Class invariants for certain non-holomorphic modular functions

Inspired by prior work of Bruinier and Ono and Mertens and Rolen, we study class polynomials for non-holomorphic modular functions arising from modular forms of negative weight. In particular, we give general conditions for the irreducibility of class polynomials. This allows us to easily generate infintely many new class invariants

MY EYES DUE SEE

My Eyes Due See is a multidimensional examination of the “black experience” in America. The installation is composed of a single-channel video, a music composition that utilizes music samples and live instrumentation, and sculptures made up of car parts and broomsedge grass. Each of these elements arranged in space share a nuanced and complicated view of blackness through the lens of a black man decoding personal history and American history simultaneously. Autonomy is the overarching theme throughout the work as it pertains to race, identity, urban and rural environments, and the relationship between generational trauma and nostalgia

Electrode geometry and preferential stimulation of spinal nerve fibers having different orientations: a modeling study

In a computer modeling study of epidural spinal cord stimulation using a longitudinal array of electrode contacts, the effect of contact geometry and contact combination on the threshold voltages for stimulation of dorsal column (DC) fibers and dorsal root (DR) fibers was investigated. It was concluded that DC-fiber stimulation will be favoured when a tripolar combination and small contact length and spacing are used, while DR-fiber stimulation will be favoured when unipolar stimulation and large contact length are used

Extraordinary exciton conductance induced by strong coupling

We demonstrate that exciton conductance in organic materials can be enhanced by several orders of magnitude when the molecules are strongly coupled to an electromagnetic mode. Using a 1D model system, we show how the formation of a collective polaritonic mode allows excitons to bypass the disordered array of molecules and jump directly from one end of the structure to the other. This finding could have important implications in the fields of exciton transistors, heat transport, photosynthesis, and biological systems in which exciton transport plays a key role.Comment: Main text: 5 pages, 4 figures; Supplemental: 2 pages, 1 figure. Version 2: Updated reference to related work arXiv:1409.2550. Version 3: Updated to version accepted for publication in Physical Review Letter

Three-form inflation and non-Gaussianity

We calculate the perturbed action, at second and third order, for a massive three-form field minimally coupled to gravity, and use it to explore the observational predictions of three-form inflation. One intriguing result is that the value of the spectral index is nearly independent of the three-form potential, being fixed solely by the number of e-folds of inflation, with n_s=0.97 for the canonical number of 60. Considering the bispectrum, we employ standard techniques to give explicit results for two models, one of which produces a large non-Gaussianity. Finally, we confirm our results by employing a duality relating the three-form theory to a non-canonical scalar field theory and explicitly re-computing results in this dual picture.Comment: 23 pages, 6 figures. Typos corrected and addition of one appendix. Accepted in JCA