Geometric characterizations for strong minima with applications to nuclear norm minimization problems

In this paper, we introduce several geometric characterizations for strong minima of optimization problems. Applying these results to nuclear norm minimization problems allows us to obtain new necessary and sufficient quantitative conditions for this important property. Our characterizations for strong minima are weaker than the Restricted Injectivity and Nondegenerate Source Condition, which are usually used to identify solution uniqueness of nuclear norm minimization problems. Consequently, we obtain the minimum (tight) bound on the number of measurements for (strong) exact recovery of low-rank matrices.Comment: 41 page

How to select the right cost-effectiveness model?

Objective: In the current study, we propose an approach for selection of a model that is transferable to a specific decision-making context (in this case, the Netherlands), using the case of rheumatoid arthritis (RA). The objectives of this study were (a) to perform a systematic literature review to identify existing health economic evaluation models for economic evaluation of disease-modifying antirheumatic drugs (DMARDs) in RA; and (b) to test the appropriateness of a stepwise model-selection process. Methods: First, we searched Medline and Embase to identify relevant studies in the English language, published between 1 January 2002 and 31 August 2012. From the included studies, all unique models were identified. Second, we applied a multi-step approach to model selection. Models that did not meet all minimal methodological and structural requirements based on the Outcome Measures in Rheumatology (OMERACT) criteria were excluded. Next, models were assessed on the basis of their fit when transferred to the Dutch health care setting. The criteria for model fit were transferability factors, as published by Welte et al., after exclusion of those that were deemed transferable by simple adaptation. Finally, the remaining models underwent a general quality check using the Philips checklist. Models showing good fit and high quality were considered to be transferable to the Dutch health care setting, using simple adaptation. Results: The systematic literature search identified 498 articles, which included 33 unique health economic evaluation models. O

ADI method based on C2-continuous two-node integrated-RBF elements for viscous flows

We propose a C2-continuous alternating direction implicit (ADI) method for the solution of the streamfunction-vorticity equations governing steady 2D incompressible viscous fluid flows. Discretisation is simply achieved with Cartesian grids. Local two-node integrated radial basis function elements (IRBFEs) [D.-A. An-Vo, N. Mai-Duy, T. Tran-Cong, A C2-continuous control-volume technique based on Cartesian grids and two-node integrated-RBF elements for second-order elliptic problems, CMES: Computer Modeling in Engineering & Sciences 72 (2011) 299-334] are used for the discretisation of the diffusion terms, and then the convection terms are incorporated into system matrices by treating nodal derivatives as unknowns. ADI procedure is applied for the time integration. Following ADI factorisation, the two-dimensional problem becomes a sequence of one-dimensional problems. The solution strategy consists of multiple use of a one-dimensional sparse matrix algorithm that helps saving the computational cost. High levels of accuracy and efficiency of the present methods are demonstrated with solutions of several benchmark problems defined on rectangular and non-rectangular domains

Development of a life expectancy table for individuals with type 1 diabetes

Aims/hypothesis:Tables reporting life expectancies by common risk factors are available for individuals with type 2 diabetes; however, there is currently no published equivalent for individuals with type 1 diabetes. We aimed to develop a life expectancy table using a recently published simulation model for individuals with type 1 diabetes.Methods: The simulation model was developed using data from a real-world population of patients with type 1 diabetes selected from the Swedish National Diabetes Register. The following six important risk factors were included in the life table: sex; age; current smoking status; BMI; eGFR; and HbA1c. For each of 1024 cells in the life expectancy table, a synthetic cohort containing 1000 individuals was created, with other risk factors assigned values representative of the real-world population. The simulations were executed for all synthetic cohorts and life expectancy for each cell was calculated as mean survival time of the individuals in the respective cohort.Results: There was a substantial variation in life expectancy across patients with different risk factor levels. Life expectancy of 20-year-old men varied from 29.3 years to 50.6 years, constituting a gap of 21.3 years between those with worst and best risk factor levels. In 20-year-old women, this gap was 18.9 years (life expectancy range 35.0-53.9 years). The variation in life expectancy was a function of the combination of risk factor values, with HbA1c and eGFR consistently showing a negative and positive correlation, respectively, with life expectancy at any level combination of other risk factors. Individuals with the lowest level (20 kg/m2) and highest level of BMI (35 kg/m2) had a lower life expectancy compared with those with a BMI of 25 kg/m2. Non-smokers and women had a higher life expectancy than smokers and men, respectively, with the difference in life expectancy ranging from 0.4 years to 2.7 years between non-smokers and smokers, and from 1.9 years to 5.9 years between women and men, depending on levels of other risk factors.Conclusions/interpretation: The life expectancy table generated in this study shows a substantial variation in life expectancy across individuals with different modifiable risk factors. The table allows for rapid communications of risk in an easily understood format between healthcare professionals, health economists, researchers, policy makers and patients. Particularly, it supports clinicians in their discussion with patients about the benefits of improving risk factors

Isolation and selection of Bacillus strains with high potential probiotic that used in catfish farming (Pangasianodon hypophthalmus)

In this study, we isolated 28 strains of Bacillus spp. from water samples, catfish pond mud samples and earthworm manure (Perionyx excavates). By the cross-streak agar methods, 22 Bacillus strains showed the inhibition ability to Edwardsiella ictaluri, which caused Bacillary Necrosis Pangasius (BNP) in catfish (Pangasianodon hypophthalmus). Both Bacillus sp. Q16 and Q111 strains showed the highest inhibition to E. ictaluri by the double-layer agar methods. Finally, two Bacillus strains (Q16, Q111) were selected as a source of potential probiotic because of the ability of extracellular enzyme secretion (protease, amylase, cellulose) strong growth at 0,1-1% salt concentrations, survival within the pH range 6-8, resistance to low pH and low bile salts, inability to produce haemolysin enzyme, sensitivity to eight antibiotics in the three impacting groups (inhibition of wall synthesis, inhibition mechanism of protein synthesis, inhibition of nucleic acid synthesis). Two Bacillus strains (Q16, Q111) were identified that they belong to Bacillus subtilis by biochemical method and 16S rRNA gene sequencing method. This study indicated that two Bacillus strains (Q16, Q111) isolated from catfish pond can be applied as high potential probiotics that used to farm catfish