On optimization, dynamics and uncertainty: A tutorial for gene-environment networks

Weber, Gerhard‐Wilhelm; Uğur, Ömür; Taylan, Pakize; Tezel, Aysun

doi:10.1016/j.dam.2008.06.030

Cited by 25 publications

(60 citation statements)

References 32 publications

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“…If the reader is interested in closer explanations and motivations about intervals, he/she may refer to [21,27,75,90,99,101].…”

Section: Modeling By Intervalsmentioning

confidence: 99%

“…Herewith, we permit regulation of the network's edge density in a more refined and soft way, and we can more confidently guarantee existence and tractability of genetic and metabolic processes. In [90,[97][98][99]101], we connected the discrete mathematics of networks with GSIP, by this introducing a new and pioneering scientific approach into computational biology. GSIP is an advancing wide problem class with many motivations, results, future challenges, and many practical applications even today [76,78,96].…”

Section: Introductionmentioning

confidence: 99%

“…In particular, for a large number of genes, the expression levels can easily be monitored by DNA-microarray experiments [18], but despite the fast technological advances, it is nevertheless affected with imprecision, ambivalence, and uncertainty [90,99,101]. Therefore, we included these errors into our model.…”

Section: Introductionmentioning

confidence: 99%

“…Likewise, for the environmental levels and concentrations, we are facing measurement and reliability problems, such that we represent them in error terms, too [55]. As introduced in [90,99,101], we represent various kinds of errors by intervals.…”

Section: Introductionmentioning

confidence: 99%

“…A simple additive shift included on the right-hand side of differential equations served to appropriately extend the model space; we interpret the shift by the relevant environmental factors. In [89,90,[97][98][99]101], we firstly extended genetic networks to gene-environment networks. In this study, the new nodes are environmental items such as poison in soil, groundwater, air or food, emissions, radiation, but also the welfare and living conditions, temperature (concerning, e.g., global warming), but also education and campaigns for a healthy lifestyle.…”

Section: Introductionmentioning

confidence: 99%

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A New Mathematical Approach in Environmental and Life Sciences: Gene–Environment Networks and Their Dynamics

Weber¹,

Gök

Söyler

2008

Environ Model Assess

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An important research area in life sciences is devoted to modeling, prediction, and dynamics of geneexpression patterns. As clearly understood in these days, this enterprise cannot become satisfactory without acknowledging the role of the environment. To a representation of past, present, and most likely future states, we also encounter measurement errors and uncertainties. This paper surveys and improves recent advances in understanding the foundations and interdisciplinary implications of the newly introduced geneenvironment networks, and it integrates the important theme of carbon dioxide emission reduction into the networks and dynamics. We also introduce some operational and managerial issues of practical working and decision making, expressed in terms of sliding windows, quadrants (modules) of parametric effects, and navigating (controlling) between such effects and directing them. Given data from DNA microarray experiments and environmental records, we extract nonlinear ordinary differential equations that contain parameters that have to be determined. For this, we employ modern (Chebychevian) approximation and (generalized semi-infinite) optimization. After this is provided, timediscretized dynamical systems are studied. A combinatorial algorithm with polyhedra sequences allows to detect the region of parametric stability. Finally, we analyze the topological landscape of gene-environment networks with its structural (in)stability. By embedding as a module and investigating CO 2 emission control and figuring out game theoretical aspects, we conclude. This pioneering work is theoretically elaborated, practically devoted to health care, medicine, education, living conditions, and environmental protection, and it invites the readers to future research.

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“…If the reader is interested in closer explanations and motivations about intervals, he/she may refer to [21,27,75,90,99,101].…”

Section: Modeling By Intervalsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A New Mathematical Approach in Environmental and Life Sciences: Gene–Environment Networks and Their Dynamics

Weber¹,

Gök

Söyler

2008

Environ Model Assess

Self Cite

View full text Add to dashboard Cite

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A review on data mining and continuous optimization applications in computational biology and medicine

Weber

Özöğür‐Akyüz

Kropat

2009

Birth Defects Research Pt C

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An emerging research area in computational biology and biotechnology is devoted to mathematical modeling and prediction of gene-expression patterns; it nowadays requests mathematics to deeply understand its foundations. This article surveys data mining and machine learning methods for an analysis of complex systems in computational biology. It mathematically deepens recent advances in modeling and prediction by rigorously introducing the environment and aspects of errors and uncertainty into the genetic context within the framework of matrix and interval arithmetics. Given the data from DNA microarray experiments and environmental measurements, we extract nonlinear ordinary differential equations which contain parameters that are to be determined. This is done by a generalized Chebychev approximation and generalized semi-infinite optimization. Then, time-discretized dynamical systems are studied. By a combinatorial algorithm which constructs and follows polyhedra sequences, the region of parametric stability is detected. In addition, we analyze the topological landscape of gene-environment networks in terms of structural stability. As a second strategy, we will review recent model selection and kernel learning methods for binary classification which can be used to classify microarray data for cancerous cells or for discrimination of other kind of diseases. This review is practically motivated and theoretically elaborated; it is devoted to a contribution to better health care, progress in medicine, a better education, and more healthy living conditions.

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Advanced Mathematical and Statistical Tools in the Dynamic Modeling and Simulation of Gene-Environment Regulatory Networks

Defterli

Purutçuoğlu

Weber

2014

Springer Proceedings in Mathematics &Amp; Statistics

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On optimization, dynamics and uncertainty: A tutorial for gene-environment networks

Cited by 25 publications

References 32 publications

A New Mathematical Approach in Environmental and Life Sciences: Gene–Environment Networks and Their Dynamics

A New Mathematical Approach in Environmental and Life Sciences: Gene–Environment Networks and Their Dynamics

A review on data mining and continuous optimization applications in computational biology and medicine

Advanced Mathematical and Statistical Tools in the Dynamic Modeling and Simulation of Gene-Environment Regulatory Networks

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