Time Dependent Floquet Theory and Absence of an Adiabatic Limit

Quantum systems subject to time periodic fields of finite amplitude, lambda, have conventionally been handled either by low order perturbation theory, for lambda not too large, or by exact diagonalization within a finite basis of N states. An adiabatic limit, as lambda is switched on arbitrarily slowly, has been assumed. But the validity of these procedures seems questionable in view of the fact that, as N goes to infinity, the quasienergy spectrum becomes dense, and numerical calculations show an increasing number of weakly avoided crossings (related in perturbation theory to high order resonances). This paper deals with the highly non-trivial behavior of the solutions in this limit. The Floquet states, and the associated quasienergies, become highly irregular functions of the amplitude, lambda. The mathematical radii of convergence of perturbation theory in lambda approach zero. There is no adiabatic limit of the wave functions when lambda is turned on arbitrarily slowly. However, the quasienergy becomes independent of time in this limit. We introduce a modification of the adiabatic theorem. We explain why, in spite of the pervasive pathologies of the Floquet states in the limit N goes to infinity, the conventional approaches are appropriate in almost all physically interesting situations.Comment: 13 pages, Latex, plus 2 Postscript figure

Postinflammatory hyperpigmentation after human cold pain testing

Abstract. Changes in cold temperature sensitivity are often associated with chronic pain conditions. Progress in understanding the neurobiological mechanism underlying these changes and resulting development of effective therapies has been slowed by the accessibility and affordability of devices used to measure thermal sensitivity in humans. To address this gap, we developed an inexpensive method to measure cold pain thresholds in healthy adult volunteers using dry ice and a thermode. However, early in preliminary testing, a subject presented with epidermal postinflammatory hyperpigmentation that lasted for >200 days. Although this response was unique among the small number of subjects in development of the assay, it raised questions as to the safety of the assay design

Coronavirus infection and PARP expression dysregulate the NAD metabolome: An actionable component of innate immunity

Poly(ADP-ribose) polymerase (PARP) superfamily members covalently link either a single ADP-ribose (ADPR) or a chain of ADPR units to proteins using NAD as the source of ADPR. Although the well-known poly(ADP-ribosylating) (PARylating) PARPs primarily function in the DNA damage response, many noncanonical mono(ADP-ribosylating) (MARylating) PARPs are associated with cellular antiviral responses. We recently demonstrated robust up-regulation of several PARPs following infection with murine hepatitis virus (MHV), a model coronavirus. Here we show that SARS-CoV-2 infection strikingly up-regulates MARylating PARPs and induces the expression of genes encoding enzymes for salvage NAD synthesis from nicotinamide (NAM) and nicotinamide riboside (NR), while down-regulating other NAD biosynthetic pathways. We show that overexpression of PARP10 is sufficient to depress cellular NAD and that the activities of the transcriptionally induced enzymes PARP7, PARP10, PARP12 and PARP14 are limited by cellular NAD and can be enhanced by pharmacological activation of NAD synthesis. We further demonstrate that infection with MHV induces a severe attack on host cell NAD+ and NADP+. Finally, we show that NAMPT activation, NAM, and NR dramatically decrease the replication of an MHV that is sensitive to PARP activity. These data suggest that the antiviral activities of noncanonical PARP isozyme activities are limited by the availability of NAD and that nutritional and pharmacological interventions to enhance NAD levels may boost innate immunity to coronaviruses

The hagfish genome and the evolution of vertebrates

As the only surviving lineages of jawless fishes, hagfishes and lampreys provide a crucial window into early vertebrate evolution1,2,3. Here we investigate the complex history, timing and functional role of genome-wide duplications4,5,6,7 and programmed DNA elimination8,9 in vertebrates in the light of a chromosome-scale genome sequence for the brown hagfish Eptatretus atami. Combining evidence from syntenic and phylogenetic analyses, we establish a comprehensive picture of vertebrate genome evolution, including an auto-tetraploidization (1RV) that predates the early Cambrian cyclostome–gnathostome split, followed by a mid–late Cambrian allo-tetraploidization (2RJV) in gnathostomes and a prolonged Cambrian–Ordovician hexaploidization (2RCY) in cyclostomes. Subsequently, hagfishes underwent extensive genomic changes, with chromosomal fusions accompanied by the loss of genes that are essential for organ systems (for example, genes involved in the development of eyes and in the proliferation of osteoclasts); these changes account, in part, for the simplification of the hagfish body plan1,2. Finally, we characterize programmed DNA elimination in hagfish, identifying protein-coding genes and repetitive elements that are deleted from somatic cell lineages during early development. The elimination of these germline-specific genes provides a mechanism for resolving genetic conflict between soma and germline by repressing germline and pluripotency functions, paralleling findings in lampreys10,11. Reconstruction of the early genomic history of vertebrates provides a framework for further investigations of the evolution of cyclostomes and jawed vertebrates

Colorectal Cancer Screening in Vulnerable Patients

Low-income, low-literacy, limited English–proficient populations have low colorectal cancer (CRC) screening rates and experience poor patient–provider communication and decision-making processes around screening. The purpose of this study was to test the effect of a CRC screening decision aid on screening-related communication and decision making in primary care visits

A Small Conductance Calcium-Activated K⁺ Channel in C. elegans, KCNL-2, Plays a Role in the Regulation of the Rate of Egg-Laying

In the nervous system of mice, small conductance calcium-activated potassium (SK) channels function to regulate neuronal excitability through the generation of a component of the medium afterhyperpolarization that follows action potentials. In humans, irregular action potential firing frequency underlies diseases such as ataxia, epilepsy, schizophrenia and Parkinson's disease. Due to the complexity of studying protein function in the mammalian nervous system, we sought to characterize an SK channel homologue, KCNL-2, in C. elegans, a genetically tractable system in which the lineage of individual neurons was mapped from their early developmental stages. Sequence analysis of the KCNL-2 protein reveals that the six transmembrane domains, the potassium-selective pore and the calmodulin binding domain are highly conserved with the mammalian homologues. We used widefield and confocal fluorescent imaging to show that a fusion construct of KCNL-2 with GFP in transgenic lines is expressed in the nervous system of C. elegans. We also show that a KCNL-2 null strain, kcnl-2(tm1885), demonstrates a mild egg-laying defective phenotype, a phenotype that is rescued in a KCNL-2-dependent manner. Conversely, we show that transgenic lines that overexpress KCNL-2 demonstrate a hyperactive egg-laying phenotype. In this study, we show that the vulva of transgenic hermaphrodites is highly innervated by neuronal processes and by the VC4 and VC5 neurons that express GFP-tagged KCNL-2. We propose that KCNL-2 functions in the nervous system of C. elegans to regulate the rate of egg-laying. © 2013 Chotoo et al

Strichartz estimates on Schwarzschild black hole backgrounds

We study dispersive properties for the wave equation in the Schwarzschild space-time. The first result we obtain is a local energy estimate. This is then used, following the spirit of earlier work of Metcalfe-Tataru, in order to establish global-in-time Strichartz estimates. A considerable part of the paper is devoted to a precise analysis of solutions near the trapping region, namely the photon sphere.Comment: 44 pages; typos fixed, minor modifications in several place