Properties of Gradient maps associated with Action of Real reductive Group

Let $(Z,\omega)$ be a Kahler manifold and let $U$ be a compact connected Lie group with Lie algebra $\mathfrak{u}$ acting on $Z$ and preserving $\omega$. We assume that the $U$-action extends holomorphically to an action of the complexified group $U^{\mathbb C}$ and the $U$-action on $Z$ is Hamiltonian. Then there exists a $U$-equivariant momentum map $\mu : Z\to \mathfrak{u}$. If $G\subset U^{\mathbb C}$ is a closed subgroup such that the Cartan decomposition $U^{\mathbb C} = U\text{exp}(i\mathfrak{u})$ induces a Cartan decomposition $G = K\text{exp}(\mathfrak{p}),$ where $K = U\cap G$, $\mathfrak{p} = \mathfrak{g}\cap i\mathfrak{u}$ and $\mathfrak{g}=\mathfrak k \oplus \mathfrak p$ is the Lie algebra of $G$, there is a corresponding gradient map $\mu_\mathfrak{p} : Z\longrightarrow \mathfrak{p}$. If $X$ is a $G$-invariant compact and connected real submanifold of $Z,$ we may consider $\mu_{\mathfrak p}$ as a mapping $\mu_\mathfrak{p} : X\longrightarrow \mathfrak{p}.$ Given an $\mathrm{Ad}(K)$-invariant scalar product on $\mathfrak p$, we obtain a Morse like function $f=\frac{1}{2}\parallel \mu_{\mathfrak p} \parallel^2$ on $X$. We point out that, without the assumption that $X$ is real analytic manifold, the Lojasiewicz gradient inequality holds for $f$. Therefore the limit of the negative gradient flow of $f$ exists and it is unique. Moreover, we prove that any $G$-orbit collapses to a single $K$-orbit and two critical points of $f$ which are in the same $G$-orbit belong to the same $K$-orbit. We also investigate convexity properties of the gradient map $\mu_\mathfrak{p}$ in the Abelian and Non-Abelian cases. In particular, we study two orbits variety $X$ and we investigate topological and cohomological properties of $X$.Comment: 38 page

Common Singularities of Commuting Vector Fields

We study the singularities of commuting vector fields of a real submanifold of a K\"ahler manifold $Z$.Comment: arXiv admin note: substantial text overlap with arXiv:2205.0439

COMPACT ORBITS OF PARABOLIC SUBGROUPS

We study the action of a real reductive group G on a real submanifold X of a Kähler manifold Z. We suppose that the action of a compact connected Lie group U with Lie algebra u extends holomorphically to an action of the complexified group U^C and that the U-action on Z is Hamiltonian. If G⊂U^C is compatible, there exists a gradient map μ:X⟶p where g=k⊕p is a Cartan decomposition of g . In this paper, we describe compact orbits of parabolic subgroups of G in terms of the gradient map μ

A Hilbert-Mumford Criterion for polystability for actions of real reductive Lie groups

We presented a Hilbert-Mumford criterion for polystablility associated with an action of a real reductive Lie group $G$ on a real submanifold $X$ of a Kahler manifold $Z$. Suppose the action of a compact Lie group with Lie algebra $\mathfrak{u}$ extends holomorphically to an action of the complexified group $U^\mathbb{C}$ and that the $U$-action on $Z$ is Hamiltonian. If $G\subset U^\mathbb{C}$ is compatible, there is a corresponding gradient map $\mu_\mathfrak{p}: X\to \mathfrak{p}$, where $\mathfrak{g} = \mathfrak{k} \oplus \mathfrak{p}$ is a Cartan decomposition of the Lie algebra of $G$. Under some mild restrictions on the $G$-action on $X,$ we characterize which $G$-orbits in $X$ intersect $\mu_\mathfrak{p}^{-1}(0)$ in terms of the maximal weight function, which we viewed as a collection of maps defined on the boundary at infinity ($\partial_\infty G/K$) of the symmetric space $G/K$

Mechanics of CNC Nanofilm

In the past decade, many researchers have studied mechanical properties of polymer reinforced nanocomposites to understand and improve the performance of materials. In this research, we would develop a tool that would conduct a mechanical test on structures of a nanocomposite called Crystalline Nano Cellulose. Crystalline Nano Cellulose (CNC) is a strong and natural molecular structure that we could obtain from processing a regular cellulose cell we could obtain from ordinary plants through acid hydrolysis. The mechanical test on these structures of CNC would be able to provide information about the type of failure and the effect of length and arrangement of CNC structures on the mechanical properties. The main goal to the research is to evaluate the effect of CNC aspect ratio (length / width), the effect of angular distribution and the effect of microstructure on the mechanical properties. A tool would be built on nanoHUB that used Python as the programming language and Rappture as the GUI designer. The tool would accept user’s desired molecule length, the variance of the length, angular alignment of the molecules and variance of the angle values. In addition, the tool would accept these parameters to produce a visualization of the structure specified, run a mechanical test on the structure and provide a graphical feedback. The results that could be expected from the tool is a visualization of both the initial structure and simulation of the test on the structure. A series of feedback graph and data file of the test

An empirical limit on the kilonova rate from the DLT40 one day cadence Supernova Survey

Binary neutron star mergers are important to understand stellar evolution, the chemical enrichment of the universe via the r-process, the physics of short gamma-ray bursts, gravitational waves and pulsars. The rates at which these coalescences happen is uncertain, but it can be constrained in different ways. One of those is to search for the optical transients produced at the moment of the merging, called a kilonova, in ongoing SN searches. However, until now, only theoretical models for kilonovae light curve were available to estimate their rates. The recent kilonova discovery AT~2017gfo/DLT17ck gives us the opportunity to constrain the rate of kilonovae using the light curve of a real event. We constrain the rate of binary neutron star mergers using the DLT40 Supernova search, and the native AT~2017gfo/DLT17ck light curve obtained with the same telescope and software system. Excluding AT~2017gfo/DLT17ck due to visibility issues, which was only discovered thanks to the aLIGO/aVirgo trigger, no other similar transients detected during 13 months of daily cadence observations of $\sim$ 2200 nearby ($<$40 Mpc) galaxies. We find that the rate of BNS mergers is lower than 0.47 - 0.55 kilonovae per 100 years per $10^{10}$ $L_{B_{\odot}}$ (depending on the adopted extinction distribution). In volume, this translates to <0.99\times 10^{-4}\,_{-0.15}^{+0.19},\rm{Mpc^{-3}}\,\rm{yr^{-1}}(SNe Ia-like extinction distribution), consistent with previous BNS coalescence rates. Based on our rate limit, and the sensitivity of aLIGO/aVirgo during O2, it is very unlikely that kilonova events are lurking in old pointed galaxy SN search datasets.Comment: 3 figures, 2 table

The discovery of the electromagnetic counterpart of GW170817: kilonova AT 2017gfo/DLT17ck

During the second observing run of the Laser Interferometer gravitational- wave Observatory (LIGO) and Virgo Interferometer, a gravitational-wave signal consistent with a binary neutron star coalescence was detected on 2017 August 17th (GW170817), quickly followed by a coincident short gamma-ray burst trigger by the Fermi satellite. The Distance Less Than 40 (DLT40) Mpc supernova search performed pointed follow-up observations of a sample of galaxies regularly monitored by the survey which fell within the combined LIGO+Virgo localization region, and the larger Fermi gamma ray burst error box. Here we report the discovery of a new optical transient (DLT17ck, also known as SSS17a; it has also been registered as AT 2017gfo) spatially and temporally coincident with GW170817. The photometric and spectroscopic evolution of DLT17ck are unique, with an absolute peak magnitude of Mr = -15.8 \pm 0.1 and an r-band decline rate of 1.1mag/d. This fast evolution is generically consistent with kilonova models, which have been predicted as the optical counterpart to binary neutron star coalescences. Analysis of archival DLT40 data do not show any sign of transient activity at the location of DLT17ck down to r~19 mag in the time period between 8 months and 21 days prior to GW170817. This discovery represents the beginning of a new era for multi-messenger astronomy opening a new path to study and understand binary neutron star coalescences, short gamma-ray bursts and their optical counterparts.Comment: ApJL in press, 4 figure

CD32-RNA Co-localizes with HIV-RNA in CD3+ Cells Found within Gut Tissues from Viremic and ART-Suppressed Individuals.

BackgroundIdentifying biomarkers for cells harboring replication-competent HIV is a major research priority. Recently, there have been mixed reports addressing the possibility that CD32-expressing T cells are enriched for HIV. There is growing evidence that CD32 expression increases with cellular activation that may be related to, but not necessarily specific for, infection with HIV. However, the relationship of CD32 expression to HIV-infection in subtypes of tissue-resident leukocytes is unclear.MethodsFirst, we used duplex chromogenic in situ hybridization to identify cells actively transcribing RNA for both CD32 and HIV on human gut tissues. Then we performed multiplexed immunofluorescence and in situ hybridization (mIFISH) on sections from the same tissues to determine the phenotype of individual cells co-expressing HIV-RNA and CD32-RNA.ResultsHIV-RNA+ cells were more abundant in tissues from viremic individuals than in those receiving suppressive anti-retroviral therapy (ART). However, staining by both methods indicated that a higher proportion of HIV-RNA+ cells co-expressed CD32-RNA in ART-suppressed individuals than in those with viremia. The majority of HIV-RNA+ cells were CD3+.ConclusionsOur data suggest that the transcription of CD32-RNA is correlated with HIV transcriptional activity in CD3+ cells found within human gut tissue. Whether or not up-regulation of CD32-RNA is a direct result of HIV transcription or more global T-cell activation remains unclear

Implementing and Evaluating Security in O-RAN: Interfaces, Intelligence, and Platforms

The Open Radio Access Network (RAN) is a networking paradigm that builds on top of cloud-based, multi-vendor, open and intelligent architectures to shape the next generation of cellular networks for 5G and beyond. While this new paradigm comes with many advantages in terms of observatibility and reconfigurability of the network, it inevitably expands the threat surface of cellular systems and can potentially expose its components to several cyber attacks, thus making securing O-RAN networks a necessity. In this paper, we explore the security aspects of O-RAN systems by focusing on the specifications and architectures proposed by the O-RAN Alliance. We address the problem of securing O-RAN systems with an holistic perspective, including considerations on the open interfaces used to interconnect the different O-RAN components, on the overall platform, and on the intelligence used to monitor and control the network. For each focus area we identify threats, discuss relevant solutions to address these issues, and demonstrate experimentally how such solutions can effectively defend O-RAN systems against selected cyber attacks. This article is the first work in approaching the security aspect of O-RAN holistically and with experimental evidence obtained on a state-of-the-art programmable O-RAN platform, thus providing unique guideline for researchers in the field.Comment: 7 pages, 5 figures, 1 table, submitted to IEEE Network Magazin

One Year Follow-up of a Randomized, Double-Blind, Placebo-Controlled Trial of Percutaneous Peripheral Nerve Stimulation for Chronic Neuropathic Pain Following Amputation

Abstract INTRODUCTION Over 85% of patients experience residual limb (RLP) and/or phantom limb (PLP) pain following amputation. Peripheral nerve stimulation (PNS) is a non-opioid approach to relieve postamputation neuropathic pain. A recent multicenter, randomized, double-blind, placebo-controlled study using a novel percutaneous PNS system demonstrated clinically and statistically significant improvements in pain and pain interference with PNS compared to placebo (Gilmore et al, 2019). This work presents prospective 1-yr follow-up to assess durability of pain relief and functional improvements. METHODS Over 85% of patients experience residual limb (RLP) and/or phantom limb (PLP) pain following amputation. Peripheral nerve stimulation (PNS) is a non-opioid approach to relieve post-amputation neuropathic pain. A recent multicenter, randomized, double-blind, placebo-controlled study using a novel percutaneous PNS system demonstrated clinically and statistically significant improvements in pain and pain interference with PNS compared to placebo (Gilmore et al, 2019). This work presents prospective one-year follow-up to assess durability of pain relief and functional improvements. RESULTS A significantly greater proportion of subjects who completed the 12-mo visit reported&nbsp;=&nbsp;50% pain relief on the BPI-SF (5/8, 63%; average pain relief&nbsp;=&nbsp;73% among responders) compared to the placebo group at the time of crossover (0/14, 0%, P&nbsp;=&nbsp;.003; average pain relief&nbsp;=&nbsp;23%). A majority of subjects also reported&nbsp;=&nbsp;50% reductions in pain interference at 12 mo (5/8, 63%). Two of 13 (15%) subjects in the placebo group reported sustained improvements in pain interference (P&nbsp;=&nbsp;.06). Average reduction in pain interference among responders in the PNS group was 87%. CONCLUSION This work suggests that PNS delivered over 60 d may provide clinically significant and enduring pain relief, enabling improved function and potentially reducing the need for a permanently implanted system