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

An ultraweak space-Time variational formulation for the wave equation: Analysis and efficient numerical solution

We introduce an ultraweak space-time variational formulation for the wave equation, prove its well-posedness (even in the case of minimal regularity) and optimal inf-sup stability. Then, we introduce a tensor product-style space-time Petrov–Galerkin discretization with optimal discrete inf-sup stability, obtained by a non-standard definition of the trial space. As a consequence, the numerical approximation error is equal to the residual, which is particularly useful for a posteriori error estimation. For the arising discrete linear systems in space and time, we introduce efficient numerical solvers that appropriately exploit the equation structure, either at the preconditioning level or in the approximation phase by using a tailored Galerkin projection. This Galerkin method shows competitive behavior concerning wall-clock time, accuracy and memory as compared with a standard time-stepping method in particular in low regularity cases. Numerical experiments with a 3D (in space) wave equation illustrate our findings

Hydrogen Energy Storage: New Techno-Economic Emergence Solution Analysis

International audienceThe integration of various renewable energy sources as well as the liberalization of electricity markets are established facts in modern electrical power systems. The increased share of renewable sources within power systems intensifies the supply variability and intermittency. Therefore, energy storage is deemed as one of the solutions for stabilizing the supply of electricity to maintain generation-demand balance and to guarantee uninterrupted supply of energy to users. In the context of sustainable development and energy resources depletion, the question of the growth of renewable energy electricity production is highly linked to the ability to propose new and adapted energy storage solutions. The purpose of this multidisciplinary paper is to highlight the new hydrogen production and storage technology, its efficiency and the impact of the policy context on its development. A comprehensive techno/socio/economic study of long term hydrogen based storage systems in electrical networks is addressed. The European policy concerning the different energy storage systems and hydrogen production is explicitly discussed. The state of the art of the techno-economic features of the hydrogen production and storage is introduced. Using Matlab-Simulink for a power system of rated 70 kW generator, the excess produced hydrogen during high generation periods or low demand can be sold either directly to the grid owners or as filled hydrogen bottles. The affordable use of Hydrogen-based technologies for long term electricity storage is verified

Identifying breast cancer patients at risk for Central Nervous System (CNS) metastases in trials of the International Breast Cancer Study Group (IBCSG)

Background: We sought to determine whether a high-risk group could be defined among patients with operable breast cancer in whom a search of occult central nervous system (CNS) metastases was justified. Patients and methods: We evaluated data from 9524 women with early breast cancer (42% node-negative) who were randomized in International Breast Cancer Study Group clinical trials between 1978 and 1999, and treated without anthracyclines, taxanes, or trastuzumab. We identified patients whose site of first event was CNS and those who had a CNS event at any time. Results: Median follow-up was 13 years. The 10-year incidence (10-yr) of CNS relapse was 5.2% (1.3% as first recurrence). Factors predictive of CNS as first recurrence included: node-positive disease (10-yr = 2.2% for > 3 N+), estrogen receptor-negative (2.3%), tumor size > 2 cm (1.7%), tumor grade 3 (2.0%), < 35 years old (2.2%), HER2-positive (2.7%), and estrogen receptor-negative and node-positive (2.6%). The risk of subsequent CNS recurrence was elevated in patients experiencing lung metastases (10-yr = 16.4%). Conclusion: Based on this large cohort we were able to define risk factors for CNS metastases, but could not define a group at sufficient risk to justify routine screening for occult CNS metastase

Menstrual cycle and timing of breast surgery in premenopausal node-positive breast cancer: Results of the International Breast Cancer Study Group (IBCSG) Trial VI

Purpose It has been postulated that breast cancer surgery performed during the follicular phase of the menstrual cycle is associated with poorer outcome. Patients and methods We tested this hypothesis by evaluating disease-free survival (DFS) for 1033 premenopausal patients who received definitive surgery either during the follicular phase (n = 358) or the luteal phase (n = 675). All patients were enrolled in a randomized trial conducted between July 1986 and April 1993. All had node positive breast cancer and randomization was stratified by estrogen receptor (ER) status. AU patients received at least three cycles of adjuvant cyclophosphamide, methotrexate, and 5-fluorouracil (CMF). The median follow-up was 60 months. Results Patients who underwent definitive surgery for breast cancer in the follicular phase had a slightly worse disease-free survival than those operated on during the luteal phase (five-year DFS percentage: 53% versus 58%; hazard ratio, 1.13; 95% confidence interval (CI), 0.94-1.38; P = 0.20). The effect was significantly greater for the subpopulation of 300 patients with ER-negative primaries (P = 0.02 interaction effect; five-year DFS percentages 42% vs. 59%; hazard ratio 1.60; 95% CI, 1.12-2.25; P 0.008). The effect of timing of surgery diminished for analyses based on lesser surgical procedures, e.g., excisional biopsies. In particular, no effect of timing was observed for fine needle aspiration procedures. Conclusion Surgical procedures which are more extensive than a fine needle aspiration biopsy might be associated with worse prognosis if conducted during the follicular phase of the menstrual cycle. This phenomenon was seen predominantly for high risk breast cancer with low levels or no estrogen receptors in the primary tumo

Thermodynamics, Disequilibrium, Evolution: Far-From-Equilibrium Geological and Chemical Considerations for Origin-Of-Life Research

The authors wish to thank the Earth-Life Science Institute of the Tokyo Institute of Technology for supporting and hosting the TDE Focus Group meeting on which this publication is based. The Thermodynamics, Disequilibrium, Evolution (TDE) Focus Group is supported by the NASA Astrobiology Institute (NAI). Parts of this work were carried out at the Jet Propulsion Laboratory, California Institute of Technology under a contract with the National Aeronautics and Space Administration; LMB and MJR are supported by NAI (Icy Worlds). ES thanks the ORIGINS COST Action (TD1308) for the STSM Reference Number: COST-STSM-TD1308-26973. ES is supported by Agreement ASI/INAF 2015 - 002 - R.O. JHEC acknowledges the financial support of the Spanish MINCINN project FIS2013-48444-C2-2-P

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

Extracapsular tumor spread and the risk of local, axillary and supraclavicular recurrence in node-positive, premenopausal patients with breast cancer

Background: Extracapsular tumor spread (ECS) has been identified as a possible risk factor for breast cancer recurrence, but controversy exists regarding its role in decision making for regional radiotherapy. This study evaluates ECS as a predictor of local, axillary, and supraclavicular recurrence. Patients and methods: International Breast Cancer Study Group Trial VI accrued 1475 eligible pre- and perimenopausal women with node-positive breast cancer who were randomly assigned to receive three to nine courses of classical combination chemotherapy with cyclophosphamide, methotrexate, and fluorouracil. ECS status was determined retrospectively in 933 patients based on review of pathology reports. Cumulative incidence and hazard ratios (HRs) were estimated using methods for competing risks analysis. Adjustment factors included treatment group and baseline patient and tumor characteristics. The median follow-up was 14 years. Results: In univariable analysis, ECS was significantly associated with supraclavicular recurrence (HR = 1.96; 95% confidence interval 1.23-3.13; P = 0.005). HRs for local and axillary recurrence were 1.38 (P = 0.06) and 1.81 (P = 0.11), respectively. Following adjustment for number of lymph node metastases and other baseline prognostic factors, ECS was not significantly associated with any of the three recurrence types studied. Conclusions: Our results indicate that the decision for additional regional radiotherapy should not be based solely on the presence of EC

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]