19 papers · ranked by Valyu relevance
Haijun Li
Regular and rapid variation have been extensively studied in the literature and applied across various fields, particularly in extreme value theory. In this paper, we examine regular and rapid variation through the lens of generalized hazard rates, with a focus on the behavior of survival and density functions of…
Raluca M. Balan
In this article, we consider a series X(t) = P j≥1 Ψj (t)Zj (t), t ∈ [0, 1] of random processes with sample paths in the space D of c`adl`ag functions (i.e. right-continuous functions with left limits) on [0, 1]. We assume that (Zj )j≥1 are i.i.d. processes with sample paths in D and (Ψj )j≥1 are processes with…
Bojan Basrak, Nikolina Milinčević, Ilya Molchanov
Since its introduction by J. Karamata, regular variation has evolved from a purely mathematical concept into a cornerstone of theoretical probability and data analysis. It is extensively studied and applied in different areas. Its significance lies in characterising large deviations, determining the limits of partial…
Bikramjit Das, Marie Kratz
We analyze risk diversification in a portfolio of heavy-tailed risk factors under the assumption of second order multivariate regular variation. Asymptotic limits for a measure of diversification benefit are obtained when considering, for instance, the value-at-risk . The asymptotic limits are computed in a few…
Adrien S. Hitz, Robin J. Evans
We introduce the notion of one-component regular variation to describe a function that is regularly varying in its first component. We extend the representation and Karamata's theorem to one-component regularly varying functions, probability distributions and densities, and explain why these results are fundamental in…
Ed Manley, Chen Zhong, Michael Batty
New smart card datasets are providing new opportunities to explore travel behaviour in much greater depth than anything accomplished hitherto. Part of this quest involves measuring the great array of regular patterns within such data and explaining these relative to less regular patterns which have often been treated…
Chen Zhong, Michael Batty, Ed Manley, Jiaqiu Wang + 4 more
'Feng Chen' 'Gerhard Schmitt' 'Tobias Preis'] To discover regularities in human mobility is of fundamental importance to our understanding of urban dynamics, and essential to city and transport planning, urban management and policymaking. Previous research has revealed universal regularities at mainly aggregated…
Haijun Li
Operator regular variation reveals general power-law distribution tail decay phenomena using operator scaling, that includes multivariate regular variation with scalar scaling as a special case. In this paper, we show that a multivariate Liouville distribution is operator regularly varying if its driving function is…
Marisol Espinoza-Monroy, Victor de Lafuente
Perceiving the temporal regularity in a sequence of repetitive sensory events facilitates the preparation and execution of relevant behaviors with tight temporal constraints. How we estimate temporal regularity from repeating patterns of sensory stimuli is not completely understood. We developed a decision-making task…
Xiaoming Ye
- Variance is the evaluation of probability interval of an error, instead of the dispersion of measured value defined by the existing measurement theory. The dispersion of measured value is 0. - Variance is expressed by the dispersion of all possible values of error. - All possible values refer to the test values under…
Patrick W. Keeley, Benjamin E. Reese
Retinal neurons are often arranged as non-random distributions called “mosaics,” as their somata minimize proximity to neighboring cells of the same type. The horizontal cells serve as an example of such a mosaic, but little is known about the developmental mechanisms that underlie their patterning. To identify genes…
Jan Kalina, Anna Schlenker
The Minimum Redundancy Maximum Relevance (MRMR) approach to supervised variable selection represents a successful methodology for dimensionality reduction, which is suitable for high-dimensional data observed in two or more different groups. Various available versions of the MRMR approach have been designed to search…
Giorgio L. Manenti, Caspar M. Schwiedrzik
Perceptual learning improves sensory discrimination, yet the brain must balance specificity and generalization, especially in variable environments. To investigate how variability shapes perceptual learning, we used functional magnetic resonance imaging while human subjects performed an orientation discrimination task…
Scott Wolf, Diogo Melo, Kristina M. Garske, Luisa F. Pallares + 2 more
Gene expression variance has been linked to organismal function and fitness but remains a commonly ne-glected aspect of molecular research. As a result, we lack a comprehensive understanding of the patterns of transcriptional variance across genes, and how this variance is linked to context-specific gene regulation and…
Ally Dworetsky, Benjamin A. Seitzman, Babatunde Adeyemo, Ashley N. Nielsen + 6 more
The cortex has a characteristic layout with specialized functional areas forming distributed large-scale networks. However, substantial work shows striking variation in this organization across people, which relates to differences in behavior. While most prior work treats all individual differences as equivalent and…
Julien F. Ayroles, Sean M. Buchanan, Chelsea Jenney, Kyobi Skutt-Kakaria + 4 more
Variability is ubiquitous in nature and a fundamental feature of complex systems. Few studies, however, have investigated variance itself as a trait under genetic control. By focusing primarily on trait means and ignoring the effect of alternative alleles on trait variability, we may be missing an important axis of…
Sarah Friedrich, Andreas Groll, Katja Ickstadt, Thomas Kneib + 3 more
methods and their applications Authors: ['Sarah Friedrich' 'Andreas Groll' 'Katja Ickstadt' 'Thomas Kneib' 'Markus Pauly' 'Jörg Rahnenführer' 'Tim Friede'] A range of regularization approaches have been proposed in the data sciences to overcome overfitting, to exploit sparsity or to improve prediction. Using a broad…
Zhenghao Wu, Tianhang Zhou
In the realm of multiscale molecular simulations, structure-based coarse graining is a prominent approach for creating efficient coarse-grained (CG) representations of soft matter systems such as polymers. This involves optimizing CG interactions by matching static correlation functions of corresponding degrees of…
Mohammed Ahmed Alomair, Syed Aflake Hussain Shah Gardazi
This study is completed for the estimation of unknown population variance for the variable of mean and variance of interest. To accomplish this task, a new generalized class of robust kind of variance estimators proposed utilizing known descriptives of auxiliary variable, for example, Mid-range, Hodges-Lehmann Mean…