Lack of superstable trajectories in linear viscoelasticity: a numerical approach

Given a positive operator $A$ on some Hilbert space, and a nonnegative decreasing summable function $\mu$, we consider the abstract equation with memory $$\ddot u(t)+ A u(t)- \int_0^t \mu(s)Au(t-s) ds=0$$ modeling the dynamics of linearly viscoelastic solids. The purpose of this work is to provide numerical evidence of the fact that the energy \E(t)=\Big(1-\int_0^t\mu(s)ds\Big)\|u(t)\|^2_1+\|\dot u(t)\|^2 +\int_0^t\mu(s)\|u(t)-u(t-s)\|^2_1ds, of any nontrivial solution cannot decay faster than exponential, no matter how fast might be the decay of the memory kernel $\mu$. This will be accomplished by simulating the integro-differential equation for different choices of the memory kernel $\mu$ and of the initial data

Delayed benign surgery during the COVID-19 pandemic. The other side of the coin

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Exponential stability of the wave equation with memory and time delay

We study the asymptotic behaviour of the wave equation with viscoelastic damping in presence of a time-delayed damping. We prove exponential stability if the amplitude of the time delay term is small enough

Efficacy and epigenetic interactions of novel DNA hypomethylating agent guadecitabine (SGI-110) in preclinical models of hepatocellular carcinoma

Hepatocellular carcinoma (HCC) is a deadly malignancy characterized at the epigenetic level by global DNA hypomethylation and focal hypermethylation on the promoter of tumor suppressor genes. In most cases it develops on a background of liver steatohepatitis, fibrosis, and cirrhosis. Guadecitabine (SGI-110) is a second-generation hypomethylating agent, which inhibits DNA methyltransferases. Guadecitabine is formulated as a dinucleotide of decitabine and deoxyguanosine that is resistant to cytidine deaminase (CDA) degradation and results in prolonged in vivo exposure to decitabine following small volume subcutaneous administration of guadecitabine. Here we found that guadecitabine is an effective demethylating agent and is able to prevent HCC progression in pre-clinical models. In a xenograft HCC HepG2 model, guadecitabine impeded tumor growth and inhibited angiogenesis, while it could not prevent liver fibrosis and inflammation in a mouse model of steatohepatitis. Demethylating efficacy of guadecitabine on LINE-1 elements was found to be the highest 8 d post-infusion in blood samples of mice. Analysis of a panel of human HCC vs. normal tissue revealed a signature of hypermethylated tumor suppressor genes (CDKN1A, CDKN2A, DLEC1, E2F1, GSTP1, OPCML, E2F1, RASSF1, RUNX3, and SOCS1) as detected by methylation-specific PCR. A pronounced demethylating effect of guadecitabine was obtained also in the promoters of a subset of tumor suppressors genes (CDKN2A, DLEC1, and RUNX3) in HepG2 and Huh-7 HCC cells. Finally, we analyzed the role of macroH2A1, a variant of histone H2A, an oncogene upregulated in human cirrhosis/HCC that synergizes with DNA methylation in suppressing tumor suppressor genes, and it prevents the inhibition of cell growth triggered by decitabine in HCC cells. Guadecitabine, in contrast to decitabine, blocked growth in HCC cells overexpressing macroH2A1 histones and with high CDA levels, despite being unable to fully demethylate CDKN2A, RUNX3, and DLEC1 promoters altered by macroH2A1. Collectively, our findings in human and mice models reveal novel epigenetic anti-HCC effects of guadecitabine, which might be effective specifically in advanced states of the disease

A Bayesian estimation of the Milky Way's circular velocity curve using Gaia DR3

Our goal is to calculate the circular velocity curve of the Milky Way, along with corresponding uncertainties that quantify various sources of systematic uncertainty in a self-consistent manner. The observed rotational velocities are described as circular velocities minus the asymmetric drift. The latter is described by the radial axisymmetric Jeans equation. We thus reconstruct the circular velocity curve between Galactocentric distances from 5 kpc to 14 kpc using a Bayesian inference approach. The estimated error bars quantify uncertainties in the Sun's Galactocentric distance and the spatial-kinematic morphology of the tracer stars. As tracers, we used a sample of roughly 0.6 million stars on the red giant branch stars with six-dimensional phase-space coordinates from Gaia data release 3 (DR3). More than 99% of the sample is confined to a quarter of the stellar disc with mean radial, rotational, and vertical velocity dispersions of $(35\pm 18)\,\rm km/s$, $(25\pm 13)\,\rm km/s$, and $(19\pm 9)\,\rm km/s$, respectively. We find a circular velocity curve with a slope of $0.4\pm 0.6\,\rm km/s/kpc$, which is consistent with a flat curve within the uncertainties. We further estimate a circular velocity at the Sun's position of $v_c(R_0)=233\pm7\, \rm km/s$ and that a region in the Sun's vicinity, characterised by a physical length scale of $\sim 1\,\rm kpc$, moves with a bulk motion of $V_{LSR} =7\pm 7\,\rm km/s$. Finally, we estimate that the dark matter (DM) mass within 14 kpc is $\log_{10}M_{\rm DM}(R<14\, {\rm kpc})/{\rm M_{\odot}}= \left(11.2^{+2.0}_{-2.3}\right)$ and the local spherically averaged DM density is $\rho_{\rm DM}(R_0)=\left(0.41^{+0.10}_{-0.09}\right)\,{\rm GeV/cm^3}=\left(0.011^{+0.003}_{-0.002}\right)\,{\rm M_\odot/pc^3}$. In addition, the effect of biased distance estimates on our results is assessed

Melanoma’s sentinel node biopsy: comparison between two clinical hospitals over 5 years

University of Medicine and Pharmacy of Targu Mures, Romania, University Hospital of Parma, ItalyIntroduction. Sentinel lymph node (SLN) is defined as the first lymph node localized on the direct lymphatic drainage pathway from a primary tumor. The sentinel lymph node biopsy (SLNB) is largely used in breast cancer and melanoma but it may also be useful in other epithelial skin cancers as well as in tumors located in the upper or lower gastrointestinal tract, lungs, thyroid, cervix and vulva. SLNB in melanoma is essential for an accurate staging, to estimate the risk of extension to other lymph nodes or organs and to evaluate the prognosis. Melanoma, even if it is not as common as the basal cell carcinoma or squamous cell carcinoma among the skin tumors, presents an increasing incidence and a higher mortality

Detection of an optical transient following the 13 March 2000 short/hard gamma-ray burst

We imaged the error box of a gamma-ray burst of the short (0.5 s), hard type (GRB 000313), with the BOOTES-1 experiment in southern Spain, starting 4 min after the gamma-ray event, in the I-band. A bright optical transient (OT 000313) with I = 9.4 +/- 0.1 was found in the BOOTES-1 image, close to the error box (3-sigma) provided by BATSE. Late time VRIK'-band deep observations failed to reveal an underlying host galaxy. If the OT 000313 is related to the short, hard GRB 000313, this would be the first optical counterpart ever found for this kind of events (all counterparts to date have been found for bursts of the long, soft type). The fact that only prompt optical emission has been detected (but no afterglow emission at all, as supported by theoretical models) might explain why no optical counterparts have ever been found for short, hard GRBs.This fact suggests that most short bursts might occur in a low-density medium and favours the models that relate them to binary mergers in very low-density enviroments.Comment: Revised version. Accepted for publication in Astronomy and Astrophysics Letters, 5 pages, 3 figure