Bochner-Martinelli formula in superspace

In a series of recent papers, a harmonic and hypercomplex function theory in superspace has been established and amply developed. In this paper, we address the problem of establishing Cauchy integral formulae in the framework of Hermitian Clifford analysis in superspace. This allows us to obtain a successful extension of the classical Bochner-Martinelli formula to superspace by means of the corresponding projections on the space of spinor-valued superfunctions.Comment: 29 pages. arXiv admin note: text overlap with arXiv:1804.0096

Drosophila modifier screens to identify novel neuropsychiatric drugs including aminergic agents for the possible treatment of Parkinson's disease and depression.

Small molecules that increase the presynaptic function of aminergic cells may provide neuroprotection in Parkinson's disease (PD) as well as treatments for attention deficit hyperactivity disorder (ADHD) and depression. Model genetic organisms such as Drosophila melanogaster may enhance the detection of new drugs via modifier or 'enhancer/suppressor' screens, but this technique has not been applied to processes relevant to psychiatry. To identify new aminergic drugs in vivo, we used a mutation in the Drosophila vesicular monoamine transporter (dVMAT) as a sensitized genetic background and performed a suppressor screen. We fed dVMAT mutant larvae ∼ 1000 known drugs and quantitated rescue (suppression) of an amine-dependent locomotor deficit in the larva. To determine which drugs might specifically potentiate neurotransmitter release, we performed an additional secondary screen for drugs that require presynaptic amine storage to rescue larval locomotion. Using additional larval locomotion and adult fertility assays, we validated that at least one compound previously used clinically as an antineoplastic agent potentiates the presynaptic function of aminergic circuits. We suggest that structurally similar agents might be used to development treatments for PD, depression and ADHD, and that modifier screens in Drosophila provide a new strategy to screen for neuropsychiatric drugs. More generally, our findings demonstrate the power of physiologically based screens for identifying bioactive agents for select neurotransmitter systems

Global well-posedness for a nonlocal Gross-Pitaevskii equation with non-zero condition at infinity

We study the Gross-Pitaevskii equation involving a nonlocal interaction potential. Our aim is to give sufficient conditions that cover a variety of nonlocal interactions such that the associated Cauchy problem is globally well-posed with non-zero boundary condition at infinity, in any dimension. We focus on even potentials that are positive definite or positive tempered distributions.Comment: Communications in Partial Differential Equations (2010

Boundaries of Siegel Disks: Numerical Studies of their Dynamics and Regularity

Siegel disks are domains around fixed points of holomorphic maps in which the maps are locally linearizable (i.e., become a rotation under an appropriate change of coordinates which is analytic in a neighborhood of the origin). The dynamical behavior of the iterates of the map on the boundary of the Siegel disk exhibits strong scaling properties which have been intensively studied in the physical and mathematical literature. In the cases we study, the boundary of the Siegel disk is a Jordan curve containing a critical point of the map (we consider critical maps of different orders), and there exists a natural parametrization which transforms the dynamics on the boundary into a rotation. We compute numerically this parameterization and use methods of harmonic analysis to compute the global Holder regularity of the parametrization for different maps and rotation numbers. We obtain that the regularity of the boundaries and the scaling exponents are universal numbers in the sense of renormalization theory (i.e., they do not depend on the map when the map ranges in an open set), and only depend on the order of the critical point of the map in the boundary of the Siegel disk and the tail of the continued function expansion of the rotation number. We also discuss some possible relations between the regularity of the parametrization of the boundaries and the corresponding scaling exponents. (C) 2008 American Institute of Physics.NSFMathematic

Plane - Chain coupling in YBa_{2}Cu_{3}O_{7} : temperature dependence of the penetration depth

We have studied the penetration depth for a model of $YBa_{2}Cu_{3}O_{7}$ involving pairing both in the $CuO_{2}$ planes and in the CuO chains. In this model pairing in the planes is due to an attractive interaction, while Coulomb repulsion induces in the chains an order parameter with opposite sign. Due to the anticrossing produced by hybridization between planes and chains, one obtains a d-wave like order parameter which changes sign on a single sheet of the Fermi surface and has nodes in the gap. We find that our model accounts quite well for the anisotropy of the penetration depth and for the absolute values. We reproduce fairly well the whole temperature dependence for both the a and the b directions, including the linear dependence at low temperature. We use a set of parameters which are all quite reasonable physically. Our results for the c direction are also satisfactory, although the situation is less clear both experimentally and theoretically.Comment: 11 pages, revtex, 6 figure

An Acidic Motif Retains Vesicular Monoamine Transporter 2 on Large Dense Core Vesicles

The release of biogenic amines from large dense core vesicles (LDCVs) depends on localization of the vesicular monoamine transporter VMAT2 to LDCVs. We now find that a cluster of acidic residues including two serines phosphorylated by casein kinase 2 is required for the localization of VMAT2 to LDCVs. Deletion of the acidic cluster promotes the removal of VMAT2 from LDCVs during their maturation. The motif thus acts as a signal for retention on LDCVs. In addition, replacement of the serines by glutamate to mimic phosphorylation promotes the removal of VMAT2 from LDCVs, whereas replacement by alanine to prevent phosphorylation decreases removal. Phosphorylation of the acidic cluster thus appears to reduce the localization of VMAT2 to LDCVs by inactivating a retention mechanism

The role of glacier mice in the invertebrate colonisation of glacial surfaces: the moss balls of the Falljökull, Iceland

Glacier surfaces have a surprisingly complex ecology. Cryoconite holes contain diverse invertebrate communities while other invertebrates, such as Collembola often graze on algae and windblown dead organic on the glacier surface. Glacier mice (ovoid unattached moss balls) occur on some glaciers worldwide. Studies of these glacier mice have concentrated on their occurrence and mode of formation. There are no reports of the invertebrate communities. But, such glacier mice may provide a suitable favourable habitat and refuge for a variety of invertebrate groups to colonise the glacier surface. Here we describe the invertebrate fauna of the glacier mice (moss balls) of the Falljökull, Iceland. The glacier mice were composed of Racomitrium sp. and varied in size from 8.0 to 10.0 cm in length. All glacier mice studied contained invertebrates. Two species of Collembola were present. Pseudisotoma sensibilis (Tullberg, 1876) was numerically dominant with between 12 and 73 individuals per glacier mouse while Desoria olivacea (Tullberg, 1871) occurred but in far lower numbers. Tardigrada and Nematoda had mean densities of approximately 200 and 1,000 respectively. No Acari, Arachnida or Enchytraeidae were observed which may be related to the difficulty these groups have in colonizing the glacier mice. We suggest that glacier mice provide an unusual environmentally ameliorated microhabitat for an invertebrate community dwelling on a glacial surface. The glacier mice thereby enable an invertebrate fauna to colonise an otherwise largely inhospitable location with implications for carbon flow in the system

Are Large Physiological Reactions to Acute Psychological Stress Always Bad for Health?

How we react physiologically to stress has long been considered to have implications for our health. There is now persuasive evidence that individuals who show large cardiovascular reactions to stress are at increased risk of developing cardiovascular disease, particularly hypertension. By implication, low reactivity is protective or benign. However, there is recent evidence that low reactivity may predict elevated risk for a range of adverse health outcomes, such as depression, obesity, poor self-reported health, and compromised immunity. In addition, low cortisol and cardiovascular reactivity may be a characteristic of individuals with addictions to tobacco and alcohol, as well as those at risk of addiction and those who relapse from abstinence. Our ideas about reactivity may have to be revised in the light of such findings