Pattern recognition and machine learning - In machine learning (ML), pattern recognition is the process of discovering similarities within small problems to solve larger, more complicated problems. Pattern …

 
Fig. 4: D and σ obtained from pattern recognition and machine learning. a Experimentally obtained magnetic domain images using a magnetic microscope equipped with a MTJ sensor.. How do i turn a picture into a pdf

2024 IEEE the 5th International Conference on Pattern Recognition and Machine Learning (PRML 2024) will take place in Chongqing, China from July 12-14, 2024. It is co-sponsored by IEEE Beijing Section and Sichuan University, and hosted by Chongqing Jianzhu College. The conference will include keynote and invited speeches, special sessions, and ... This week: overview on pattern recognition (related to machine learning) This week: overview on pattern recognition (related to machine learning). Non-review of chapters 6/7. Z-transforms Convolution Sampling/aliasing Linear difference equations Resonances FIR/IIR filtering DFT/FFT. Speech Pattern Recognition. 506 views • 35 slidesPattern Recognition and Machine Learning Browse Computer Science: Pattern Recognition and Machine Learning. Relevant books. View all. Book; Machine Learning Evaluation; Nathalie Japkowicz, Zois Boukouvalas, Mohak Shah; Textbook; Linear Algebra for Data Science, Machine Learning, and Signal Processing; Jeffrey A. Fessler, Raj …Pattern recognition is a facet of machine learning that focuses on the identification of patterns and regularities in data. In essence, it is about classifying data based on either …Learn what pattern recognition is, how it works, and its applications in computer science. Pattern recognition is the process of recognizing patterns by using …In machine learning (ML), pattern recognition is the process of discovering similarities within small problems to solve larger, more complicated problems. Pattern …(Only for Supervised Learning and follows Bishop) Pattern Recognition: Indian Institute of Science (I personally like this course as I have attended it, but this course requires you to know probability theory.) Both the courses are maths oriented, for a lighter course on machine learning would be "Machine Learning" by UdacityWherever it is a matter of recognizing patterns in large data volumes, it is expected that machines will bring great benefit to humanity. Following the classical …Pattern Recognition and Machine Learning. Bharadwaj, K. Prakash, G. Kanagachidambaresan. Published in Programming with TensorFlow 2021. Computer Science. Programming with TensorFlow. studyguide for pattern recognition and machine learning by bishop christopher m brand new 44 55 list price previous price 53 46 buy it …" Pattern Recognition and Machine Learning." Technometrics, 49(3), p. 366. Reprints and Corporate Permissions. Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content? To request a reprint or corporate permissions for this article, please click on the …Bishop Pattern Recognition and Machine Learning. sun kim. Download Free PDF View PDF. Pattern Recognition Letters. Pattern recognition and beyond: Alfredo Petrosino’s scientific results. Lucia Maddalena. Download Free PDF View PDF. Information Science and Statistics. Nohemi Magallanes. Download Free PDF View PDF. A Bird's-Eye View …Pattern recognition is the process of identifying patterns in data. Machine learning is a method of teaching computers to learn from data. Together, these two fields can be used to create systems ...Pattern perception, Pattern recognition systems, Machine learning, Reconnaissance des formes (Informatique) -- Manuels d'enseignement superieur, Apprentissage automatique -- Manuels d'enseignement superieur, Reconnaissance des formes (Informatique) -- Problemes et exercices, Apprentissage automatique -- … Microsoft It is a combination of technologies such as machine learning, pattern recognition, and artificial intelligence. With the help of OCR, you can store the information more compactly and easily search for the necessary entry without having to dig through tons of papers, etc. This data can be a training dataset for other machine learning …The domains of Pattern Recognition and Machine Learning have experienced exceptional interest and growth, however the overwhelming number of methods and applications can make the fields seem bewildering. This text offers an accessible and conceptually rich introduction, a solid mathematical development …Pattern recognition has its origins in engineering, whereas machine learning grew out of computer science. However, these activities can be viewed as two …Machine learning based pattern recognition is used to generate, analyze, and translate text. Hence, patterns are used to understand human language and generate text messages. Accordingly, text recognition on …Christopher M. Bishop. 4.32. 1,817 ratings75 reviews. Pattern recognition has its origins in engineering, whereas machine learning grew out of computer science. However, these activities can be viewed as two facets of the same field, and together they have undergone substantial development over the past ten years.This is the solutions manual (web-edition) for the book Pattern Recognition and Machine Learning (PRML; published by Springer in 2006). It contains solutions to the www exercises. This release was created September 8, 2009. Future releases with corrections to errors will be published on the PRML web-site (see below).Learn what pattern recognition is, how it works, and why it is important for machine learning. Explore the applications, methods, and examples of pattern recognition in data analysis, computer vision, …This book is one of the most up-to-date and cutting-edge texts available on the rapidly growing application area of neural networks. Neural Networks and Pattern Recognition focuses on the use of neural networksin pattern recognition, a very important application area for neural networks technology. The contributors are widely known and highly ...This new textbook reacts these recent developments while providing a comprehensive introduction to the fields of pattern recognition and machine learning. It is aimed at advanced undergraduates or first year PhD students, as wellas researchers and practitioners, and assumes no previous knowledge of pattern recognition or - chine …Pattern Recognition and Machine Learning provides excellent intuitive descriptions and appropriate-level technical details on modern pattern recognition and machine learning. It can be used to teach a course or for self-study, as well as for a reference. … I strongly recommend it for the intended audience and note that Neal (2007) also has given this …Christopher M. Bishop. 4.32. 1,817 ratings75 reviews. Pattern recognition has its origins in engineering, whereas machine learning grew out of computer science. However, these activities can be viewed as two facets of the same field, and together they have undergone substantial development over the past ten years.Introduction to pattern analysis and machine intelligence designed for advanced undergraduate and graduate students. Topics include Bayes decision theory, learning parametric distributions, non-parametric methods, regression, Adaboost, perceptrons, support vector machines, principal components analysis, nonlinear dimension reduction, …Machine learning based pattern recognition and classification framework development Abstract: In this paper we describe implementation of several step pattern recognition framework. Pattern recognition is the main aspect for different important areas such as video surveillance, biometrics, interactive game applications, human computer …A textbook by Paul Fieguth that covers the fundamentals and applications of pattern recognition and machine learning. It …Aug 17, 2006 · Pattern Recognition and Machine Learning. Christopher M. Bishop. Springer, Aug 17, 2006 - Computers - 738 pages. This is the first textbook on pattern recognition to present the Bayesian viewpoint. The book presents approximate inference algorithms that permit fast approximate answers in situations where exact answers are not feasible. Sep 21, 2011 · This document lists corrections and clarifications for the first printing1 of Pattern Recognition and Machine Learning by Christopher M. Bishop, first published by Springer in 2006. It is intended to be complete, in that it includes also trivial ty-pographical errors and provides clarifications that some readers may find helpful. Pattern Recognition and Machine Learning. Christopher M. Bishop. Springer, Aug 17, 2006 - Computers - 738 pages. This is the first textbook on pattern recognition to present the Bayesian viewpoint. The book presents approximate inference algorithms that permit fast approximate answers in situations where exact answers are …Bishop Pattern Recognition and Machine Learning. sun kim. Download Free PDF View PDF. Pattern Recognition Letters. Pattern recognition and beyond: Alfredo Petrosino’s scientific results. Lucia Maddalena. Download Free PDF View PDF. Information Science and Statistics. Nohemi Magallanes. Download Free PDF View PDF. A Bird's-Eye View …Large-Scale Data Analytics with Python and Spark. A Hands-on Guide to Implementing Machine Learning Solutions. Triguero, Isaac. Galar, Mikel. Published: Not yet published - available from February 2024. $39.99 (C) Paperback. Pre-order Order examination. Look Inside.Aug 17, 2006 · Computer Science, Mathematics. Technometrics. 1999. TLDR. This chapter presents techniques for statistical machine learning using Support Vector Machines (SVM) to recognize the patterns and classify them, predicting structured objects using SVM, k-nearest neighbor method for classification, and Naive Bayes classifiers. Expand. Christopher Bishop, Pattern Recognition and Machine Learning, First Edition, Springer-Verlag New York, 2006. [ Open-Access] Ethem Alpaydin, Introduction to Machine Learning, Third Edition, The MIT Press, September 2014. Trevor Hastie, Robert Tibshirani, Jerome Friedman, The Elements of Statistical Learning, Second Edition, Springer, 2009.Pattern Recognition and Machine Learning (Information Science and Statistics) یک کتاب فوق العاده در زمینه یادگیری ماشین که تئوری مسائل مربوط به ماشین لرنینگ رو طورکامل بررسی می کند. این کتاب که به کتاب بی شاپ معروف است نوشته Christopher M. Bishop از دانشمندان هوش مصنوعی است.. این کتاب میتواند مرجعی مناسب در کنار منابع ...Bishop Pattern Recognition and Machine Learning. sun kim. Download Free PDF View PDF. Pattern Recognition Letters. Pattern recognition and beyond: Alfredo Petrosino’s scientific results. Lucia Maddalena. Download Free PDF View PDF. Information Science and Statistics. Nohemi Magallanes. Download Free PDF View PDF. A Bird's-Eye View …Chris is the author of two highly cited and widely adopted machine learning text books: Neural Networks for Pattern Recognition (1995) and Pattern Recognition and Machine Learning (2006). He has also worked on a broad range of applications of machine learning in domains ranging from computer vision to healthcare. Chris is a keen … graphical models to machine learning. No previous knowledge of pattern recognition or machine learning concepts is assumed. Familiarity with multivariate calculus and basic linear algebra is required, and some experience in the use of probabilities would be helpful though not essential as the book includes a self-contained introduction to bas... Computer Science > Computer Vision and Pattern Recognition. arXiv:2404.11461 (cs) ... In this article, we demonstrate how modern game engines …Pattern Recognition and Machine Learning. January 2006. Journal of Electronic Imaging 16 (4):140-155. DOI: 10.1117/1.2819119. In book: Stat Sci (pp.140-155)Pattern recognition and machine learning . 1992. Abstract. No abstract available. ... Anzai seeks to provide a basic knowledge of pattern recognition, learning concepts based on symbolic representations, and learning concepts as implemented in neural networks. It is intended as a college-level text needing as background only the …Sep 21, 2011 · This document lists corrections and clarifications for the first printing1 of Pattern Recognition and Machine Learning by Christopher M. Bishop, first published by Springer in 2006. It is intended to be complete, in that it includes also trivial ty-pographical errors and provides clarifications that some readers may find helpful. Pattern Recognition in Machine Learning. What is Pattern Recognition: Pattern Recognition is the modernized Acknowledgment of models and textures in data. It has …Pattern Recognition in Machine Learning refers to identifying and detecting the regularities and patterns in data. This process involves training a machine learning …Statistical learning theory. PAC learning, empirical risk minimization, uniform convergence and VC-dimension. Support vector machines and kernel methods. Ensemble Methods. Bagging, Boosting. Multilayer neural networks. Feedforward networks, backpropagation. Mixture densities and EM algorithm. Clustering.DOI: 10.1007/978-0-387-45528-0. Corpus ID: 31993898. Pattern Recognition and Machine Learning. Radford M. Neal. Published in Technometrics 17 … Microsoft We expect this special issue addresses the research issues in the closely related areas of Pattern Recognition, such as Machine Learning, Data Mining, Computer Vision and Image Processing. We encourage the interdisciplinary research and applications of these areas. We welcome high-quality submissions with important new theories, …Machine Learning (ML) vs. Pattern Recognition vs. Data Mining. It is always a challenge to describe the difference between the three fields since there is considerable confusion because of significant overlap regarding the objectives and approaches. Pattern recognition is the most ancient of the three fields, dating back to …We expect this special issue addresses the research issues in the closely related areas of Pattern Recognition, such as Machine Learning, Data Mining, Computer Vision and Image Processing. We encourage the interdisciplinary research and applications of these areas. We welcome high-quality submissions with important new theories, …Difference Between Machine Learning and Pattern Recognition. In simple terms, Machine learning is a broader field that encompasses various techniques for developing models that can learn from data, while pattern recognition is a specific subfield that focuses on the identification and interpretation of patterns within data.Nov 13, 2022 · Pattern recognition is a process that looks at the available data and tries to see whether there are any regularities within it. There are two main parts: The explorative part, where the algorithms are looking for patterns in general. The descriptive part, where the algorithms start to categorize the found patterns. For example, in Computer Vision (CV) for facial recognition, one way of building its machine learning model is by using linear regression, which applies the following equation: ð ‘“ð ‘“ (𠑥𠑥) = ð ‘Šð ‘Š × 𠑥𠑥 (1) W = parameter (weight vector) x = input 2.2. Pattern Recognition Pattern recognition ...Welcome to the 10 th International Conference on Pattern Recognition and Machine Intelligence (PReMI'23). The primary goal of the conference is to provide a platform for presenting state-of-the-art scientific results, enabling academic and industrial interactions, and promoting collaborative research activities in Pattern Recognition, Machine …CS5691: Pattern Recognition and Machine Learning. Vectors, Inner product, Outer product, Inverse of a matrix, Eigenanalysis, Singular value decomposition, Probability distributions - Discrete distributions and Continuous distributions; Independence of events, Conditional probability distribution and Joint probability distribution, Bayes theorem ...Introduction Pattern recognition, a key component of Artificial Intelligence (AI) and machine learning, is increasingly transforming our society, revolutionizing the way we live and work. These technologies, equipped with the ability to sift through massive datasets and discern patterns and trends, make informed predictions or decisions.Apr 11, 2023 · Pattern recognition methodologies are incredibly popular in computer vision. We can put pattern recognition methodologies to use to programmatically develop applications that derive knowledge from images, and effectively understand them as a human being might. Machine Learning Graduate Certificate in Pattern Recognition Systems. Duration. 5 days. Course Time. 9.00am - 5.00pm. Enquiry. Please email [email protected] for more details. Machine learning uses statistical techniques to give computers the ability to "learn" with data without being explicitly programmed. With the most recent breakthrough in the area of deep ...Thesupport-vector network is a new learning machine for two-group classification problems. The machine conceptually implements the following idea: input vectors are …This document contains solutions to selected exercises from the book \Pattern Recognition and Machine Learning" by Christopher M. Bishop. Written in 2006, PRML is one of the most popular books in the eld of machine learning. It’s clearly written, never boring and exposes the reader to details without being terse or dry. At the time of …Pattern recognition and machine learning detect arrangements of characteristics of data that uncover information about a given data set or system and is …Machine Learning & Pattern Recognition Fourth-Year Option Course. Data is generated by most scientific disciplines. The science of pattern recognition enables analysis of this data. This course explores the issues involved in data-driven machine learning and, in particular, the detection and recognition of patterns within it. Pattern recognition …Since Machine Learning and Pattern Recognition encompasses hundreds of algorithms and mathematical concepts, the goal of this course is not to give an overview of each one of them. Rather, it is to impart to students a strong fundamental background on these topics (such as feature clustering, dimensionality reduction, classification, and neural networks) …Python codes implementing algorithms described in Bishop's book "Pattern Recognition and Machine Learning" Required Packages. python 3; numpy; scipy; jupyter (optional: to run jupyter notebooks) matplotlib (optional: to plot results in the notebooks) sklearn (optional: to fetch data)Pattern Recognition and Machine Learning. Bharadwaj, K. Prakash, G. Kanagachidambaresan. Published in Programming with TensorFlow 2021. Computer Science. Programming with TensorFlow. studyguide for pattern recognition and machine learning by bishop christopher m brand new 44 55 list price previous price 53 46 buy it …During the past decade there has been a considerable growth of interest in problems of pattern recognition and machine learn­ ing. In designing an optimal pattern recognition or control system, if all the a priori information about the process under study is known and can be described deterministically, the optimal system is usually designed by …This paper presents different machine learning-based pattern recognition approaches to recognize an object. The first step in building an automatic classification is separating the objects from ...Our analysis suggests that a new categorization of old-world plant oils is possible as revealed by machine learning patterns. ... Yu, Z. et al. Pattern recognition based on machine learning ...Pattern Recognition and Machine Learning. Christopher M. Bishop. Springer, Aug 17, 2006 - Computers - 738 pages. This is the first textbook on pattern recognition to present the Bayesian viewpoint. The book presents approximate inference algorithms that permit fast approximate answers in situations where exact answers are …This leading textbook provides a comprehensive introduction to the fields of pattern recognition and machine learning. It is aimed at advanced undergraduates or first-year PhD students, as well as researchers and practitioners.Pattern recognition has its origins in engineering, whereas machine learning grew out of computer science. However, these activities can be viewed as two facets of the same ?eld, and together they have undergone substantial development over the past ten years. In particular, Bayesian methods have grown from a specialist niche …Introduction to pattern analysis and machine intelligence designed for advanced undergraduate and graduate students. Topics include Bayes decision theory, learning parametric distributions, non-parametric methods, regression, Adaboost, perceptrons, support vector machines, principal components analysis, nonlinear dimension reduction, …This self-contained textbook bridges the gap between mathematical and machine learning texts, introducing the mathematical concepts with a minimum of prerequisites. It uses these concepts to derive four central machine learning methods: linear regression, principal component analysis, Gaussian mixture models and support …The following abbreviations are used in this document: PRML (Pattern Recog-nition and Machine Learning), l.h.s. (left hand side) and r.h.s. (right hand side). Acknowledgements We would like to thank all of the readers who have reported mistakes in PRML. In particular, we are grateful to the Japanese translation team, Dr Xiaobo Jin of theThe course is an introduction to the theoretical foundations of machine learning and pattern recognition. A variety of classical and recent results in machine learning and statistical pattern classification are discussed. Topics include Bayesian classification, regression, regularization, maximum margin classification, kernels, neural networks a...The following abbreviations are used in this document: PRML (Pattern Recog-nition and Machine Learning), l.h.s. (left hand side) and r.h.s. (right hand side). Acknowledgements We would like to thank all of the readers who have reported mistakes in PRML. In particular, we are grateful to the Japanese translation team, Dr Xiaobo Jin of thePattern recognition is the process of recognizing regularities in data by a machine that uses machine learning algorithms. In the heart of the process lies the classification of events based on statistical information, historical data, or the machine’s memory. A pattern is a regularity in the world or in abstract notions. Chris is the author of two highly cited and widely adopted machine learning text books: Neural Networks for Pattern Recognition (1995) and Pattern Recognition and Machine Learning (2006). He has also worked on a broad range of applications of machine learning in domains ranging from computer vision to healthcare. Pattern Recognition and Machine Learning provides excellent intuitive descriptions and appropriate-level technical details on modern pattern recognition and machine learning. It can be used to teach a course or for self-study, as well as for a reference. … I strongly recommend it for the intended audience and note that Neal …Starting in the 1990s, researchers realized machine learning could help them make pattern recognition algorithms faster than before. That’s because machine learning requires less human intervention. Closing Thoughts on Pattern Recognition and Machine Learning. It should be obvious now that there are numerous similarities …Pattern recognition is the process of identifying patterns in data. Machine learning is a method of teaching computers to learn from data. Together, these two fields can be used to create systems ... 2008) will deal with practical aspects of pattern recognition and machine learning, and will be accompanied by Matlab software implementing most of the algorithms discussed in this book. Acknowledgements First of all I would like to express my sincere thanks to Markus Svensen who´ CS5691: Pattern Recognition and Machine Learning. Vectors, Inner product, Outer product, Inverse of a matrix, Eigenanalysis, Singular value decomposition, Probability distributions - Discrete distributions and Continuous distributions; Independence of events, Conditional probability distribution and Joint probability distribution, Bayes theorem ...Solutions for Pattern Recognition and Machine Learning - Christopher M. Bishop View on GitHub This repo contains (or at least will eventually contain) solutions to all the exercises in Pattern Recognition and Machine Learning - Christopher M. Bishop , along with useful code snippets to illustrate certain concepts. Course Description. This course introduces fundamental concepts, theories, and algorithms for pattern recognition and machine learning, which are used in computer vision, speech recognition, data mining, statistics, information retrieval, and bioinformatics. His main research interests include machine learning, particularly deep learning, and its applications to speech and audio processing, natural language processing, and computer vision. Over the past 30 years, he has worked on a wide range of research problems from these areas and published hundreds of technical articles and papers in the mainstream …Pattern recognition and machine learning; Pattern recognition and machine learning. Results. Refine results. Refine results Clear all. Series Select series Format. Paperback (28) Hardback (78) eBook (80) Rating. 5 stars (4) 4 stars (1) 3 stars (0) 2 stars (0) 1 stars (0) All reviews (5) Show me. Unavailable titles (12) Textbooks (26) Titles with examination …Large-Scale Data Analytics with Python and Spark. A Hands-on Guide to Implementing Machine Learning Solutions. Triguero, Isaac. Galar, Mikel. Published: Not yet published - available from February 2024. $39.99 (C) Paperback. Pre-order Order examination. Look Inside.

Pattern recognition and machine learning toolbox. Contribute to weilinear/PRML development by creating an account on GitHub.. App store for games

pattern recognition and machine learning

Christopher M. Bishop. 4.32. 1,817 ratings75 reviews. Pattern recognition has its origins in engineering, whereas machine learning grew out of computer science. However, these activities can be viewed as two facets of the same field, and together they have undergone substantial development over the past ten years.Solutions for Pattern Recognition and Machine Learning - Christopher M. Bishop View on GitHub This repo contains (or at least will eventually contain) solutions to all the exercises in Pattern Recognition and Machine Learning - Christopher M. Bishop , along with useful code snippets to illustrate certain concepts. Ng's research is in the areas of machine learning and artificial intelligence. He leads the STAIR (STanford Artificial Intelligence Robot) project, whose goal is to develop a home assistant robot that can perform tasks such as tidy up a room, load/unload a dishwasher, fetch and deliver items, and prepare meals using a kitchen. Learn the concept of pattern recognition and its significance within the realm of machine learning. Explore the key techniques of statistical, syntactic, and …Pattern Clustering: Criterion functions for clustering, Techniques for clustering -- K-means clustering, Hierarchical clustering, Density based clustering and Spectral clustering; Cluster validation. (6 Lectures) Text Books. C.M.Bishop, Pattern Recognition and Machine Learning, Springer, 2006Our analysis suggests that a new categorization of old-world plant oils is possible as revealed by machine learning patterns. ... Yu, Z. et al. Pattern recognition based on machine learning ...In machine learning (ML), pattern recognition is the process of discovering similarities within small problems to solve larger, more complicated problems. Pattern recognition techniques are crucial in intelligent systems and prove useful in many application domains. Pattern recognition incorporates two distinct learning …Tools used for Pattern Recognition in Machine Learning. Amazon Lex – It is an open-source software/service provided by Amazon for building intelligent conversation agents such as chatbots by using text and speech recognition. Google Cloud AutoML – This technology is used for building high-quality machine learning models with …Machine Learning and Pattern Recognition (MLPR), Autumn 2023. Machine learning is about developing algorithms that adapt their behaviour to data, to provide useful representations or make predictions. This course is for those wanting to research and develop machine learning methods in future. Those who want a more practical course, …This self-contained textbook bridges the gap between mathematical and machine learning texts, introducing the mathematical concepts with a minimum of prerequisites. It uses these concepts to derive four central machine learning methods: linear regression, principal component analysis, Gaussian mixture models and support …It is a combination of technologies such as machine learning, pattern recognition, and artificial intelligence. With the help of OCR, you can store the information more compactly and easily search for the necessary entry without having to dig through tons of papers, etc. This data can be a training dataset for other machine learning …In statistical machine learning, pattern recognition and data mining, data is represented as a pattern matrix or data matrix. We illustrate it using the data in Figure 2.1 which is represented using the matrix shown in Table 2.1. Note that in Table 2.1, there are eight patterns which are represented using height in feet and weight in Kilograms.CS5691: Pattern recognition and machine learning Quiz - 1 Course Instructor : Prashanth L. A. Date : Feb-1, 2019 Duration : 30 minutes Name of the student : Roll No : INSTRUCTIONS: For MCQ questions, you do not have to justify the answer. For the rest, provide proper justi cation for the answers. Please use rough sheets for any calculations …Pattern recognition has its origins in engineering, whereas machine learning grew out of computer science. However, these activities can be viewed as two facets of the same field, and together they have undergone substantial development over the past ten years. In particular, Bayesian methods have grown from a specialist niche toDec 27, 2023 · Machine learning and pattern recognition work in tandem to enhance a system’s ability to make decisions, learn from experiences, and predict outcomes. By employing these techniques, machines can simulate the pattern identification capabilities of the human brain, but at a scale and speed that is unattainable for humans. A complex application can be in medical field, such as recognition of disease from patient data. The course covers following. (1) Pattern recognition problems in Bayesian framework. Forming optimal cost functions, and then establishing maximum-likelihood (ML) and maximum-a-posteriori (MAP) rules for classification. (2) Discriminant functions..

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