Order reduction approaches for the algebraic Riccati equation and the LQR problem

We explore order reduction techniques for solving the algebraic Riccati equation (ARE), and investigating the numerical solution of the linear-quadratic regulator problem (LQR). A classical approach is to build a surrogate low dimensional model of the dynamical system, for instance by means of balanced truncation, and then solve the corresponding ARE. Alternatively, iterative methods can be used to directly solve the ARE and use its approximate solution to estimate quantities associated with the LQR. We propose a class of Petrov-Galerkin strategies that simultaneously reduce the dynamical system while approximately solving the ARE by projection. This methodology significantly generalizes a recently developed Galerkin method by using a pair of projection spaces, as it is often done in model order reduction of dynamical systems. Numerical experiments illustrate the advantages of the new class of methods over classical approaches when dealing with large matrices

Thinking ahead of disasters: the role of risk regulation in the European Union

The need to reduce the vulnerability of society against disasters has fostered the introduction of regulatory instruments which can anticipate protection before a danger is imminent and an emergency phase starts. Disaster risk regulation has therefore become a significant field of legislation aimed at complementing and supporting disaster relief measures through precautionary action. It however represents a specific issue of disaster management: given the low probability of high impact disasters, it is difficult to assess related risks, so their regulation involves balancing different rights and interests at stake with uncertain scenarios. The need to rationalise such precautionary protection requires regulatory instruments that take into account the very nature of disaster risks (low probability, high impact) as well as other competing situations of rights and interests which can be affected by regulatory measures. Moreover, in view of the aim of reducing vulnerability, disaster-related policies aim at achieving resilience against disasters. Being resilient means having the abilities to resist, adapt to stressful changes and to bounce back to the original structure. In a resilience-oriented context, what disaster risk mitigation should do is to facilitate the process of adaptation under stress by anticipating impact scenarios and the instruments of protection. This article examines the European Union\u2019s (EU) approach to the regulation of risks of potential catastrophic impact by framing it in the context of resilience. In so doing, it argues that this approach is shaped by the multilevel interdependencies that exist between the EU, national administrations, and private parties. These relationships, which govern the functioning of the EU legal order itself, impact on how protection against disaster is designed, shape the nature of regulation and create a number of challenges for regulators. The modes which disaster risk regulation follows in the EU are therefore analysed as a key issue for enhancing the understanding of this complex regulatory approach

On Convergence of the Inexact Rayleigh Quotient Iteration with the Lanczos Method Used for Solving Linear Systems

For the Hermitian inexact Rayleigh quotient iteration (RQI), the author has established new local general convergence results, independent of iterative solvers for inner linear systems. The theory shows that the method locally converges quadratically under a new condition, called the uniform positiveness condition. In this paper we first consider the local convergence of the inexact RQI with the unpreconditioned Lanczos method for the linear systems. Some attractive properties are derived for the residuals, whose norms are $\xi_{k+1}$'s, of the linear systems obtained by the Lanczos method. Based on them and the new general convergence results, we make a refined analysis and establish new local convergence results. It is proved that the inexact RQI with Lanczos converges quadratically provided that $\xi_{k+1}\leq\xi$ with a constant $\xi\geq 1$. The method is guaranteed to converge linearly provided that $\xi_{k+1}$ is bounded by a small multiple of the reciprocal of the residual norm $\|r_k\|$ of the current approximate eigenpair. The results are fundamentally different from the existing convergence results that always require $\xi_{k+1}<1$, and they have a strong impact on effective implementations of the method. We extend the new theory to the inexact RQI with a tuned preconditioned Lanczos for the linear systems. Based on the new theory, we can design practical criteria to control $\xi_{k+1}$ to achieve quadratic convergence and implement the method more effectively than ever before. Numerical experiments confirm our theory.Comment: 20 pages, 8 figures. arXiv admin note: text overlap with arXiv:0906.223

Measuring societal awareness of the rural agrarian landscape: indicators and scale issues

The work presented in this report is part of the effort to define the landscape state and diversity indicator in the frame of COM (2006) 508 “Development of agri-environmental indicators for monitoring the integration of environmental concerns into the common agricultural policy”. The Communication classifies the indicators according to their level of development, which, for the landscape indicator is “in need of substantial improvements in order to become fully operational”. For this reason a full re-definition of the indicator has been carried out, following the initial proposal presented in the frame of the IRENA operation (“Indicator Reporting on the Integration of Environmental Concerns into Agricultural Policy”). The new proposal for the landscape state and diversity indicator is structured in three components: the first concerns the degree of naturalness, the second landscape structure, the third the societal appreciation of the rural landscape. While the first two components rely on a strong bulk of existing literature, the development of the methodology has made evident the need for further analysis of the third component, which is based on a newly proposed top-down approach. This report presents an in-depth analysis of such component of the indicator, and the effort to include a social dimension in large scale landscape assessment

Dexamethasone-Induced Expression of Endothelial Mitogen-Activated Protein Kinase Phosphatase-1 Involves Activation of the Transcription Factors Activator Protein-1 and 3',5'-Cyclic Adenosine 5'-Monophosphate Response Element-Binding Protein and the Generation of Reactive Oxygen Species

We have recently identified the MAPK phosphatase (MKP)-1 as a novel mediator of the antiinflammatory properties of glucocorticoids (dexamethasone) in the human endothelium. However, nothing is as yet known about the signaling pathways responsible for the up-regulation of MKP-1 by dexamethasone in endothelial cells. Knowledge of the molecular basis of this new alternative way of glucocorticoid action could facilitate the identification of new antiinflammatory drug targets. Thus, the aim of our study was to elucidate the underlying molecular mechanisms. Using Western blot analysis, we found that dexamethasone rapidly activates ERK, c-jun Nterminal kinase (JNK), and p38 MAPK in human umbilical vein endothelial cells. By applying the kinase inhibitors PD98059 (MAPK kinase-1) and SP600125 (JNK), ERK and JNK were shown to be crucial for the induction of MKP-1. Using EMSA and a decoy oligonucleotide approach, the transcription factors activator protein-1 (activated by ERK and JNK) and cAMP response element-binding protein (activated by ERK) were found to be involved in the up-regulation of MKP-1 by dexamethasone. Interestingly, dexamethasone induces the generation of reactive oxygen species (measured by dihydrofluorescein assay), which participate in the signaling process by triggering JNK activation. Our work elucidates a novel alternative mechanism for transducing antiinflammatory effects of glucocorticoids in the human endothelium. Thus, our study adds valuable information to the efforts made to find new antiinflammatory principles utilized by glucocorticoids. This might help to gain new therapeutic options to limit glucocorticoid side effects and to overcome resistance

A Knot Not to Be Cut? The Legacy of Brexit over the CJEU

What was the role of the Court of Justice of the European Union (CJEU) in the Brexit saga? And what will the impact of Brexit be over the future structure and activity of the CJEU? This article deals with this twofold question and explores three different issues. Firstly, we will offer a reflection on the questions and the risks raised by the Wightman case, where the CJEU ruled on the unilateral revocation of the UK notification of its intention to withdraw from the European Union under Art. 50 Treaty of the EU. Secondly, we will analyse the impact of Brexit on the composition of the CJEU and, particularly, the risks for the independence of the Court raised by the advanced termination of the mandate of the British Advocate General. Thirdly, we will provide some insights on the scope of the jurisdiction of the CJEU in the post-Brexit Union, emphasising how the Withdrawal Agreement maintained its jurisdiction during and even beyond the transition period. This article reflects the events that took place up to 6 October 2020

Wightman and the perils of Britain's withdrawal

On 10 December 2018, the Court of Justice (CJEU) delivered the Wightman judgment and recognized the unilateral revocability of the notification ex Art. 50 Treaty on European Union (TEU). This article offers a critical analysis of the decision by insisting above all on the national background of the ruling and the political risks stemming from the decision. The article is structured as follows. Firstly, it analyses the legal questions of the Scottish case, which constituted the ground for the admissibility of the preliminary ruling and showed the perils for the exercise of national sovereign rights embedded in the lack of clarity on revocation options. It thus reconstructs the critical aspects of the preliminary ruling of the CJEU. Subsequently, the article examines the implications of the ruling for the EU legal order. On the one hand, the analysis considers the conception of the EU membership by comparing the approach of the CJEU and that of Advocate General Campos Sánchez Bordona in Wightman

Mellowing Meroni: how ESMA can help build the single market

On January 22nd, the Court of Justice of the European Union (CJEU) gave its longawaited opinion in the case concerning the European Securities and Markets Authority (ESMA).1 The ruling is important in order to appreciate the modern understanding of the Meroni non-delegation doctrine. It is not the purpose of this CEPS Commentary to provide a fully-fledged analysis of the ESMA ruling,2 but rather to extract the potential implications of the ESMA case for the place and significance of the Meroni doctrine in building up the single market. We aim to demonstrate that the ESMA case is yet another manifestation of a slow process of \u201cmellowing Meroni\u2019. This is a critical condition for a new single market strategy aiming to end the remaining fragmentation of the single market \u2013 not only in financial markets but also in network industries \u2013 and ensure its \u2018proper functioning\u2019

The nuclear receptors of Biomphalaria glabrata and Lottia gigantea: Implications for developing new model organisms

© 2015 Kaur et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are creditedNuclear receptors (NRs) are transcription regulators involved in an array of diverse physiological functions including key roles in endocrine and metabolic function. The aim of this study was to identify nuclear receptors in the fully sequenced genome of the gastropod snail, Biomphalaria glabrata, intermediate host for Schistosoma mansoni and compare these to known vertebrate NRs, with a view to assessing the snail's potential as a invertebrate model organism for endocrine function, both as a prospective new test organism and to elucidate the fundamental genetic and mechanistic causes of disease. For comparative purposes, the genome of a second gastropod, the owl limpet, Lottia gigantea was also investigated for nuclear receptors. Thirty-nine and thirty-three putative NRs were identified from the B. glabrata and L. gigantea genomes respectively, based on the presence of a conserved DNA-binding domain and/or ligand-binding domain. Nuclear receptor transcript expression was confirmed and sequences were subjected to a comparative phylogenetic analysis, which demonstrated that these molluscs have representatives of all the major NR subfamilies (1-6). Many of the identified NRs are conserved between vertebrates and invertebrates, however differences exist, most notably, the absence of receptors of Group 3C, which includes some of the vertebrate endocrine hormone targets. The mollusc genomes also contain NR homologues that are present in insects and nematodes but not in vertebrates, such as Group 1J (HR48/DAF12/HR96). The identification of many shared receptors between humans and molluscs indicates the potential for molluscs as model organisms; however the absence of several steroid hormone receptors indicates snail endocrine systems are fundamentally different.The National Centre for the Replacement, Refinement and Reduction of Animals in Research, Grant Ref:G0900802 to CSJ, LRN, SJ & EJR [www.nc3rs.org.uk]

Differential efficacy of three cycles of CMF followed by tamoxifen in patients with ER-positive and ER-negative tumors: Long-term follow up on IBCSG Trial IX

Background: The benefit of adjuvant chemotherapy in postmenopausal patients with estrogen receptor (ER)-positive lymph node-negative breast cancer is being reassessed. Patients and methods: After stratification by ER status, 1669 postmenopausal patients with operable lymph node-negative breast cancer were randomly assigned to three 28-day courses of ‘classical' CMF (cyclophosphamide, methotrexate, 5-fluorouracil) chemotherapy followed by tamoxifen for 57 months (CMF→tamoxifen) or to tamoxifen alone for 5 years. Results: ERs were positive in 81% of tumors. At a median follow-up of 13.1 years, patients with ER-positive breast cancers did not benefit from CMF [13-year disease-free survival (DFS) 64% CMF→tamoxifen, 66% tamoxifen; P = 0.99], whereas CMF substantially improved the prognosis of patients with ER-negative breast cancer (13-year DFS 73% versus 57%, P = 0.001). Similarly, breast cancer-free interval (BCFI) was identical in the ER-positive cohort but significantly improved by chemotherapy in the ER-negative cohort (13-year BCFI 80% versus 63%, P = 0.001). CMF had no influence on second nonbreast malignancies or deaths from other causes. Conclusion: CMF is not beneficial in postmenopausal patients with node-negative ER-positive breast cancer but is highly effective within the ER-negative cohort. In the future, other markers of chemotherapy response may define a subset of patients with ER-positive tumors who may benefit from adjuvant chemotherap