Blow-up phenomena for linearly perturbed Yamabe problem on manifolds with umbilic boundary

We build blowing-up solutions for linear perturbation of the Yamabe problem on manifolds with umbilic boundary, provided the Weyl tensor is nonzero everywhere on the boundary and the dimension of the manifold is n>10

The role of the scalar curvature in some singularly perturbed coupled elliptic systems on Riemannian manifolds

Given a 3-dimensional Riemannian manifold (M,g), we investigate the existence of positive solutions of singularly perturbed Klein-Gordon-Maxwell systems and Schroedinger-Maxwell systems on M, with a subcritical nonlinearity. We prove that when the perturbation parameter epsilon is small enough, any stable critical point x_0 of the scalar curvature of the manifold (M,g) generates a positive solution (u_eps,v_eps) to both the systems such that u_eps concentrates at xi_0 as epsilon goes to zero

On Yamabe type problems on Riemannian manifolds with boundary

Let $(M,g)$ be a $n-$dimensional compact Riemannian manifold with boundary. We consider the Yamabe type problem \begin{equation} \left\{ \begin{array}{ll} -\Delta_{g}u+au=0 & \text{ on }M \\ \partial_\nu u+\frac{n-2}{2}bu= u^{{n\over n-2}\pm\varepsilon} & \text{ on }\partial M \end{array}\right. \end{equation} where $a\in C^1(M),$ $b\in C^1(\partial M)$, $\nu$ is the outward pointing unit normal to $\partial M$ and $\varepsilon$ is a small positive parameter. We build solutions which blow-up at a point of the boundary as $\varepsilon$ goes to zero. The blowing-up behavior is ruled by the function $b-H_g ,$ where $H_g$ is the boundary mean curvature

QAOA with N⋅p≥200N\cdot p\geq 200

One of the central goals of the DARPA Optimization with Noisy Intermediate-Scale Quantum (ONISQ) program is to implement a hybrid quantum/classical optimization algorithm with high $N\cdot p$, where $N$ is the number of qubits and $p$ is the number of alternating applications of parameterized quantum operators in the protocol. In this note, we demonstrate the execution of the Quantum Approximate Optimization Algorithm (QAOA) applied to the MaxCut problem on non-planar 3-regular graphs with $N\cdot p$ of up to $320$ on the Quantinuum H1-1 and H2 trapped-ion quantum processors. To the best of our knowledge, this is the highest $N\cdot p$ demonstrated on hardware to date. Our demonstration highlights the rapid progress of quantum hardware.Comment: Experiments on H2 processor with $N\cdot p = 320$ added in v

Access-rights Analysis in the Presence of Subjects

Modern software development and run-time environments, such as Java and the Microsoft .NET Common Language Runtime (CLR), have adopted a declarative form of access control. Permissions are granted to code providers, and during execution, the platform verifies compatibility between the permissions required by a security-sensitive operation and those granted to the executing code. While convenient, configuring the access-control policy of a program is not easy. If a code component is not granted sufficient permissions, authorization failures may occur. Thus, security administrators tend to define overly permissive policies, which violate the Principle of Least Privilege (PLP). A considerable body of research has been devoted to building program-analysis tools for computing the optimal policy for a program. However, Java and the CLR also allow executing code under the authority of a subject (user or service), and no program-analysis solution has addressed the challenges of determining the policy of a program in the presence of subjects. This paper introduces Subject Access Rights Analysis (SARA), a novel analysis algorithm for statically computing the permissions required by subjects at run time. We have applied SARA to 348 libraries in IBM WebSphere Application Server - a commercial enterprise application server written in Java that consists of >2 million lines of code and is required to support the Java permission- and subject-based security model. SARA detected 263 PLP violations, 219 cases of policies with missing permissions, and 29 bugs that led code to be unnecessarily executed under the authority of a subject. SARA corrected all these vulnerabilities automatically, and additionally synthesized fresh policies for all the libraries, with a false-positive rate of 5% and an average running time of 103 seconds per library. SARA also implements mechanisms for mitigating the risk of false negatives due to reflection and native code; according to a thorough result evaluation based on testing, no false negative was detected. SARA enabled IBM WebSphere Application Server to receive the Common Criteria for Information Technology Security Evaluation Assurance Level 4 certification

Not proper ROC curves as new tool for the analysis of differentially expressed genes in microarray experiments

<p>Abstract</p> <p>Background</p> <p>Most microarray experiments are carried out with the purpose of identifying genes whose expression varies in relation with specific conditions or in response to environmental stimuli. In such studies, genes showing similar mean expression values between two or more groups are considered as not differentially expressed, even if hidden subclasses with different expression values may exist. In this paper we propose a new method for identifying differentially expressed genes, based on the area between the ROC curve and the rising diagonal (<it>ABCR</it>). <it>ABCR </it>represents a more general approach than the standard area under the ROC curve (<it>AUC</it>), because it can identify both proper (<it>i.e.</it>, concave) and not proper ROC curves (NPRC). In particular, NPRC may correspond to those genes that tend to escape standard selection methods.</p> <p>Results</p> <p>We assessed the performance of our method using data from a publicly available database of 4026 genes, including 14 normal B cell samples (NBC) and 20 heterogeneous lymphomas (namely: 9 follicular lymphomas and 11 chronic lymphocytic leukemias). Moreover, NBC also included two sub-classes, <it>i.e.</it>, 6 heavily stimulated and 8 slightly or not stimulated samples. We identified 1607 differentially expressed genes with an estimated False Discovery Rate of 15%. Among them, 16 corresponded to NPRC and all escaped standard selection procedures based on <it>AUC </it>and <it>t </it>statistics. Moreover, a simple inspection to the shape of such plots allowed to identify the two subclasses in either one class in 13 cases (81%).</p> <p>Conclusion</p> <p>NPRC represent a new useful tool for the analysis of microarray data.</p

L’infinito intrattenimento. Dickens dalla pagina alle illustrazioni, agli schermi del “primo” cinema

The knowledge and the fortune of Charles Dickens’s works are also due to the beautiful illustrations of his short and long novels. The illustrations – painted by Cruikshank, Phiz, Leech – were reproduced as slides for the Magic Lantern. But, since the beginning of the Twentieth Century, cinema was the main medium of Dickens’ s fortune all over the world. This study tries to connect the several passages from one form – for instance the book illustrations – to another – the slides for the Magic Lantern, up to the cinematographic frames. The analysis of some interesting films of the silent era and – especially – of the beginning of cinema and their relationships with the diversified ‘world’ of other images, is the focus of this study