Computational Algorithms Research Articles

Novel Partitioned Time-Stepping Algorithms for Fast Computation of Random Interface-Coupled Problems with Uncertain Parameters

Novel Partitioned Time-Stepping Algorithms for Fast Computation of Random Interface-Coupled Problems with Uncertain Parameters

An efficient healthcare system by cloud computing and clustering-based hybrid machine learning algorithm

Cloud computing, deep learning, clustering, genetic, and ensemble algorithms in healthcare are gaining popularity. This research highlights the relevance and complex repercussions of this integration. Cloud computing is transforming healthcare by providing scalable data storage and application access. It streamlines data exchange between hospitals, researchers, and institutions. Deep learning allows healthcare systems to use artificial intelligence for diagnostics, predictive analytics, and customized medication. Clustering algorithms segment patients, improving therapy and intervention customization. Genetic algorithms can optimize healthcare processes like treatment planning and resource allocation. Ensemble algorithms combine multiple models to improve predicted accuracy, enabling strong healthcare decision-making. This connection has several benefits. Healthcare systems become more efficient and scalable, resulting in cost-effective resource allocation. Access to patient data and apps promotes collaborative research and real-time healthcare. Deep learning algorithms can recognize complex medical data patterns, improving illness diagnosis and treatment results. Clustering algorithms streamline customized healthcare by stratifying individuals by clinical variables. Genetic algorithms optimize resource allocation, assuring healthcare resource efficiency. Ensemble algorithms improve predicted accuracy and clinical decision support system dependability. Its efficiency, accessibility, and prediction accuracy are positives, but security, resource constraints, interpretability, and ethical issues are obstacles.

Cryptographic Application of Elliptic Curve Generated through Centered Hexadecagonal Numbers

Background/Objectives: Elliptic Curve Cryptography (ECC) is a public-key encryption method that is similar to RSA. ECC uses the mathematical concept of elliptic curves to achieve the same level of security with significantly smaller keys, whereas RSA's security depends on large prime numbers. Elliptic curves and their applications in cryptography will be discussed in this paper. The elliptic curve is formed by the extension of a Diophantine pair of Centered Hexadecagonal numbers to a Diophantine triple with property D(8). Method: The Diffie–Hellman key exchange, named for Whitfield Diffie and Martin Hellman, was developed by Ralph Merkle and is a mathematical technique for safely transferring cryptographic keys over a public channel. Based on the Diffie–Hellman key exchange, the ElGamal encryption system is an asymmetric key encryption algorithm for public-key cryptography. The generation of keys, encryption and decryption are the three main operations of the ElGamal cryptosystem. Findings: Given the relative modesty of our objectives, the fundamental algebraic and geometric characteristics of elliptic curves shall be delineated. Then the behaviour of elliptic curves modulo p: ultimately, there is a fairly strong analogy between the structure of the points on an elliptic curve modulo p and the integers modulo n will be studied. In the end, elliptic curve ElGamal encryption analogues of Diffie–Hellman key exchange will be created. Novelty: Elliptic curves are encountered in a multitude of mathematical contexts and have a varied and fascinating history. Elliptic curves are very significant in number theory and are a focus of much recent work. The earlier research works in Elliptic Curve Cryptography has concentrated on computer algorithms and pairing – based algorithms. In this paper, the concept of polygonal numbers and its extension from Diophantine pair to triples is encountered, thus forming an elliptic curve and perform the encryption-decryption process. MSC Classification Number: 11D09, 11D99,11T71,11G05. Keywords: Elliptic curves, Cryptography, Encryption, Decryption, Centered polygonal numbers

Variable Neighborhood Search Based Human Learning Optimization Algorithm for Secure Data Analysis and Computing

Variable Neighborhood Search Based Human Learning Optimization Algorithm for Secure Data Analysis and Computing

ESTIMATION OF THE POSTMORTEM INTERVAL BY CRANIOENCEPHALIC THERMOMETRY WITH A SINGLE DISCRETE DECREASE IN AMBIENT TEMPERATURE

Aim– development of a method implemented in the format of a computer program for determining the postmortem interval (PMI) by cranioencephalic temperature (CT) of a corpse under conditions of cooling with a single discrete decrease in ambient temperature. Material and methods. Analytical and finite element modeling of CT dynamics with a single discrete decrease in ambient temperature is performed. Results. A mathematical model has been developed for determining the PMI and the uncertainty of its estimates with a single discrete decrease in the ambient temperature. The values of the constants of the model equation and their variances are determined on the basis of finite element modeling of CT dynamics under the specified cooling conditions. The computational algorithm of the specified method for determining PMI and contraindications to its use are implemented in the C# language in the form of the Warm Bodies DSC program. Conclusion. The developed method and the application implementing it are recommended for use in forensic medical practice to determine the PMI with a single discrete decrease in ambient temperature.

Abstract IA022: AI in bladder cancer pathology and research: What can we expect and what not?

Abstract Artificial intelligence (AI) applications are rapidly evolving, disruptive technologies that recently attracted tremendous public awareness including euphoria, bull runs at stock exchanges but also criticism and skepticism. Pathology, a crucial clinical diagnostic discipline, faces significant challenges despite its critical role and broad scope. A notable issue is the declining interest among medical graduates in pursuing further training in Surgical Pathology and Molecular Pathology. This disinterest is compounded by a trend towards part-time work and the aging demographic in Western industrial nations, which increases the demand for precise cancer diagnoses, molecular pathology and advanced oncological treatments. As the need for skilled pathologists grows, the availability of these professionals is steadily decreasing. Furthermore, political policies in heavily regulated healthcare systems (e.g., Germany) are exacerbating the shortage by limiting residency and specialist training positions despite the growing need. Adding to the reluctance among medical graduates to consider pathology as discipline is the looming “threat”” of replacing the field with Artificial Intelligence (AI) technologies. However, historical precedents suggest that necessity often spurs significant innovation. AI's role in pathology is expanding, reshaping the field with new technological advancements. AI, broadly encompassing various computational algorithms designed to perform tasks typically requiring human intelligence such as learning, reasoning, and pattern recognition, is now being applied extensively across different domains including medical diagnostics. Recent implementations in pathology include AI-driven algorithms that automate processes such as the Gleason grading of prostate biopsies, lymph node metastasis detection, detection of molecular bladder cancer subtypes or grading of kidney cancer showing high accuracy levels, speed and reproducibility in delivering results. These tools, while they do not replace pathologists, significantly reduce their workload by automating routine tasks, thus freeing up time for more complex diagnostic activities or simply dealing with the increasing workload. Despite the exciting possibilities, the use of AI in predicting molecular alterations, such as FGFR3 mutations in bladder cancer, faces limitations due to insufficient sensitivity and specificity, indicating that such technologies are not yet suitable for screening purposes. In conclusion, AI is increasingly vital in addressing the challenges of modern pathology, particularly in compensating for the shortage of pathologists. As technology advances, its integration into clinical practice offers promising solutions to enhance diagnostic accuracy and efficiency in uropathology, paving the way for more personalized and effective patient care. Citation Format: Markus Eckstein. AI in bladder cancer pathology and research: What can we expect and what not? [abstract]. In: Proceedings of the AACR Special Conference on Bladder Cancer: Transforming the Field; 2024 May 17-20; Charlotte, NC. Philadelphia (PA): AACR; Clin Cancer Res 2024;30(10_Suppl):Abstract nr IA022.

Attitude solving aided UWB/IMU integrated algorithm with real-time NLOS suppression

In response to the challenges posed by non-line-of-sight (NLOS) errors and inadequate attitude estimation accuracy in ultra-wideband and inertial measurement unit (UWB/IMU) integrated navigation algorithms in the complex environment, a robust UWB/IMU integrated positioning scheme is proposed. On one hand, the utilization of the robust local weighted regression algorithm (RLWR) is employed to mitigate the impact of NLOS errors on UWB data. RLWR incorporates information from nodes with known pseudo-range within local time intervals into the regression model, enhancing the identification of NLOS errors and improving positioning accuracy. On the other hand, the variational Bayesian filter algorithm based on adaptive conjugate gradient descent (ACGD) is proposed to improve the accuracy of IMU attitude calculation. The algorithm leverages an ACGD approach to optimize the attitude output of the accelerometer and magnetometer. The output is then incorporated into the variational Bayesian filtering system alongside the gyroscopic attitude output compensated by integrated positioning. Compared to conventional quaternion calculation and gradient descent linear filtering methods, the approach exhibits superior precision and stability. The experimental findings demonstrate that the amalgamation of the proposed NLSO identification suppression algorithm and the enhanced attitude computation algorithm confers significant advantages in terms of both localization accuracy and attitude estimation precision in complex environments. Moreover, the robust solution presented in the paper ensures the preservation of filter performance in the event of UWB measurement failure.

A Comparative Smart Computation Algorithm for Economic And Emission Dispatch Optimization of Tanjung Jati Power Plant

This research delves into optimization strategies for enhancing power generation efficiency and reducing costs in PLTU Tanjung Jati. The study explores three computational algorithms for optimization: Grey Wolf Optimization (GWO), Genetic Algorithm (GA), and Particle Swarm Optimization (PSO), focusing on optimizing power generation costs while considering penalty costs and emissions. Through extensive simulations and evaluations, the results indicate that the GWO algorithm achieves the most optimal outcomes in terms of cost optimization, demonstrating fast convergence and lesser simulation time compared to the other algorithms. The research provides valuable insights into selecting optimal algorithms for complex optimization problems like Combined Economic Emission Dispatch (CEED) in power generation systems, ultimately contributing to more efficient and cost-effective power generation.

Creating Patterns for Handicrafts and Embroidery

In this era of design and fashion , matching technology with aesthetics , selecting colors plays a major role in enhancing the beauty of designs .colors are a vital part of design artists to realm the designs , emotions , and make the paintings appear real .The color combination generator in this abstract deals with the enhancing of colors with the computational algorithms and make it simple for artisans compute the color for their use . The colors they use play a vital role in developing paintings and all other delusions such as combinations of arts , and creativity.This paper deals with the enhancing of handicrafts with the modern cultures trends such as coding , developing codes for several patterns in handicrafts to reduce the efforts of craftsmen engaged in the crafting , and framing of crafts such as ceramic crafts , pottery crafts , textile crafts , decorative and jewelry crafts.

A comparison of computational algorithms for the Bayesian analysis of clinical trials.

Clinical trials are increasingly using Bayesian methods for their design and analysis. Inference in Bayesian trials typically uses simulation-based approaches such as Markov Chain Monte Carlo methods. Markov Chain Monte Carlo has high computational cost and can be complex to implement. The Integrated Nested Laplace Approximations algorithm provides approximate Bayesian inference without the need for computationally complex simulations, making it more efficient than Markov Chain Monte Carlo. The practical properties of Integrated Nested Laplace Approximations compared to Markov Chain Monte Carlo have not been considered for clinical trials. Using data from a published clinical trial, we aim to investigate whether Integrated Nested Laplace Approximations is a feasible and accurate alternative to Markov Chain Monte Carlo and provide practical guidance for trialists interested in Bayesian trial design. Data from an international Bayesian multi-platform adaptive trial that compared therapeutic-dose anticoagulation with heparin to usual care in non-critically ill patients hospitalized for COVID-19 were used to fit Bayesian hierarchical generalized mixed models. Integrated Nested Laplace Approximations was compared to two Markov Chain Monte Carlo algorithms, implemented in the software JAGS and stan, using packages available in the statistical software R. Seven outcomes were analysed: organ-support free days (an ordinal outcome), five binary outcomes related to survival and length of hospital stay, and a time-to-event outcome. The posterior distributions for the treatment and sex effects and the variances for the hierarchical effects of age, site and time period were obtained. We summarized these posteriors by calculating the mean, standard deviations and the 95% equitailed credible intervals and presenting the results graphically. The computation time for each algorithm was recorded. The average overlap of the 95% credible interval for the treatment and sex effects estimated using Integrated Nested Laplace Approximations was 96% and 97.6% compared with stan, respectively. The graphical posterior densities for these effects overlapped for all three algorithms. The posterior mean for the variance of the hierarchical effects of age, site and time estimated using Integrated Nested Laplace Approximations are within the 95% credible interval estimated using Markov Chain Monte Carlo but the average overlap of the credible interval is lower, 77%, 85.6% and 91.3%, respectively, for Integrated Nested Laplace Approximations compared to stan. Integrated Nested Laplace Approximations and stan were easily implemented in clear, well-established packages in R, while JAGS required the direct specification of the model. Integrated Nested Laplace Approximations was between 85 and 269 times faster than stan and 26 and 1852 times faster than JAGS. Integrated Nested Laplace Approximations could reduce the computational complexity of Bayesian analysis in clinical trials as it is easy to implement in R, substantially faster than Markov Chain Monte Carlo methods implemented in JAGS and stan, and provides near identical approximations to the posterior distributions for the treatment effect. Integrated Nested Laplace Approximations was less accurate when estimating the posterior distribution for the variance of hierarchical effects, particularly for the proportional odds model, and future work should determine if the Integrated Nested Laplace Approximations algorithm can be adjusted to improve this estimation.

A general framework for developing computable clinical phenotype algorithms.

Present a general framework providing high-level guidance to developers of computable algorithms for identifying patients with specific clinical conditions (phenotypes) through a variety of approaches, including but not limited to machine learning and natural language processing methods to incorporate rich electronic health record data. Drawing on extensive prior phenotyping experiences and insights derived from three algorithm development projects conducted specifically for this purpose, our team with expertise in clinical medicine, statistics, informatics, pharmacoepidemiology, and healthcare data science methods conceptualized stages of development and corresponding sets of principles, strategies, and practical guidelines for improving the algorithm development process. We propose five stages of algorithm development and corresponding principles, strategies, and guidelines: 1) assessing fitness-for-purpose, 2) creating gold standard data, 3) feature engineering, 4) model development, and 5) model evaluation. This framework is intended to provide practical guidance and serve as a basis for future elaboration and extension.

The speech neuroprosthesis.

Loss of speech after paralysis is devastating, but circumventing motor-pathway injury by directly decoding speech from intact cortical activity has the potential to restore naturalcommunication and self-expression. Recent discoveries have defined how key features of speech production are facilitated by the coordinated activity of vocal-tract articulatory and motor-planning cortical representations. In this Review, we highlight such progress and how it has led to successful speech decoding, first in individuals implanted with intracranial electrodes for clinicalepilepsy monitoringand subsequently in individuals with paralysis as part ofearlyfeasibility clinical trials to restore speech. We discuss high-spatiotemporal-resolution neural interfaces and the adaptation of state-of-the-art speech computational algorithms that have driven rapidandsubstantial progress indecoding neural activity into text, audible speech, and facial movements. Although restoring natural speech is a long-term goal, speech neuroprostheses already have performance levels that surpass communication rates offered by current assistive-communication technology. Given this accelerated rate of progress in the field, we propose key evaluation metrics for speed and accuracy, among others, to help standardize across studies. We finish by highlighting several directions to more fully explore the multidimensional feature space of speech and language, which will continue to accelerate progress towards a clinically viable speech neuroprosthesis.

An evaluation of computational methods for aggregate data meta-analyses of diagnostic test accuracy studies

BackgroundA Generalized Linear Mixed Model (GLMM) is recommended to meta-analyze diagnostic test accuracy studies (DTAs) based on aggregate or individual participant data. Since a GLMM does not have a closed-form likelihood function or parameter solutions, computational methods are conventionally used to approximate the likelihoods and obtain parameter estimates. The most commonly used computational methods are the Iteratively Reweighted Least Squares (IRLS), the Laplace approximation (LA), and the Adaptive Gauss-Hermite quadrature (AGHQ). Despite being widely used, it has not been clear how these computational methods compare and perform in the context of an aggregate data meta-analysis (ADMA) of DTAs.MethodsWe compared and evaluated the performance of three commonly used computational methods for GLMM - the IRLS, the LA, and the AGHQ, via a comprehensive simulation study and real-life data examples, in the context of an ADMA of DTAs. By varying several parameters in our simulations, we assessed the performance of the three methods in terms of bias, root mean squared error, confidence interval (CI) width, coverage of the 95% CI, convergence rate, and computational speed.ResultsFor most of the scenarios, especially when the meta-analytic data were not sparse (i.e., there were no or negligible studies with perfect diagnosis), the three computational methods were comparable for the estimation of sensitivity and specificity. However, the LA had the largest bias and root mean squared error for pooled sensitivity and specificity when the meta-analytic data were sparse. Moreover, the AGHQ took a longer computational time to converge relative to the other two methods, although it had the best convergence rate.ConclusionsWe recommend practitioners and researchers carefully choose an appropriate computational algorithm when fitting a GLMM to an ADMA of DTAs. We do not recommend the LA for sparse meta-analytic data sets. However, either the AGHQ or the IRLS can be used regardless of the characteristics of the meta-analytic data.

Bio-inspired foveal super-resolution method for multi-focal-length images based on local gradient constraints

Most existing super-resolution (SR) imaging systems, inspired by the bionic compound eye, utilize image registration and reconstruction algorithms to overcome the angular resolution limitations of individual imaging systems. This article introduces a multi-aperture multi-focal-length imaging system and a multi-focal-length image super-resolution algorithm, mimicking the foveal imaging of the human eye. Experimental results demonstrate that with the proposed imaging system and an SR imaging algorithm inspired by the human visual system, the proposed method can enhance the spatial resolution of the foveal region by up to 4 × compared to the original acquired image. These findings validate the effectiveness of the proposed imaging system and computational imaging algorithm in enhancing image texture and spatial resolution.

Basic Computational Algorithms for Representing an Aircraft Flight (Calculation of 3D Displacement and Displaying)

This manuscript describes the computational process to calculate an airplane path and display it in a 2D and 3D coordinate system on a computer screen. The airplane movement is calculated as a function of its dynamic’s conditions according to physical and logical theory. Here, the flight is divided into maneuvers and the aircraft conditions are defined as boundary conditions. Then the aircraft position is calculated using nested loops, which execute the calculation procedure at every step time (Δt). The calculation of the aircraft displacement is obtained as a function of the aircraft speed and heading angles. The simulator was created using the C++ programming language, and each part of the algorithm was compiled independently to reduce the source code, allow easy modification, and improve the programming efficiency. Aerial navigation involves very complex phenomena to be considered for an appropriate representation; moreover, in this manuscript, the influence of the mathematical approach to properly represent the aircraft flight is described in detail. The flight simulator was successfully tested by simulating some basic theoretical flights with different maneuvers, which include stationary position, running along the way, take off, and some movements in the airspace. The maximum aircraft speed tested was 120 km/h, the maximum maneuver time was 12 min, and the space for simulation was assumed to be without obstacles. Here, the geometrical description of path and speed is analyzed according to the symmetric and asymmetric results. Finally, an analysis was conducted to evaluate the approach of the numerical methods used; after that, it was possible to confirm that precision increased as the step time was reduced. According to this analysis, no more than 500 steps are required for a good approach in the calculation of the aircraft displacement.

A Stepwise Cosimulation Framework for Modeling Critical Elements in Copper Porphyry Deposits

AbstractThe increased attention given to batteries has given rise to apprehensions regarding their availability; they have thus been categorized as essential commodities. Cobalt (Co), copper (Cu), lithium (Li), nickel (Ni), and molybdenum (Mo) are frequently selected as the primary metallic elements in lithium-ion batteries. The principal aim of this study was to develop a computational algorithm that integrates geostatistical methods and machine learning techniques to assess the resources of critical battery elements within a copper porphyry deposit. By employing a hierarchical/stepwise cosimulation methodology, the algorithm detailed in this research paper successfully represents both soft and hard boundaries in the simulation results. The methodology is evaluated using several global and local statistical studies. The findings indicate that the proposed algorithm outperforms the conventional approach in estimating these five elements, specifically when utilizing a stepwise estimation strategy known as cascade modeling. The proposed algorithm is also validated against true values by using a jackknife method, and it is shown that the method is precise and unbiased in the prediction of critical battery elements.

PLEIADES: A numerical framework dedicated to the multiphysics and multiscale nuclear fuel behavior simulation

The aim of this paper is to introduce the PLEIADES framework offering a set of services and numerical tools to model and simulate the behavior of nuclear fuels of different concepts of reactors. The framework provides in particular the following features: interfaces to manipulate meshes and fields, services to deal with different physical solvers, setup of coupling trees to realize multiphysics partitioned (accelerated) fixed point couplings, automated time-marching algorithm, checkpoint/restart strategies, capability to realize on-the-fly multiscale couplings. It is built with a permanent concern for sustainability, scalability and maintainability. PLEIADES framework supports multidimensional simulations, typically 1D, 2D and 3D, possibly multilayered. To date, this framework relies on the generic thermomechanical finite elements solver Cast3M to deal with partial derivative problems (mechanical, thermal or diffusion problems) at the scale of the structure or the (heterogeneous) microstructure. It also makes use of so-called point models (mainly based on ODE — ordinary differential equations) to describe the local (mesoscale) evolution of the material through the physics of irradiation. Several software applications are built on the PLEIADES framework, they can use its parallel features to use multiple processors. The multilayered calculation scheme provides a way to loosen the computations and access to a good parallel performance up to hundred cores. It is also possible to achieve efficient scalable concurrent multiscale simulations through finite element square (FE2) computational homogenization algorithms.

Current Applications of Artificial Intelligence in the Neonatal Intensive Care Unit

Artificial intelligence (AI) refers to computer algorithms that replicate the cognitive function of humans. Machine learning is widely applicable using structured and unstructured data, while deep learning is derived from the neural networks of the human brain that process and interpret information. During the last decades, AI has been introduced in several aspects of healthcare. In this review, we aim to present the current application of AI in the neonatal intensive care unit. AI-based models have been applied to neurocritical care, including automated seizure detection algorithms and electroencephalogram-based hypoxic-ischemic encephalopathy severity grading systems. Moreover, AI models evaluating magnetic resonance imaging contributed to the progress of the evaluation of the neonatal developing brain and the understanding of how prenatal events affect both structural and functional network topologies. Furthermore, AI algorithms have been applied to predict the development of bronchopulmonary dysplasia and assess the extubation readiness of preterm neonates. Automated models have been also used for the detection of retinopathy of prematurity and the need for treatment. Among others, AI algorithms have been utilized for the detection of sepsis, the need for patent ductus arteriosus treatment, the evaluation of jaundice, and the detection of gastrointestinal morbidities. Finally, AI prediction models have been constructed for the evaluation of the neurodevelopmental outcome and the overall mortality of neonates. Although the application of AI in neonatology is encouraging, further research in AI models is warranted in the future including retraining clinical trials, validating the outcomes, and addressing serious ethics issues.

Counting \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal{N}$$\\end{document} = 8 black holes as algebraic varieties

We calculate the helicity trace index B14 for \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal{N}$$\\end{document} = 8 pure D-brane black holes using various techniques of computational algebraic geometry and find perfect agreement with the existing results in the literature. For these black holes, microstate counting is equivalent to finding the number of supersymmetric vacua of a multi-variable supersymmetric quantum mechanics which in turn is equivalent to solving a set of multi-variable polynomial equations modulo gauge symmetries. We explore four different techniques to solve a set of polynomial equations, namely Newton Polytopes, Homotopy continuation, Monodromy and Hilbert series. The first three methods rely on a mixture of symbolic and high precision numerics whereas the Hilbert series is symbolic and admit a gauge invariant analysis. Furthermore, exploiting various exchange symmetries, we show that quartic and higher order terms are absent in the potential, which if present would have spoiled the counting. Incorporating recent developments in algebraic geometry focusing on computational algorithms, we have extended the scope of one of the authors previous works [1, 2] and presented a new perspective for the black hole microstate counting problem. This further establishes the pure D-brane system as a consistent model, bringing us a step closer to \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal{N}$$\\end{document} = 2 black hole microstate counting.

Improved Test Procedure and Sample Size Calculation for Assessing Similarity in Two-Group Comparative Studies with Heterogeneous Variances

AbstractThe two one-sided tests (TOST) method for mean equivalence or average equivalence has been extended to assessing similarity or switchability for individual equivalence in clinical trials. Tolerance interval procedures are available to establish similarity with respect to the proportion of the response differences covered by a prespecified threshold range. However, the extended TOST procedures based on tolerance intervals are potentially susceptible to the control of Type I errors. This article aims to present an exact approach with the specified Type I error probability for appraising similarity between two treatments in comparative studies with heterogeneous variances. Analytic examination and numerical comparison are conducted to clarify the utility of the suggested similarity test and the drawback of the current TOST procedures. To enhance the usefulness of the described exact method, the related power and sample size issues are also considered. Computer algorithms are provided to implement the proposed test procedure, power calculation, and sample size determination in similarity studies.