Particle approximation for Lagrangian Stochastic Models with specular boundary condition

In this paper, we prove a particle approximation, in the sense of the propagation of chaos, of a Lagrangian stochastic model submitted to specular boundary condition and satisfying the mean no-permeability condition

Clarification and complement to "Mean-field description and propagation of chaos in networks of Hodgkin-Huxley and FitzHugh-Nagumo neurons"

In this note, we clarify the well-posedness of the limit equations to the mean-field $N$-neuron models proposed in Baladron et al. and we prove the associated propagation of chaos property. We also complete the modeling issue in Baladron et al. by discussing the well-posedness of the stochastic differential equations which govern the behavior of the ion channels and the amount of available neurotransmitters

Nash equilibrium for coupling of CO2 allowances and electricity markets

In this note, we present an existence result of a Nash equilibrium between electricity producers selling their production on an electricity market and buying CO2 emission allowances on an auction carbon market. The producers' strategies integrate the coupling of the two markets via the cost functions of the electricity production. We set out a clear Nash equilibrium that can be used to compute equilibrium prices on both markets as well as the related electricity produced and CO2 emissions covered

Game theory analysis for carbon auction market through electricity market coupling

In this paper, we analyze Nash equilibria between electricity producers selling their production on an electricity market and buying CO2 emission allowances on an auction carbon market. The producers' strategies integrate the coupling of the two markets via the cost functions of the electricity production. We set out a clear Nash equilibrium on the power market that can be used to compute equilibrium prices on both markets as well as the related electricity produced and CO2 emissions released.Comment: arXiv admin note: text overlap with arXiv:1311.153

Overcoming the acoustic diffraction limit in photoacoustic imaging by localization of flowing absorbers

The resolution of photoacoustic imaging deep inside scattering media is limited by the acoustic diffraction limit. In this work, taking inspiration from super-resolution imaging techniques developed to beat the optical diffraction limit, we demonstrate that the localization of individual optical absorbers can provide super-resolution photoacoustic imaging well beyond the acoustic diffraction limit. As a proof-of-principle experiment, photoacoustic cross-sectional images of microfluidic channels were obtained with a 15 MHz linear CMUT array while absorbing beads were flown through the channels. The localization of individual absorbers allowed to obtain super-resolved cross-sectional image of the channels, by reconstructing both the channel width and position with an accuracy better than $\lambda/10$. Given the discrete nature of endogenous absorbers such as red blood cells, or that of exogenous particular contrast agents, localization is a promising approach to push the current resolution limits of photoacoustic imaging

Photoacoustic generation by a gold nanosphere: From linear to nonlinear thermoelastics in the long-pulse illumination regime

We investigate theoretically the photoacoustic generation by a gold nanosphere in water in the thermoelastic regime. Specifically, we consider the long-pulse illumination regime, in which the time for electron-phonon thermalisation can be neglected and photoacoustic wave generation arises solely from the thermo-elastic stress caused by the temperature increase of the nanosphere or its liquid environment. Photoacoustic signals are predicted computed based on the successive resolution of a thermal diffusion problem and a thermoelastic problem, taking into account the finite size of the gold nanosphere and the temperature-dependence of the thermal expansion coefficient of water. For sufficiently high illumination fluences, this temperature dependence yields a nonlinear relationship between the photoacoustic amplitude and the fluence. For nanosecond pulses in the linear regime, we show that more than 90 % of the emitted photoacoustic energy is generated in water, and the thickness of the generating layer around the particle scales close to the square root of the pulse duration. Our results demonstrate that the point-absorber model introduced by Calasso et al.[17] significantly overestimates the amplitude of photoacoustic waves in the nonlinear regime. We therefore provide quantitative estimates of a critical energy, defined as the absorbed energy required such that the nonlinear contribution is equal to that of the linear contribution. Our results suggest that the critical energy scales as the volume of water over which heat diffuses during the illumination pulse. Moreover, thermal nonlinearity is shown to be expected only for sufficiently high ultrasound frequency. Finally, we show that the relationship between the photoacoustic amplitude and the equilibrium temperature at sufficiently high fluence reflects the thermal diffusion at the nanoscale around the gold nanosphere.Comment: Published in Physical Review B, 16 pages, 14 figure

Clearing the Brain’s Cobwebs: The Role of Autophagy in Neuroprotection

Protein aggregates or inclusion bodies are common hallmarks of age-related neurodegenerative disorders. Why these aggregates form remains unclear. Equally debated is whether they are toxic, protective, or simple by-products. Increasing evidence, however, supports the notion that in general aggregates confer toxicity and disturb neuronal function by hampering axonal transport, synaptic integrity, transcriptional regulation, and mitochondrial function. Thus, neuroscientists in search of effective treatments to slow neural loss during neurodegeneration have long been interested in finding new ways to clear inclusion bodies. Intriguingly, two studies using conditional neuron-specific gene ablations of autophagy regulators in mice revealed that autophagy loss elicits inclusion body formation and a neurodegenerative cascade.Such studies indicate autophagy may be a built-in defense mechanism to clear the nervous system of inclusion bodies.This new finding has implications for our understanding of aging and neurodegeneration and the development of new therapies. First, we discuss the pathways underlying autophagy and its controversial role in cell death and survival regulation.We then discuss the physiological role of autophagy in the aging process of the nervous system. In the final portion of this review, we discuss the therapeutic promise of inducing autophagy and the potential side effects of such treatments