Some mathematical properties of the absolute area of a difference spectrum

1993 ◽  
Vol 99 (9) ◽  
pp. 6330-6335 ◽  
Author(s):  
R. Gaufrès ◽  
Y. Arab
Keyword(s):  
Difference Spectrum ◽  
Mathematical Properties ◽  
The Absolute

The Bayesian Model

2020 ◽  
pp. 19-60
Author(s):  
Scott Sturgeon
Keyword(s):  
Bayesian Model ◽  
Mental States ◽  
Probability Functions ◽  
Venn Diagrams ◽  
Mathematical Properties ◽  
The Absolute ◽  
Conditional Credence ◽  
Truth Tables

Chapter 2 introduces the Bayesian Model of rational credence. The mathematical properties of classic probability are explained—their linearity, cardinality, and so on—as well as the use of probability functions to model mental states. A game with balls is created and diagrammed to make visually vivid how probability works. Venn diagrams and truth-tables are used to illustrate everything for the absolute beginner. Conditional Credence is explained with intuitive examples, and the standard ratio formula is introduced. A game with marbles is then created and diagrammed to pump intuition about change of probability, which leads directly to Jeffrey-style kinematics. The chapter closes by describing a notionally possible agent, Creda, whose psychology matches the Bayesian Model.

scholarly journals Measuring the Magnitude of Health Inequality Between 2 Population Subgroup Proportions

2020 ◽  
Vol 189 (9) ◽  
pp. 987-996
Author(s):  
Makram Talih ◽  
Ramal Moonesinghe ◽  
David T Huang
Keyword(s):  
Health Disparities ◽  
Absolute Difference ◽  
Measurement Unit ◽  
Z Score ◽  
Underlying Distribution ◽  
Standard Measurement ◽  
Mathematical Properties ◽  
Population Subgroup ◽  
The Absolute ◽  
Measures Of Inequality

Abstract In this paper, we evaluate 11 measures of inequality, d(p1, p2), between 2 proportions p1 and p2, some of which are new to the health disparities literature. These measures are selected because they are continuous, nonnegative, equal to 0 if and only if |p1 − p2| = 0, and maximal when |p1 − p2| = 1. They are also symmetrical [d(p1, p2) = d(p2, p1)] and complement-invariant [d(p1, p2) = d(1 − p2, 1 − p1)]. To study intermeasure agreement, 5 of the 11 measures, including the absolute difference, are retained, because they remain finite and are maximal if and only if |p1 − p2| = 1. Even when the 2 proportions are assumed to be drawn at random from a shared distribution—interpreted as the absence of an avoidable difference—the expected value of d(p1, p2) depends on the shape of the distribution (and the choice of d) and can be quite large. To allow for direct comparisons among measures, we propose a standard measurement unit akin to a z score. For skewed underlying beta distributions, 4 of the 5 retained measures, once standardized, offer more conservative assessments of the magnitude of inequality than the absolute difference. We conclude that, even for measures that share the highlighted mathematical properties, magnitude comparisons are most usefully assessed relative to an elicited or estimated underlying distribution for the 2 proportions.

Bulk standards for low-temperature biological x-ray microanalysis

1984 ◽  
Vol 42 ◽  
pp. 282-283
Author(s):  
P. Echlin ◽  
M. McKoon ◽  
E.S. Taylor ◽  
C.E. Thomas ◽  
K.L. Maloney ◽  
...  
Keyword(s):  
Phase Separation ◽  
Low Temperature ◽  
Analytical Method ◽  
Salt Solutions ◽  
Absolute Concentration ◽  
Cooling Process ◽  
X Ray ◽  
The Absolute ◽  
Analytical Procedures ◽  
Electrical Conductors

Although sections of frozen salt solutions have been used as standards for x-ray microanalysis, such solutions are less useful when analysed in the bulk form. They are poor thermal and electrical conductors and severe phase separation occurs during the cooling process. Following a suggestion by Whitecross et al we have made up a series of salt solutions containing a small amount of graphite to improve the sample conductivity. In addition, we have incorporated a polymer to ensure the formation of microcrystalline ice and a consequent homogenity of salt dispersion within the frozen matrix. The mixtures have been used to standardize the analytical procedures applied to frozen hydrated bulk specimens based on the peak/background analytical method and to measure the absolute concentration of elements in developing roots.

An example of spectrum imaging used for comparison of EELS quantitative analysis techniques on Al-Li

1991 ◽  
Vol 49 ◽  
pp. 726-727
Author(s):  
John A. Hunt
Keyword(s):  
Quantitative Analysis ◽  
Large Data ◽  
Difference Spectrum ◽  
Large Data Sets ◽  
Foil Thickness ◽  
Data Sets ◽  
Analysis Techniques ◽  
Spectrum Imaging ◽  
Normal Spectrum ◽  
Electron Energy Loss

Spectrum-imaging is a useful technique for comparing different processing methods on very large data sets which are identical for each method. This paper is concerned with comparing methods of electron energy-loss spectroscopy (EELS) quantitative analysis on the Al-Li system. The spectrum-image analyzed here was obtained from an Al-10at%Li foil aged to produce δ' precipitates that can span the foil thickness. Two 1024 channel EELS spectra offset in energy by 1 eV were recorded and stored at each pixel in the 80x80 spectrum-image (25 Mbytes). An energy range of 39-89eV (20 channels/eV) are represented. During processing the spectra are either subtracted to create an artifact corrected difference spectrum, or the energy offset is numerically removed and the spectra are added to create a normal spectrum. The spectrum-images are processed into 2D floating-point images using methods and software described in [1].

A Quantitative Ultrastructural Study of Peripheral Blood Lymphocytes Containing Parallel Tubular Arrays in Epstein-Barr Virus and Cytomegalo-Virus Mononucleosis

1981 ◽  
Vol 39 ◽  
pp. 454-455
Author(s):  
C. M. Payne ◽  
P. M. Tennican
Keyword(s):  
Peripheral Blood ◽  
Lymphocyte Count ◽  
Epstein Barr Virus ◽  
Absolute Lymphocyte Count ◽  
Peripheral Blood Lymphocytes ◽  
Clinical State ◽  
Barr Virus ◽  
The Absolute ◽  
Epstein Barr ◽  
Tubular Arrays

In the normal peripheral circulation there exists a sub-population of lymphocytes which is ultrastructurally distinct. This lymphocyte is identified under the electron microscope by the presence of cytoplasmic microtubular-like inclusions called parallel tubular arrays (PTA) (Figure 1), and contains Fc-receptors for cytophilic antibody. In this study, lymphocytes containing PTA (PTA-lymphocytes) were quantitated from serial peripheral blood specimens obtained from two patients with Epstein -Barr Virus mononucleosis and two patients with cytomegalovirus mononucleosis. This data was then correlated with the clinical state of the patient.It was determined that both the percentage and absolute number of PTA- lymphocytes was highest during the acute phase of the illness. In follow-up specimens, three of the four patients' absolute lymphocyte count fell to within normal limits before the absolute PTA-lymphocyte count.In one patient who was followed for almost a year, the absolute PTA- lymphocyte count was consistently elevated (Figure 2). The estimation of absolute PTA-lymphocyte counts was determined to be valid after a morphometric analysis of the cellular areas occupied by PTA during the acute and convalescent phases of the disease revealed no statistical differences.

Polarity Determination in Sphalerite and Wurtzite Structures

1990 ◽  
Vol 48 (2) ◽  
pp. 500-501
Author(s):  
Stuart McKernan ◽  
C. Barry Carter
Keyword(s):  
Opposite Polarity ◽  
Single Domain ◽  
Polar Material ◽  
Electron Microscopic ◽  
Dynamical Interaction ◽  
X Ray ◽  
Polarity Determination ◽  
The Absolute ◽  
Microscopic Techniques

The determination of the absolute polarity of a polar material is often crucial to the understanding of the defects which occur in such materials. Several methods exist by which this determination may be performed. In bulk, single-domain specimens, macroscopic techniques may be used, such as the different etching behavior, using the appropriate etchant, of surfaces with opposite polarity. X-ray measurements under conditions where Friedel’s law (which means that the intensity of reflections from planes of opposite polarity are indistinguishable) breaks down can also be used to determine the absolute polarity of bulk, single-domain specimens. On the microscopic scale, and particularly where antiphase boundaries (APBs), which separate regions of opposite polarity exist, electron microscopic techniques must be employed. Two techniques are commonly practised; the first [1], involves the dynamical interaction of hoLz lines which interfere constructively or destructively with the zero order reflection, depending on the crystal polarity. The crystal polarity can therefore be directly deduced from the relative intensity of these interactions.

516: A Simplified Method to Estimate the Absolute Renal Uptake of 99MTC-DMSA: Evaluation with a New Model using the Radioactivity of Nephrectomy Specimens as Reference

2005 ◽  
Vol 173 (4S) ◽  
pp. 140-141
Author(s):  
Mariana Lima ◽  
Celso D. Ramos ◽  
Sérgio Q. Brunetto ◽  
Marcelo Lopes de Lima ◽  
Carla R.M. Sansana ◽  
...  
Keyword(s):  
New Model ◽  
Renal Uptake ◽  
Simplified Method ◽  
The Absolute

Translocation Relative to Range

Methodology ◽  
2008 ◽  
Vol 4 (3) ◽  
pp. 132-138 ◽  
Author(s):  
Michael Höfler
Keyword(s):  
Risk Difference ◽  
Binary Outcomes ◽  
Number Needed To Treat ◽  
Likert Scales ◽  
Psychological Science ◽  
The Absolute ◽  
The Difference ◽  
Variance Parameters ◽  
Standardized Index ◽  
Maximum Possible Magnitude

A standardized index for effect intensity, the translocation relative to range (TRR), is discussed. TRR is defined as the difference between the expectations of an outcome under two conditions (the absolute increment) divided by the maximum possible amount for that difference. TRR measures the shift caused by a factor relative to the maximum possible magnitude of that shift. For binary outcomes, TRR simply equals the risk difference, also known as the inverse number needed to treat. TRR ranges from –1 to 1 but is – unlike a correlation coefficient – a measure for effect intensity, because it does not rely on variance parameters in a certain population as do effect size measures (e.g., correlations, Cohen’s d). However, the use of TRR is restricted on outcomes with fixed and meaningful endpoints given, for instance, for meaningful psychological questionnaires or Likert scales. The use of TRR vs. Cohen’s d is illustrated with three examples from Psychological Science 2006 (issues 5 through 8). It is argued that, whenever TRR applies, it should complement Cohen’s d to avoid the problems related to the latter. In any case, the absolute increment should complement d.

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