Pole structure of the Hamiltonian ζ\zeta-function for a singular potential

We study the pole structure of the $\zeta$-function associated to the Hamiltonian $H$ of a quantum mechanical particle living in the half-line $\mathbf{R}^+$, subject to the singular potential $g x^{-2}+x^2$. We show that $H$ admits nontrivial self-adjoint extensions (SAE) in a given range of values of the parameter $g$. The $\zeta$-functions of these operators present poles which depend on $g$ and, in general, do not coincide with half an integer (they can even be irrational). The corresponding residues depend on the SAE considered.Comment: 12 pages, 1 figure, RevTeX. References added. Version to appear in Jour. Phys. A: Math. Ge

Honey bee foraging distance depends on month and forage type

To investigate the distances at which honey bee foragers collect nectar and pollen, we analysed 5,484 decoded waggle dances made to natural forage sites to determine monthly foraging distance for each forage type. Firstly, we found significantly fewer overall dances made for pollen (16.8 %) than for non-pollen, presumably nectar (83.2 %; P < 2.2 × 10−23). When we analysed distance against month and forage type, there was a significant interaction between the two factors, which demonstrates that in some months, one forage type is collected at farther distances, but this would reverse in other months. Overall, these data suggest that distance, as a proxy for forage availability, is not significantly and consistently driven by need for one type of forage over the other

A review of hippocampal activation in post‐traumatic stress disorder

Post‐traumatic stress disorder (PTSD) is often characterized by deficits in memory encoding and retrieval and aberrant fear and extinction learning. The hippocampus plays a critical role in memory and contextual processing and has been implicated in intrinsic functional connectivity networks involved in self‐referential thought and memory‐related processes. This review focuses on hippocampal activation findings during memory and fear and extinction learning tasks, as well as resting state hippocampal connectivity in individuals with PTSD. A preponderance of functional neuroimaging studies to date, using memory, fear learning, and extinction tasks, report decreased or “controls comparable” hippocampal activation in individuals with PTSD, which is usually associated with poorer performance on the task imaged. Existing evidence thus raises the possibility that greater hippocampal recruitment in PTSD participants may be required for similar performance levels. Studies of resting state functional connectivity in PTSD predominantly report reduced within‐network connectivity in the default mode network (DMN), as well as greater coupling between the DMN and salience network (SN) via the hippocampus. Together, these findings suggest that deficient hippocampal activation in PTSD may be associated with poorer performance during memory, extinction recall, and fear renewal tasks. Furthermore, studies of resting state connectivity implicate the hippocampus in decreased within‐network DMN connectivity and greater coupling with SN regions characteristic of PTSD.The hippocampus plays a key role in memory, fear learning and extinction, and default mode network resting state connectivity, all processes which have known deficits in post‐traumatic stress disorder (PTSD). In this review, we examine recent fMRI studies on hippocampal function in PTSD and controls and identify critical areas for future research to explore.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/153031/1/psyp13357.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/153031/2/psyp13357_am.pd

Bandit Models of Human Behavior: Reward Processing in Mental Disorders

Drawing an inspiration from behavioral studies of human decision making, we propose here a general parametric framework for multi-armed bandit problem, which extends the standard Thompson Sampling approach to incorporate reward processing biases associated with several neurological and psychiatric conditions, including Parkinson's and Alzheimer's diseases, attention-deficit/hyperactivity disorder (ADHD), addiction, and chronic pain. We demonstrate empirically that the proposed parametric approach can often outperform the baseline Thompson Sampling on a variety of datasets. Moreover, from the behavioral modeling perspective, our parametric framework can be viewed as a first step towards a unifying computational model capturing reward processing abnormalities across multiple mental conditions.Comment: Conference on Artificial General Intelligence, AGI-1

The Melanocortin-4 Receptor Integrates Circadian Light Cues and Metabolism

The melanocortin system directs diverse physiological functions from coat color to body weight homoeostasis. A commonality among melanocortin-mediated processes is that many animals modulate similar processes on a circannual basis in response to longer, summer days, suggesting an underlying link between circadian biology and the melanocortin system. Despite key neuroanatomical substrates shared by both circadian and melanocortin-signaling pathways, little is known about the relationship between the two. Here we identify a link between circadian disruption and the control of glucose homeostasis mediated through the melanocortin-4 receptor (Mc4r). Mc4r-deficient mice exhibit exaggerated circadian fluctuations in baseline blood glucose and glucose tolerance. Interestingly, exposure to lighting conditions that disrupt circadian rhythms improve their glucose tolerance. This improvement occurs through an increase in glucose clearance by skeletal muscle and is food intake and body weight independent. Restoring Mc4r expression to the paraventricular nucleus prevents the improvement in glucose tolerance, supporting a role for the paraventricular nucleus in the integration of circadian light cues and metabolism. Altogether these data suggest that Mc4r signaling plays a protective role in minimizing glucose fluctuations due to circadian rhythms and environmental light cues and demonstrate a previously undiscovered connection between circadian biology and glucose metabolism mediated through the melanocortin system

The Politics of Commerce : The Congress of Chambers of Commerce of the Empire, 1886-1914

Peer reviewedPublisher PD

Analytic and Reidemeister torsion for representations in finite type Hilbert modules

For a closed Riemannian manifold we extend the definition of analytic and Reidemeister torsion associated to an orthogonal representation of fundamental group on a Hilbert module of finite type over a finite von Neumann algebra. If the representation is of determinant class we prove, generalizing the Cheeger-M\"uller theorem, that the analytic and Reidemeister torsion are equal. In particular, this proves the conjecture that for closed Riemannian manifolds with positive Novikov-Shubin invariants, the L2 analytic and Reidemeister torsions are equal.Comment: 78 pages, AMSTe

Diagrams for heat kernel expansions

A diagramatic heat kernel expansion technique is presented. The method is especially well suited to the small-derivative expansion of the heat kernel, but it can also be used to reproduce the results obtained by the approach known as covariant perturbation theory. The new technique gives an expansion for the heat kernel at coincident points. It can also be used to obtain the derivative of the heat kernel and this is useful for evaluating the expectation values of the stress-energy tensor.Comment: 17 pages, 4 figures, ReVTe