Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

Exponential Functions with Base e

Exponential Functions with Base e

Exponential functions with base e are essential for modeling continuous processes of growth and decay. The constant e, approximately 2.718, naturally arises in systems where change occurs proportionally to the current value. A positive exponent represents continuous growth, while a negative exponent represents continuous decay. These functions are especially useful for describing situations where change happens smoothly over time rather than in discrete steps.One clear example of exponential...

Introduction to Exponential Functions

Introduction to Exponential Functions

Exponential functions are fundamental in modeling dynamic processes where the rate of change is proportional to the current value. Defined by f(x) = bx, where b is a positive constant not equal to one, they form the basis for describing processes of growth and decay depending on whether the base b is greater than or less than one.Exponential models describe situations where change occurs at a rate proportional to the current amount. These include phenomena such as bacterial proliferation,...

Protein Families

Protein Families

Protein families are groups of homologous proteins; that is, they have similarities in amino acid sequences and three-dimensional structures. Protein families usually occur because of gene duplication, where an additional copy of a gene is inserted into the genome of an organism. Mutations that change the amino acids but still allow the protein to be properly synthesized, will lead to new protein family members. If these new proteins contain similar amino acids in key...

Protein Families

Protein Families

Gene Families

Gene Families

Gene families consist of groups of genes proposed to have originated from a common ancestor. Typically these arise through events in which a gene or genes are mistakenly duplicated during cell division. Unlike their parent genes (which are subject to selection pressure to maintain function), these gene copies do not need to preserve their sequences and may evolve at a relatively faster rate.
Occasionally these regions can be adapted to take on new roles within the organism, becoming novel genes...

Gene Families

Gene Families

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by

Same author

Tracking the longitudinal course of physiologic and mental health functioning among individuals in substance use disorder treatment.

Frontiers in psychiatry·2026

Same author

Multilevel functional quantile principal component analysis.

Biostatistics (Oxford, England)·2026

Same author

Associations of accelerometry-derived time in major activity intensities with cognitive outcomes: a compositional data analysis approach.

The journals of gerontology. Series A, Biological sciences and medical sciences·2026

Same author

Spinal cord stimulation for upper limb motor function in people with chronic post-stroke hemiparesis: a feasibility trial.

Nature medicine·2026

Same author

Correcting Measurement Error and Zero Inflation in Functional Covariates for Scalar-on-Function Quantile Regression.

Statistics in medicine·2026

Same author

Oregon's Hospital Rate Cap: A Questionable Measure.

Health affairs (Project Hope)·2026

Same journal

Fast penalized generalized estimating equations for large longitudinal functional datasets.

Biometrics·2026

Same journal

Causally-interpretable random-effects meta-analysis.

Biometrics·2026

Same journal

Statistical inference for mean function of partially observed functional time series.

Biometrics·2026

Same journal

Subgroup identification via Interaction Tree and Mixed Model for Repeated Measures with application to Alzheimer's disease.

Biometrics·2026

Same journal

Finite mixtures of linear quantile regressions with concomitant variables: a solution to endogeneity in longitudinal data modeling.

Biometrics·2026

Same journal

Discussion on "INTACT: a method for integration of longitudinal physical activity data from multiple sources" by Jingru Zhang, Erjia Cui, Hongzhe Li, and Haochang Shou.

Biometrics·2026

See all related articles

Search research articles

Related Experiment Video

Updated: Feb 6, 2026

Examining BCL-2 Family Function with Large Unilamellar Vesicles

Examining BCL-2 Family Function with Large Unilamellar Vesicles

Published on: October 5, 2012

Registration for exponential family functional data.

Julia Wrobel¹, Vadim Zipunnikov², Jennifer Schrack^3,4

¹Department of Biostatistics, Mailman School of Public Health, Columbia University, New York, New York, U.S.A.

|August 22, 2018

Summary

This summary is machine-generated.

We developed a new, efficient method to analyze functional data by separating amplitude and phase variability. This approach improves the clarity of patterns in complex datasets, like activity timing from aging studies.

Keywords:

Accelerometers Alignment Binary functional data Functional principal component analysis Generalized functional data Warping

More Related Videos

Brain Infarct Segmentation and Registration on MRI or CT for Lesion-symptom Mapping

Brain Infarct Segmentation and Registration on MRI or CT for Lesion-symptom Mapping

Published on: September 25, 2019

Four-Dimensional CT Analysis Using Sequential 3D-3D Registration

Four-Dimensional CT Analysis Using Sequential 3D-3D Registration

Published on: November 23, 2019

Related Experiment Videos

Last Updated: Feb 6, 2026

Examining BCL-2 Family Function with Large Unilamellar Vesicles

Examining BCL-2 Family Function with Large Unilamellar Vesicles

Published on: October 5, 2012

Brain Infarct Segmentation and Registration on MRI or CT for Lesion-symptom Mapping

Brain Infarct Segmentation and Registration on MRI or CT for Lesion-symptom Mapping

Published on: September 25, 2019

Four-Dimensional CT Analysis Using Sequential 3D-3D Registration

Four-Dimensional CT Analysis Using Sequential 3D-3D Registration

Published on: November 23, 2019

Area of Science:

Statistics
Functional Data Analysis
Biostatistics

Background:

Functional data analysis often struggles with separating amplitude and phase variability.
Existing registration methods for discrete functional data can be computationally intensive and require pre-smoothing.

Purpose of the Study:

To introduce a novel, computationally efficient method for separating amplitude and phase variability in exponential family functional data.
To address limitations of existing methods for discrete functional data registration.

Main Methods:

Alternating between generalized functional principal components analysis (gFPCA) for template functions and estimation of smooth warping functions.
Focusing on the likelihood of observed data, avoiding pre-smoothing steps.
Implementing computationally efficient algorithms for both steps.

Main Results:

The proposed method effectively separates amplitude and phase variability in functional data.
Demonstrated improved accuracy and computational efficiency compared to competing approaches in simulations.
Successfully analyzed binary functional data from the Baltimore Longitudinal Study on Aging, revealing clear diurnal activity patterns after alignment.

Conclusions:

The novel method offers an accurate and efficient approach to functional data registration, particularly for discrete data.
The technique enhances the interpretability of complex functional data by aligning curves.
Publicly available code facilitates reproducibility and application of the method.