Applications of Hilbert Module Approach to Multivariable Operator Theory

A commuting $n$-tuple $(T_1, \ldots, T_n)$ of bounded linear operators on a Hilbert space \clh associate a Hilbert module $\mathcal{H}$ over $\mathbb{C}[z_1, \ldots, z_n]$ in the following sense: $$\mathbb{C}[z_1, \ldots, z_n] \times \mathcal{H} \rightarrow \mathcal{H}, \quad \quad (p, h) \mapsto p(T_1, \ldots, T_n)h,$$where $p \in \mathbb{C}[z_1, \ldots, z_n]$ and $h \in \mathcal{H}$. A companion survey provides an introduction to the theory of Hilbert modules and some (Hilbert) module point of view to multivariable operator theory. The purpose of this survey is to emphasize algebraic and geometric aspects of Hilbert module approach to operator theory and to survey several applications of the theory of Hilbert modules in multivariable operator theory. The topics which are studied include: generalized canonical models and Cowen-Douglas class, dilations and factorization of reproducing kernel Hilbert spaces, a class of simple submodules and quotient modules of the Hardy modules over polydisc, commutant lifting theorem, similarity and free Hilbert modules, left invertible multipliers, inner resolutions, essentially normal Hilbert modules, localizations of free resolutions and rigidity phenomenon. This article is a companion paper to "An Introduction to Hilbert Module Approach to Multivariable Operator Theory".Comment: 46 pages. This is a companion paper to arXiv:1308.6103. To appear in Handbook of Operator Theory, Springe

Take-off mechanics in hummingbirds (Trochilidae)

Initiating flight is challenging, and considerable effort has focused on understanding the energetics and aerodynamics of take-off for both machines and animals. For animal flight, the available evidence suggests that birds maximize their initial flight velocity using leg thrust rather than wing flapping. The smallest birds, hummingbirds (Order Apodiformes), are unique in their ability to perform sustained hovering but have proportionally small hindlimbs that could hinder generation of high leg thrust. Understanding the take-off flight of hummingbirds can provide novel insight into the take-off mechanics that will be required for micro-air vehicles. During take-off by hummingbirds, we measured hindlimb forces on a perch mounted with strain gauges and filmed wingbeat kinematics with high-speed video. Whereas other birds obtain 80–90% of their initial flight velocity using leg thrust, the leg contribution in hummingbirds was 59% during autonomous take-off. Unlike other species, hummingbirds beat their wings several times as they thrust using their hindlimbs. In a phylogenetic context, our results show that reduced body and hindlimb size in hummingbirds limits their peak acceleration during leg thrust and, ultimately, their take-off velocity. Previously, the influence of motivational state on take-off flight performance has not been investigated for any one organism. We studied the full range of motivational states by testing performance as the birds took off: (1) to initiate flight autonomously, (2) to escape a startling stimulus or (3) to aggressively chase a conspecific away from a feeder. Motivation affected performance. Escape and aggressive take-off featured decreased hindlimb contribution (46% and 47%, respectively) and increased flight velocity. When escaping, hummingbirds foreshortened their body movement prior to onset of leg thrust and began beating their wings earlier and at higher frequency. Thus, hummingbirds are capable of modulating their leg and wingbeat kinetics to increase take-off velocity

SUPPLY RESPONSE TO TECHNOLOGICAL CHANGE AND REGULATION: THE CASE OF MECHANICALLY DEBONED POULTRY

Research and Development/Tech Change/Emerging Technologies,

Hypervelocity runaways from the Large Magellanic Cloud

We explore the possibility that the observed population of Galactic hypervelocity stars (HVSs) originate as runaway stars from the Large Magellanic Cloud (LMC). Pairing a binary evolution code with an N-body simulation of the interaction of the LMC with the Milky Way, we predict the spatial distribution and kinematics of an LMC runaway population. We find that runaway stars from the LMC can contribute Galactic HVSs at a rate of $3 \times 10^{-6}\;\mathrm{yr}^{-1}$. This is composed of stars at different points of stellar evolution, ranging from the main-sequence to those at the tip of the asymptotic giant branch. We find that the known B-type HVSs have kinematics which are consistent with an LMC origin. There is an additional population of hypervelocity white dwarfs whose progenitors were massive runaway stars. Runaways which are even more massive will themselves go supernova, producing a remnant whose velocity will be modulated by a supernova kick. This latter scenario has some exotic consequences, such as pulsars and supernovae far from star-forming regions, and a small rate of microlensing from compact sources around the halo of the LMC.Comment: MNRAS, in pres

Large Deformation Behavior of Long Shallow Cylindrical Composite Panels

An exact solution is presented for the large deformation response of a simply supported orthotropic cylindrical panel subjected to a uniform line load along a cylinder generator. The cross section of the cylinder is circular and deformations up to the fully snapped through position are investigated. The orthotropic axes are parallel to the generator and circumferential directions. The governing equations are derived using laminated plate theory, nonlinear strain-displacement relations, and applying variational principles. The response is investigated for the case of a panel loaded exactly at midspan and for a panel with the load offset from midspan. The mathematical formulation is one dimensional in the circumferential coordinate. Solutions are obtained in closed-form. An experimental apparatus was designed to load the panels. Experimental results of displacement controlled tests performed on graphite-epoxy curved panels are compared with analytical predictions

Abnormal Perceptual Sensitivity in Body-Focused Repetitive Behaviors

Objective Several compulsive grooming habits such as hair pulling, skin picking, and nail biting are collectively known as body-focused repetitive behaviors (BFRBs). Although subclinical BFRBs are common and benign, more severe and damaging manifestations exist that are difficult to manage. Researchers have suggested that BFRBs are maintained by various cognitive, affective, and sensory contingencies. Although the involvement of cognitive and affective processes in BFRBs has been studied, there is a paucity of research on sensory processes. Methods The current study tested whether adults with subclinical or clinical BFRBs would report abnormal patterns of sensory processing as compared to a healthy control sample. Results Adults with clinical BFRBs (n = 26) reported increased sensory sensitivity as compared to persons with subclinical BFRBs (n = 48) and healthy individuals (n = 33). Elevations in sensation avoidance differentiated persons with clinical versus subclinical BFRBs. Sensation seeking patterns were not different between groups. Unexpectedly, BFRB severity was associated with lower registration of sensory stimuli, but this finding may be due to high psychiatric comorbidity rates in the BFRB groups. Conclusions These findings suggest that several sensory abnormalities may underlie BFRBs. Implications for the etiology and treatment of BFRBs are discussed

Amygdala reactivity predicts adolescent antisocial behavior but not callous-unemotional traits.

Recent neuroimaging studies have suggested divergent relationships between antisocial behavior (AB) and callous-unemotional (CU) traits and amygdala reactivity to fearful and angry facial expressions in adolescents. However, little work has examined if these findings extend to dimensional measures of behavior in ethnically diverse, non-clinical samples, or if participant sex, ethnicity, pubertal stage, and age moderate associations. We examined links between amygdala reactivity and dimensions of AB and CU traits in 220 Hispanic and non-Hispanic Caucasian adolescents (age 11-15; 49.5% female; 38.2% Hispanic), half of whom had a family history for depression and thus were at relatively elevated risk for late starting, emotionally dysregulated AB. We found that AB was significantly related to increased right amygdala reactivity to angry facial expressions independent of sex, ethnicity, pubertal stage, age, and familial risk status for depression. CU traits were not related to fear- or anger-related amygdala reactivity. The present study further demonstrates that AB is related to increased amygdala reactivity to interpersonal threat cues in adolescents, and that this relationship generalizes across sex, ethnicity, pubertal stage, age, and familial risk status for depression