L\'evy Processes on Uq(g)U_q(g) as Infinitely Divisible Representations

L\'evy processes on bialgebras are families of infinitely divisible representations. We classify the generators of L\'evy processes on the compact forms of the quantum algebras $U_q(g)$, where $g$ is a simple Lie algebra. Then we show how the processes themselves can be reconstructed from their generators and study several classical stochastic processes that can be associated to these processes.Comment: 13 pages, LATEX file, ASI-TPA/13/99 (TU Clausthal); 6/99 (Preprint-Reihe Mathmatik, Univ. Greifswald)

Absence of a consistent classical equation of motion for a mass-renormalized point charge

The restrictions of analyticity, relativistic (Born) rigidity, and negligible O(a) terms involved in the evaluation of the self electromagnetic force on an extended charged sphere of radius "a" are explicitly revealed and taken into account in order to obtain a classical equation of motion of the extended charge that is both causal and conserves momentum-energy. Because the power-series expansion used in the evaluation of the self force becomes invalid during transition time intervals immediately following the application and termination of an otherwise analytic externally applied force, transition forces must be included during these transition time intervals to remove the noncausal pre-acceleration and pre-deceleration from the solutions to the equation of motion without the transition forces. For the extended charged sphere, the transition forces can be chosen to maintain conservation of momentum-energy in the causal solutions to the equation of motion within the restrictions of relativistic rigidity and negligible O(a) terms under which the equation of motion is derived. However, it is shown that renormalization of the electrostatic mass to a finite value as the radius of the charge approaches zero introduces a violation of momentum-energy conservation into the causal solutions to the equation of motion of the point charge if the magnitude of the external force becomes too large. That is, the causal classical equation of motion of a point charge with renormalized mass experiences a high acceleration catastrophe.Comment: 13 pages, No figure

Chapter 6 - Cerebrospinal fluid in the dementias

Alzheimer disease, vascular dementia, dementia with Lewy bodies, and frontotemporal dementia are the most common central nervous system disorders that cause progressive neurocognitive dysfunction and ultimately dementia. A number of biomarkers for pathologies reflecting each condition have been developed. Here, we review these and give an overview of the current state of practice and research regarding cerebrospinal fluid biomarkers for these disorders. The chapter discusses both established (most of which are tau- and amyloid β-related) and upcoming biomarkers and details, wherever appropriate, clinical use and differential diagnostics aspects

Self-forces on extended bodies in electrodynamics

In this paper, we study the bulk motion of a classical extended charge in flat spacetime. A formalism developed by W. G. Dixon is used to determine how the details of such a particle's internal structure influence its equations of motion. We place essentially no restrictions (other than boundedness) on the shape of the charge, and allow for inhomogeneity, internal currents, elasticity, and spin. Even if the angular momentum remains small, many such systems are found to be affected by large self-interaction effects beyond the standard Lorentz-Dirac force. These are particularly significant if the particle's charge density fails to be much greater than its 3-current density (or vice versa) in the center-of-mass frame. Additional terms also arise in the equations of motion if the dipole moment is too large, and when the `center-of-electromagnetic mass' is far from the `center-of-bare mass' (roughly speaking). These conditions are often quite restrictive. General equations of motion were also derived under the assumption that the particle can only interact with the radiative component of its self-field. These are much simpler than the equations derived using the full retarded self-field; as are the conditions required to recover the Lorentz-Dirac equation.Comment: 30 pages; significantly improved presentation; accepted for publication in Phys. Rev.

Blood Biomarkers for Alzheimer's Disease: Much Promise, Cautious Progress

Biomarkers in Alzheimer's disease (AD) have the potential to allow early and more accurate diagnosis, predict disease progression, stratify individuals and track response to candidate therapies in drug trials. The first fluid biomarkers reflecting aspects of AD neuropathology were identified in cerebrospinal fluid (CSF) in the 1990s. Three CSF biomarkers (amyloid-β 1-42, total tau and phospho-tau) have consistently been shown to have diagnostic utility and are incorporated into the new diagnostic criteria for AD. These markers have also been shown in longitudinal studies to predict conversion of mild cognitive impairment to AD. However, a key issue with the use of CSF biomarkers as a screening test is the invasiveness of lumbar puncture. Over the last 20 years there has been an active quest for blood biomarkers, which could be easily acquired and tested repeatedly throughout the disease course. One approach to identifying such markers is to attempt to measure candidates that have already been identified in CSF. Until recently, this approach has been limited by assay sensitivity, but newer platforms now allow single molecule-level detection. Another approach is identification of candidates in large multiplex panels that allow for multiple analytes to be quantified in parallel. While both approaches show promise, to date no blood-based biomarker or combination of biomarkers has sufficient predictive value to have utility in clinical practice. In this review, an overview of promising blood protein candidates is provided, and the challenges of validating and converting these into practicable tests are discussed

Membrane-Bound Catechol-O-Methyl Transferase in Cortical Neurons and Glial Cells is Intracellularly Oriented

Catechol-O-methyl transferase (COMT) is involved in the inactivation of dopamine in brain regions in which the dopamine transporter (DAT1) is sparsely expressed. The membrane-bound isoform of COMT (MB-COMT) is the predominantly expressed form in the mammalian central nervous system (CNS). It has been a matter of debate whether in neural cells of the CNS the enzymatic domain of MB-COMT is oriented toward the cytoplasmic or the extracellular compartment. Here we used live immunocytochemistry on cultured neocortical neurons and glial cells to investigate the expression and membrane orientation of native COMT and of transfected MB-COMT fused to green fluorescent protein (GFP). After live staining, COMT immunoreactivity was reliably detected in both neurons and glial cells after permeabilization, but not on unpermeabilized cells. Similarly, autofluorescence of COMT-GFP fusion protein and antibody fluorescence showed overlap only in permeabilized neurons. Our data provide converging evidence for an intracellular membrane orientation of MB-COMT in neurons and glial cells, suggesting the presence of a DAT1-independent postsynaptic uptake mechanism for dopamine, prior to its degradation via COMT

Molecular tuning of the magnetic response in organic semiconductors

The tunability of high-mobility organic semi-conductors (OSCs) holds great promise for molecular spintronics. In this study, we show this extreme variability - and therefore potential tunability - of the molecular gyromagnetic coupling ("g-") tensor with respect to the geometric and electronic structure in a much studied class of OSCs. Composed of a structural theme of phenyl- and chalcogenophene (group XVI element containing, five-membered) rings and alkyl functional groups, this class forms the basis of several intensely studied high-mobility polymers and molecular OSCs. We show how in this class the g-tensor shifts, $\Delta g$, are determined by the effective molecular spin-orbit coupling (SOC), defined by the overlap of the atomic spin-density and the heavy atoms in the polymers. We explain the dramatic variations in SOC with molecular geometry, chemical composition, functionalization, and charge life-time using a first-principles theoretical model based on atomic spin populations. Our approach gives a guide to tuning the magnetic response of these OSCs by chemical synthesis