Vibrational modes of circular free plates under tension

The vibrational frequencies of a plate under tension are given by the eigenvalues $\omega$ of the equation $\Delta^2u-\tau\Delta u=\omega u$. This paper determines the eigenfunctions and eigenvalues of this bi-Laplace problem on the ball under natural (free) boundary conditions. In particular, the fundamental modes --- the eigenfunctions of the lowest nonzero eigenvalue --- are identified and found to have simple angular dependence.Comment: 17 pages. To be submitted for publication shortly

On a classical spectral optimization problem in linear elasticity

We consider a classical shape optimization problem for the eigenvalues of elliptic operators with homogeneous boundary conditions on domains in the $N$-dimensional Euclidean space. We survey recent results concerning the analytic dependence of the elementary symmetric functions of the eigenvalues upon domain perturbation and the role of balls as critical points of such functions subject to volume constraint. Our discussion concerns Dirichlet and buckling-type problems for polyharmonic operators, the Neumann and the intermediate problems for the biharmonic operator, the Lam\'{e} and the Reissner-Mindlin systems.Comment: To appear in the proceedings of the workshop `New Trends in Shape Optimization', Friedrich-Alexander Universit\"{a}t Erlangen-Nuremberg, 23-27 September 201

Analyticity and criticality results for the eigenvalues of the biharmonic operator

We consider the eigenvalues of the biharmonic operator subject to several homogeneous boundary conditions (Dirichlet, Neumann, Navier, Steklov). We show that simple eigenvalues and elementary symmetric functions of multiple eigenvalues are real analytic, and provide Hadamard-type formulas for the corresponding shape derivatives. After recalling the known results in shape optimization, we prove that balls are always critical domains under volume constraint.Comment: To appear on the proceedings of the conference "Geometric Properties for Parabolic and Elliptic PDE's - 4th Italian-Japanese Workshop" held in Palinuro (Italy), May 25-29, 201

Approximation of the critical buckling factor for composite panels

This article is concerned with the approximation of the critical buckling factor for thin composite plates. A new method to improve the approximation of this critical factor is applied based on its behavior with respect to lamination parameters and loading conditions. This method allows accurate approximation of the critical buckling factor for non-orthotropic laminates under complex combined loadings (including shear loading). The influence of the stacking sequence and loading conditions is extensively studied as well as properties of the critical buckling factor behavior (e.g concavity over tensor D or out-of-plane lamination parameters). Moreover, the critical buckling factor is numerically shown to be piecewise linear for orthotropic laminates under combined loading whenever shear remains low and it is also shown to be piecewise continuous in the general case. Based on the numerically observed behavior, a new scheme for the approximation is applied that separates each buckling mode and builds linear, polynomial or rational regressions for each mode. Results of this approach and applications to structural optimization are presented

A Survey on the Krein-von Neumann Extension, the corresponding Abstract Buckling Problem, and Weyl-Type Spectral Asymptotics for Perturbed Krein Laplacians in Nonsmooth Domains

In the first (and abstract) part of this survey we prove the unitary equivalence of the inverse of the Krein--von Neumann extension (on the orthogonal complement of its kernel) of a densely defined, closed, strictly positive operator, $S\geq \varepsilon I_{\mathcal{H}}$ for some $\varepsilon >0$ in a Hilbert space $\mathcal{H}$ to an abstract buckling problem operator. This establishes the Krein extension as a natural object in elasticity theory (in analogy to the Friedrichs extension, which found natural applications in quantum mechanics, elasticity, etc.). In the second, and principal part of this survey, we study spectral properties for $H_{K,\Omega}$, the Krein--von Neumann extension of the perturbed Laplacian $-\Delta+V$ (in short, the perturbed Krein Laplacian) defined on $C^\infty_0(\Omega)$, where $V$ is measurable, bounded and nonnegative, in a bounded open set $\Omega\subset\mathbb{R}^n$ belonging to a class of nonsmooth domains which contains all convex domains, along with all domains of class $C^{1,r}$, $r>1/2$.Comment: 68 pages. arXiv admin note: extreme text overlap with arXiv:0907.144

A Naturally Occurring Mutation in ropB Suppresses SpeB Expression and Reduces M1T1 Group A Streptococcal Systemic Virulence

Epidemiological studies of group A streptococcus (GAS) have noted an inverse relationship between SpeB expression and invasive disease. However, the role of SpeB in the course of infection is still unclear. In this study we utilize a SpeB-negative M1T1 clinical isolate, 5628, with a naturally occurring mutation in the gene encoding the regulator RopB, to elucidate the role of RopB and SpeB in systemic virulence. Allelic exchange mutagenesis was used to replace the mutated ropB allele in 5628 with the intact allele from the well characterized isolate 5448. The inverse allelic exchange was also performed to replace the intact ropB in 5448 with the mutated allele from 5628. An intact ropB was found to be essential for SpeB expression. While the ropB mutation was shown to have no effect on hemolysis of RBC's, extracellular DNase activity or survival in the presence of neutrophils, strains with the mutated ropB allele were less virulent in murine systemic models of infection. An isogenic SpeB knockout strain containing an intact RopB showed similarly reduced virulence. Microarray analysis found genes of the SpeB operon to be the primary target of RopB regulation. These data show that an intact RopB and efficient SpeB production are necessary for systemic infection with GAS

Polycation-π Interactions Are a Driving Force for Molecular Recognition by an Intrinsically Disordered Oncoprotein Family

Molecular recognition by intrinsically disordered proteins (IDPs) commonly involves specific localized contacts and target-induced disorder to order transitions. However, some IDPs remain disordered in the bound state, a phenomenon coined "fuzziness", often characterized by IDP polyvalency, sequence-insensitivity and a dynamic ensemble of disordered bound-state conformations. Besides the above general features, specific biophysical models for fuzzy interactions are mostly lacking. The transcriptional activation domain of the Ewing's Sarcoma oncoprotein family (EAD) is an IDP that exhibits many features of fuzziness, with multiple EAD aromatic side chains driving molecular recognition. Considering the prevalent role of cation-π interactions at various protein-protein interfaces, we hypothesized that EAD-target binding involves polycation- π contacts between a disordered EAD and basic residues on the target. Herein we evaluated the polycation-π hypothesis via functional and theoretical interrogation of EAD variants. The experimental effects of a range of EAD sequence variations, including aromatic number, aromatic density and charge perturbations, all support the cation-π model. Moreover, the activity trends observed are well captured by a coarse-grained EAD chain model and a corresponding analytical model based on interaction between EAD aromatics and surface cations of a generic globular target. EAD-target binding, in the context of pathological Ewing's Sarcoma oncoproteins, is thus seen to be driven by a balance between EAD conformational entropy and favorable EAD-target cation-π contacts. Such a highly versatile mode of molecular recognition offers a general conceptual framework for promiscuous target recognition by polyvalent IDPs. © 2013 Song et al

Echinocandin Treatment of Pneumocystis Pneumonia in Rodent Models Depletes Cysts Leaving Trophic Burdens That Cannot Transmit the Infection

Fungi in the genus Pneumocystis cause pneumonia (PCP) in hosts with debilitated immune systems and are emerging as co-morbidity factors associated with chronic diseases such as COPD. Limited therapeutic choices and poor understanding of the life cycle are a result of the inability of these fungi to grow outside the mammalian lung. Within the alveolar lumen, Pneumocystis spp., appear to have a bi-phasic life cycle consisting of an asexual phase characterized by binary fission of trophic forms and a sexual cycle resulting in formation of cysts, but the life cycle stage that transmits the infection is not known. The cysts, but not the trophic forms, express β -1,3-D-glucan synthetase and contain abundant β -1,3-D-glucan. Here we show that therapeutic and prophylactic treatment of PCP with echinocandins, compounds which inhibit the synthesis of β -1,3-D-glucan, depleted cysts in rodent models of PCP, while sparing the trophic forms which remained in significant numbers. Survival was enhanced in the echincandin treated mice, likely due to the decreased β -1,3-D-glucan content in the lungs of treated mice and rats which coincided with reductions of cyst numbers, and dramatic remodeling of organism morphology. Strong evidence for the cyst as the agent of transmission was provided by the failure of anidulafungin-treated mice to transmit the infection. We show for the first time that withdrawal of anidulafungin treatment with continued immunosuppression permitted the repopulation of cyst forms. Treatment of PCP with an echinocandin alone will not likely result in eradication of infection and cessation of echinocandin treatment while the patient remains immunosuppressed could result in relapse. Importantly, the echinocandins provide novel and powerful chemical tools to probe the still poorly understood bi-phasic life cycle of this genus of fungal pathogens

Five insights from the Global Burden of Disease Study 2019

The Global Burden of Diseases, Injuries, and Risk Factors Study (GBD) 2019 provides a rules-based synthesis of the available evidence on levels and trends in health outcomes, a diverse set of risk factors, and health system responses. GBD 2019 covered 204 countries and territories, as well as first administrative level disaggregations for 22 countries, from 1990 to 2019. Because GBD is highly standardised and comprehensive, spanning both fatal and non-fatal outcomes, and uses a mutually exclusive and collectively exhaustive list of hierarchical disease and injury causes, the study provides a powerful basis for detailed and broad insights on global health trends and emerging challenges. GBD 2019 incorporates data from 281 586 sources and provides more than 3.5 billion estimates of health outcome and health system measures of interest for global, national, and subnational policy dialogue. All GBD estimates are publicly available and adhere to the Guidelines on Accurate and Transparent Health Estimate Reporting. From this vast amount of information, five key insights that are important for health, social, and economic development strategies have been distilled. These insights are subject to the many limitations outlined in each of the component GBD capstone papers.Peer reviewe