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

Definite Integral

Definite Integral

Consider a real-valued function defined on a closed interval. One of the fundamental objectives in calculus is to determine the area under the graph of such a function. When an exact computation is not readily available, this area can be estimated by dividing the interval into a finite number of equal subintervals. Each subinterval corresponds to a rectangle whose width is the length of the subinterval and whose height is determined by the value of the function at a selected point within that...

Definition of z-Transform

Definition of z-Transform

The z-transform is a powerful mathematical tool used in the analysis of discrete-time signals and systems. It is an essential analytical tool, analogous to the Laplace transform used in continuous-time systems. It plays a crucial role in the analysis of signals and systems, complementing the discrete-time Fourier transform. Both the z-transform and the Laplace transform convert differential or difference equations into algebraic equations, simplifying the process of solving complex problems.

Properties of Definite Integral I

Properties of Definite Integral I

A car’s motion over time can be effectively analyzed using integral calculus, particularly through the concept of the definite integral applied to a velocity–time relationship. The definite integral describes how velocity accumulates over a specified time interval to produce total displacement. From a geometric perspective, this displacement is interpreted as the area under the velocity–time curve. Several key properties of definite integrals make it easier to analyze motion...

The Precise Definition of a Limit

The Precise Definition of a Limit

Understanding the formal definition of a limit is essential for precise mathematical analysis. This concept allows us to rigorously determine how a function behaves near a particular point without relying on ambiguous notions such as "getting close." The ε-δ definition plays a foundational role in calculus, ensuring analytical clarity and logical consistency in limit evaluation.The formal definition states that the limit of a function f(x) as x approaches a is L, written asif for...

Properties of Definite Integral II

Properties of Definite Integral II

Definite integrals are essential tools in calculus, used to quantify accumulated change over an interval. A common physical application is calculating the total displacement from a velocity-time graph. If a velocity function, v(t), describes the motion of an object over time, the definite integral gives the net displacement between times a and b. This integral corresponds to the signed area under the velocity curve between those two points.Two fundamental properties of definite integrals aid in...

Integration by Parts: Definite Integrals

Integration by Parts: Definite Integrals

Definite integrals involving the product of two functions over a fixed interval can be evaluated using integration by parts. This method rewrites the integral as the difference of a product evaluated at the endpoints and a remaining definite integral that is often simpler to compute.A representative example is the definite integral of the inverse tangent function. Since there is no direct integration formula for arctan ⁡x, the integrand is rewritten as a product of arctan⁡ x and the...

You might also read

Related Articles

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

Sort by

Same author

Clinical and prognostic implications of circulating pentraxin 3 levels in non ST-elevation acute coronary syndrome.

Clinical biochemistry·2013

Same author

Electronic health records based phenotyping in next-generation clinical trials: a perspective from the NIH Health Care Systems Collaboratory.

Journal of the American Medical Informatics Association : JAMIA·2013

Same author

Postmarket surveillance and returned product analysis: success but not transparency.

Heart rhythm·2013

Same author

Predictors of stroke in patients with impaired glucose tolerance: results from the Nateglinide and Valsartan in Impaired Glucose Tolerance Outcomes Research trial.

Stroke·2013

Same author

Global variation in quality of care among patients hospitalized with acute heart failure in an international trial: findings from the acute study clinical effectiveness of nesiritide in decompensated heart failure trial (ASCEND-HF).

Circulation. Cardiovascular quality and outcomes·2013

Same author

Forging stronger partnerships between academic health centers and patient-driven organizations.

Academic medicine : journal of the Association of American Medical Colleges·2013

Search research articles

Related Experiment Video

Updated: Feb 14, 2026

Biomarkers in an Animal Model for Revealing Neural, Hematologic, and Behavioral Correlates of PTSD

Biomarkers in an Animal Model for Revealing Neural, Hematologic, and Behavioral Correlates of PTSD

Published on: October 10, 2012

Biomarker definitions and their applications.

Robert M Califf^1,2,3

¹1 12277 School of Medicine, Duke University , Durham, NC 27710, USA.

Experimental Biology and Medicine (Maywood, N.J.)

|February 7, 2018

Summary

This summary is machine-generated.

Clarifying biomarker definitions and applications is crucial for medical research and patient care. This review details FDA-NIH biomarker classifications, aiding rational therapeutic development and clinical practice.

Keywords:

Biomarkers cardiovascular epidemiology medicine monitoring pharmacology/toxicology

More Related Videos

Microarray-based Identification of Individual HERV Loci Expression: Application to Biomarker Discovery in Prostate Cancer

Microarray-based Identification of Individual HERV Loci Expression: Application to Biomarker Discovery in Prostate Cancer

Published on: November 2, 2013

Ecotoxicological Methodologies to Evaluate Biomarkers at Different Scales in Neotropical Anurans

Ecotoxicological Methodologies to Evaluate Biomarkers at Different Scales in Neotropical Anurans

Published on: April 28, 2023

Related Experiment Videos

Last Updated: Feb 14, 2026

Biomarkers in an Animal Model for Revealing Neural, Hematologic, and Behavioral Correlates of PTSD

Biomarkers in an Animal Model for Revealing Neural, Hematologic, and Behavioral Correlates of PTSD

Published on: October 10, 2012

Microarray-based Identification of Individual HERV Loci Expression: Application to Biomarker Discovery in Prostate Cancer

Microarray-based Identification of Individual HERV Loci Expression: Application to Biomarker Discovery in Prostate Cancer

Published on: November 2, 2013

Ecotoxicological Methodologies to Evaluate Biomarkers at Different Scales in Neotropical Anurans

Ecotoxicological Methodologies to Evaluate Biomarkers at Different Scales in Neotropical Anurans

Published on: April 28, 2023

Area of Science:

Biomedical research
Translational science
Regulatory science

Background:

Biomarker definitions and applications are often unclear, hindering medical therapeutics development, especially in chronic disease and nutrition.
Confusion in biomarker concepts impacts research and clinical practice, necessitating standardized definitions.

Purpose of the Study:

To review and clarify biomarker definitions using the joint FDA-NIH Biomarkers, EndpointS, and other Tools (BEST) resource.
To contextualize biomarker definitions within patient care, clinical research, and therapeutic development.
To explore emerging trends like composite and digital biomarkers and their implications.

Main Methods:

Review of recently established biomarker definitions from the FDA-NIH BEST resource.
Analysis of distinctions between biomarkers and clinical outcome assessments.
Exploration of various biomarker types: diagnostic, monitoring, predictive, prognostic, safety, and susceptibility/risk.

Main Results:

Established definitions provide context for biomarker use in different medical applications.
Identified key biomarker categories including diagnostic, monitoring, predictive, prognostic, safety, and susceptibility/risk.
Highlighted trends in complex composite and digital biomarkers, predictive toxicology, and systems pharmacology.

Conclusions:

Clear biomarker definitions and understanding their applications are vital for advancing medical diagnostics and therapeutics.
Emphasizes the need for quality, reproducibility, and interdisciplinary collaboration in biomarker development.
Biomarker-driven approaches, including digital tools, are reshaping medical product development.