Active hair-bundle movements can amplify a hair cell’s response to oscillatory mechanical stimuli

To enhance their mechanical sensitivity and frequency selectivity, hair cells amplify the mechanical stimuli to which they respond. Although cell-body contractions of outer hair cells are thought to mediate the active process in the mammalian cochlea, vertebrates without outer hair cells display highly sensitive, sharply tuned hearing and spontaneous otoacoustic emissions. In these animals the amplifier must reside elsewhere. We report physiological evidence that amplification can stem from active movement of the hair bundle, the hair cell’s mechanosensitive organelle. We performed experiments on hair cells from the sacculus of the bullfrog. Using a two-compartment recording chamber that permits exposure of the hair cell’s apical and basolateral surfaces to different solutions, we examined active hair-bundle motion in circumstances similar to those in vivo. When the apical surface was bathed in artificial endolymph, many hair bundles exhibited spontaneous oscillations of amplitudes as great as 50 nm and frequencies in the range 5 to 40 Hz. We stimulated hair bundles with a flexible glass probe and recorded their mechanical responses with a photometric system. When the stimulus frequency lay within a band enclosing a hair cell’s frequency of spontaneous oscillation, mechanical stimuli as small as ±5 nm entrained the hair-bundle oscillations. For small stimuli, the bundle movement was larger than the stimulus. Because the energy dissipated by viscous drag exceeded the work provided by the stimulus probe, the hair bundles powered their motion and therefore amplified it.

Synchronization of oscillatory responses in visual cortex correlates with perception in interocular rivalry

In subjects suffering from early onset strabismus, signals conveyed by the two eyes are not perceived simultaneously but in alternation. We exploited this phenomenon of interocular suppression to investigate the neuronal correlate of binocular rivalry in primary visual cortex of awake strabismic cats. Monocularly presented stimuli that were readily perceived by the animal evoked synchronized discharges with an oscillatory patterning in the γ-frequency range. Upon dichoptic stimulation, neurons responding to the stimulus that continued to be perceived increased the synchronicity and the regularity of their oscillatory patterning while the reverse was true for neurons responding to the stimulus that was no longer perceived. These differential changes were not associated with modifications of discharge rate, suggesting that at early stages of visual processing the degree of synchronicity rather than the amplitude of responses determines which signals are perceived and control behavioral responses.

Singular value decomposition for genome-wide expression data processing and modeling

We describe the use of singular value decomposition in transforming genome-wide expression data from genes × arrays space to reduced diagonalized “eigengenes” × “eigenarrays” space, where the eigengenes (or eigenarrays) are unique orthonormal superpositions of the genes (or arrays). Normalizing the data by filtering out the eigengenes (and eigenarrays) that are inferred to represent noise or experimental artifacts enables meaningful comparison of the expression of different genes across different arrays in different experiments. Sorting the data according to the eigengenes and eigenarrays gives a global picture of the dynamics of gene expression, in which individual genes and arrays appear to be classified into groups of similar regulation and function, or similar cellular state and biological phenotype, respectively. After normalization and sorting, the significant eigengenes and eigenarrays can be associated with observed genome-wide effects of regulators, or with measured samples, in which these regulators are overactive or underactive, respectively.

Behavior of several two-dimensional fluid equations in singular scenarios

We give conditions that rule out formation of sharp fronts for certain two-dimensional incompressible flows. We show that a necessary condition of having a sharp front is that the flow has to have uncontrolled velocity growth. In the case of the quasi-geostrophic equation and two-dimensional Euler equation, we obtain estimates on the formation of semi-uniform fronts.

Quantum groups with invariant integrals

Quantum groups have been studied intensively for the last two decades from various points of view. The underlying mathematical structure is that of an algebra with a coproduct. Compact quantum groups admit Haar measures. However, if we want to have a Haar measure also in the noncompact case, we are forced to work with algebras without identity, and the notion of a coproduct has to be adapted. These considerations lead to the theory of multiplier Hopf algebras, which provides the mathematical tool for studying noncompact quantum groups with Haar measures. I will concentrate on the *-algebra case and assume positivity of the invariant integral. Doing so, I create an algebraic framework that serves as a model for the operator algebra approach to quantum groups. Indeed, the theory of locally compact quantum groups can be seen as the topological version of the theory of quantum groups as they are developed here in a purely algebraic context.

Turbulent diffusion phase transition is due to singular energy spectrum.

The phase transition for turbulent diffusion, reported by Avellaneda and Majda [Avellaneda, M. & Majda, A. J. (1994) Philos. Trans. R. Soc. London A 346, 205-233, and several earlier papers], is traced to a modeling assumption in which the energy spectrum of the turbulent fluid is singularly dependent on the viscosity in the inertial range. Phenomenological models of turbulence and intermittency, by contrast, require that the energy spectrum be independent of the viscosity in the inertial range. When the energy spectrum is assumed to be consistent with the phenomenological models, there is no phase transition for turbulent diffusion.