Singular normal form for the Painlev\'e equation P1

We show that there exists a rational change of coordinates of Painlev\'e's P1 equation $y''=6y^2+x$ and of the elliptic equation $y''=6y^2$ after which these two equations become analytically equivalent in a region in the complex phase space where $y$ and $y'$ are unbounded. The region of equivalence comprises all singularities of solutions of P1 (i.e. outside the region of equivalence, solutions are analytic). The Painlev\'e property of P1 (that the only movable singularities are poles) follows as a corollary. Conversely, we argue that the Painlev\'e property is crucial in reducing P1, in a singular regime, to an equation integrable by quadratures

Ionization in damped time-harmonic fields

We study the asymptotic behavior of the wave function in a simple one dimensional model of ionization by pulses, in which the time-dependent potential is of the form $V(x,t)=-2\delta(x)(1-e^{-\lambda t} \cos\omega t)$, where $\delta$ is the Dirac distribution. We find the ionization probability in the limit $t\to\infty$ for all $\lambda$ and $\omega$. The long pulse limit is very singular, and, for $\omega=0$, the survival probability is $const \lambda^{1/3}$, much larger than $O(\lambda)$, the one in the abrupt transition counterpart, $V(x,t)=\delta(x)\mathbf{1}_{\{t\ge 1/\lambda\}}$ where $\mathbf{1}$ is the Heaviside function

The big and intricate dreams of little organelles: Embracing complexity in the study of membrane traffic

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/138421/1/tra12497_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/138421/2/tra12497-sup-0001-EditorialProcess.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/138421/3/tra12497.pd

Decay versus survival of a localized state subjected to harmonic forcing: exact results

We investigate the survival probability of a localized 1-d quantum particle subjected to a time dependent potential of the form $rU(x)\sin{\omega t}$ with $U(x)=2\delta (x-a)$ or $U(x)= 2\delta(x-a)-2\delta (x+a)$. The particle is initially in a bound state produced by the binding potential $-2\delta (x)$. We prove that this probability goes to zero as $t\to\infty$ for almost all values of $r$, $\omega$, and $a$. The decay is initially exponential followed by a $t^{-3}$ law if $\omega$ is not close to resonances and $r$ is small; otherwise the exponential disappears and Fermi's golden rule fails. For exceptional sets of parameters $r,\omega$ and $a$ the survival probability never decays to zero, corresponding to the Floquet operator having a bound state. We show similar behavior even in the absence of a binding potential: permitting a free particle to be trapped by harmonically oscillating delta function potential

Differing roles of autophagy in HIV-associated neurocognitive impairment and encephalitis with implications for morphine co-exposure

We investigated the role of autophagy in HIV-infected subjects with neurocognitive impairment (NCI) ± HIV encephalitis (HIVE), many of which had a history of polysubstance abuse/dependence, using post-mortem brain tissues to determine whether differences in autophagy related factors may be more associated with NCI or NCI-encephalitis. Using qRT-PCR, we detected significant differences in gene expression levels with SQSTM1, LAMP1 higher in HIV-infected subjects without NCI while ATG5, SQSTM1 were then lower in HIV infection/NCI and ATG7, SQSTM1 being higher in NCI-HIVE. Immunohistochemical labeling of these autophagy associated proteins (also including Beclin 1 and LC3B) in Iba1-positive microglial cells showed generally higher immunoreactivity in the NCI and NCI-HIVE groups with more focal vs. diffuse patterns of expression in the NCI-HIVE group. Furthermore, analysis of microarray data from these same subjects found significantly higher levels of LAMP1 in NCI-HIVE compared to uninfected subjects in the basal ganglia. Finally, we tested the effect of supernatant from HIV-1-infected microglia and HIV-1 Tat protein in combination with morphine on neurons in vitro and found opposing events with both significant inhibition of autophagic flux and reduced dendrite length for morphine and supernatant treatment while Tat and morphine exposure resulted in lower autophagic activity at an earlier time point and higher levels in the later. These results suggest autophagy genes and their corresponding proteins may be differentially regulated at the transcriptional, translational, and post-translational levels in the brain during various stages of the HIV disease and that infected individuals exposed to morphine can experience mixed signaling of autophagic activity which could lead to more severe NCI than those without opioid use

Cohomological BRST aspects of the massless tensor field with the mixed symmetry (k,k)

The main BRST cohomological properties of a free, massless tensor field that transforms in an irreducible representation of GL(D,R), corresponding to a rectangular, two-column Young diagram with k>2 rows are studied in detail. In particular, it is shown that any non-trivial co-cycle from the local BRST cohomology group H(s|d) can be taken to stop either at antighost number (k+1) or k, its last component belonging to the cohomology of the exterior longitudinal derivative H(gamma) and containing non-trivial elements from the (invariant) characteristic cohomology H^{inv}(delta|d).Comment: Latex, 50 pages, uses amssym

Akt-ing Up Just About Everywhere: Compartment-Specific Akt Activation and Function in Receptor Tyrosine Kinase Signaling

The serine/threonine kinase Akt is a master regulator of many diverse cellular functions, including survival, growth, metabolism, migration, and differentiation. Receptor tyrosine kinases are critical regulators of Akt, as a result of activation of phosphatidylinositol-3-kinase (PI3K) signaling leading to Akt activation upon receptor stimulation. The signaling axis formed by receptor tyrosine kinases, PI3K and Akt, as well as the vast range of downstream substrates is thus central to control of cell physiology in many different contexts and tissues. This axis must be tightly regulated, as disruption of PI3K-Akt signaling underlies the pathology of many diseases such as cancer and diabetes. This sophisticated regulation of PI3K-Akt signaling is due in part to the spatial and temporal compartmentalization of Akt activation and function, including in specific nanoscale domains of the plasma membrane as well as in specific intracellular membrane compartments. Here, we review the evidence for localized activation of PI3K-Akt signaling by receptor tyrosine kinases in various specific cellular compartments, as well as that of compartment-specific functions of Akt leading to control of several fundamental cellular processes. This spatial and temporal control of Akt activation and function occurs by a large number of parallel molecular mechanisms that are central to regulation of cell physiology

Hamiltonian BRST deformation of a class of n-dimensional BF-type theories

Consistent Hamiltonian interactions that can be added to an abelian free BF-type class of theories in any n greater or equal to 4 spacetime dimensions are constructed in the framework of the Hamiltonian BRST deformation based on cohomological techniques. The resulting model is an interacting field theory in higher dimensions with an open algebra of on-shell reducible first-class constraints. We argue that the Hamiltonian couplings are related to a natural structure of Poisson manifold on the target space.Comment: 27 pages, uses JHEP3.cl

Evolution of the one-phonon 2(1,ms)(+) mixed-symmetry state in N=80 isotones as a local measure for the proton-neutron quadrupole interaction

An inverse kinematics Coulomb excitation experiment was performed to obtain absolute E2 and M1 transition strengths in 134Xe. The measured transition strengths indicate that the 23+ state of 134Xe is the dominant fragment of the one-phonon 21, ms+ mixed-symmetry state. Comparing the energy of the 21, ms+ mixed-symmetry state in 134Xe to that of the 21, ms+ levels in the N = 80 isotonic chain indicates that the separation in energy between the fully-symmetric 21+ state and the 21, ms+ level increases as a function of the number of proton pairs outside the Z = 50 shell closure. This behavior can be understood as resulting from the mixing of the basic components of a two-fluid quantum system. A phenomenological fit based on this concept was performed. It provides the first experimental estimate of the strength of the proton-neutron quadrupole interaction derived from nuclear collective states with symmetric and antisymmetric nature