Work in Progress: A Literature Review On Computational & Numerical Methods in Engineering Education
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2022 ASEE Annual Conference & Exposition
August 23, 2022
June 26, 2022
June 29, 2022
Computers in Education 5 - Modulus 4
Nicolas leger florida international university.
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Nicolas Léger is currently an engineering and computing education Ph.D. student in the School of Universal Computing, Construction, and Engineering Education (SUCCEED) at Florida International University. He earned a B.S. in Chemical and Biomolecular Engineering from the University of Maryland at College Park in May 2021 and began his Ph.D. studies the following fall semester. His research interests center on numerical and computational methods in STEM education and in Engineering Entrepreneurship.
Bruk Berhane Florida International University
Scholars within computing and engineering education have broadly explored how students understand computing-related disciplines. Existing studies have led to publications on promising practices for teaching computing, such as evidence-based strategies for teaching computer science principles and programming languages like C++ and Java. However, other education research on computer-based technologies that students in engineering disciplines often use, such as MATLAB, Mathematica, Mathcad, Excel, and Aspen Plus, is limited. Initial analysis reveals that most of the published work on numerical and computational methods (NCM) in engineering education is in the form of textbooks used to introduce these software packages. However, a gap in the literature exists between understanding the technical content that these textbooks provide, and the degree to which effective pedagogy is used to teach this content. In other words, while textbooks exist to introduce these concepts, few studies have been done to measure the effectiveness of teaching these concepts. Understanding how to effectively teach these computing resources is important because it provides a foundation to allow engineering students to tackle their day-to-day calculations and be prepared with essential tools in the 21st century to tackle modern projects. Literature indicates that very little has been done to understand the impact of these computational technologies both on students as well as the perspective of faculty who teach these courses. As part of this literature review, we will review published scholarship to understand ways in which scholars have investigated the way that computational and numerical methods have been taught so far. This is a work in progress that will serve as a foundation for a broader study to understand effective pedagogies in computational and numerical methods in computing and engineering education.
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Leger, N., & Berhane, B. (2022, August), Work in Progress: A Literature Review On Computational & Numerical Methods in Engineering Education Paper presented at 2022 ASEE Annual Conference & Exposition, Minneapolis, MN. https://peer.asee.org/41195
ASEE holds the copyright on this document. It may be read by the public free of charge. Authors may archive their work on personal websites or in institutional repositories with the following citation: © 2022 American Society for Engineering Education. Other scholars may excerpt or quote from these materials with the same citation. When excerpting or quoting from Conference Proceedings, authors should, in addition to noting the ASEE copyright, list all the original authors and their institutions and name the host city of the conference. - Last updated April 1, 2015
Review of Numerical Methods for the Analysis of Arbitrarily-Shaped Microwave and Optical Dielectric Waveguides
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Numerical Methods with Applications
Autar K. Kaw , University of South Florida Follow Egwu K. Kalu , Florida A&M University Duc Nguyen , Old Dominion University
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This book entitled Numerical Methods with Applications is written primarily for engineering and science undergraduates taking a course in Numerical Methods. The textbook offers a unique treatise to numerical methods which is based on a holistic approach and short chapters. This book is a product of many years of work on educational projects funded since 2002 by the National Science Foundation. Since our belief continues to embrace open and uncomplicated dissemination, individual chapters of the book in pdf form are always available free of charge.
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Applied Mathematics | Mathematics
Contributors : Glen Besterfield, Sudeep Sarkar, Henry Welch, Ali Yalcin, Venkat Bhethanabotla
The material in the book is based upon work supported by the National Science Foundation under Grant# 0126793, 0341468 and 071624. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the National Science Foundation.
Kaw, Autar K.; Kalu, Egwu K.; and Nguyen, Duc, "Numerical Methods with Applications" (2011). Textbooks Collection . 11. https://digitalcommons.usf.edu/oa_textbooks/11
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Quantitative methods emphasize objective measurements and the statistical, mathematical, or numerical analysis of data collected through polls, questionnaires, and surveys, or by manipulating pre-existing statistical data using computational techniques . Quantitative research focuses on gathering numerical data and generalizing it across groups of people or to explain a particular phenomenon.
Babbie, Earl R. The Practice of Social Research . 12th ed. Belmont, CA: Wadsworth Cengage, 2010; Muijs, Daniel. Doing Quantitative Research in Education with SPSS . 2nd edition. London: SAGE Publications, 2010.
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Characteristics of Quantitative Research
Your goal in conducting quantitative research study is to determine the relationship between one thing [an independent variable] and another [a dependent or outcome variable] within a population. Quantitative research designs are either descriptive [subjects usually measured once] or experimental [subjects measured before and after a treatment]. A descriptive study establishes only associations between variables; an experimental study establishes causality.
Quantitative research deals in numbers, logic, and an objective stance. Quantitative research focuses on numeric and unchanging data and detailed, convergent reasoning rather than divergent reasoning [i.e., the generation of a variety of ideas about a research problem in a spontaneous, free-flowing manner].
Its main characteristics are :
- The data is usually gathered using structured research instruments.
- The results are based on larger sample sizes that are representative of the population.
- The research study can usually be replicated or repeated, given its high reliability.
- Researcher has a clearly defined research question to which objective answers are sought.
- All aspects of the study are carefully designed before data is collected.
- Data are in the form of numbers and statistics, often arranged in tables, charts, figures, or other non-textual forms.
- Project can be used to generalize concepts more widely, predict future results, or investigate causal relationships.
- Researcher uses tools, such as questionnaires or computer software, to collect numerical data.
The overarching aim of a quantitative research study is to classify features, count them, and construct statistical models in an attempt to explain what is observed.
Things to keep in mind when reporting the results of a study using quantitative methods :
- Explain the data collected and their statistical treatment as well as all relevant results in relation to the research problem you are investigating. Interpretation of results is not appropriate in this section.
- Report unanticipated events that occurred during your data collection. Explain how the actual analysis differs from the planned analysis. Explain your handling of missing data and why any missing data does not undermine the validity of your analysis.
- Explain the techniques you used to "clean" your data set.
- Choose a minimally sufficient statistical procedure ; provide a rationale for its use and a reference for it. Specify any computer programs used.
- Describe the assumptions for each procedure and the steps you took to ensure that they were not violated.
- When using inferential statistics , provide the descriptive statistics, confidence intervals, and sample sizes for each variable as well as the value of the test statistic, its direction, the degrees of freedom, and the significance level [report the actual p value].
- Avoid inferring causality , particularly in nonrandomized designs or without further experimentation.
- Use tables to provide exact values ; use figures to convey global effects. Keep figures small in size; include graphic representations of confidence intervals whenever possible.
- Always tell the reader what to look for in tables and figures .
NOTE: When using pre-existing statistical data gathered and made available by anyone other than yourself [e.g., government agency], you still must report on the methods that were used to gather the data and describe any missing data that exists and, if there is any, provide a clear explanation why the missing data does not undermine the validity of your final analysis.
Babbie, Earl R. The Practice of Social Research . 12th ed. Belmont, CA: Wadsworth Cengage, 2010; Brians, Craig Leonard et al. Empirical Political Analysis: Quantitative and Qualitative Research Methods . 8th ed. Boston, MA: Longman, 2011; McNabb, David E. Research Methods in Public Administration and Nonprofit Management: Quantitative and Qualitative Approaches . 2nd ed. Armonk, NY: M.E. Sharpe, 2008; Quantitative Research Methods. Writing@CSU. Colorado State University; Singh, Kultar. Quantitative Social Research Methods . Los Angeles, CA: Sage, 2007.
Basic Research Design for Quantitative Studies
Before designing a quantitative research study, you must decide whether it will be descriptive or experimental because this will dictate how you gather, analyze, and interpret the results. A descriptive study is governed by the following rules: subjects are generally measured once; the intention is to only establish associations between variables; and, the study may include a sample population of hundreds or thousands of subjects to ensure that a valid estimate of a generalized relationship between variables has been obtained. An experimental design includes subjects measured before and after a particular treatment, the sample population may be very small and purposefully chosen, and it is intended to establish causality between variables. Introduction The introduction to a quantitative study is usually written in the present tense and from the third person point of view. It covers the following information:
- Identifies the research problem -- as with any academic study, you must state clearly and concisely the research problem being investigated.
- Reviews the literature -- review scholarship on the topic, synthesizing key themes and, if necessary, noting studies that have used similar methods of inquiry and analysis. Note where key gaps exist and how your study helps to fill these gaps or clarifies existing knowledge.
- Describes the theoretical framework -- provide an outline of the theory or hypothesis underpinning your study. If necessary, define unfamiliar or complex terms, concepts, or ideas and provide the appropriate background information to place the research problem in proper context [e.g., historical, cultural, economic, etc.].
Methodology The methods section of a quantitative study should describe how each objective of your study will be achieved. Be sure to provide enough detail to enable the reader can make an informed assessment of the methods being used to obtain results associated with the research problem. The methods section should be presented in the past tense.
- Study population and sampling -- where did the data come from; how robust is it; note where gaps exist or what was excluded. Note the procedures used for their selection;
- Data collection – describe the tools and methods used to collect information and identify the variables being measured; describe the methods used to obtain the data; and, note if the data was pre-existing [i.e., government data] or you gathered it yourself. If you gathered it yourself, describe what type of instrument you used and why. Note that no data set is perfect--describe any limitations in methods of gathering data.
- Data analysis -- describe the procedures for processing and analyzing the data. If appropriate, describe the specific instruments of analysis used to study each research objective, including mathematical techniques and the type of computer software used to manipulate the data.
Results The finding of your study should be written objectively and in a succinct and precise format. In quantitative studies, it is common to use graphs, tables, charts, and other non-textual elements to help the reader understand the data. Make sure that non-textual elements do not stand in isolation from the text but are being used to supplement the overall description of the results and to help clarify key points being made. Further information about how to effectively present data using charts and graphs can be found here .
- Statistical analysis -- how did you analyze the data? What were the key findings from the data? The findings should be present in a logical, sequential order. Describe but do not interpret these trends or negative results; save that for the discussion section. The results should be presented in the past tense.
Discussion Discussions should be analytic, logical, and comprehensive. The discussion should meld together your findings in relation to those identified in the literature review, and placed within the context of the theoretical framework underpinning the study. The discussion should be presented in the present tense.
- Interpretation of results -- reiterate the research problem being investigated and compare and contrast the findings with the research questions underlying the study. Did they affirm predicted outcomes or did the data refute it?
- Description of trends, comparison of groups, or relationships among variables -- describe any trends that emerged from your analysis and explain all unanticipated and statistical insignificant findings.
- Discussion of implications – what is the meaning of your results? Highlight key findings based on the overall results and note findings that you believe are important. How have the results helped fill gaps in understanding the research problem?
- Limitations -- describe any limitations or unavoidable bias in your study and, if necessary, note why these limitations did not inhibit effective interpretation of the results.
Conclusion End your study by to summarizing the topic and provide a final comment and assessment of the study.
- Summary of findings – synthesize the answers to your research questions. Do not report any statistical data here; just provide a narrative summary of the key findings and describe what was learned that you did not know before conducting the study.
- Recommendations – if appropriate to the aim of the assignment, tie key findings with policy recommendations or actions to be taken in practice.
- Future research – note the need for future research linked to your study’s limitations or to any remaining gaps in the literature that were not addressed in your study.
Black, Thomas R. Doing Quantitative Research in the Social Sciences: An Integrated Approach to Research Design, Measurement and Statistics . London: Sage, 1999; Gay,L. R. and Peter Airasain. Educational Research: Competencies for Analysis and Applications . 7th edition. Upper Saddle River, NJ: Merril Prentice Hall, 2003; Hector, Anestine. An Overview of Quantitative Research in Composition and TESOL . Department of English, Indiana University of Pennsylvania; Hopkins, Will G. “Quantitative Research Design.” Sportscience 4, 1 (2000); "A Strategy for Writing Up Research Results. The Structure, Format, Content, and Style of a Journal-Style Scientific Paper." Department of Biology. Bates College; Nenty, H. Johnson. "Writing a Quantitative Research Thesis." International Journal of Educational Science 1 (2009): 19-32; Ouyang, Ronghua (John). Basic Inquiry of Quantitative Research . Kennesaw State University.
Strengths of Using Quantitative Methods
Quantitative researchers try to recognize and isolate specific variables contained within the study framework, seek correlation, relationships and causality, and attempt to control the environment in which the data is collected to avoid the risk of variables, other than the one being studied, accounting for the relationships identified.
Among the specific strengths of using quantitative methods to study social science research problems:
- Allows for a broader study, involving a greater number of subjects, and enhancing the generalization of the results;
- Allows for greater objectivity and accuracy of results. Generally, quantitative methods are designed to provide summaries of data that support generalizations about the phenomenon under study. In order to accomplish this, quantitative research usually involves few variables and many cases, and employs prescribed procedures to ensure validity and reliability;
- Applying well established standards means that the research can be replicated, and then analyzed and compared with similar studies;
- You can summarize vast sources of information and make comparisons across categories and over time; and,
- Personal bias can be avoided by keeping a 'distance' from participating subjects and using accepted computational techniques .
Babbie, Earl R. The Practice of Social Research . 12th ed. Belmont, CA: Wadsworth Cengage, 2010; Brians, Craig Leonard et al. Empirical Political Analysis: Quantitative and Qualitative Research Methods . 8th ed. Boston, MA: Longman, 2011; McNabb, David E. Research Methods in Public Administration and Nonprofit Management: Quantitative and Qualitative Approaches . 2nd ed. Armonk, NY: M.E. Sharpe, 2008; Singh, Kultar. Quantitative Social Research Methods . Los Angeles, CA: Sage, 2007.
Limitations of Using Quantitative Methods
Quantitative methods presume to have an objective approach to studying research problems, where data is controlled and measured, to address the accumulation of facts, and to determine the causes of behavior. As a consequence, the results of quantitative research may be statistically significant but are often humanly insignificant.
Some specific limitations associated with using quantitative methods to study research problems in the social sciences include:
- Quantitative data is more efficient and able to test hypotheses, but may miss contextual detail;
- Uses a static and rigid approach and so employs an inflexible process of discovery;
- The development of standard questions by researchers can lead to "structural bias" and false representation, where the data actually reflects the view of the researcher instead of the participating subject;
- Results provide less detail on behavior, attitudes, and motivation;
- Researcher may collect a much narrower and sometimes superficial dataset;
- Results are limited as they provide numerical descriptions rather than detailed narrative and generally provide less elaborate accounts of human perception;
- The research is often carried out in an unnatural, artificial environment so that a level of control can be applied to the exercise. This level of control might not normally be in place in the real world thus yielding "laboratory results" as opposed to "real world results"; and,
- Preset answers will not necessarily reflect how people really feel about a subject and, in some cases, might just be the closest match to the preconceived hypothesis.
Finding Examples of How to Apply Different Types of Research Methods
SAGE publications is a major publisher of studies about how to design and conduct research in the social and behavioral sciences. Their SAGE Research Methods Online and Cases database includes contents from books, articles, encyclopedias, handbooks, and videos covering social science research design and methods including the complete Little Green Book Series of Quantitative Applications in the Social Sciences and the Little Blue Book Series of Qualitative Research techniques. The database also includes case studies outlining the research methods used in real research projects. This is an excellent source for finding definitions of key terms and descriptions of research design and practice, techniques of data gathering, analysis, and reporting, and information about theories of research [e.g., grounded theory]. The database covers both qualitative and quantitative research methods as well as mixed methods approaches to conducting research.
SAGE Research Methods Online and Cases
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Review of Some Numerical Methods for Solving Initial Value Problems for Ordinary Differential Equations
Fadugba Sunday Emmanuel 1 , Adebayo Kayode James 1 , Ogunyebi Segun Nathaniel 1 , Okunlola Joseph Temitayo 2
1 Department of Mathematics, Ekti State University, Ado Ekiti, Nigeria
2 Department of Mathematical and Physical Sciences, Afe Babalola University, Ado Ekiti, Nigeria
Numerical analysis is a subject that is concerned with how to solve real life problems numerically. Numerical methods form an important part of solving differential equations emanated from real life situations, most especially in cases where there is no closed-form solution or difficult to obtain exact solutions. The main aim of this paper is to review some numerical methods for solving initial value problems of ordinary differential equations. The comparative study of the Third Order Convergence Numerical Method (FS), Adomian Decomposition Method (ADM) and Successive Approximation Method (SAM) in the context of the exact solution is presented. The methods will be compared in terms of convergence, accuracy and efficiency. Five illustrative examples/test problems were solved successfully. The results obtained show that the three methods are approximately the same in terms of accuracy and convergence in the case of first order linear ordinary differential equations. It is also observed that FS, ADM and SAM were found to be computationally efficient for the linear ordinary differential equations. In the case of the non-linear ordinary differential equations, SAM is found to be more accurate and converges faster to the exact solution than the FS and ADM. Hence, It is clearly seen that the ADM is found to be better than the FS and SAM in the case of non-linear differential equations in terms of computational efficiency.
Accuracy, Adomian Decomposition Method, Convergence, Differential Equation, Efficiency, Initial Value Problem, Successive Approximation Method
Fadugba Sunday Emmanuel, Adebayo Kayode James, Ogunyebi Segun Nathaniel, Okunlola Joseph Temitayo. (2020). Review of Some Numerical Methods for Solving Initial Value Problems for Ordinary Differential Equations. International Journal of Applied Mathematics and Theoretical Physics , 6 (1), 7-13. https://doi.org/10.11648/j.ijamtp.20200601.12
Copyright © 2020 Authors retain the copyright of this article. This article is an open access article distributed under the Creative Commons Attribution License ( http://creativecommons.org/licenses/by/4.0/ ) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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Lau F, Kuziemsky C, editors. Handbook of eHealth Evaluation: An Evidence-based Approach [Internet]. Victoria (BC): University of Victoria; 2017 Feb 27.
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From: Chapter 9 Methods for Literature Reviews
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Specific Heat Smoothing Methods for Numerical Heat Transfer Analysis Involving Phase Change in a Model Food System
- Shengyue Shan 1 ,
- Dennis R. Heldman 1 , 2 &
- Osvaldo H. Campanella 1 , 3
Food Engineering Reviews ( 2023 ) Cite this article
For high-moisture foods, the water latent heat of fusion during a phase change process causes a significant discontinuity in the temperature-dependent apparent specific heat of food products, which leads to complications during the numerical solution of heat transfer problems. The discontinuity in the apparent specific heat as a function of temperature can be alleviated by smoothing. Previously, a piecewise approximation smoothing method was developed and extensively used. In this study, different approaches which are based on curve fitting, the use of a sigmoid function, and data interpolation were developed. The performance of these methods in numerical simulations of food freezing and thawing processes was evaluated. The heat transfer model was implemented with the MATLAB PDE Toolbox. Simulated temperature profiles of representative freezing/thawing processes showed a reasonable agreement with experimental values collected from the literature. The optimal smoothing method showed comparatively less numerical oscillation, higher accuracy, faster computation speed, and simplicity in implementation. Recommendations were provided for the utilization of the smoothing methods under different circumstances.
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The authors thank Professor Edward Overman from the Department of Mathematics at The Ohio State University for the fruitful discussions.
This work was supported by the Dale A. Seiberling Endowment Fund and Carl E. Haas Endowed Chair Fund from College of Food, Agricultural and Environmental Sciences at the Ohio State University.
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Department of Food Science and Technology, The Ohio State University, 2015 Fyffe Road, 43210, Columbus, OH, USA
Shengyue Shan, Dennis R. Heldman & Osvaldo H. Campanella
Department of Food, Agricultural and Biological Engineering, The Ohio State University, 590 Woody Hayes Drive, 43210, Columbus, OH, USA
Dennis R. Heldman
Whistler Center for Carbohydrate Research, Purdue University, 745 Agriculture Mall Drive, 47907, West Lafayette, IN, USA
Osvaldo H. Campanella
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All the authors have read the manuscript and agreed to submit to Food Engineering Reviews. The contribution of each author can be seen below: Shenyue Shan (SS): Conceptualization, data curation, formal analysis, investigation, methodology, writing original manuscript. Dennis R. Heldman (DRH): Draft review & editing, funding. Osvaldo H Campanella (OHC): investigation, methodology, data analysis, writing- review & editing, funding.
Correspondence to Osvaldo H. Campanella .
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Shan, S., Heldman, D.R. & Campanella, O.H. Specific Heat Smoothing Methods for Numerical Heat Transfer Analysis Involving Phase Change in a Model Food System. Food Eng Rev (2023). https://doi.org/10.1007/s12393-023-09359-x
Received : 03 July 2023
Accepted : 28 September 2023
Published : 08 November 2023
DOI : https://doi.org/10.1007/s12393-023-09359-x
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This article is part of the research topic.
Community Series in Mental Illness, Culture, and Society: Dealing with the COVID-19 Pandemic, volume VIII
Arts Therapies for mental disorders in COVID-19 patients: A comprehensive review
- 1 Macau University of Science and Technology, Macao, SAR China
- 2 Faculty of Humanities and Arts, Macau University of Science and Technology, China
- 3 The Fourth People's Hospital of Qinghai Province, China
- 4 Guangzhou Wanqu Cooperative Institute of Design, China
- 5 State Key Laboratory of Quality Research in Chinese Medicines, Macau University of Science and Technology, China
- 6 Faculty of Chinese Medicine, Macau University of Science and Technology, China
- 7 Guangdong-Hong Kong-Macao Joint Laboratory for Contaminants Exposure and Health, Guangdong University of Technology, China
The final, formatted version of the article will be published soon.
Background and objective: The COVID-19 global pandemic has necessitated the urgency for innovative mental health interventions. We performed a comprehensive review of the available literature on the utility and efficacy of arts therapies in treating mental health problems, with special emphasis on their deployment during the COVID-19 pandemic, aiming to provide some evidence for the application of this therapy. Methods: The potential studies were systematically sourced from 5 authoritative databases: PubMed, Embase, the Cochrane Library, Web of Science, and the CNKI database. The evaluation of these studies was conducted based on stringent criteria, including validity, suitability, therapeutic potential, and consistency. Each piece of included literature was meticulously scored in accordance with these criteria, thus ensuring the inclusion of only the most robust studies in this review. The data from these Randomized Controlled Trials (RCTs) were carefully extracted using the PICO(S) framework, ensuring a comprehensive and systemic approach to data collection. In order to emphasize the variability in the effects of differing arts therapies on COVID-19-induced psychiatric disturbances, the sourced literature was systematically categorized and scrutinized based on distinct modalities. Results: Out of the 7,250 sourced articles, 16 satisfied the inclusion conditions. The therapies were predominantly meditation (n=7), supplemented by individual studies on color therapy (n=3), music therapy (n=2), and single studies on horticultural therapy, dance therapy, mindfulness and music therapy, and yoga and music therapy (n=4 collectively). These various forms of arts therapies had a positive short to medium-term impact on the mental health of COVID-19 patients. Besides improving patients' physical and mental health, these therapies can also be employed to mitigate mental health issues among healthcare professionals. Conclusion: The COVID-19 pandemic has profound and long-lasting implications for public mental health. Diverse forms of arts therapies are potentially effective in addressing related psychiatric symptoms. The integration of artificial intelligence might further enhance the efficacy and scalability of arts therapies in future implementations.
Keywords: Mental Disorders, COVID-19, post-acute COVID-19 syndrome, arts therapies, Psychotherapy
Received: 06 Sep 2023; Accepted: 13 Nov 2023.
Copyright: © 2023 Luo, Zhang, Shi, He, WANG, Wu and Huang. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY) . The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
* Correspondence: Dr. JUE WANG, State Key Laboratory of Quality Research in Chinese Medicines, Macau University of Science and Technology, Macau, China Prof. Qibiao Wu, State Key Laboratory of Quality Research in Chinese Medicines, Macau University of Science and Technology, Macau, China Dr. Guanghui Huang, Faculty of Humanities and Arts, Macau University of Science and Technology, Macau, China