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Interval Level of Measurement

Interval Level of Measurement

For effective statistical analysis, data are classified into four levels of measurement—nominal, ordinal, interval, and ratio.
Data measured using the interval scale are similar to ordinal level data because they have a definite arrangement. However, in the interval level of measurement, the differences between data values are meaningful even though the data does not have a starting point.
Temperature is measured using the interval scale. It is measurable data, and the difference between...

Prediction Intervals

Prediction Intervals

The interval estimate of any variable is known as the prediction interval. It helps decide if a point estimate is dependable.
However, the point estimate is most likely not the exact value of the population parameter, but close to it. After calculating point estimates, we construct interval estimates, called confidence intervals or prediction intervals. This prediction interval comprises a range of values unlike the point estimate and is a better predictor of the observed sample value, y.

Norton's Theorem

Norton's Theorem

Norton's theorem is a fundamental principle stating that a linear two-terminal circuit can be substituted with an equivalent circuit, which comprises a current source (ⅠN) in parallel with a resistor (RN). Here, ⅠN represents the short-circuit current flowing through the terminals, and RN stands for the input or equivalent resistance at the terminals when all independent sources are deactivated. This implies that the circuit illustrated in Figure (a) can be exchanged with the one depicted...

Routh-Hurwitz Criterion II

Routh-Hurwitz Criterion II

In the application of the Routh-Hurwitz criterion, two specific scenarios can arise that complicate stability analysis.
The first scenario occurs when a singular zero appears in the first column of the Routh table. This situation creates a division by zero issues. To resolve this, a small positive or negative number, denoted as epsilon (∈), is substituted for the zero. The stability analysis proceeds by assuming a sign for ∈. If ∈ is positive, any sign change in the first...

Critical Numbers and the Closed Interval Method

Critical Numbers and the Closed Interval Method

Understanding the maximum and minimum values of a function is essential for analyzing its overall behavior. These values, often referred to as extrema, provide insight into how a function behaves across its domain. In mathematical terms, extrema can be either local—representing peaks and valleys within a limited region—or absolute, indicating the highest or lowest points over an entire interval.A function’s extrema occur at critical numbers, which are values in the domain...

The Intermediate Value Theorem

The Intermediate Value Theorem

The Intermediate Value Theorem is a foundational result in calculus that guarantees the existence of solutions within certain intervals for continuous functions. Formally, the Intermediate Value Theorem states that if a function f is continuous on the closed interval [a, b], and if N is any value between f(a) and f(b), then there exists at least one c ∈ (a, b) such that f(c) = N. This theorem is instrumental in proving the existence of roots and in analyzing the behavior of continuous...

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BEDCrypt: Privacy-preserving interval analytics with homomorphic encryption.

Kimon Antonios Provatas, Ilias Georgakopoulos-Soares

|March 11, 2026

Summary

This summary is machine-generated.

BEDCrypt protects sensitive genomic data during analysis using homomorphic encryption. This privacy-preserving system enables secure interval analytics without revealing data to third-party servers.

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Area of Science:

Genomics
Bioinformatics
Cryptography

Background:

Genomic data contains sensitive information.
Outsourcing genomic analysis to third-party infrastructure poses privacy risks.
Protecting both data and queried loci is crucial.

Purpose of the Study:

To develop a privacy-preserving system for genomic interval analytics.
To enable secure analysis of genomic data on untrusted servers.

Main Methods:

Utilized homomorphic encryption for privacy preservation.
Developed BEDCrypt, a system operating on encrypted genomic interval data.
Implemented an honest-but-curious server model.

Main Results:

BEDCrypt enables core genomic interval analytics on encrypted data.
Functionalities include coverage summaries, interval intersections, and proximity queries.
The system returns encrypted results, with decryption performed client-side.

Conclusions:

BEDCrypt offers a robust solution for privacy-preserving genomic interval analytics.
It safeguards sensitive genomic data and query loci in outsourced environments.
Enables secure execution of various genomic analyses without data exposure.