Diffusion of new products in risk-sensitive markets

Diffusion of new products may be deterred by consumers' uncertainties about how they will perform. This paper introduces a decision-theoretic framework for modeling the diffusion of consumables, in which consumers choose between a current and new product so as to maximize expected utility. Consumers that are sufficiently risk-averse delay adoption, and change their prior uncertainties in a Bayesian fashion using information generated by early adopters. Under certain assumptions about the underlying consumer choice process and the market dynamics, the result is logistic growth in the share of consumers that choose the new product. The model can be generalized by allowing for consumer heterogeneity with respect to performance of the new product. The paper concludes with a discussion of applications for market forecasting, design of market trials and other extensions.     

Imaging cortical correlates of illusion in early visual cortex

Exploring visual illusions reveals fundamental principles of cortical processing. Illusory motion perception of non-moving stimuli was described almost a century ago by Gestalt psychologists. However, the underlying neuronal mechanisms remain unknown. To explore cortical mechanisms underlying the 'line-motion' illusion, we used real-time optical imaging, which is highly sensitive to subthreshold activity. We examined, in the visual cortex of the anaesthetized cat, responses to five stimuli: a stationary small square and a long bar; a moving square; a drawn-out bar; and the well-known line-motion illusion, a stationary square briefly preceding a long stationary bar presentation. Whereas flashing the bar alone evoked the expected localized, short latency and high amplitude activity patterns, presenting a square 60-100 ms before a bar induced the dynamic activity patterns resembling that of fast movement. The preceding square, even though physically non-moving, created gradually propagating subthreshold cortical activity that must contribute to illusory motion, because it was indistinguishable from cortical representations of real motion in this area. These findings demonstrate the effect of spatio-temporal patterns of subthreshold synaptic potentials on cortical processing and the shaping of perception.     

Transport and Anderson localization in disordered two-dimensional photonic lattices

One of the most interesting phenomena in solid-state physics is Anderson localization, which predicts that an electron may become immobile when placed in a disordered lattice. The origin of localization is interference between multiple scatterings of the electron by random defects in the potential, altering the eigenmodes from being extended (Bloch waves) to exponentially localized. As a result, the material is transformed from a conductor to an insulator. Anderson's work dates back to 1958, yet strong localization has never been observed in atomic crystals, because localization occurs only if the potential (the periodic lattice and the fluctuations superimposed on it) is time-independent. However, in atomic crystals important deviations from the Anderson model always occur, because of thermally excited phonons and electron-electron interactions. Realizing that Anderson localization is a wave phenomenon relying on interference, these concepts were extended to optics. Indeed, both weak and strong localization effects were experimentally demonstrated, traditionally by studying the transmission properties of randomly distributed optical scatterers (typically suspensions or powders of dielectric materials). However, in these studies the potential was fully random, rather than being 'frozen' fluctuations on a periodic potential, as the Anderson model assumes. Here we report the experimental observation of Anderson localization in a perturbed periodic potential: the transverse localization of light caused by random fluctuations on a two-dimensional photonic lattice. We demonstrate how ballistic transport becomes diffusive in the presence of disorder, and that crossover to Anderson localization occurs at a higher level of disorder. Finally, we study how nonlinearities affect Anderson localization. As Anderson localization is a universal phenomenon, the ideas presented here could also be implemented in other systems (for example, matter waves), thereby making it feasible to explore experimentally long-sought fundamental concepts, and bringing up a variety of intriguing questions related to the interplay between disorder and nonlinearity.     

Detachment fronts and the onset of dynamic friction

The dynamics of friction have been studied for hundreds of years, yet many aspects of these everyday processes are not understood. One such aspect is the onset of frictional motion (slip). First described more than 200 years ago as the transition from static to dynamic friction, the onset of slip is central to fields as diverse as physics, tribology, mechanics of earthquakes and fracture. Here we show that the onset of frictional slip is governed by three different types of coherent crack-like fronts: these are observed by real-time visualization of the net contact area that forms the interface separating two blocks of like material. Two of these fronts, which propagate at subsonic and intersonic velocities, have been the subject of intensive recent interest. We show that a third type of front, which propagates an order of magnitude more slowly, is the dominant mechanism for the rupture of the interface. No overall motion (sliding) of the blocks occurs until either of the slower two fronts traverses the entire interface.