Transition Decomposition of Quantum Mechanical Evolution

We show that the existence of the family of self-adjoint Lyapunov operators introduced in [J. Math. Phys. 51, 022104 (2010)] allows for the decomposition of the state of a quantum mechanical system into two parts: A past time asymptote, which is asymptotic to the state of the system at t goes to minus infinity and vanishes at t goes to plus infinity, and a future time asymptote, which is asymptotic to the state of the system at t goes to plus infinity and vanishes at t goes to minus infinity. We demonstrate the usefulness of this decomposition for the description of resonance phenomena by considering the resonance scattering of a particle off a square barrier potential. We show that the past time asymptote captures the behavior of the resonance. In particular, it exhibits the expected exponential decay law and spatial probability distribution.Comment: Accepted for publication in Int. J. Theor. Phy

Extrapolating SMBH correlations down the mass scale: the case for IMBHs in globular clusters

Empirical evidence for both stellar mass black holes M_bh<10^2 M_sun) and supermassive black holes (SMBHs, M_bh>10^5 M_sun) is well established. Moreover, every galaxy with a bulge appears to host a SMBH, whose mass is correlated with the bulge mass, and even more strongly with the central stellar velocity dispersion sigma_c, the `M-sigma' relation. On the other hand, evidence for "intermediate-mass" black holes (IMBHs, with masses in the range 1^2 - 10^5 M_sun) is relatively sparse, with only a few mass measurements reported in globular clusters (GCs), dwarf galaxies and low-mass AGNs. We explore the question of whether globular clusters extend the M-sigma relationship for galaxies to lower black hole masses and find that available data for globular clusters are consistent with the extrapolation of this relationship. We use this extrapolated M-sigma relationship to predict the putative black hole masses of those globular clusters where existence of central IMBH was proposed. We discuss how globular clusters can be used as a constraint on theories making specific predictions for the low-mass end of the M-sigma relation.Comment: 14 pages, 3 figures, accepted for publication in Astrophysics and Space Science; fixed typos and a quote in Sec.

Horizontal Branch Stars: The Interplay between Observations and Theory, and Insights into the Formation of the Galaxy

We review HB stars in a broad astrophysical context, including both variable and non-variable stars. A reassessment of the Oosterhoff dichotomy is presented, which provides unprecedented detail regarding its origin and systematics. We show that the Oosterhoff dichotomy and the distribution of globular clusters (GCs) in the HB morphology-metallicity plane both exclude, with high statistical significance, the possibility that the Galactic halo may have formed from the accretion of dwarf galaxies resembling present-day Milky Way satellites such as Fornax, Sagittarius, and the LMC. A rediscussion of the second-parameter problem is presented. A technique is proposed to estimate the HB types of extragalactic GCs on the basis of integrated far-UV photometry. The relationship between the absolute V magnitude of the HB at the RR Lyrae level and metallicity, as obtained on the basis of trigonometric parallax measurements for the star RR Lyrae, is also revisited, giving a distance modulus to the LMC of (m-M)_0 = 18.44+/-0.11. RR Lyrae period change rates are studied. Finally, the conductive opacities used in evolutionary calculations of low-mass stars are investigated. [ABRIDGED]Comment: 56 pages, 22 figures. Invited review, to appear in Astrophysics and Space Scienc

Context conditioning in humans using commercially available immersive Virtual Reality

Despite a wealth of knowledge on how humans and nonhuman animals learn to associate meaningful events with cues in the environment, far less is known about how humans learn to associate these events with the environment itself. Progress on understanding spatiotemporal contextual processes in humans has been slow in large measure by the methodological constraint of generating and manipulating immersive spatial environments in well-controlled laboratory settings. Fortunately, immersive Virtual Reality (iVR) technology has improved appreciably and affords a relatively straightforward methodology to investigate the role of context on learning, memory, and emotion while maintaining experimental control. Here, we review context conditioning literature in humans and describe challenges to study contextual learning in humans. We then provide details for a novel context threat (fear) conditioning paradigm in humans using a commercially available VR headset and a cross-platform game engine. This paradigm resulted in the acquisition of subjective threat, threat-conditioned defensive responses, and explicit threat memory. We make the paradigm publicly available and describe obstacles and solutions to optimize future studies of context conditioning using iVR. As computer technology advances to replicate the sensation of realistic environments, there are increasing opportunities to bridge the translational gap between rodent and human research on how context modulates cognition, which may ultimately lead to more optimal treatment strategies for anxiety- and stress-related disorders

Investigating the efficacy of the reminder-extinction procedure to disrupt contextual threat memories in humans using immersive Virtual Reality

Contains fulltext : 226248.pdf (publisher's version ) (Open Access

Peripheral inflammatory biomarkers predict the deposition and progression of amyloid-β in cognitively unimpaired older adults

Introduction Systemic inflammation has been increasingly implicated in the pathogenesis of Alzheimer’s disease (AD), yet the mechanistic and temporal specificity of this relationship is poorly understood. We aimed to characterize the cross-sectional and longitudinal associations between peripheral inflammatory biomarkers, cognition, and Aβ deposition in oldest-old cognitively unimpaired (CU) adults. Methods A large sample of 139 CU older adults (mean age (range) = 85.4 (82–95)) underwent neuropsychological testing, Pittsburgh compound-B (PiB)-PET imaging and structural MRI. Hierarchical regression models examined associations between circulating inflammatory biomarkers (Interleukin-6 (IL-6), soluble Tumor Necrosis Factor receptors 1 and 2 (sTNFr1 and sTNFr2), soluble cluster of differentiation 14 (sCD14), C-reactive protein (CRP)), cognition, and global and regional Aβ deposition at baseline and over follow-up. Indices of preclinical disease, including pathologic Aβ status and hippocampal volume, were incorporated to assess conditional associations. Results At baseline evaluation, higher concentrations of IL-6 and sTNFr2 were associated with greater global Aβ burden in those with lower hippocampal volume. In longitudinal models, IL-6 predicted subsequent conversion to MCI and both IL-6 and CRP predicted greater change in global and regional Aβ deposition specifically among participants PiB-positive at baseline. These relationships withstood adjustment for demographic factors, anti-hypertensive medication use, history of diabetes, heart disease, APOE ε4 carrier status, and white matter lesions. Discussion In a large prospective sample of CU adults aged 80 and over, peripheral inflammatory biomarkers were associated with and predictive of the progression of Aβ deposition. This was specific to those with biomarker evidence of preclinical AD at baseline, supporting recent evidence of disease-state-dependent differences in inflammatory expression profiles. Chronic, low-level systemic inflammation may exacerbate the deposition of Aβ pathology among those with emerging disease processes, and place individuals at a higher risk of developing clinically significant cognitive impairment