scholarly journals Type and Cotype Constants and the Linear Stability of Wigner’s Symmetry Theorem

Symmetry ◽  
2019 ◽  
Vol 11 (9) ◽  
pp. 1107
Author(s):  
Javier Cuesta
Keyword(s):  
Banach Spaces ◽  
Linear Stability ◽  
Linear Extension ◽  
Transition Probabilities ◽  
Linear Map ◽  
Additive Error ◽  
Type And Cotype

We study the relation between almost-symmetries and the geometry of Banach spaces. We show that any almost-linear extension of a transformation that preserves transition probabilities up to an additive error admits an approximation by a linear map, and the quality of the approximation depends on the type and cotype constants of the involved spaces.

scholarly journals A NON-EXTENDABLE BOUNDED LINEAR MAP BETWEEN C*-ALGEBRAS

2001 ◽  
Vol 44 (2) ◽  
pp. 241-248 ◽  
Author(s):  
Narutaka Ozawa
Keyword(s):  
Linear Extension ◽  
Subject Classification ◽  
Primary 46L05 ◽  
Bounded Linear ◽  
Linear Map ◽  
C Algebras ◽  
Secondary 46L07

AbstractWe present an example of a $C^*$-subalgebra $A$ of $\mathbb{B}(H)$ and a bounded linear map from $A$ to $\mathbb{B}(K)$ which does not admit any bounded linear extension. This generalizes the result of Robertson and gives the answer to a problem raised by Pisier. Using the same idea, we compute the exactness constants of some Q-spaces. This solves a problem raised by Oikhberg. We also construct a Q-space which is not locally reflexive.AMS 2000 Mathematics subject classification: Primary 46L05. Secondary 46L07

Type and Cotype of Banach Spaces

1991 ◽  
pp. 236-271 ◽  
Author(s):  
Michel Ledoux ◽  
Michel Talagrand
Keyword(s):  
Banach Spaces ◽  
Type And Cotype

Bounds and good policies in stationary finite–stage Markovian decision problems

1980 ◽  
Vol 12 (1) ◽  
pp. 154-173 ◽  
Author(s):  
Gerhard Hübner
Keyword(s):  
Decision Model ◽  
Transition Probabilities ◽  
Planning Horizon ◽  
Decision Problems ◽  
Optimal Decisions ◽  
Optimal Value ◽  
Action Spaces ◽  
Stationary Problems ◽  
Markovian Decision Problems

A stationary Markovian decision model is considered with general state and action spaces where the transition probabilities are weakened to be bounded transition measures (this is useful for many applications). New and improved bounds are given for the optimal value of stationary problems with a large planning horizon if either only a few steps of iteration are carried out or, in addition, a solution of the infinite-stage problem is known. Similar estimates are obtained for the quality of policies which are composed of nearly optimal decisions from the first few steps or from the infinite-stage solution.

On the type and cotype of Banach spaces

1979 ◽  
Vol 32 (1) ◽  
pp. 32-38 ◽  
Author(s):  
L. Tzafriri
Keyword(s):  
Banach Spaces ◽  
Type And Cotype

Atomic structure calculations for Br-like ions

2015 ◽  
Vol 93 (5) ◽  
pp. 487-495 ◽  
Author(s):  
Arun Goyal ◽  
Indu Khatri ◽  
Sunny Aggarwal ◽  
A.K. Singh ◽  
Man Mohan
Keyword(s):  
Transition Probabilities ◽  
Energy Levels ◽  
Oscillator Strengths ◽  
Atomic Data ◽  
Plasma Diagnostic ◽  
Fusion Plasma ◽  
Atomic Structure Calculations ◽  
Structure Calculations ◽  
Good Agreement

Energy levels, wavefunction compositions, and lifetimes are computed for all levels of 4s24p5, 4s24p44d, and 4s4p6 configurations in Br-like ions (Z = 47–50). We use the multiconfigurational Dirac–Fock method to generate the wavefunctions. We also present the transition wavelengths, oscillator strengths, transition probabilities, and line strengths for the electric dipole (E1) transition from the ground state configuration. We compare our calculated results with the available data in the literature and good agreement is obtained, which confirms the quality of our results. Moreover, we predict some new atomic data that have not been available so far and may be important for plasma diagnostic analysis in fusion plasma.

scholarly journals Comparison of risk-of-bias assessment approaches for selection of studies reporting prevalence for economic analyses

BMJ Open ◽  
2020 ◽  
Vol 10 (9) ◽  
pp. e037324
Author(s):  
Matthew J Glasgow ◽  
Richard Edlin ◽  
Jane E Harding
Keyword(s):  
Convergent Validity ◽  
Transition Probabilities ◽  
Risk Of Bias ◽  
Control Group ◽  
Decision Analysis Model ◽  
Neonatal Hypoglycaemia ◽  
Analysis Model ◽  
Prevalence Studies ◽  
Economic Analyses

ObjectivesWithin cost-effectiveness models, prevalence figures can inform transition probabilities. The methodological quality of studies can inform the choice of prevalence figures but no single obvious candidate tool exists for assessing quality of the observational epidemiological studies for selecting prevalence estimates. We aimed to compare different tools to assess the risk of bias of studies reporting prevalence, and develop and compare possible numerical scoring systems using these tools to set a threshold for inclusion of reports of prevalence in an economic analysis of neonatal hypoglycaemia.DesignAssessments of bias using two tools (Joanna Briggs Institute (JBI) Checklist for Prevalence Studies and a modified version of Risk Of Bias In Non-randomised Studies-of Interventions (ROBINS-I)) were compared for 18 studies relevant to a single setting (neonatal hypoglycaemia). Inclusions of studies for use in a decision analysis model were considered based on summary scores derived from these tools.ResultsBoth tools were considered easy to use and produced dispersed scores for each of the 40 study–outcome combinations. The modified ROBINS-I scores were more skewed than the JBI scores, particularly at higher thresholds. The studies selected for inclusion are generally the same using either tool; if 50% was used as the cut-off threshold using the Applicable Score both tools would yield the same results. However, the JBI tool is shorter and may be easier to interpret and apply to studies that do not involve a control group, while the modified ROBINS-I tool assesses more methodological detail in studies that include a control group.ConclusionBoth tools performed well for systematically assessing studies that report on outcome prevalence and provided similar discrimination between studies for risk of bias. This convergent validity supports use of both tools for the purpose of assessing risk of bias and selecting studies that report prevalence for inclusion in economic analyses.

Model to assess the cost-effectiveness of new treatments for depression

2006 ◽  
Vol 22 (4) ◽  
pp. 469-477 ◽  
Author(s):  
Patrik Sobocki ◽  
Mattias Ekman ◽  
Hans Ågren ◽  
Bengt Jönsson ◽  
Clas Rehnberg
Keyword(s):  
Quality Of Life ◽  
Cost Effectiveness ◽  
Standard Care ◽  
Transition Probabilities ◽  
Sensitivity Analyses ◽  
Full Remission ◽  
Life Years ◽  
New Treatment ◽  
The Cost

Objectives: The objective of this study was to develop a model to assess the cost-effectiveness of a new treatment for patients with depression.Methods: A Markov simulation model was constructed to evaluate standard care for depression as performed in clinical practice compared with a new treatment for depression. Costs and effects were estimated for time horizons of 6 months to 5 years. A naturalistic longitudinal observational study provided data on costs, quality of life, and transition probabilities. Data on long-term consequences of depression and mortality risks were collected from the literature. Cost-effectiveness was quantified as quality-adjusted life-years (QALYs) gained from the new treatment compared with standard care, and the societal perspective was taken. Probabilistic analyses were conducted to present the uncertainty in the results, and sensitivity analyses were conducted on key parameters used in the model.Results: Compared with standard care, the new hypothetical therapy was predicted to substantially decrease costs and was also associated with gains in QALYs. With an improved treatment effect of 50 percent on achieving full remission, the net cost savings were 20,000 Swedish kronor over a 5-year follow-up time, given equal costs of treatments. Patients gained .073 QALYs over 5 years. The results are sensitive to changes in assigned treatment effects.Conclusions: The present study provides a new model for assessing the cost-effectiveness of treatments for depression by incorporating full remission as the treatment goal and QALYs as the primary outcome measure. Moreover, we show the usefulness of naturalistic real-life data on costs and quality of life and transition probabilities when modeling the disease over time.

scholarly journals Type and cotype numbers of operators on Banach spaces

1990 ◽  
Vol 96 (1) ◽  
pp. 21-37 ◽  
Author(s):  
Albrecht Pietsch
Keyword(s):  
Banach Spaces ◽  
Type And Cotype

scholarly journals An evaluation of daily precipitation from atmospheric reanalyses over Australia

2019 ◽  
Author(s):  
Suwash Chandra Acharya ◽  
Rory Nathan ◽  
Quan J. Wang ◽  
Chun-Hsu Su ◽  
Nathan Eizenberg
Keyword(s):  
Daily Precipitation ◽  
Transition Probabilities ◽  
Reanalysis Dataset ◽  
Atmospheric Processes ◽  
Precipitation Estimates ◽  
Spatio Temporal ◽  
Regional Reanalysis ◽  
Global Reanalysis ◽  
Better Than

Abstract. An accurate representation of spatio-temporal characteristics of precipitation fields is fundamental for many hydro-meteorological analyses but is often limited by the paucity of gauges. Reanalysis models provide systematic methods of representing atmospheric processes to produce datasets of spatio-temporal precipitation estimates. The precipitation from the reanalysis datasets should, however, be evaluated thoroughly before use because it is inferred from physical parameterization. In this paper, we evaluated the precipitation dataset from the Bureau of Meteorology Atmospheric high-resolution Regional Reanalysis for Australia (BARRA) and compared it against (a) gauged point observations, (b) an interpolated gridded dataset based on gauged point observations (AWAP), and (c) a global reanalysis dataset (ERA-Interim). We utilized a range of evaluation metrics such as continuous metrics (correlation, bias, variability, modified Kling-Gupta efficiency), categorical metrics, and other statistics (wet day frequency, transition probabilities and quantiles) to ascertain the quality of the dataset. BARRA, in comparison with ERA-Interim, shows a better representation of rainfall of larger magnitude at both point and grid scale of 5 km. BARRA also consistently reproduces the distribution of wet days and transition probabilities. The performance of BARRA varies spatially, with better performance in the temperate zone than in the arid and tropical zones. A point-to-grid evaluation based on correlation, bias and modified Kling-Gupta efficiency (KGE') indicates that ERA-Interim performs on par or better than BARRA. However, on a spatial scale, BARRA outperforms AWAP in terms of KGE' score and the components of the KGE' score. Our evaluation illustrates that BARRA, with richer spatial variations in climatology of daily precipitation, provides an improved representation of precipitation compared with the coarser ERA-Interim. It is a useful complement to existing precipitation datasets for Australia, especially in sparsely gauged regions.

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