The large-N limit of the threshold values in Mandelbrot's fractal percolation process

1989 ◽  
Vol 22 (11) ◽  
pp. L501-L506 ◽  
Author(s):  
J T Chayes ◽  
L Chayes
Keyword(s):  
Threshold Values ◽  
Percolation Process ◽  
Fractal Percolation ◽  
Large N

Random fractals and their intersection with winning sets

2021 ◽  
pp. 1-30
Author(s):  
YIFTACH DAYAN
Keyword(s):  
Hausdorff Dimension ◽  
General Result ◽  
Countable Collection ◽  
Percolation Process ◽  
Fractal Percolation ◽  
Random Fractals ◽  
Affine Hyperplane ◽  
Badly Approximable

Abstract We show that fractal percolation sets in $\mathbb{R}^{d}$ almost surely intersect every hyperplane absolutely winning (HAW) set with full Hausdorff dimension. In particular, if $E\subset\mathbb{R}^{d}$ is a realisation of a fractal percolation process, then almost surely (conditioned on $E\neq\emptyset$ ), for every countable collection $\left(f_{i}\right)_{i\in\mathbb{N}}$ of $C^{1}$ diffeomorphisms of $\mathbb{R}^{d}$ , $\dim_{H}\left(E\cap\left(\bigcap_{i\in\mathbb{N}}f_{i}\left(\text{BA}_{d}\right)\right)\right)=\dim_{H}\left(E\right)$ , where $\text{BA}_{d}$ is the set of badly approximable vectors in $\mathbb{R}^{d}$ . We show this by proving that E almost surely contains hyperplane diffuse subsets which are Ahlfors-regular with dimensions arbitrarily close to $\dim_{H}\left(E\right)$ . We achieve this by analysing Galton–Watson trees and showing that they almost surely contain appropriate subtrees whose projections to $\mathbb{R}^{d}$ yield the aforementioned subsets of E. This method allows us to obtain a more general result by projecting the Galton–Watson trees against any similarity IFS whose attractor is not contained in a single affine hyperplane. Thus our general result relates to a broader class of random fractals than fractal percolation.

scholarly journals Geometric functionals of fractal percolation

2020 ◽  
Vol 52 (4) ◽  
pp. 1085-1126
Author(s):  
Michael A. Klatt ◽  
Steffen Winter
Keyword(s):  
Topological Phase ◽  
Explicit Formulas ◽  
Percolation Process ◽  
Intrinsic Volumes ◽  
Fractal Percolation ◽  
Fractal Models ◽  
Topological Phase Transition ◽  
Finite Approximations ◽  
Percolation Thresholds ◽  
Transition Points

AbstractFractal percolation exhibits a dramatic topological phase transition, changing abruptly from a dust-like set to a system-spanning cluster. The transition points are unknown and difficult to estimate. In many classical percolation models the percolation thresholds have been approximated well using additive geometric functionals, known as intrinsic volumes. Motivated by the question of whether a similar approach is possible for fractal models, we introduce corresponding geometric functionals for the fractal percolation process F. They arise as limits of expected functionals of finite approximations of F. We establish the existence of these limit functionals and obtain explicit formulas for them as well as for their finite approximations.

Desynchronosis markers in risk assessment of metabolic syndrome development

2019 ◽  
Vol 1 (4) ◽  
pp. 21-26 ◽  
Author(s):  
O. V. Bobko ◽  
O. V. Tikhomirova ◽  
N. N. Zybina ◽  
O. A. Klitsenko
Keyword(s):  
Risk Assessment ◽  
Metabolic Syndrome ◽  
Threshold Values ◽  
Fat Tissue ◽  
Diurnal Dynamics ◽  
Laboratory Markers ◽  
Dyscirculatory Encephalopathy ◽  
Melatonin Production ◽  
Pai 1 ◽  
Logistic Regression Equation

The objective of the study is to show significance of desynchronosis laboratory markers in risk assessment of metabolic syndrome (MS) development. Materials and Methods. There were examined 98 men, aged 43-88, diagnosed with dyscirculatory encephalopathy showing one and more risk factors for development of cardiovascular diseases. They were divided into 2 groups according to the international guidelines of 2009: with MS (n = 61) and without MS (n = 37). Parameters of fats, glucose metabolism, inflammatory mediators, fat tissue metabolism markers, melatonin metabolite excretion (6-sulfatoxymelatonin) were defined in blood serum and urine. Results. The article presents data on changes in leptin, adiponectin, PAI-1, testosterone production and 6-sulfatoxymela-tonin excretion in patients with MS. There are calculated threshold values of these markers definitely increasing MS risk and logistic regression equation which allows assessing MS risk for an individual patient. Conclusion. Detected disorders of melatonin synthesis diurnal dynamics in patients with MS and interconnection between melatonin production and adiponectin, leptin, PAI-1, testosterone synthesis allow considering these parameters as desynchronosis markers significant for MS development.

A study on the odor threshold values of the fatty acids and VOCs of specified offensive odor substances

2014 ◽  
Vol 13 (4) ◽  
pp. 313-325 ◽  
Author(s):  
Jin-Soo Choi ◽  
◽  
Jin-Seok Han ◽  
Bu-Ju Gong ◽  
Seok-Yong Hong ◽  
...  
Keyword(s):  
Fatty Acids ◽  
Odor Threshold ◽  
Threshold Values

Using Item-level Analyses to Better Understand the Consequences of Partialing Procedures: An Example Using the Dark Triad

2019 ◽  
Author(s):  
Colin Vize ◽  
Katherine Collison ◽  
Donald Lynam ◽  
Josh Miller
Keyword(s):  
Psychological Research ◽  
Dark Triad ◽  
Small Samples ◽  
Residual Content ◽  
Fine Grained ◽  
Large N ◽  
Dirty Dozen ◽  
Item Level ◽  
Variable Content ◽  
Small N

Objective: Partialing procedures are frequently used in psychological research. The present study sought to further explore the consequences of partialing, focusing on the replicability of partialing-based results. Method: We used popular measures of the Dark Triad (DT; Machiavellianism, narcissism, and psychopathy) to explore the replicability of partialing procedures. We examined whether the residual content of popular DT scales are similar to the residual content of DT scales derived from separate samples based on relations with individual items from the IPIP-NEO-120, allowing for a fine-grained analysis of residual variable content. Results: Profiles were compared using three sample sizes (Small N=156-157, Moderate N = 313-314, Large N = 627-628) randomly drawn from a large MTurk sample (N = 1,255). There was low convergence among original/residual DT scales within samples. Additionally, results showed the content of residual Dirty Dozen scales was not similar across samples. Similar results were found for Short Dark Triad-Machiavellianism, but only in the moderate and small samples. Conclusion: The results indicate that there are important issues that arise when using partialing procedures, including replicability issues surrounding residual variables. Reasons for the observed results are discussed and further research examining the replicability of residual-based results is recommended.

Political identity over personal impact: Early US reactions to the COVID-19 pandemic

2020 ◽  
Author(s):  
Robert N Collins ◽  
David R. Mandel ◽  
Sarah S. Schywiola
Keyword(s):  
Emotional Distress ◽  
Strong Influence ◽  
Political Identity ◽  
Organizational Response ◽  
Threat Perception ◽  
Attitudes And Beliefs ◽  
Value Differences ◽  
Personal Impact ◽  
Large N ◽  
Weak Influence

Research suggests political identity has strong influence over individuals’ attitudes and beliefs, which in turn can affect their behavior. Likewise, firsthand experience with an issue can also affect attitudes and beliefs. A large (N = 10,362) survey (Pew Research and Ipsos W64) of Americans was analyzed to investigate the effects of both political identity and personal impact on individuals’ reactions to the COVID-19 pandemic. Results show that political identity (i.e., Democrat or Republican) and personal impact (i.e., personally affected or not) influenced different aspects of the American public’s reaction to COVID-19. Political identity exerted a strong influence on self-reports of emotional distress, threat perception, discomfort with exposure, support for restrictions, and perception of under/overreaction by individuals and institutions. Personal impact exerted a comparatively weaker influence on reported emotional distress and threat perception. Both factors had a weak influence on appraisal of individual and organizational and community responses. The dominating influence of political identity carried over into the bivariate relations among these responses. In particular, the appraisal of organizational response divided along party lines, tied to opposing views of whether there has been over- or under-reaction to the pandemic. The dominance of political identity has important implications for crisis management and reflects the influence of normative value differences between the parties, partisan messaging on the pandemic, and polarization in American politics.

OnPoint: A package for online experiments in motor control and motor learning

2020 ◽  
Author(s):  
Jonathan Sanching Tsay ◽  
Alan S. Lee ◽  
Guy Avraham ◽  
Darius E. Parvin ◽  
Jeremy Ho ◽  
...  
Keyword(s):  
Motor Control ◽  
Motor Learning ◽  
Open Source Software ◽  
Research Progress ◽  
Global Pandemic ◽  
Large N ◽  
Open Source Software Package ◽  
Potential Applications ◽  
Temporal And Spatial ◽  
The One

Motor learning experiments are typically run in-person, exploiting finely calibrated setups (digitizing tablets, robotic manipulandum, full VR displays) that provide high temporal and spatial resolution. However, these experiments come at a cost, not limited to the one-time expense of purchasing equipment but also the substantial time devoted to recruiting participants and administering the experiment. Moreover, exceptional circumstances that limit in-person testing, such as a global pandemic, may halt research progress. These limitations of in-person motor learning research have motivated the design of OnPoint, an open-source software package for motor control and motor learning researchers. As with all online studies, OnPoint offers an opportunity to conduct large-N motor learning studies, with potential applications to do faster pilot testing, replicate previous findings, and conduct longitudinal studies (GitHub repository: https://github.com/alan-s-lee/OnPoint).

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