Riesz Transforms and Spectral Multipliers of the Hodge-Laguerre Operator

On $\mathbb{R}^d_+$, endowed with the Laguerre probability measure $\mu_\alpha$, we define a Hodge-Laguerre operator $\mathbb{L}_\alpha=\delta\delta^*+\delta^* \delta$ acting on differential forms. Here $\delta$ is the Laguerre exterior differentiation operator, defined as the classical exterior differential, except that the partial derivatives $\partial_{x_i}$ are replaced by the "Laguerre derivatives" $\sqrt{x_i}\partial_{x_i}$, and $\delta^*$ is the adjoint of $\delta$ with respect to inner product on forms defined by the Euclidean structure and the Laguerre measure $\mu_\alpha$. We prove dimension-free bounds on $L^p$, $1<p<\infty$, for the Riesz transforms $\delta \mathbb{L}_\alpha^{-1/2}$ and $\delta^* \mathbb{L}_ \alpha^{-1/2}$. As applications we prove the strong Hodge-de Rahm-Kodaira decomposition for forms in $L^p$ and deduce existence and regularity results for the solutions of the Hodge and de Rham equations in $L^p$. We also prove that for suitable functions $m$ the operator $m(\mathbb{L}^\alpha)$ is bounded on $L^p$, $1<p<\infty$.Comment: 49 page

Higher order Riesz transforms on noncompact symmetric spaces

In this note we prove various sharp boundedness results on suitable Hardy type spaces for Riesz transforms of arbitrary order on noncompact symmetric spaces of arbitrary rank.Comment: v2: the first version has been revised and splitted up in two papers, of which this new version is one par

Estimates for functions of the Laplacian on manifolds with bounded geometry

In this paper we consider a complete connected noncompact Riemannian manifold M with Ricci curvature bounded from below and positive injectivity radius. Denote by L the Laplace-Beltrami operator on M. We assume that the kernel associated to the heat semigroup generated by L satisfies a mild decay condition at infinity. We prove that if m is a bounded holomorphic function in a suitable strip of the complex plane, and satisfies Mihlin-Hormander type conditions of appropriate order at infinity, then the operator m(L) extends to an operator of weak type 1. This partially extends a celebrated result of J. Cheeger, M. Gromov and M. Taylor, who proved similar results under much stronger curvature assumptions on M, but without any assumption on the decay of the heat kernel.Comment: 19 page

Activating the MSH2/MSH6 Apoptotic Pathway in Cancer Cells Using Non-Reserpine Compounds

DNA mismatch repair (MMR) is a system that is highly conserved in both prokaryotes and eukaryotes. The heterodimeric protein MutSα and a suite of associated proteins are essential in the recognition and repair of DNA afflicted with mispaired bases and short insertion/deletion loops, but are also implicated in funneling damaged cells towards apoptosis via a key conformational change in a subunit of the MutSα complex. This conformation can be bound specifically by the small molecule reserpine. Molecular dynamics modeling and virtual screening were used to identify additional small molecule novel ligands with the predicted ability to selectively bind this “death” conformation of MutSα. These novel ligands were demonstrated to possess cytotoxicity similar to that of reserpine. As MMR deficiency has been demonstrated to confer a degree of resistance to some chemotherapeutic agents, exploiting this novel apoptotic pathway may prove to be a valid niche treatment in particular classes of cancers in which MMR proteins have been mutated

Short-Term Neurodevelopmental Outcome in Term Neonates Treated with Phenobarbital versus Levetiracetam: A Single-Center Experience

BACKGROUND: Phenobarbital (PB) has been traditionally used as the first-line treatment for neonatal seizures. More recently, levetiracetam (LEV) has been increasingly used as a promising newer antiepileptic medication for treatment of seizures in neonates. OBJECTIVES: The aim of our study was to compare the effect of PB vs. LEV on short-term neurodevelopmental outcome in infants treated for neonatal seizures. METHOD: This randomized, one-blind prospective study was conducted on term neonates admitted to the Neonatal Intensive Care Unit of S. Bambino Hospital, University Hospital "Policlinico-Vittorio Emanuele," Catania, Italy, from February 2016 to February 2018. Thirty term neonates with seizures were randomized to receive PB or LEV; the Hammersmith Neonatal Neurological Examination (HNNE) was used at baseline (T0) and again one month after the initial treatment (T1). RESULTS: We found a significantly positive HNNE score for the developmental outcomes, specifically tone and posture, in neonates treated with LEV. There was no significant improvement in the HNNE score at T1 in the neonates treated with PB. CONCLUSION: This study suggests a positive effect of levetiracetam on tone and posture in term newborns treated for neonatal seizures. If future randomized-controlled studies also show better efficacy of LEV in the treatment of neonatal seizures, LEV might potentially be considered as the first-line anticonvulsant in this age grou

Reducing the anxiety of patients undergoing an oral biopsy by means of graphic novels: an open-label randomized clinical trial

Background: The use of graphic novels is a trending topic in health communication as a new form of visual storytelling which explores narratives of health care, cancer, healing, and disability. The objective of the present study was to evaluate - for the first time in the literature - the effect of graphic novels in reducing the anxiety of patients waiting for an incisional biopsy in an oral oncology setting. Material and methods: This open-label randomized clinical trial comprised 50 patients with a clinical suspicion of oral potentially malignant disorders. Twenty-five patients were randomly allocated to the test group, and a colourful graphic novel was provided. Subsequently, the Beck Depression Inventory and the Depression Anxiety Stress Scales-21 were administered to all 50 recruited patients, after which a biopsy was performed on each patient. Results: No statistically significant difference was observed between the test and control groups for the variables regarding the demographic data (p&gt;0.2). There was a significant difference after the introduction of the graphic novel, regardless of which questionnaire was used. The graphic novel demonstrated an improvement in the ability of the test group to tolerate anxiety while waiting for an oral biopsy in both psychological tests (p&lt;0.05). Conclusions: In light of these initial positive results, the authors of this study would like to suggest the use of graphic novels in oral oncology, dentistry, and medicine with the aim of reducing patient anxiety