Existence and uniqueness of limit cycles in a class of second order ODE's with inseparable mixed terms

We prove a uniqueness result for limit cycles of the second order ODE $\ddot x + \dot x \phi(x,\dot x) + g(x) = 0$. Under mild additional conditions, we show that such a limit cycle attracts every non-constant solution. As a special case, we prove limit cycle's uniqueness for an ODE studied in \cite{ETA} as a model of pedestrians' walk. This paper is an extension to equations with a non-linear $g(x)$ of the results presented in \cite{S}

Shaping the auditory peripersonal space with motor planning in immersive virtual reality

Immersive audio technologies require personalized binaural synthesis through headphones to provide perceptually plausible virtual and augmented reality (VR/AR) simulations. We introduce and apply for the first time in VR contexts the quantitative measure called premotor reaction time (pmRT) for characterizing sonic interactions between humans and the technology through motor planning. In the proposed basic virtual acoustic scenario, listeners are asked to react to a virtual sound approaching from different directions and stopping at different distances within their peripersonal space (PPS). PPS is highly sensitive to embodied and environmentally situated interactions, anticipating the motor system activation for a prompt preparation for action. Since immersive VR applications benefit from spatial interactions, modeling the PPS around the listeners is crucial to reveal individual behaviors and performances. Our methodology centered around the pmRT is able to provide a compact description and approximation of the spatiotemporal PPS processing and boundaries around the head by replicating several well-known neurophysiological phenomena related to PPS, such as auditory asymmetry, front/back calibration and confusion, and ellipsoidal action fields

Spin-dependent direct gap emission in tensile-strained Ge films on Si substrates

The circular polarization of direct gap emission of Ge is studied in optically-excited tensile-strained Ge-on-Si heterostructures as a function of doping and temperature. Owing to the spin-dependent optical selection rules, the radiative recombinations involving strain-split light (cG-LH) and heavy hole (cG-HH) bands are unambiguously resolved. The fundamental cG-LH transition is found to have a low temperature circular polarization degree of about 85% despite an off-resonance excitation of more than 300 meV. By photoluminescence (PL) measurements and tight binding calculations we show that this exceptionally high value is due to the peculiar energy dependence of the optically-induced electron spin population. Finally, our observation of the direct gap doublet clarifies that the light hole contribution, previously considered to be negligible, can dominate the room temperature PL even at low tensile strain values of about 0.2%

Beyond variability: Subjective timing and the neurophysiology of motor cognition.

Movement simulation helps increasing the chances to reach goals. A cognitive task used to study the neuro-behavioral aspects of movement simulation is mental rotation: people mentally re-orient rotated pictures of hands. However, the involvement of the primary motor cortex (M1) in mental rotation is largely controversial. Such inconsistency could arise from potential methodological flaws in experimental procedures and data analysis. In particular, until now, the timing of M1 activity has been computed in absolute terms: from the onset of mental rotation (onset-locked), neglecting intra- and inter-subject variability. A novel phase-locked approach is introduced to synchronize the same phases of cognitive processing among different subjects and sessions. This approach was validated in the particular case of corticospinal excitability of the motor cortex during mental rotation. We identified the relative time-windows during which the excitability of M1 is effector-specifically modulated by different features of mental rotation. These time windows correspond to the 55%-85% of the subjective timing. In sum, (i) we introduce a new method to study the neurophysiology of motor cognition, and (ii) validating this method, we shed new light on the involvement of M1 in movement simulation

Geometric and analytic views in existence theorems for optimal control. III. Weak solutions

Existence theorems are proved for weak optimal solutions of problems of optimization with distributed and boundary control. Many examples are given. Application is made of recent remarks on closure properties of linear and nonlinear operators. Recent geometric, topological, and analytical views are brought to bear on the underlying seminormality conditions.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45209/1/10957_2004_Article_BF00934060.pd