Towards a Theory of Experimentation for Expected Improvement

2005 ◽  
Author(s):  
Daniel D. Frey ◽  
Hungjen Wang
Keyword(s):  
Mathematical Model ◽  
Engineering Design ◽  
Parameter Design ◽  
Expected Improvement ◽  
Simple Mathematical Model ◽  
Adaptive Process ◽  
Design Alternatives ◽  
Factor Interactions ◽  
Main Effects

This paper concerns the role of experimentation in engineering design, especially the process of making improvements through parameter design. A simple mathematical model is proposed for studying experimentation including a model of adaptive one-factor-at-a-time experimentation. Theorems are proven concerning the expected value of the improvement provided by adaptive experimentation. Theorems are also proven regarding the probability that factor effects will be exploited by the process. The results suggest that adaptive one-factor-at-a-time plans tend to exploit two-factor interactions when they are large or otherwise exploit main effects if interactions are small. As a result, the adaptive process provides around 80% of the improvements achievable via parameter design while exploring a small fraction of the design alternatives (less than 20% if the system has more than five variables).

A study of the geometric design and gas port of the claw-type rotor

2009 ◽  
Vol 223 (9) ◽  
pp. 2063-2069 ◽  
Author(s):  
C-F Hsieh
Keyword(s):  
Mathematical Model ◽  
Geometric Design ◽  
Parameter Design ◽  
Simple Mathematical Model ◽  
Area Efficiency ◽  
Pumping Efficiency ◽  
Rotor Profiles

This article presents a simple mathematical model for the geometric design of a claw-type rotor. Based on the parameter design, the different claw shapes can be produced, and the design of gas ports and the fluid carryover will be discussed. Hence, a better design course will be proposed for the design of gas ports. Additionally, feasible design regions of the parameters are determined for avoiding the interference between two rotor profiles. Finally, the pumping efficiency will be estimated by the comparisons of carryover area and area efficiency in varied parameters designs. These results can indicate a better design course for the designer.

scholarly journals Gender and societies: a grassroots approach to women in science

2019 ◽  
Vol 6 (9) ◽  
pp. 190633 ◽  
Author(s):  
Alex James ◽  
Rose Chisnall ◽  
Michael J. Plank
Keyword(s):  
Mathematical Model ◽  
Gender Bias ◽  
Gender Gap ◽  
Women In Science ◽  
Male Dominance ◽  
Simple Mathematical Model ◽  
Lower Status ◽  
The Status ◽  
Analyse Data

Women are under-represented in science. We show that the extent of the gender gap varies depending on the status of the position in question and there are simple steps that can be taken to improve diversity. We analyse data on the activities of over 30 science societies spanning four countries and five distinct discipline areas. Our results show that women tend to be equally represented in lower status roles and awards, e.g. student prizes and editorships, but under-represented in higher status roles, e.g. late-career awards and chief editorships. We develop a simple mathematical model to explore the role of homophily in decision making and quantify the effect of simple steps that can be taken to improve diversity. We conclude that, when the stakes are low, efforts to tackle historic gender bias towards men have been at least partially successful, but when the stakes are higher male dominance is often still the norm.

Article Commentary: Epidermal Wound Healing: The Clinical Implications of a Simple Mathematical Model

1992 ◽  
Vol 1 (5) ◽  
pp. 365-371 ◽  
Author(s):  
Jonathan A. Sherratt ◽  
J.D. Murray
Keyword(s):  
Mathematical Model ◽  
Wound Healing ◽  
Experimental Research ◽  
Healing Time ◽  
Clinical Implications ◽  
Simple Mathematical Model ◽  
New Ideas ◽  
Healing Wounds ◽  
The Subject

The role of biochemical regulation in the healing of epidermal wounds remains the subject of much biological debate. We have previously developed a mathematical model which focusses on the role of mitogenic autoregulation in reepithelialization (23–25). Here, we discuss some predictions of our model and their clinical relevance. We investigate both the effects of adding mitotic regulators to healing wounds and the dependence of healing time on wound shape. The latter study suggests a possible mechanism for the control of changes in wound shape during healing. The predictions we make are amenable to experimental verification, and suggest new ideas for experimental research.

A Possible Role of Adenylate Metabolism in Human Erythrocytes: Simple Mathematical Model

1996 ◽  
Vol 179 (1) ◽  
pp. 75-86 ◽  
Author(s):  
Fazoil I. Ataullakhanov ◽  
Svetlana V. Komarova ◽  
Victor M. Vitvitsky
Keyword(s):  
Mathematical Model ◽  
Human Erythrocytes ◽  
Simple Mathematical Model

scholarly journals Multidimensional generalization of phyllotaxis

2019 ◽  
pp. 153-160 ◽  
Author(s):  
Andrei Lodkin
Keyword(s):  
Mathematical Model ◽  
Fixed Points ◽  
Bifurcation Diagram ◽  
Large Family ◽  
Divergence Angle ◽  
Simple Mathematical Model ◽  
Biological Objects ◽  
Golden Number ◽  
Living Objects

The regular spiral arrangement of various parts of biological objects (leaves, florets, etc.), known as phyllotaxis, could not find an explanation during several centuries. Some quantitative parameters of the phyllotaxis (the divergence angle being the principal one) show that the organization in question is, in a sense, the same in a large family of living objects, and the values of the divergence angle that are close to the golden number prevail. This was a mystery, and explanations of this phenomenon long remained “lyrical”. Later, similar patterns were discovered in inorganic objects. After a series of computer models, it was only in the XXI century that the rigorous explanation of the appearance of the golden number in a simple mathematical model has been given. The resulting pattern is related to stable fixed points of some operator and depends on a real parameter. The variation of this parameter leads to an interesting bifurcation diagram where the limiting object is the SL(2;Z)-orbit of the golden number on the segment [0,1]. We present a survey of the problem and introduce a multidimensional analog of phyllotaxis patterns. A conjecture about the object that plays the role of the golden number is given.

The Role of Positive and Negative Affectivity in Healthy and Unhealthy Work-Related Behavior and Experiences

2019 ◽  
Vol 26 (2) ◽  
pp. 56-67 ◽  
Author(s):  
Hanna Hofmann ◽  
Carl-Walter Kohlmann
Keyword(s):  
Negative Affectivity ◽  
Coping Behavior ◽  
Common Method ◽  
Positive Affectivity ◽  
Work Related ◽  
Teacher Students ◽  
And Behaviors ◽  
Main Effects ◽  
Positive And Negative Affectivity

Abstract. Positive affectivity (PA) and negative affectivity (NA) are basic traits that affect work-related perceptions and behaviors and should be considered in any assessment of these variables. A quite common method to assess healthy or unhealthy types of work-related perceptions and behaviors is the questionnaire on Work-Related Coping Behavior and Experience Patterns (WCEP). However, the association of PA and NA with WCEP remained unclear. In a sample of teachers, physiotherapists, and teacher students ( N = 745; Mage = 35.07, SD = 12.49; 78% females), we aimed to identify the relevance of these basic traits. After controlling for age, gender, and type of occupation, we found main effects of PA and NA, with the specific combination of PA and NA being decisive for predicting the assignment to a WCEP type. The results highlight the need to include PA and NA in future assessments with the WCEP questionnaire.

The role of copper ions in hydrogen peroxide bleaching: Their origin, removal, and effect on pulp quality

TAPPI Journal ◽  
2012 ◽  
Vol 11 (7) ◽  
pp. 37-46 ◽  
Author(s):  
PEDRO E.G. LOUREIRO ◽  
SANDRINE DUARTE ◽  
DMITRY V. EVTUGUIN ◽  
M. GRAÇA V.S. CARVALHO
Keyword(s):  
Hydrogen Peroxide ◽  
Copper Ions ◽  
Peroxide Bleaching ◽  
Metals Removal ◽  
Peroxide Decomposition ◽  
Equipment Corrosion ◽  
And Performance ◽  
And Control ◽  
Main Effects

This study puts particular emphasis on the role of copper ions in the performance of hydrogen peroxide bleaching (P-stage). Owing to their variable levels across the bleaching line due to washing filtrates, bleaching reagents, and equipment corrosion, these ions can play a major role in hydrogen peroxide decomposition and be detrimental to polysaccharide integrity. In this study, a Cu-contaminated D0(EOP)D1 prebleached pulp was subjected to an acidic washing (A-stage) or chelation (Q-stage) before the alkaline P-stage. The objective was to understand the isolated and combined role of copper ions in peroxide bleaching performance. By applying an experimental design, it was possible to identify the main effects of the pretreatment variables on the extent of metals removal and performance of the P-stage. The acid treatment was unsuccessful in terms of complete copper removal, magnesium preservation, and control of hydrogen peroxide consumption in the following P-stage. Increasing reaction temperature and time of the acidic A-stage improved the brightness stability of the D0(EOP)D1AP bleached pulp. The optimum conditions for chelation pretreatment to maximize the brightness gains obtained in the subsequent P-stage with the lowest peroxide consumption were 0.4% diethylenetriaminepentaacetic acid (DTPA), 80ºC, and 4.5 pH.

The Impact of Light Polarisation on Light Field of Scenes with Multiple Reflections

2020 ◽  
pp. 108-115 ◽  
Author(s):  
Vladimir P. Budak ◽  
Anton V. Grimaylo
Keyword(s):  
Mathematical Model ◽  
Light Field ◽  
Global Illumination ◽  
Multiple Reflections ◽  
Software Environment ◽  
The Monte Carlo Method ◽  
Mueller Matrices ◽  
Volume Integration ◽  
The Impact

The article describes the role of polarisation in calculation of multiple reflections. A mathematical model of multiple reflections based on the Stokes vector for beam description and Mueller matrices for description of surface properties is presented. On the basis of this model, the global illumination equation is generalised for the polarisation case and is resolved into volume integration. This allows us to obtain an expression for the Monte Carlo method local estimates and to use them for evaluation of light distribution in the scene with consideration of polarisation. The obtained mathematical model was implemented in the software environment using the example of a scene with its surfaces having both diffuse and regular components of reflection. The results presented in the article show that the calculation difference may reach 30 % when polarisation is taken into consideration as compared to standard modelling.

Forms, Importance, and Ineffability of Factor Interactions to Define Personality Disorders: Comment on Lilienfeld et al. (2019)

2019 ◽  
Author(s):  
Stephen D Benning ◽  
Edward Smith
Keyword(s):  
Personality Disorders ◽  
False Positive Rate ◽  
Empirical Work ◽  
Design Studies ◽  
Linear Threshold ◽  
Positive Rate ◽  
Saturation Effects ◽  
Factor Interactions ◽  
Main Effects ◽  
Criterion Variables

The emergent interpersonal syndrome (EIS) approach conceptualizes personality disorders as the interaction among their constituent traits to predict important criterion variables. We detail the difficulties we have experienced finding such interactive predictors in our empirical work on psychopathy, even when using uncorrelated traits that maximize power. Rather than explaining a large absolute proportion of variance in interpersonal outcomes, EIS interactions might explain small amounts of variance relative to the main effects of each trait. Indeed, these interactions may necessitate samples of almost 1,000 observations for 80% power and a false positive rate of .05. EIS models must describe which specific traits’ interactions constitute a particular EIS, as effect sizes appear to diminish as higher-order trait interactions are analyzed. Considering whether EIS interactions are ordinal with non-crossing slopes, disordinal with crossing slopes, or entail non-linear threshold or saturation effects may help researchers design studies, sampling strategies, and analyses to model their expected effects efficiently.

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