Subsequence generators for ergodic group translations

LetT be an ergodic translation on a compact abelian group. For every infinite set of integers {n _i} and ε >0 there is a setA of measure less than ε such that {T ⁿ _iA} generates the σ-algebra of measurable sets. Research partially supported by National Science Foundation Grants MCS7703659 (first author) and MCS7606735A01 (second author).     

Optical polarimetry of random fields

The state of polarization of an optical field provides detailed information concerning both the radiation emission processes and the intricate interaction between light and matter. We report here a novel approach for characterizing the polarization properties of electromagnetic fields for which the electric field vector at a point may fluctuate in three dimensions. Using probes which couple all three components of the field, we were able to extract the polarized and unpolarized components of such fields. Our results constitute the proof of concept for what could be called three-dimensional optical polarimetry.     

Multiple Critical Behavior of Probabilistic Limit Theorems in the Neighborhood of a Tricritical Point

We derive probabilistic limit theorems that reveal the intricate structure of the phase transitions in a mean-field version of the Blume–Emery–Griffiths model [Phys. Rev. A 4 (1971) 1071–1077]. These probabilistic limit theorems consist of scaling limits for the total spin and moderate deviation principles (MDPs) for the total spin. The model under study is defined by a probability distribution that depends on the parameters n, β, and K, which represent, respectively, the number of spins, the inverse temperature, and the interaction strength. The intricate structure of the phase transitions is revealed by the existence of 18 scaling limits and 18 MDPs for the total spin. These limit results are obtained as (β,K) converges along appropriate sequences (β_n, kn) to points belonging to various subsets of the phase diagram, which include a curve of second-order points and a tricritical point. The forms of the limiting densities in the scaling limits and of the rate functions in the MDPs reflect the influence of one or more sets that lie in neighborhoods of the critical points and the tricritical point. Of all the scaling limits, the structure of those near the tricritical point is by far the most complex, exhibiting new types of critical behavior when observed in a limit-theorem phase diagram in the space of the two parameters that parametrize the scaling limits. American Mathematical Society 2000 Subject Classifications. Primary 60F10, 60F05, Secondary 82B20     

Thermodynamically Stable,Photoreversible Pharmacology in Neurons with One‐ and Two‐Photon Excitation

Photoswitchable bioprobes enable bidirectional control of cell physiology with different wavelengths of light. Many current photoswitches use cytotoxic UV light and are limited by the need for constant illumination owing to thermal relaxation in the dark. Now a photoswitchable tetrafluoroazobenzene(4FAB)‐based ion channel antagonist has been developed that can be efficiently isomerized in two separate optical channels with visible light. Importantly, the metastable cis configuration showed very high stability in the dark over the course of days at room temperature. In neurons, the 4FAB antagonist reversibly blocks voltage‐gated ion channels with violet and green light. Furthermore, photoswitching could also be achieved with two‐photon excitation yielding high spatial resolution. 4FAB probes have the potential to enable long‐term biological studies where both ON and OFF states can be maintained in the absence of irradiation.