Decompositions and coalescing eigenvalues of symmetric definite pencils depending on parameters

In this work, we consider symmetric positive definite pencils depending on two parameters. That is, we are concerned with the generalized eigenvalue problem $A(x)-\lambda B(x)$, where $A$ and $B$ are symmetric matrix valued functions in ${\mathbb R}^{n\times n}$, smoothly depending on parameters $x\in \Omega\subset {\mathbb R}^2$; further, $B$ is also positive definite. In general, the eigenvalues of this multiparameter problem will not be smooth, the lack of smoothness resulting from eigenvalues being equal at some parameter values (conical intersections). We first give general theoretical results on the smoothness of eigenvalues and eigenvectors for the present generalized eigenvalue problem, and hence for the corresponding projections, and then perform a numerical study of the statistical properties of coalescing eigenvalues for pencils where $A$ and $B$ are either full or banded, for several bandwidths. Our numerical study will be performed with respect to a random matrix ensemble which respects the underlying engineering problems motivating our study.Comment: 34 pages, 4 figure

C1q-Mediated Complement Activation and C3 Opsonization Trigger Recognition of Stealth Poly(2-methyl-2-oxazoline)-Coated Silica Nanoparticles by Human Phagocytes

Poly(2-methyl-2-oxazoline) (PMOXA) is an alternative promising polymer to poly(ethylene glycol) (PEG) for design and engineering of macrophage-evading nanoparticles (NPs). Although PMOXA-engineered NPs have shown comparable pharmacokinetics and in vivo performance to PEGylated stealth NPs in the murine model, its interaction with elements of the human innate immune system has not been studied. From a translational angle, we studied the interaction of fully characterized PMOXA-coated vinyltriethoxysilane-derived organically modified silica NPs (PMOXA-coated NPs) of approximately 100 nm in diameter with human complement system, blood leukocytes, and macrophages and compared their performance with PEGylated and uncoated NP counterparts. Through detailed immunological and proteomic profiling, we show that PMOXA-coated NPs extensively trigger complement activation in human sera exclusively through the classical pathway. Complement activation is initiated by the sensing molecule C1q, where C1q binds with high affinity (Kd = 11 \ub1 1 nM) to NP surfaces independent of immunoglobulin binding. C1q-mediated complement activation accelerates PMOXA opsonization with the third complement protein (C3) through the amplification loop of the alternative pathway. This promoted NP recognition by human blood leukocytes and monocyte-derived macrophages. The macrophage capture of PMOXA-coated NPs correlates with sera donor variability in complement activation and opsonization but not with other major corona proteins, including clusterin and a wide range of apolipoproteins. In contrast to these observations, PMOXA-coated NPs poorly activated the murine complement system and were marginally recognized by mouse macrophages. These studies provide important insights into compatibility of engineered NPs with elements of the human innate immune system for translational steps

Current Knowledge on Endocrine Disrupting Chemicals (EDCs) from Animal Biology to Humans, from Pregnancy to Adulthood: Highlights from a National Italian Meeting

Wildlife has often presented and suggested the effects of endocrine disrupting chemicals (EDCs). Animal studies have given us an important opportunity to understand the mechanisms of action of many chemicals on the endocrine system and on neurodevelopment and behaviour, and to evaluate the effects of doses, time and duration of exposure. Although results are sometimes conflicting because of confounding factors, epidemiological studies in humans suggest effects of EDCs on prenatal growth, thyroid function, glucose metabolism and obesity, puberty, fertility, and on carcinogenesis mainly through epigenetic mechanisms. This manuscript reviews the reports of a multidisciplinary national meeting on this topic

How future surgery will benefit from SARS-COV-2-related measures: a SPIGC survey conveying the perspective of Italian surgeons

COVID-19 negatively affected surgical activity, but the potential benefits resulting from adopted measures remain unclear. The aim of this study was to evaluate the change in surgical activity and potential benefit from COVID-19 measures in perspective of Italian surgeons on behalf of SPIGC. A nationwide online survey on surgical practice before, during, and after COVID-19 pandemic was conducted in March-April 2022 (NCT:05323851). Effects of COVID-19 hospital-related measures on surgical patients' management and personal professional development across surgical specialties were explored. Data on demographics, pre-operative/peri-operative/post-operative management, and professional development were collected. Outcomes were matched with the corresponding volume. Four hundred and seventy-three respondents were included in final analysis across 14 surgical specialties. Since SARS-CoV-2 pandemic, application of telematic consultations (4.1% vs. 21.6%; p < 0.0001) and diagnostic evaluations (16.4% vs. 42.2%; p < 0.0001) increased. Elective surgical activities significantly reduced and surgeons opted more frequently for conservative management with a possible indication for elective (26.3% vs. 35.7%; p < 0.0001) or urgent (20.4% vs. 38.5%; p < 0.0001) surgery. All new COVID-related measures are perceived to be maintained in the future. Surgeons' personal education online increased from 12.6% (pre-COVID) to 86.6% (post-COVID; p < 0.0001). Online educational activities are considered a beneficial effect from COVID pandemic (56.4%). COVID-19 had a great impact on surgical specialties, with significant reduction of operation volume. However, some forced changes turned out to be benefits. Isolation measures pushed the use of telemedicine and telemetric devices for outpatient practice and favored communication for educational purposes and surgeon-patient/family communication. From the Italian surgeons' perspective, COVID-related measures will continue to influence future surgical clinical practice

One dimensional collocation at Gaussian points and superconvergence at interior nodal points

In questo lavoro vengono estesi e completati i risultati ottenuti da M. Bakker [1 ] sulla proprietà di superconvergenza in punti interni del metodo di Collocazione ai punti di Gauss. In particolare, sotto opportune ipotesi di regolarità (cfr. De Boor e Swartz [2]), vengono individuati in ogni intervallo della partizione tutti i punti in cui l’ordine di convergenza del metodo è superiore ali ordine ottimo di convergenza globale.Here we extend and complete the results that M. Bakker [1] recently proved about a special kind of superconvergence of the method of Collocation at Gaussian points: the superconvergence at interior nodal points. We will prove that under the smoothness assumptions made by De Boor and Swartz in [2] there exist particular points inside each segment of the partition in which the rates of convergence are one order better than the optimal global one