplectic maps close to a map with a quadratic homoclinic tangency were studied. The existence of one- and two-parameter cascades of elliptic periodic orbits was proved.

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We establish a one-to-one correspondence between the renormalizations and proper totally invariant closed sets (i.e., α-limit sets) of expanding Lorenz map, which enable us to distinguish periodic and non-periodic renormalizations. We describe the minimal renormalization by constructing the minimal totally invariant closed set, so that we can define the renormalization operator. Using consecutive renormalizations, we obtain complete topological characteriza- tion of α-limit sets and nonwandering set decomposition. For piecewise linear Lorenz map with slopes ≥ 1, we show that each renormalization is periodic and every proper α-limit set is countable.

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Report for the scientific sojourn at the Stanford University from January until June 2007. Music is well known for affecting human emotional states, yet the relationship between specific musical parameters and emotional responses is still not clear. With the advent of new human-computer interaction (HCI) technologies, it is now possible to derive emotion-related information from physiological data and use it as an input to interactive music systems. Providing such implicit musical HCI will be highly relevant for a number of applications including music therapy, diagnosis, nteractive gaming, and physiologically-based musical instruments. A key question in such physiology-based compositions is how sound synthesis parameters can be mapped to emotional states of valence and arousal. We used both verbal and heart rate responses to evaluate the affective power of five musical parameters. Our results show that a significant correlation exists between heart rate and the subjective evaluation of well-defined musical parameters. Brightness and loudness showed to be arousing parameters on subjective scale while harmonicity and even partial attenuation factor resulted in heart rate changes typically associated to valence. This demonstrates that a rational approach to designing emotion-driven music systems for our public installations and music therapy applications is possible.

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Continuity of set-valued maps is hereby revisited: after recalling some basic concepts of variational analysis and a short description of the State-of-the-Art, we obtain as by-product two Sard type results concerning local minima of scalar and vector valued functions. Our main result though, is inscribed in the framework of tame geometry, stating that a closed-valued semialgebraic set-valued map is almost everywhere continuous (in both topological and measure-theoretic sense). The result –depending on stratification techniques– holds true in a more general setting of o-minimal (or tame) set-valued maps. Some applications are briefly discussed at the end.