806 research outputs found
Stokes matrices for confluent hypergeometric equations
We apply the method of [arXiv:1705.07610] to compute the Stokes matrices of
non-resonant confluent hypergeometric differential equations. We discuss the
ambiguity of the presentation of the Stokes matrices regarding different
choices. The results rely on an explicit description of the perverse sheaf
associated to the non-confluent regular singular hypergeometric system arising
via Fourier-Laplace transform. We give assumptions on the parameter such that
the Stokes matrices have rational or real values. Under some more restrictive
conditions, the Stokes matrices had been computed by Duval-Mitschi before. We
compare our results with their formulae in the unramified case.Comment: 34 pages, 5 figures v4: section on the ramified case added, will be
published in International Mathematics Research Notice
Periods for rank 1 irregular singular connections on surfaces
We define a period pairing for flat, irregular singular, rank one
connections, satisfying a technical condition regarding its stationary set, on
complex surfaces between de Rham cohomology of the connection and a modified
singular homology, the rapid decay homology. We prove that this gives a perfect
duality. A 2-dimensional version of confluent hypergeometrics are contructed as
an example.Comment: 28 pages; previous version partly incorrect (for higher rank case),
new version contains case of line bundles and a new example. v3: technical
assumption inserted (Definition 1.1
Integral representations for solutions of exponential Gauss-Manin systems
Let f,g be two algebraically independent regular functions from the smooth
affine complex variety U to the affine line. The associated exponential
Gauss-Manin systems on the affine line are defined to be the cohomology sheaves
of the direct image of the exponential differential system
with respect to f. We prove that its holomorphic solutions admit
representations in terms of period integrals over topological chains with
possibly closed support and with rapid decay condition.Comment: 16 page
The local Laplace transform of an elementary irregular meromorphic connection
We give a definition of the topological local Laplace transformation for a
Stokes-filtered local system on the complex affine line and we compute in a
topological way the Stokes data of the Laplace transform of a differential
system of elementary type.Comment: 56 pages, 21 figures. V2: Final version to appear in Rend. Sem. Mat.
Univ. Padov
Topological computation of some Stokes phenomena on the affine line
Let be a holonomic algebraic -module on the affine
line, regular everywhere including at infinity. Malgrange gave a complete
description of the Fourier-Laplace transform , including
its Stokes multipliers at infinity, in terms of the quiver of . Let
be the perverse sheaf of holomorphic solutions to . By the
irregular Riemann-Hilbert correspondence, is determined
by the enhanced Fourier-Sato transform of . Our aim here is
to recover Malgrange's result in a purely topological way, by computing
using Borel-Moore cycles. In this paper, we also consider some
irregular 's, like in the case of the Airy equation, where our
cycles are related to steepest descent paths.Comment: 50 pages, to appear at Annales de l'Institut Fourier, v3: some minor
(editorial) correction
Periods for flat algebraic connections
In previous work, we established a duality between the algebraic de Rham
cohomology of a flat algebraic connection on a smooth quasi-projective surface
over the complex numbers and the rapid decay homology of the dual connection
relying on a conjecture by C. Sabbah, which has been proved recently by T.
Mochizuki for algebraic connections in any dimension. In the present article,
we verify that Mochizuki's results allow to generalize these duality results to
arbitrary dimensions also
Analyzing immune cell infiltration of cancer spheroids in a 3D cell culture platform
The adoption of in vitro 3D cell culture models as a bridge between conventional 2D cell culture models and the complex in vivo animal
models has been increasing. A carefully designed 3D model can run biological assays with animal model-like complexities but with the
simplicity and affordability of traditional cell culture. For example, traditional 2D and transwell assays of immune cell infiltration efficiency are
unrealistic, as cell migration is gravity-driven. AIM 3D cell culture chips offer a more realistic immune cell infiltration model by
compartmentalizing immune cells and cancer spheroids in parallel channels. The chips consist of a 3D hydrogel channel and two flanking
media channels. Cancer spheroids are cultured within the hydrogel channel while immune cells are seeded in one of the media channels. The
seeded immune cells are required to actively invade and seek out target cancer cells in 3D hydrogel in AIM chips before they can infiltrate the
cancer spheroids. This is a process similar to immune cell infiltration in vivo. By utilizing high content confocal imaging, fluorescent-labeled
immune cells that migrate into the 3D hydrogel can be visualized and quantified. This assay, in combination with adoptive T cell therapy or
immune checkpoint blockade, can determine the roles of tumor infiltrated lymphocytes in immunotherapy through quantifying the live: dead
ratio of cancer spheroids in the chips. This is particularly useful as a quality control tool for cellular adoptive immunotherapy where the
infiltration efficiency and tumoricidal activity of engineered immune cells can be accessed in vitro. In summary, AIM 3D cell culture chips
create a more physiologically relevant 3D microenvironment for visualizing immune cell infiltration of cancer spheroids
Distinct firing activities of the hypothalamic arcuate nucleus neurons to appetite hormones
The hypothalamic arcuate nucleus (Arc) is a central unit that controls the appetite through the integration of metabolic, hormonal, and neuronal afferent inputs. Agouti-related protein (AgRP), proopiomelanocortin (POMC), and dopaminergic neurons in the Arc differentially regulate feeding behaviors in response to hunger, satiety, and appetite, respectively. At the time of writing, the anatomical and electrophysiological characterization of these three neurons has not yet been intensively explored. Here, we interrogated the overall characterization of AgRP, POMC, and dopaminergic neurons using genetic mouse models, immunohistochemistry, and whole-cell patch recordings. We identified the distinct geographical location and intrinsic properties of each neuron in the Arc with the transgenic lines labelled with cell-specific reporter proteins. Moreover, AgRP, POMC, and dopaminergic neurons had different firing activities to ghrelin and leptin treatments. Ghrelin led to the increased firing rate of dopaminergic and AgRP neurons, and the decreased firing rate of POMC. In sharp contrast, leptin resulted in the decreased firing rate of AgRP neurons and the increased firing rate of POMC neurons, while it did not change the firing rate of dopaminergic neurons in Arc. These findings demonstrate the anatomical and physiological uniqueness of three hypothalamic Arc neurons to appetite control
Distinct Firing Activities of the Hypothalamic Arcuate Nucleus Neurons to Appetite Hormones
The hypothalamic arcuate nucleus (Arc) is a central unit that controls the appetite through
the integration of metabolic, hormonal, and neuronal afferent inputs. Agouti-related protein (AgRP),
proopiomelanocortin (POMC), and dopaminergic neurons in the Arc differentially regulate feeding
behaviors in response to hunger, satiety, and appetite, respectively. At the time of writing, the anatomical
and electrophysiological characterization of these three neurons has not yet been intensively
explored. Here, we interrogated the overall characterization of AgRP, POMC, and dopaminergic
neurons using genetic mouse models, immunohistochemistry, and whole-cell patch recordings.
We identified the distinct geographical location and intrinsic properties of each neuron in the Arc
with the transgenic lines labelled with cell-specific reporter proteins. Moreover, AgRP, POMC, and
dopaminergic neurons had different firing activities to ghrelin and leptin treatments. Ghrelin led to
the increased firing rate of dopaminergic and AgRP neurons, and the decreased firing rate of POMC.
In sharp contrast, leptin resulted in the decreased firing rate of AgRP neurons and the increased
firing rate of POMC neurons, while it did not change the firing rate of dopaminergic neurons in Arc.
These findings demonstrate the anatomical and physiological uniqueness of three hypothalamic Arc
neurons to appetite control
Discovery of Two Distant Type Ia Supernovae in the Hubble Deep Field North with the Advanced Camera for Surveys
We present observations of the first two supernovae discovered with the
recently installed Advanced Camera for Surveys (ACS) on the Hubble Space
Telescope. The supernovae were found in Wide Field Camera images of the Hubble
Deep Field North taken with the F775W, F850LP, and G800L optical elements as
part of the ACS guaranteed time observation program. Spectra extracted from the
ACS G800L grism exposures confirm that the objects are Type Ia supernovae (SNe
Ia) at redshifts z=0.47 and z=0.95. Follow-up HST observations have been
conducted with ACS in F775W and F850LP and with NICMOS in the near-infrared
F110W bandpass, yielding a total of 9 flux measurements in the 3 bandpasses
over a period of 50 days in the observed frame. We discuss many of the
important issues in doing accurate photometry with the ACS. We analyze the
multi-band light curves using two different fitting methods to calibrate the
supernovae luminosities and place them on the SNe Ia Hubble diagram. The
resulting distances are consistent with the redshift-distance relation of the
accelerating universe model, although evolving intergalactic grey dust remains
as a less likely possibility. The relative ease with which these SNe Ia were
found, confirmed, and monitored demonstrates the potential ACS holds for
revolutionizing the field of high-redshift SNe Ia, and therefore of testing the
accelerating universe cosmology and constraining the "epoch of deceleration".Comment: 11 pages, 8 embedded figures. Accepted for publication in Ap
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