Rough Fuzzy Pattern Recognition

Learn how to apply rough-fuzzy computing techniques to solve problems in bioinformatics and medical image processing Emphasizing applications in bioinformatics and medical image processing, this text offers a clear framework that enables ...

Author: Pradipta Maji

Publisher: John Wiley & Sons

ISBN: 111800440X

Category: Technology & Engineering

Page: 312

View: 455

Learn how to apply rough-fuzzy computing techniques to solve problems in bioinformatics and medical image processing Emphasizing applications in bioinformatics and medical image processing, this text offers a clear framework that enables readers to take advantage of the latest rough-fuzzy computing techniques to build working pattern recognition models. The authors explain step by step how to integrate rough sets with fuzzy sets in order to best manage the uncertainties in mining large data sets. Chapters are logically organized according to the major phases of pattern recognition systems development, making it easier to master such tasks as classification, clustering, and feature selection. Rough-Fuzzy Pattern Recognition examines the important underlying theory as well as algorithms and applications, helping readers see the connections between theory and practice. The first chapter provides an introduction to pattern recognition and data mining, including the key challenges of working with high-dimensional, real-life data sets. Next, the authors explore such topics and issues as: Soft computing in pattern recognition and data mining A mathematical framework for generalized rough sets, incorporating the concept of fuzziness in defining the granules as well as the set Selection of non-redundant and relevant features of real-valued data sets Selection of the minimum set of basis strings with maximum information for amino acid sequence analysis Segmentation of brain MR images for visualization of human tissues Numerous examples and case studies help readers better understand how pattern recognition models are developed and used in practice. This text—covering the latest findings as well as directions for future research—is recommended for both students and practitioners working in systems design, pattern recognition, image analysis, data mining, bioinformatics, soft computing, and computational intelligence.

Rough Fuzzy Image Analysis

Near sets are a recent generalization of rough sets that have proven to be useful
in image analysis and pattern 0-2 recognition*******. This volume fully reflects the
diversity and richness. *See, e.g., Zadeh, L.A., Fuzzy sets. Information and ...

Author: Sankar K. Pal

Publisher: CRC Press

ISBN: 9781439803301

Category: Mathematics

Page: 266

View: 468

Fuzzy sets, near sets, and rough sets are useful and important stepping stones in a variety of approaches to image analysis. These three types of sets and their various hybridizations provide powerful frameworks for image analysis. Emphasizing the utility of fuzzy, near, and rough sets in image analysis, Rough Fuzzy Image Analysis: Foundations and Methodologies introduces the fundamentals and applications in the state of the art of rough fuzzy image analysis. In the first chapter, the distinguished editors explain how fuzzy, near, and rough sets provide the basis for the stages of pictorial pattern recognition: image transformation, feature extraction, and classification. The text then discusses hybrid approaches that combine fuzzy sets and rough sets in image analysis, illustrates how to perform image analysis using only rough sets, and describes tolerance spaces and a perceptual systems approach to image analysis. It also presents a free, downloadable implementation of near sets using the Near Set Evaluation and Recognition (NEAR) system, which visualizes concepts from near set theory. In addition, the book covers an array of applications, particularly in medical imaging involving breast cancer diagnosis, laryngeal pathology diagnosis, and brain MR segmentation. Edited by two leading researchers and with contributions from some of the best in the field, this volume fully reflects the diversity and richness of rough fuzzy image analysis. It deftly examines the underlying set theories as well as the diverse methods and applications.

Granular Neural Networks Pattern Recognition and Bioinformatics

13(9), 3944–3955 (2013) Pal, S.K., Meher, S.K., Dutta, S.: Class-dependent
rough-fuzzy granular space, dispersion index and classification. Pattern Recogn.
45(7), 2690–2707 (2012) Pal, S.K., Mitra, P.: Multispectral image segmentation
using ...

Author: Sankar K. Pal

Publisher: Springer

ISBN: 331957115X

Category: Computers

Page: 227

View: 749

This book provides a uniform framework describing how fuzzy rough granular neural network technologies can be formulated and used in building efficient pattern recognition and mining models. It also discusses the formation of granules in the notion of both fuzzy and rough sets. Judicious integration in forming fuzzy-rough information granules based on lower approximate regions enables the network to determine the exactness in class shape as well as to handle the uncertainties arising from overlapping regions, resulting in efficient and speedy learning with enhanced performance. Layered network and self-organizing analysis maps, which have a strong potential in big data, are considered as basic modules,. The book is structured according to the major phases of a pattern recognition system (e.g., classification, clustering, and feature selection) with a balanced mixture of theory, algorithm, and application. It covers the latest findings as well as directions for future research, particularly highlighting bioinformatics applications. The book is recommended for both students and practitioners working in computer science, electrical engineering, data science, system design, pattern recognition, image analysis, neural computing, social network analysis, big data analytics, computational biology and soft computing.

Pattern Recognition And Big Data

Rough Sets, 5946, 106–129 (2010). S. K. Pal, Granular mining and rough-fuzzy
pattern recognition: a way to natural computation, (Feature Article), IEEE
Intelligent Informatics Bulletin, 13(1), 3–13 (2012). S. K. Pal, S. K. Meher and S.
Dutta, ...

Author: Pal Sankar Kumar

Publisher: World Scientific

ISBN: 9813144564

Category: Computers

Page: 876

View: 775

Containing twenty six contributions by experts from all over the world, this book presents both research and review material describing the evolution and recent developments of various pattern recognition methodologies, ranging from statistical, linguistic, fuzzy-set-theoretic, neural, evolutionary computing and rough-set-theoretic to hybrid soft computing, with significant real-life applications. Pattern Recognition and Big Data provides state-of-the-art classical and modern approaches to pattern recognition and mining, with extensive real life applications. The book describes efficient soft and robust machine learning algorithms and granular computing techniques for data mining and knowledge discovery; and the issues associated with handling Big Data. Application domains considered include bioinformatics, cognitive machines (or machine mind developments), biometrics, computer vision, the e-nose, remote sensing and social network analysis.

Scalable Pattern Recognition Algorithms

IEEE Trans Syst Man Cybern Part B Cybern 37(6):1529–1540 Maji P, Pal SK (
2012) Rough-fuzzy pattern recognition: applications in bioinformatics and
medical imaging. Wiley-IEEE Computer Society Press, New Jersey Maji P, Paul S
(2011) ...

Author: Pradipta Maji

Publisher: Springer Science & Business Media

ISBN: 3319056301

Category: Computers

Page: 304

View: 622

This book addresses the need for a unified framework describing how soft computing and machine learning techniques can be judiciously formulated and used in building efficient pattern recognition models. The text reviews both established and cutting-edge research, providing a careful balance of theory, algorithms, and applications, with a particular emphasis given to applications in computational biology and bioinformatics. Features: integrates different soft computing and machine learning methodologies with pattern recognition tasks; discusses in detail the integration of different techniques for handling uncertainties in decision-making and efficiently mining large biological datasets; presents a particular emphasis on real-life applications, such as microarray expression datasets and magnetic resonance images; includes numerous examples and experimental results to support the theoretical concepts described; concludes each chapter with directions for future research and a comprehensive bibliography.

Pattern Recognition Algorithms for Data Mining

Recently, the theory of rough sets [213, 214], as explained before, is also being
used in soft computing [209]. The rough-fuzzy MLP [17], developed in 1998 for
pattern classification, is such an example for building an efficient connectionist ...

Author: Sankar K. Pal

Publisher: CRC Press

ISBN: 9780203998076

Category: Computers

Page: 280

View: 180

Pattern Recognition Algorithms for Data Mining addresses different pattern recognition (PR) tasks in a unified framework with both theoretical and experimental results. Tasks covered include data condensation, feature selection, case generation, clustering/classification, and rule generation and evaluation. This volume presents various theories, me

Neuro Fuzzy Pattern Recognition

235 – 246 , 1996 . 251 . M . Sarkar and B . Yegnanarayana , “ Rough - fuzzy set
theoretic approach to evaluate the importance of input features in classification , ”
in Proceedings of IEEE International Conference on Neural Networks ( Houston ...

Author: Sankar K. Pal

Publisher: Wiley-Interscience

ISBN:

Category: Computers

Page: 375

View: 245

The neuro-fuzzy approach to pattern recognition-a unique overview Recent years have seen a surge of interest in neuro-fuzzy computing, which combines fuzzy logic, neural networks, and soft computing techniques. This book focuses on the application of this new tool to the rapidly evolving area of pattern recognition. Written by two leaders in neural networks and soft computing research, this landmark work presents a unified, comprehensive treatment of the state of the art in the field. The authors consolidate a wealth of information previously cattered in disparate articles, journals, and edited volumes, explaining both the theory of neuro-fuzzy computing and the latest methodologies for performing different pattern recognition tasks in the neuro-fuzzy network-classification, feature evaluation, rule generation, knowledge extraction, and hybridization. Special emphasis is given to the integration of neuro-fuzzy methods with rough sets and genetic algorithms (GAs) to ensure more efficient recognition systems. Clear, concise, and fully referenced, Neuro-Fuzzy Pattern Recognition features extensive examples and highlights key applications in speech, machine learning, medicine, and forensic science. It is an extremely useful resource for scientists and engineers in laboratories and industry as well as for anyone seeking up-to-date information on the advantages of neuro-fuzzy pattern recognition in new computer technologies.

Soft Computing Approach to Pattern Recognition and Image Processing

This volume provides a collection of sixteen articles containing review and new material.

Author: Ashish Ghosh

Publisher: World Scientific

ISBN: 9789812776235

Category: Computers

Page: 371

View: 151

This volume provides a collection of sixteen articles containing review and new material. In a unified way, they describe the recent development of theories and methodologies in pattern recognition, image processing and vision using fuzzy logic, artificial neural networks, genetic algorithms, rough sets and wavelets with significant real life applications. The book details the theory of granular computing and the role of a rough-neuro approach as a way of computing with words and designing intelligent recognition systems. It also demonstrates applications of the soft computing paradigm to case based reasoning, data mining and bio-informatics with a scope for future research. The contributors from around the world present a balanced mixture of current theory, algorithms and applications, making the book an extremely useful resource for students and researchers alike. Contents: Pattern Recognition: Multiple Classifier Systems; Building Decision Trees from the Fourier Spectrum of a Tree Ensemble; Clustering Large Data Sets; Multi-objective Variable String Genetic Classifier: Application to Remote Sensing Imagery; Image Processing and Vision: Dissimilarity Measures Between Fuzzy Sets or Fuzzy Structures; Early Vision: Concepts and Algorithms; Self-organizing Neural Network for Multi-level Image Segmentation; Geometric Transformation by Moment Method with Wavelet Matrix; New Computationally Efficient Algorithms for Video Coding; Soft Computing for Computational Media Aesthetics: Analyzing Video Content for Meaning; Granular Computing and Case Based Reasoning: Towards Granular Multi-agent Systems; Granular Computing and Pattern Recognition; Case Base Maintenance: A Soft Computing Perspective; Real Life Applications: Autoassociative Neural Network Models for Pattern Recognition Tasks in Speech and Image; Protein Structure Prediction Using Soft Computing; Pattern Classification for Biological Data Mining. Readership: Upper level undergraduates, graduates, researchers, academics and industrialists.

Rough Sets Fuzzy Sets Data Mining and Granular Computing

11th International Conference, RSFDGrC 2007, Toronto, Canada, May 14-16,
2007 Aijun An, Jerzy Stefanowski, Sheela Ramanna, Witold Pedrycz, Cory Butz.
Image Pattern Recognition Using Near Sets⋆ Christopher Henry and James F.

Author: Aijun An

Publisher: Springer Science & Business Media

ISBN: 3540725296

Category: Computers

Page: 585

View: 232

This volume contains the papers selected for presentation at the 11th Int- national Conference on Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing (RSFDGrC 2007), a part of the Joint Rough Set Symposium (JRS 2007) organized by Infobright Inc. and York University. JRS 2007 was held for the ?rst time during May 14–16, 2007 in MaRS Discovery District, Toronto, Canada. It consisted of two conferences: RSFDGrC 2007 and the Second Int- national Conference on Rough Sets and Knowledge Technology (RSKT 2007). The two conferences that constituted JRS 2007 investigated rough sets as an emerging methodology established more than 25 years ago by Zdzis law Pawlak. Roughsettheoryhasbecomeanintegralpartofdiversehybridresearchstreams. In keeping with this trend, JRS 2007 encompassed rough and fuzzy sets, kno- edgetechnologyanddiscovery,softandgranularcomputing,dataprocessingand mining, while maintaining an emphasis on foundations and applications. RSFDGrC 2007 followed in the footsteps of well-established international initiatives devoted to the dissemination of rough sets research, held so far in Canada, China, Japan, Poland, Sweden, and the USA. RSFDGrC was ?rst - ganized as the 7th International Workshop on Rough Sets, Data Mining and Granular Computing held in Yamaguchi, Japan in 1999. Its key feature was to stress the role of integrating intelligent information methods to solve real-world, large, complex problems concerned with uncertainty and fuzziness. RSFDGrC achieved the status of a bi-annual international conference, starting from 2003 in Chongqing, China.

Computational Intelligence in Multi Feature Visual Pattern Recognition

Research is what I'm doing when I don't know what I'm doing Wernher von Braun
Abstract Classification of datasets with multiple features is computationally
intensive. Fuzzy-rough set based feature selection and classification requires ...

Author: Pramod Kumar Pisharady

Publisher: Springer

ISBN: 9812870563

Category: Technology & Engineering

Page: 138

View: 270

This book presents a collection of computational intelligence algorithms that addresses issues in visual pattern recognition such as high computational complexity, abundance of pattern features, sensitivity to size and shape variations and poor performance against complex backgrounds. The book has 3 parts. Part 1 describes various research issues in the field with a survey of the related literature. Part 2 presents computational intelligence based algorithms for feature selection and classification. The algorithms are discriminative and fast. The main application area considered is hand posture recognition. The book also discusses utility of these algorithms in other visual as well as non-visual pattern recognition tasks including face recognition, general object recognition and cancer / tumor classification. Part 3 presents biologically inspired algorithms for feature extraction. The visual cortex model based features discussed have invariance with respect to appearance and size of the hand, and provide good inter class discrimination. A Bayesian model of visual attention is described which is effective in handling complex background problem in hand posture recognition. The book provides qualitative and quantitative performance comparisons for the algorithms outlined, with other standard methods in machine learning and computer vision. The book is self-contained with several figures, charts, tables and equations helping the reader to understand the material presented without instruction.

Rough Set Theory and Granular Computing

Relevance of fuzzy logic, artificial neural networks, genetic algorithms and rough
sets to pattern recognition and image processing problems is described through
examples. Different integrations of these soft computing tools are illustrated.

Author: Masahiro Inuiguchi

Publisher: Springer Science & Business Media

ISBN: 9783540005742

Category: Computers

Page: 300

View: 971

This monograph presents novel approaches and new results in fundamentals and applications related to rough sets and granular computing. It includes the application of rough sets to real world problems, such as data mining, decision support and sensor fusion. The relationship of rough sets to other important methods of data analysis – Bayes theorem, neurocomputing and pattern recognition is thoroughly examined. Another issue is the rough set based data analysis, including the study of decision making in conflict situations. Recent engineering applications of rough set theory are given, including a processor architecture organization for fast implementation of basic rough set operations and results concerning advanced image processing for unmanned aerial vehicles. New emerging areas of study and applications are presented as well as a wide spectrum of on-going research, which makes the book valuable to all interested in the field of rough set theory and granular computing.

Intelligent Computing in Signal Processing and Pattern Recognition

A Novel Emitter Signal Recognition Model Based on Rough Set Guan Xin, Yi
Xiao, and He You Research Institute of ... emitter purpose is selected, and
compared with fuzzy pattern recognition and classical statistical recognition
algorithm ...

Author: De-Shuang Huang

Publisher: Springer

ISBN: 354037258X

Category: Technology & Engineering

Page: 1182

View: 890

This 1179-page book assembles the complete contributions to the International Conference on Intelligent Computing, ICIC 2006: one volume of Lecture Notes in Computer Science (LNCS); one of Lecture Notes in Artificial Intelligence (LNAI); one of Lecture Notes in Bioinformatics (LNBI); and two volumes of Lecture Notes in Control and Information Sciences (LNCIS). Include are 149 revised full papers, and a Special Session on Computing for Searching Strategies to Control Dynamic Processes.

Rough Sets Fuzzy Sets Data Mining and Granular Computing

... of Rough Set problems, Pattern Recognition/Machine Learning problems, and
Statistical Model Identification problems. In the first Rough Set situation, what we
have seen is as follows: 1) The ”granularity” should be taken so as to divide ...

Author: Dominik Slezak

Publisher: Springer Science & Business Media

ISBN: 3540286535

Category: Computers

Page: 742

View: 763

The two volume set LNAI 3641 and LNAI 3642 constitutes the refereed proceedings of the 10th International Conference on Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing, RSFDGrC 2005, held in Regina, Canada in August/September 2005. The 119 revised full papers presented were carefully reviewed and selected from a total of 277 submissions. They comprise the two volumes together with 6 invited papers, 22 approved workshop papers, and 5 special section papers that all were carefully selected and thoroughly revised. The first volume includes 75 contributions related to rough set approximations, rough-algebraic foundations, feature selection and reduction, reasoning in information systems, rough-probabilistic approaches, rough-fuzzy hybridization, fuzzy methods in data analysis, evolutionary computing, machine learning, approximate and uncertain reasoning, probabilistic network models, spatial and temporal reasoning, non-standard logics, and granular computing. The second volume contains 77 contributions and deals with rough set software, data mining, hybrid and hierarchical methods, information retrieval, image recognition and processing, multimedia applications, medical applications, web content analysis, business and industrial applications, the approved workshop papers and the papers accepted for a special session on intelligent and sapient systems.

Active Media Technology

SOFT COMPUTING PATTERN RECOGNITION , CASE GENERATION AND
DATA MINING SANKAR K. PAL Machine ... of fuzzy logic , artificial neural
networks , genetic algorithms and rough sets to pattern recognition and image
processing ...

Author: Jian Ping Li

Publisher: World Scientific

ISBN: 9789812704313

Category: Computers

Page: 536

View: 352

Seeking to capture the essence of the current state of research in active media technology, this volume identifies the changes and opportunities - both current and future - in the field. The papers are taken from the Second International Conference on Active Media Technology, held in China in 2003. Researchers such as Professor Ning Zhong from the Maebashi Institute of Technology, Professor John Yen from the Pennsylvania State University, and Professor Sanker K. Pal from the Indian Statistical Institute present their research papers.

New Frontiers in Artificial Intelligence

Pattern. Recognition: Principles,. Integrations,. and. Data. Mining. Sankar K. Pal
Machine Intelligence Unit Indian ... Relevance of fuzzy logic, artificial neural
networks, genetic algorithms and rough sets to pattern recognition and image ...

Author: Takao Terano

Publisher: Springer Science & Business Media

ISBN: 3540430709

Category: Computers

Page: 556

View: 325

This book constitutes the thoroughly refereed joint post-proceedings of five international workshops organized by the Japanese Society of Artificial Intelligence, JSAI in 2001. The 75 revised papers presented were carefully reviewed and selected for inclusion in the volume. In accordance with the five workshops documented, the book offers topical sections on social intelligence design, agent-based approaches in economic and complex social systems, rough set theory and granular computing, chance discovery, and challenges in knowledge discovery and data mining.

Pattern Recognition and Machine Intelligence

This book constitutes the refereed proceedings of the First International Conference on Pattern Recognition and Machine Intelligence, PReMI 2005, held in Kolkata, India in December 2005.

Author: Sankar K. Pal

Publisher: Springer

ISBN: 3540324208

Category: Computers

Page: 808

View: 674

This book constitutes the refereed proceedings of the First International Conference on Pattern Recognition and Machine Intelligence, PReMI 2005, held in Kolkata, India in December 2005. The 108 revised papers presented together with 6 keynote talks and 14 invited papers were carefully reviewed and selected from 250 submissions. The papers are organized in topical sections on clustering, feature selection and learning, classification, neural networks and applications, fuzzy logic and applications, optimization and representation, image processing and analysis, video processing and computer vision, image retrieval and data mining, bioinformatics application, Web intelligence and genetic algorithms, as well as rough sets, case-based reasoning and knowledge discovery.

Transactions on Rough Sets XI

Computational Theory Perception (CTP), Rough-Fuzzy Uncertainty Analysis and
Mining in Bioinformatics and Web ... Rough set-based techniques havebeen
used in the fields of pattern recognition [25,41], image processing [38], data ...

Author:

Publisher: Springer Science & Business Media

ISBN: 3642114784

Category: Computers

Page: 189

View: 206

Volume XI of the Transactions on Rough Sets (TRS) provides evidence of f- ther growth in the rough set landscape, both in terms of its foundations and applications. This volume provides further evidence of the number of research streams that were either directly or indirectly initiated by the seminal work on rough 1 sets by Zdzis law Pawlak (1926-2006) . Evidence of the growth of various rough 2 set-based research streams can be found in the rough set database . Thisvolumecontainsarticlesintroducingadvancesinthefoundationsand- plicationsofroughsets.These advancesinclude: calculusofattribute-value pairs useful in mining numerical data, de?nability and coalescence of approximations, variable consistency generalization approach to bagging controlled by measures of consistency, classical and dominance-based rough sets in the search for genes, judgementaboutsatis?abilityunderincompleteinformation,irreducibledescr- tive sets of attributes for information systems useful in the design of concurrent data models, computational theory of perceptions (CTP) and its characteristics and the relation with fuzzy-granulation, methods and algorithms of the Net- TRS system, a recursive version of the apriori algorithm designed for parallel processing, and decision table reduction method based on fuzzy rough sets. Theeditorsandauthorsofthisvolumeextendtheirgratitudetothereviewers of articles in this volume, Alfred Hofmann, Ursula Barth, Christine Reiss and the LNCS sta? at Springer for their support in making this volume of the TRS possible.

Rough Sets Fuzzy Sets Data Mining and Granular Computing

Rough Sets: Trends and Challenges Extended Abstract Andrzej Skowron1 and
James F. Peters2 1 Institute of ... to new approaches to concept approximation,
pattern identification, pattern recognition, pattern languages, clustering,
information ...

Author: Guoyin Wang

Publisher: Springer Science & Business Media

ISBN: 3540140409

Category: Computers

Page: 741

View: 518

This book constitutes the refereed proceedings of the 9th International Conference on Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing, RSFDGrC 2003, held in Chongqing, China in May 2003. The 39 revised full papers and 75 revised short papers presented together with 2 invited keynote papers and 11 invited plenary papers were carefully reviewed and selected from a total of 245 submissions. The papers are organized in topical sections on rough sets foundations and methods; fuzzy sets and systems; granular computing; neural networks and evolutionary computing; data mining, machine learning, and pattern recognition; logics and reasoning; multi-agent systems; and Web intelligence and intelligent systems.

Multiple Fuzzy Classification Systems

Classifying objects described by a set of their numerical features is one of the
basic tasks of pattern recognition and data ... The book applies fuzzy, neuro-fuzzy
and neuro-rough-fuzzy ensembles in the classification problem which is of utmost
 ...

Author: Rafał Scherer

Publisher: Springer

ISBN: 3642306047

Category: Computers

Page: 132

View: 219

Fuzzy classifiers are important tools in exploratory data analysis, which is a vital set of methods used in various engineering, scientific and business applications. Fuzzy classifiers use fuzzy rules and do not require assumptions common to statistical classification. Rough set theory is useful when data sets are incomplete. It defines a formal approximation of crisp sets by providing the lower and the upper approximation of the original set. Systems based on rough sets have natural ability to work on such data and incomplete vectors do not have to be preprocessed before classification. To achieve better performance than existing machine learning systems, fuzzy classifiers and rough sets can be combined in ensembles. Such ensembles consist of a finite set of learning models, usually weak learners. The present book discusses the three aforementioned fields – fuzzy systems, rough sets and ensemble techniques. As the trained ensemble should represent a single hypothesis, a lot of attention is placed on the possibility to combine fuzzy rules from fuzzy systems being members of classification ensemble. Furthermore, an emphasis is placed on ensembles that can work on incomplete data, thanks to rough set theory. .

Rough Fuzzy Hybridization

Pattern Recognition with Fuzzy Objective Function Algorithms . Plenum Press ,
New York , 1981 . 2 . S . B . Cho . Fuzzy aggregation of modular neural networks
with ordered weighted averaging operators . Approximate Reasoning , 13 : 359 ...

Author: Sankar K. Pal

Publisher: Springer Verlag

ISBN:

Category: Computers

Page: 454

View: 455

The present volume describes, in a unified way, the basic concepts and characteristic features of these theories and integrations, including recent developments, trends, and significant applications.