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作者： Gözükirmizi, Coşar Demiralp, Metin Istanbul Technical University Informatics Institute Group for Science and Methods of Computing Maslak 34469 Istanbul Turkey

Fluctuationlessness theorem is an important tool to approximate the matrix representation of functions. According to the theorem, matrix representation of a function may be approximated by the image of the matrix representation of its independent variable under the function. This may be used for numerical integration as long as the function and the Hilbert space used for approximation have certain properties. There are certain approaches to improve the accuracy obtained by this approximation. Extended fluctuationlessness theorem is proposed as a novel method to decompose a fluctuationlessness approximation into two additive fluctuationlessness approximations which may be calculated directly from the basis set. This work aims to form the foundations of novel divide and conquer algorithms that utilize several smaller matrix representations rather than the matrix representation of the independent variable.

关键词： Integration

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Combined small scale enhanced multivariance product representation

Combined small scale enhanced multivariance product represen...

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作者： Özay, Evrim Korkmaz Demiralp, Metin Istanbul Technical University Informatics Institute Group for Science and Methods of Computing Maslak 34469 Istanbul Türkiye Turkey

The main idea of this work, to empower High Dimensional Model Representation(HDMR) by combining two recently developed schemes, Enhanced Multivariance Product Representation(EMPR) and Combined Small Scale Model Representation (CSSHDMR). EMPR and CSSHDMR alternative methods to HDMR, because they provide better approximation comparing with HDMR not only for additive but also other kinds of functions. In this manner it is possible to obtain good quality approximations to multivariate functions with constant and univariate terms of HDMR. Using both schemes together it possible to decrease the number of HDMR components and number of CSSHDMR subgeometries.

关键词： Multivariant analysis

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Affine transformational enhanced multivariance product representation (ATEMPR) and its relation to rational approximants

Affine transformational enhanced multivariance product repre...

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作者： Kalay, Berfin Demiralp, Metin Istanbul Technical University Informatics Institute Group for Science and Methods of Computing Maslak 34469 Istanbul Türkiye Turkey

This work focuses on the development of a univariate function approximating method by using recently proposed extension to high dimensional model representation, enhanced multivariance product representation (EMPR). The method uses the target function's image under an affine transformation for EMPR instead of the function's itself. The affine transformation is a first degree polynomial in the target function with coefficients depending on the independent variable operator. These coefficients are taken as certain degree polynomials in the independent variable operator whose coefficients are to be determined by maximizing the constancy measurer of the EMPR for the image of the function under this transformation. The resulting scheme is in a rational function structure. The fundamentally conceptual and constructional issues are given here. The illustrative implementations will be given in the presentation and in the journal publication.

关键词： Rational functions

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Data completion via combined and optimized small scale high dimensional model representation

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AIP Conference Proceedings 2012年第1期1504卷 828-831页

作者： Evrim Korkmaz Metin Demiralp İstanbul Technical University Informatics Institute Group for Science and Methods of Computing Maslak 34469 İstanbul Turkey

This work deals with the data completion for a multivariate function whose values are given on the nodes, except a few ones, of an orthonormal hyperprismatic grid. The method we develop here uses a recently developed scheme we call "Combined Small Scale High Dimensional Model Representation (CSSHDMR)". This scheme is preferred to be used mostly at constant or perhaps univariate level bringing some discontinuities at the borders of subregions in the function values or its derivatives or both. In the case where certain function values or derivatives are unknown, these discontinuities can be suppressed to get those unknown values. This is done via optimisation. We try to present some details of this issue in this extended abstract.

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A Fluctuation Analysis at the Classical Limit for the Expectation Dynamics of a Single Quartic Quantum Anharmonic Oscillator

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AIP Conference Proceedings 2010年第1期1281卷 1950-1953页

作者： Muzaffer Ayvaz Metin Demiralp İstanbul Technical University Informatics Institute Group for Science and Methods of Computing Maslak 34469 İstanbul Türkiye (Turkey)

The definition of the fluctuation terms in the matrix representations of operators, especially function operators, brings a lot of facilitations to the numerical analysis of matrix representation issues. This work considers a one‐dimensional quantum oscillator with purely quartic anharmonicity and focuses on its position and momentum expectations. By using certain level commutator operation it is possible to get two ODEs as equations of motion, which are in classical nature when the fluctuation terms are omitted. To understand how fluctuation terms affect expectation dynamical analysis we add extra temporal unknowns and construct extra ODEs over them. There seem to be an infinite ODEs chain for fluctuation altough their truncations seem to be utilizable as approximations. Here basic theory is summarized. Further details will be prasented at the conference presentation.

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Numerical Studies on the Use of Enhanced Multivariance Product Representation as a Multiway Array Decomposer

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AIP Conference Proceedings 2010年第1期1281卷 1922-1925页

作者： Coşar Gözükirmizi Metin Demiralp Istanbul Technical University Informatics Institute Group for Science and Methods of Computing Maslak 34469 Ïstanbul Türkiye (Turkey)

High dimensional model representation (HDMR) is a method to approximate a multivariate function by the sum of a constant, univariate, bivariate and other higher variate functions. HDMR philosophy may also be used as a multiway array decomposer approximating an N‐way array by the sum of a constant, vector, matrix and higher way arrays. Enhanced multivariance product representation (EMPR) provides univariate factors for each term of the representation and the choice of the factors affect the quality of the truncation. In multiway array decomposition case, this approach coincides with taking the outer product of the components by certain predetermined vectors instead of vectors with all elements that are 1. This work focuses on this case, investigating the application of EMPR to multiway array decomposition.

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Validating the predictions of mathematical models describing tumor growth and treatment response

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arXiv 2025年

作者： Lorenzo, Guillermo Hormuth, David A. Wu, Chengyue Pash, Graham Chaudhuri, Anirban Lima, Ernesto A.B.F. Okereke, Lois C. Patel, Reshmi Willcox, Karen Yankeelov, Thomas E. Group of Numerical Methods in Engineering Department of Mathematics University of A Coruña Spain Oden Institute for Computational Engineering and Sciences The University of Texas at Austin AustinTX United States Livestrong Cancer Institutes The University of Texas at Austin AustinTX United States Department of Imaging Physics The University of Texas MD Anderson Cancer Center HoustonTX United States Department of Breast Imaging The University of Texas MD Anderson Cancer Center HoustonTX United States Department of Biostatistics The University of Texas MD Anderson Cancer Center HoustonTX United States Institute for Data Science in Oncology The University of Texas MD Anderson Cancer Center HoustonTX United States Texas Advanced Computing Center The University of Texas at Austin AustinTX United States Department of Biomedical Engineering The University of Texas at Austin AustinTX United States Department of Diagnostic Medicine The University of Texas at Austin AustinTX United States Department of Oncology The University of Texas at Austin AustinTX United States

Despite advances in methods to interrogate tumor biology, the observational and population-based approach of classical cancer research and clinical oncology does not enable anticipation of tumor outcomes to hasten the discovery of cancer mechanisms and personalize disease management. To address these limitations, individualized cancer forecasts have been shown to predict tumor growth and therapeutic response, inform treatment optimization, and guide experimental efforts. These predictions are obtained via computer simulations of mathematical models that are constrained with data from a patient’s cancer and experiments. This book chapter addresses the validation of these mathematical models to forecast tumor growth and treatment response. We start with an overview of mathematical modeling frameworks, model selection techniques, and fundamental metrics. We then describe the usual strategies employed to validate cancer forecasts in preclinical and clinical scenarios. Finally, we discuss existing barriers in validating these predictions along with potential strategies to address them. © 2025, CC BY-NC-ND.

关键词： Prediction models

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Symposium: Recent developments in Hilbert space tools and methodology for scientific computing

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AIP Conference Proceedings 2010年第1期1281卷 1921-1921页

作者： Demiralp, Metin Istanbul Technical University Informatics Institute Group for Science and Methods of Computing Maslak 34469 Istanbul Turkey

Metin Demiralp; Symposium: Recent Developments in Hilbert Space Tools and Methodology for Scientific computing, AIP Conference Proceedings, Volume 1281, Issue 1

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Reductive multilinear array decomposition based support functions in enhanced multivariance product representation (EMPR)

Reductive multilinear array decomposition based support func...

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作者： Demiralp, Emre Demiralp, Metin Department of Psychology University of Michigan 1012 East Hall 530 Church Street Ann Arbor MI 48109-1043 United States Istanbul Technical University Informatics Institute Group for Science and Methods of Computing Maslak 34469 Istanbul Turkey

Enhanced Multivariance Product Representation (EMPR) is a recently proposed extension to High Dimensional Model Representation (HDMR) which uses certain univariate support functions. EMPR components to a given multivariate function can be uniquely determined as long as the support functions are given. In a large number of cases the sum of the leading component of EMPR suffices as an approximation of the multivariate function of interest. In cases where this approximation is insufficient, a better match can be attained with the use of the univariate terms. The univariate truncation quality is determined by the support functions beside the target multivariate function. One simple way to get rather useful support functions is to use Reductive Multilinear Array Decomposition (RMAD) for the multilinear structures which can be obtained through a discretization of the independent variables' domains. This work considers these issues in conceptual framework and illustrative implementations will be presented in the relevant conference session and in the postconference journal publication.

关键词： Decomposition

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Do Leadership Styles Influence Employee Information Systems Security Intention? A Study of the Banking Industry

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Global Journal of Flexible Systems Management 2022年第4期23卷 535-550页

作者： Almeida, Murilo Catussi Yoshikuni, Adilson Carlos Dwivedi, Rajeev Larieira, Cláudio Luís Carvalho Group for Technology & Analytics in Management Accounting and Finance (TAMAF) Mackenzie Presbyterian University São Paulo Brazil Center of Applied Social Science Mackenzie Presbyterian University (UPM) São Paulo Brazil School of Business College of Professional Program Eastern Washington University Cheney WA United States Computing and Quantitative Methods (IMQ) at EAESP/FGV Mackenzie Presbyterian University São Paulo Brazil

The banking industry is highly prone to Information Systems (IS) security breaches from outside organizations and inside organizations. There are processes to monitor, detect, measure, and prevent IS security threats from an outside organization. However, inside organization threats to IS security are very challenging to monitor and detect, especially employee-related. The paper aims to understand how leadership plays a vital role in employee information systems security intention in the banking industry. Therefore, research applied full-range leadership style theory (FRLT) to assess the role of leadership style on employees’ information systems security intention. The study collects 517 responses from non-managerial bank employees from Brazilian banks using questionnaires and tested the theoretical relationship using partial least square structural equation modeling. The findings reveal that transformational leadership has a positive impact on the development of employee information systems security intention, whereas passive leadership harms employee intention toward information systems security. In addition to that results also show that age, education level, and work experience have moderating effects on employee intention toward information systems security. The research will help the banking industry to influence employee IS security intention through proactive and transformational leadership. In addition, it will also help leaders to understand employee intention toward information systems security aspects. The leadership role will enable IS security and flexibility in the organization. © 2022, The Author(s) under exclusive licence to Global Institute of Flexible Systems Management.

关键词： Brazilian multiple banks Full-range leadership theory (FRLT) Information systems security behavior Leadership styles

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