scholarly journals The critical window in random digraphs

2021 ◽  
pp. 1-19
Author(s):  
Matthew Coulson
Keyword(s):  
Tail Probabilities ◽  
Component Structure ◽  
Critical Window ◽  
Random Digraphs ◽  
Explicit Bounds

Abstract We consider the component structure of the random digraph D(n,p) inside the critical window $p = n^{-1} + \lambda n^{-4/3}$ . We show that the largest component $\mathcal{C}_1$ has size of order $n^{1/3}$ in this range. In particular we give explicit bounds on the tail probabilities of $|\mathcal{C}_1|n^{-1/3}$ .

On domination of tail probabilities of (super)martingales: Explicit bounds

2006 ◽  
Vol 46 (1) ◽  
pp. 1-43 ◽  
Author(s):  
V. Bentkus ◽  
N. Kalosha ◽  
M. van Zuijlen
Keyword(s):  
Tail Probabilities ◽  
Explicit Bounds

The sense of presence in virtual environments:

2003 ◽  
Vol 15 (2) ◽  
pp. 69-71 ◽  
Author(s):  
Thomas W. Schubert
Keyword(s):  
Virtual Environments ◽  
Coding Theory ◽  
Model Building ◽  
Self Report ◽  
Survey Study ◽  
Spatial Presence ◽  
Component Structure ◽  
Sense Of Presence ◽  
Being There ◽  
Measure Sense

Abstract. The sense of presence is the feeling of being there in a virtual environment. A three-component self report scale to measure sense of presence is described, the components being sense of spatial presence, involvement, and realness. This three-component structure was developed in a survey study with players of 3D games (N = 246) and replicated in a second survey study (N = 296); studies using the scale for measuring the effects of interaction on presence provide evidence for validity. The findings are explained by the Potential Action Coding Theory of presence, which assumes that presence develops from mental model building and suppression of the real environment.

Psychometric Definition of Rorschach Determinant Component Structure

1998 ◽  
Vol 14 (2) ◽  
pp. 116-123 ◽  
Author(s):  
Raymond M. Costello
Keyword(s):  
Lower Order ◽  
Three Dimensions ◽  
Comprehensive System ◽  
Empirical Examination ◽  
Component Structure ◽  
Exner's Comprehensive System ◽  
Factor Analytic ◽  
Confirmatory Factor ◽  
Components Analysis ◽  
Definition Of

This is an empirical examination of Experienced Stimulation (es) and Experience Actual (EA) from Exner's Comprehensive System (CS) for Rorschach's Test, spurred by Kleiger's theoretical critique. Principal components analysis, Cronbach's α, and inter-item correlational analyses were used to test whether 13 determinants used to code Rorschach responses (M, FM, m, CF+C, YF+Y, C'F+C', TF+T, VF+V, FC, FC', FV, FY, FT) are best represented as a one, two, or more-dimensional construct. The 13 determinants appear to reflect three dimensions, a “lower order” sensori-motor dimension (m + CF+C + YF+Y + C'F+C' + TF+T + VF+V) with a suggested label of Modified Experienced Stimulation (MES), a “higher order” sensori-motor dimension (FM + FV + FY + FT) with a suggested label of Modified Experience Potential (MEP), and a third sensori-motor dimension (M+FC+FC') for which the label of Modified Experience Actual (MEA) is suggested. These findings are consistent with Kleiger's arguments and could lead to a refinement of CS constructs by aggregating determinants along lines more theoretically congruous and more internally consistent. A RAMONA model with parameters specified was presented for replication attempts which use confirmatory factor analytic techniques.

Mathematics of networks

2018 ◽  
Author(s):  
Mark Newman
Keyword(s):  
Random Walks ◽  
Adjacency Matrix ◽  
Graph Partitioning ◽  
Dynamic Networks ◽  
Graph Laplacian ◽  
Network Visualization ◽  
Final Part ◽  
Bipartite Networks ◽  
Component Structure ◽  
Basic Properties

An introduction to the mathematical tools used in the study of networks. Topics discussed include: the adjacency matrix; weighted, directed, acyclic, and bipartite networks; multilayer and dynamic networks; trees; planar networks. Some basic properties of networks are then discussed, including degrees, density and sparsity, paths on networks, component structure, and connectivity and cut sets. The final part of the chapter focuses on the graph Laplacian and its applications to network visualization, graph partitioning, the theory of random walks, and other problems.

scholarly journals Normal approximation for mixtures of normal distributions and the evolution of phenotypic traits

2021 ◽  
Vol 53 (1) ◽  
pp. 162-188
Author(s):  
Krzysztof Bartoszek ◽  
Torkel Erhardsson
Keyword(s):  
Normal Distribution ◽  
Phenotypic Trait ◽  
Phenotypic Traits ◽  
Normal Distributions ◽  
Average Value ◽  
Conditional Moments ◽  
Mixture Of Normal Distributions ◽  
Explicit Bounds ◽  
Mixtures Of Normal Distributions ◽  
Parameter Values

AbstractExplicit bounds are given for the Kolmogorov and Wasserstein distances between a mixture of normal distributions, by which we mean that the conditional distribution given some $\sigma$ -algebra is normal, and a normal distribution with properly chosen parameter values. The bounds depend only on the first two moments of the first two conditional moments given the $\sigma$ -algebra. The proof is based on Stein’s method. As an application, we consider the Yule–Ornstein–Uhlenbeck model, used in the field of phylogenetic comparative methods. We obtain bounds for both distances between the distribution of the average value of a phenotypic trait over n related species, and a normal distribution. The bounds imply and extend earlier limit theorems by Bartoszek and Sagitov.

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