A New Chamber for Studying the Behavior of Drosophila

Methods available for quickly and objectively quantifying the behavioral phenotypes of the fruit fly, Drosophila melanogaster, lag behind in sophistication the tools developed for manipulating their genotypes. We have developed a simple, easy-to-replicate, general-purpose experimental chamber for studying the ground-based behaviors of fruit flies. The major innovative feature of our design is that it restricts flies to a shallow volume of space, forcing all behavioral interactions to take place within a monolayer of individuals. The design lessens the frequency that flies occlude or obscure each other, limits the variability in their appearance, and promotes a greater number of flies to move throughout the center of the chamber, thereby increasing the frequency of their interactions. The new chamber design improves the quality of data collected by digital video and was conceived and designed to complement automated machine vision methodologies for studying behavior. Novel and improved methodologies for better quantifying the complex behavioral phenotypes of Drosophila will facilitate studies related to human disease and fundamental questions of behavioral neuroscience

A Nanoscale Experiment Measuring Gravity's Role in Breaking the Unitarity of Quantum Dynamics

Modern, state of the art nanomechanical devices are capable of creating spatial superpositions that are massive enough to begin to experimentally access the quantum to classical crossover, and thus force us to consider the possible ways in which the usual quantum dynamics may be affected. One recent theoretical proposal describes the crossover from unitary quantum mechanics to classical dynamics as a form of spontaneous symmetry breaking. Here, we propose a specific experimental setup capable of identifying the source of unitarity breaking in such a mechanism. The experiment is aimed specifically at clarifying the role played by gravity, and distinguishes the resulting dynamics from that suggested by alternative scenarios for the quantum to classical crossover. We give both a theoretical description of the expected dynamics, and a discussion of the involved experimental parameter values and the proposed experimental protocol.Comment: 11 pages, 5 figures; final versio

A nonsymmetric version of Okounkov's BC-type interpolation Macdonald polynomials

Symmetric and nonsymmetric interpolation Laurent polynomials are introduced with the interpolation points depending on $q$ and a $n$-tuple of parameters $\tau=(\tau_1,\ldots,\tau_n)$. For the principal specialization $\tau_i=st^{n-i}$ the symmetric interpolation Laurent polynomials reduce to Okounkov's $BC$-type interpolation Macdonald polynomials and the nonsymmetric interpolation Laurent polynomials become their nonsymmetric variants. We expand the symmetric interpolation Laurent polynomials in the nonsymmetric ones. We show that Okounkov's $BC$-type interpolation Macdonald polynomials can also be obtained from their nonsymmetric versions using a one-parameter family of actions of the finite Hecke algebra of type $B_n$ in terms of Demazure-Lusztig operators. In the Appendix we give some experimental results and conjectures about extra vanishing.Comment: 30 pages, 9 figures; v4: experimental results and conjectures added about extra vanishin