Interpolating Blaschke Products and Angular Derivatives

We show that to each inner function, there corresponds at least one interpolating Blaschke product whose angular derivatives have precisely the same behavior as the given inner function. We characterize the Blaschke products invertible in the closed algebra generated by the algebra of bounded analytic functions and the conjugates of Blaschke products with angular derivative finite everywhere. We study the most well-known example of a Blaschke product with infinite angular derivative everywhere and show that it is an interpolating Blaschke product. We conclude the paper with a method for constructing thin Blaschke products with infinite angular derivative everywhere.

Rapid Facilitation of Ultrasound Production and Lordosis in Female Hamsters by Horizontal Cuts Between the Septum and Preoptic Area

Horizontal cuts between the septum and preoptic area (anterior roof deafferentation, or ARD) dramatically affect sexual behavior, and in ways that could explain a variety of differences across behavioral categories (precopulatory, copulatory), species, and the sexes. Yet little is known about how these effects develop. Such information would be useful generally and could be pivotal in clarifying the mechanism for ultrasonic vocalization in female hamsters. Ultrasounds serve these animals as precopulatory signals that can attract males and help initiate mating. Their rates can be increased by either ARD or lesions of the ventromedial hypothalamus (VMN). If these effects are independent, they would require a mechanism that includes multiple structures and pathways within the forebrain and hypothalamus. However, it currently is not clear if they are independent: VMN lesions could affect vocalization by causing incidental damage to the same fibers targeted by ARD. Fortunately, past studies of VMN lesions have described a response with a very distinctive time course. This raises the possibility of assessing the independence of the two lesion effects by describing just the development of the response to ARD. To accomplish this, female hamsters were observed for levels of ultrasound production and lordosis before and after control surgery or ARD. As expected, both behaviors were facilitated by these cuts. Further, these effects began to appear by two days after surgery and were fully developed by six days. These results extend previous descriptions of the ARD effect by describing its development and time course. In turn, the rapid responses to ARD suggest that these cuts trigger disinhibitory changes in pathways that differ from those affected by VMN lesions. 2013

Mass Transport Perspective on an Accelerated Exclusion Process: Analysis of Augmented Current and Unit-Velocity Phases

In an accelerated exclusion process (AEP), each particle can "hop" to its adjacent site if empty as well as "kick" the frontmost particle when joining a cluster of size ℓ⩽ℓ_{max}. With various choices of the interaction range, ℓ_{max}, we find that the steady state of AEP can be found in a homogeneous phase with augmented currents (AC) or a segregated phase with holes moving at unit velocity (UV). Here we present a detailed study on the emergence of the novel phases, from two perspectives: the AEP and a mass transport process (MTP). In the latter picture, the system in the UV phase is composed of a condensate in coexistence with a fluid, while the transition from AC to UV can be regarded as condensation. Using Monte Carlo simulations, exact results for special cases, and analytic methods in a mean field approach (within the MTP), we focus on steady state currents and cluster sizes. Excellent agreement between data and theory is found, providing an insightful picture for understanding this model system.