Download or read book Neural Networks in Chemical Reaction Dynamics written by Lionel Raff and published by Oxford University Press. This book was released on 2012-01-18 with total page 303 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents recent advances in neural network (NN) approaches and applications to chemical reaction dynamics. Topics covered include: (i) the development of ab initio potential-energy surfaces (PES) for complex multichannel systems using modified novelty sampling and feedforward NNs; (ii) methods for sampling the configuration space of critical importance, such as trajectory and novelty sampling methods and gradient fitting methods; (iii) parametrization of interatomic potential functions using a genetic algorithm accelerated with a NN; (iv) parametrization of analytic interatomic potential functions using NNs; (v) self-starting methods for obtaining analytic PES from ab inito electronic structure calculations using direct dynamics; (vi) development of a novel method, namely, combined function derivative approximation (CFDA) for simultaneous fitting of a PES and its corresponding force fields using feedforward neural networks; (vii) development of generalized PES using many-body expansions, NNs, and moiety energy approximations; (viii) NN methods for data analysis, reaction probabilities, and statistical error reduction in chemical reaction dynamics; (ix) accurate prediction of higher-level electronic structure energies (e.g. MP4 or higher) for large databases using NNs, lower-level (Hartree-Fock) energies, and small subsets of the higher-energy database; and finally (x) illustrative examples of NN applications to chemical reaction dynamics of increasing complexity starting from simple near equilibrium structures (vibrational state studies) to more complex non-adiabatic reactions. The monograph is prepared by an interdisciplinary group of researchers working as a team for nearly two decades at Oklahoma State University, Stillwater, OK with expertise in gas phase reaction dynamics; neural networks; various aspects of MD and Monte Carlo (MC) simulations of nanometric cutting, tribology, and material properties at nanoscale; scaling laws from atomistic to continuum; and neural networks applications to chemical reaction dynamics. It is anticipated that this emerging field of NN in chemical reaction dynamics will play an increasingly important role in MD, MC, and quantum mechanical studies in the years to come.

Download or read book Neural Networks in Chemical Reaction Dynamics written by Ranga Komanduri and published by . This book was released on with total page 303 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents recent advances in neural network (NN) approaches and applications to chemical reaction dynamics. Topics covered include: (i) the development of ab initio potential-energy surfaces (PES) for complex multichannel systems using modified novelty sampling and feedforward NNs; (ii) methods for sampling the configuration space of critical importance, such as trajectory and novelty sampling methods and gradient fitting methods; (iii) parametrization of interatomic potential functions using a genetic algorithm accelerated with a NN; (iv) parametrization of analytic interatomic potential functions using NNs; (v) self-starting methods for obtaining analytic PES from ab inito electronic structure calculations using direct dynamics; (vi) development of a novel method, namely, combined function derivative approximation (CFDA) for simultaneous fitting of a PES and its corresponding force fields using feedforward neural networks; (vii) development of generalized PES using many-body expansions, NNs, and moiety energy approximations; (viii) NN methods for data analysis, reaction probabilities, and statistical error reduction in chemical reaction dynamics; (ix) accurate prediction of higher-level electronic structure energies (e.g. MP4 or higher) for large databases using NNs, lower-level (Hartree-Fock) energies, and small subsets of the higher-energy database; and finally (x) illustrative examples of NN applications to chemical reaction dynamics of increasing complexity starting from simple near equilibrium structures (vibrational state studies) to more complex non-adiabatic reactions. The monograph is prepared by an interdisciplinary group of researchers working as a team for nearly two decades at Oklahoma State University, Stillwater, OK with expertise in gas phase reaction dynamics; neural networks; various aspects of MD and Monte Carlo (MC) simulations of nanometric cutting, tribology, and material properties at nanoscale; scaling laws from atomistic to continuum; and neural networks applications to chemical reaction dynamics. It is anticipated that this emerging field of NN in chemical reaction dynamics will play an increasingly important role in MD, MC, and quantum mechanical studies in the years to come.

Download or read book Neural Networks in Chemical Reaction Dynamics written by Lionel Raff and published by OUP USA. This book was released on 2012-01-18 with total page 303 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents recent advances in neural network (NN) approaches and applications to chemical reaction dynamics. Topics covered include: (i) the development of ab initio potential-energy surfaces (PES) for complex multichannel systems using modified novelty sampling and feedforward NNs; (ii) methods for sampling the configuration space of critical importance, such as trajectory and novelty sampling methods and gradient fitting methods; (iii) parametrization of interatomic potential functions using a genetic algorithm accelerated with a NN; (iv) parametrization of analytic interatomic potential functions using NNs; (v) self-starting methods for obtaining analytic PES from ab inito electronic structure calculations using direct dynamics; (vi) development of a novel method, namely, combined function derivative approximation (CFDA) for simultaneous fitting of a PES and its corresponding force fields using feedforward neural networks; (vii) development of generalized PES using many-body expansions, NNs, and moiety energy approximations; (viii) NN methods for data analysis, reaction probabilities, and statistical error reduction in chemical reaction dynamics; (ix) accurate prediction of higher-level electronic structure energies (e.g. MP4 or higher) for large databases using NNs, lower-level (Hartree-Fock) energies, and small subsets of the higher-energy database; and finally (x) illustrative examples of NN applications to chemical reaction dynamics of increasing complexity starting from simple near equilibrium structures (vibrational state studies) to more complex non-adiabatic reactions. The monograph is prepared by an interdisciplinary group of researchers working as a team for nearly two decades at Oklahoma State University, Stillwater, OK with expertise in gas phase reaction dynamics; neural networks; various aspects of MD and Monte Carlo (MC) simulations of nanometric cutting, tribology, and material properties at nanoscale; scaling laws from atomistic to continuum; and neural networks applications to chemical reaction dynamics. It is anticipated that this emerging field of NN in chemical reaction dynamics will play an increasingly important role in MD, MC, and quantum mechanical studies in the years to come.

Download or read book Mathematically Reduced Chemical Reaction Mechanism Using Neural Networks written by and published by . This book was released on 2006 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an annual technical report for the work done over the last year (period ending 9/30/2005) on the project titled ''Mathematically Reduced Chemical Reaction Mechanism Using Neural Networks''. The aim of the project is to develop an efficient chemistry model for combustion simulations. The reduced chemistry model will be developed mathematically without the need of having extensive knowledge of the chemistry involved. To aid in the development of the model, Neural Networks (NN) will be used via a new network topology know as Non-linear Principal Components Analysis (NPCA). We report on the significant development made in developing a truly meshfree computational fluid dynamics (CFD) flow solver to be coupled to NPCA. First, the procedure of obtaining nearly analytic accurate first order derivatives using the complex step method (CSM) is extended to include computation of accurate meshfree second order derivatives via a theorem described in this report. Next, boosted generalized regression neural network (BGRNN), described in our previous report is combined with CSM and used to obtain complete solution of a hard to solve wave dominated sample second order partial differential equation (PDE): the cubic Schrodinger equation. The resulting algorithm is a significant improvement of the meshfree technique of smooth particle hydrodynamics method (SPH). It is suggested that the demonstrated meshfree technique be termed boosted smooth particle hydrodynamics method (BSPH). Some of the advantages of BSPH over other meshfree methods include; it is of higher order accuracy than SPH; compared to other meshfree methods, it is completely meshfree and does not require any background meshes; It does not involve any construction of shape function with their associated solution of possibly ill conditioned matrix equations; compared to some SPH techniques, no equation for the smoothing parameter is required; finally it is easy to program.

Download or read book Stochastic Local Search written by Holger H. Hoos and published by Morgan Kaufmann. This book was released on 2005 with total page 678 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic local search (SLS) algorithms are among the most prominent and successful techniques for solving computationally difficult problems. Offering a systematic treatment of SLS algorithms, this book examines the general concepts and specific instances of SLS algorithms and considers their development, analysis and application.

Download or read book Quantum Chemistry in the Age of Machine Learning written by Pavlo O. Dral and published by Elsevier. This book was released on 2022-09-16 with total page 702 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum chemistry is simulating atomistic systems according to the laws of quantum mechanics, and such simulations are essential for our understanding of the world and for technological progress. Machine learning revolutionizes quantum chemistry by increasing simulation speed and accuracy and obtaining new insights. However, for nonspecialists, learning about this vast field is a formidable challenge. Quantum Chemistry in the Age of Machine Learning covers this exciting field in detail, ranging from basic concepts to comprehensive methodological details to providing detailed codes and hands-on tutorials. Such an approach helps readers get a quick overview of existing techniques and provides an opportunity to learn the intricacies and inner workings of state-of-the-art methods. The book describes the underlying concepts of machine learning and quantum chemistry, machine learning potentials and learning of other quantum chemical properties, machine learning-improved quantum chemical methods, analysis of Big Data from simulations, and materials design with machine learning. Drawing on the expertise of a team of specialist contributors, this book serves as a valuable guide for both aspiring beginners and specialists in this exciting field. Compiles advances of machine learning in quantum chemistry across different areas into a single resource Provides insights into the underlying concepts of machine learning techniques that are relevant to quantum chemistry Describes, in detail, the current state-of-the-art machine learning-based methods in quantum chemistry

Download or read book Chemical Reaction Networks written by Oleg N. Temkin and published by CRC Press. This book was released on 2020-07-24 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the last decade, increased attention to reaction dynamics, combined with the intensive application of computers in chemical studies, mathematical modeling of chemical processes, and mechanistic studies has brought graph theory to the forefront of research. It offers an advanced and powerful formalism for the description of chemical reactions and their intrinsic reaction mechanisms. Chemical Reaction Networks: A Graph-Theoretical Approach elegantly reviews and expands upon graph theory as applied to mechanistic theory, chemical kinetics, and catalysis. The authors explore various graph-theoretical approaches to canonical representation, numbering, and coding of elementary steps and chemical reaction mechanisms, the analysis of their topological structure, the complexity estimation, and classification of reaction mechanisms. They discuss topologically distinctive features of multiroute catalytic and noncatalytic and chain reactions involving metal complexes. With it's careful balance of clear language and mathematical rigor, the presentation of the authors' significant original work, and emphasis on practical applications and examples, Chemical Reaction Networks: A Graph Theoretical Approach is both an outstanding reference and valuable tool for chemical research.

Download or read book Neural Networks for Chemical Engineers written by A. B. Bulsari and published by Elsevier Publishing Company. This book was released on 1995 with total page 704 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hardbound. Although neural and connectionist models have been known for decades, their first appearance in chemical engineering was as late as 1988. This book is an attempt to expedite a cautious intake of neural networks into chemical engineering.Besides core chemical engineering, it includes applications in process engineering, biochemical engineering, and metallurgical engineering. Of the 27 chapters, six cover theoretical issues and the remaining 21 cover applications.

Download or read book New Horizons in Computational Chemistry Software written by Michael Filatov and published by Springer Nature. This book was released on 2022-07-30 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents the current status of software development in the field of computational and theoretical chemistry and gives an overview of the emerging trends. The challenges of maintaining the legacy codes and their adaptation to the rapidly growing hardware capabilities and the new programming environments are surveyed in a series of topical reviews written by the core developers and maintainers of the popular quantum chemistry and molecular dynamics programs. Special emphasis is given to new computational methodologies and practical aspects of their implementation and application in the computational chemistry codes. Modularity of the computational chemistry software is an emerging concept that enables to bypass the development and maintenance bottleneck of the legacy software and to customize the software using the best available computational procedures implemented in the form of self-contained modules. Perspectives on modular design of the computer programs for modeling molecular electronic structure, non-adiabatic dynamics, kinetics, as well as for data visualization are presented by the researchers actively working in the field of software development and application. This volume is of interest to quantum and computational chemists as well as experimental chemists actively using and developing computational software for their research. Chapters "MLatom 2: An Integrative Platform for Atomistic Machine Learning” and “Evolution of the Automatic Rhodopsin Modeling (ARM) Protocol" are available open access under a CC BY 4.0 License via link.springer.com.

Download or read book Novel Methods for Learning and Adaptation in Chemical Reaction Networks written by and published by . This book was released on 2015 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: State-of-the-art biochemical systems for medical applications and chemical computing are application-specific and cannot be re-programmed or trained once fabricated. The implementation of adaptive biochemical systems that would offer flexibility through programmability and autonomous adaptation faces major challenges because of the large number of required chemical species as well as the timing-sensitive feedback loops required for learning. Currently, biochemistry lacks a systems vision on how the user-level programming interface and abstraction with a subsequent translation to chemistry should look like. By developing adaptation in chemistry, we could replace multiple hard-wired systems with a single programmable template that can be (re)trained to match a desired input-output profile benefiting smart drug delivery, pattern recognition, and chemical computing. I aimed to address these challenges by proposing several approaches to learning and adaptation in Chemical Reaction Networks (CRNs), a type of simulated chemistry, where species are unstructured, i.e., they are identified by symbols rather than molecular structure, and their dynamics or concentration evolution are driven by reactions and reaction rates that follow mass-action and Michaelis-Menten kinetics. Several CRN and experimental DNA-based models of neural networks exist. However, these models successfully implement only the forward-pass, i.e., the input-weight integration part of a perceptron model. Learning is delegated to a non-chemical system that computes the weights before converting them to molecular concentrations. Autonomous learning, i.e., learning implemented fully inside chemistry has been absent from both theoretical and experimental research. The research in this thesis offers the first constructive evidence that learning in CRNs is, in fact, possible. I have introduced the original concept of a chemical binary perceptron that can learn all 14 linearly-separable logic functions and is robust to the perturbation of rate constants. That shows learning is universal and substrate-free. To simplify the model I later proposed and applied the "asymmetric" chemical arithmetic providing a compact solution for representing negative numbers in chemistry. To tackle more difficult tasks and to serve more complicated biochemical applications, I introduced several key modular building blocks, each addressing certain aspects of chemical information processing and learning. These parts organically combined into gradually more complex systems. First, instead of simple static Boolean functions, I tackled analog time-series learning and signal processing by modeling an analog chemical perceptron. To store past input concentrations as a sliding window I implemented a chemical delay line, which feeds the values to the underlying chemical perceptron. That allows the system to learn, e.g., the linear moving-average and to some degree predict a highly nonlinear NARMA benchmark series. Another important contribution to the area of chemical learning, which I have helped to shape, is the composability of perceptrons into larger multi-compartment networks. Each compartment hosts a single chemical perceptron and compartments communicate with each other through a channel-mediated exchange of molecular species. Besides the feedforward pass, I implemented the chemical error backpropagation analogous to that of feedforward neural networks. Also, after applying mass-action kinetics for the catalytic reactions, I succeeded to systematically analyze the ODEs of my models and derive the closed exact and approximative formulas for both the input-weight integration and the weight update with a learning rate annealing. I proved mathematically that the formulas of certain chemical perceptrons equal the formal linear and sigmoid neurons, essentially bridging neural networks and adaptive CRNs. For all my models the basic methodology was to first design species and reactions, and then set the rate constants either "empirically" by hand, automatically by a standard genetic algorithm (GA), or analytically if possible. I performed all simulations in my COEL framework, which is the first cloud-based chemistry modeling tool, accessible at http://coel-sim.org. I minimized the amount of required molecular species and reactions to make wet chemical implementation possible. I applied an automatized mapping technique, Soloveichik's CRN-to-DNA-strand-displacement transformation, to the chemical linear perceptron and the manual signalling delay line and obtained their full DNA-strand specified implementations. As an alternative DNA-based substrate, I mapped these two models also to deoxyribozyme-mediated cleavage reactions reducing the size of the displacement variant to a third. Both DNA-based incarnations could directly serve as blue-prints for wet biochemicals. Besides an actual synthesis of my models and conducting an experiment in a biochemical laboratory, the most promising future work is to employ so-called reservoir computing (RC), which is a novel machine learning method based on recurrent neural networks. The RC approach is relevant because for time-series prediction it is clearly superior to classical recurrent networks. It can also be implemented in various ways, such as electrical circuits, physical systems, such as a colony of Escherichia Coli, and water. RC's loose structural assumptions therefore suggest that it could be expressed in a chemical form as well. This could further enhance the expressivity and capabilities of chemically-embedded learning. My chemical learning systems may have applications in the area of medical diagnosis and smart medication, e.g., concentration signal processing and monitoring, and the detection of harmful species, such as chemicals produced by cancer cells in a host (cancer miRNAs) or the detection of a severe event, defined as a linear or nonlinear temporal concentration pattern. My approach could replace hard-coded solutions and would allow to specify, train, and reuse chemical systems without redesigning them. With time-series integration, biochemical computers could keep a record of changing biological systems and act as diagnostic aids and tools in preventative and highly personalized medicine.

Download or read book Wavelets in Chemistry written by Beata Walczak and published by Elsevier. This book was released on 2000-05-10 with total page 571 pages. Available in PDF, EPUB and Kindle. Book excerpt: Wavelets seem to be the most efficient tool in signal denoising and compression. They can be used in an unlimited number of applications in all fields of chemistry where the instrumental signals are the source of information about the studied chemical systems or phenomena, and in all cases where these signals have to be archived. The quality of the instrumental signals determines the quality of answer to the basic analytical questions: how many components are in the studied systems, what are these components like and what are their concentrations? Efficient compression of the signal sets can drastically speed up further processing such as data visualization, modelling (calibration and pattern recognition) and library search. Exploration of the possible applications of wavelets in analytical chemistry has just started and this book will significantly speed up the process. The first part, concentrating on theoretical aspects, is written in a tutorial-like manner, with simple numerical examples. For the reader's convenience, all basic terms are explained in detail and all unique properties of wavelets are pinpointed and compared with the other types of basis function. The second part presents applications of wavelets from many branches of chemistry which will stimulate chemists to further exploration of this exciting subject.

Download or read book Glowworm Swarm Optimization written by Krishnanand N. Kaipa and published by Springer. This book was released on 2017-01-10 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a comprehensive account of the glowworm swarm optimization (GSO) algorithm, including details of the underlying ideas, theoretical foundations, algorithm development, various applications, and MATLAB programs for the basic GSO algorithm. It also discusses several research problems at different levels of sophistication that can be attempted by interested researchers. The generality of the GSO algorithm is evident in its application to diverse problems ranging from optimization to robotics. Examples include computation of multiple optima, annual crop planning, cooperative exploration, distributed search, multiple source localization, contaminant boundary mapping, wireless sensor networks, clustering, knapsack, numerical integration, solving fixed point equations, solving systems of nonlinear equations, and engineering design optimization. The book is a valuable resource for researchers as well as graduate and undergraduate students in the area of swarm intelligence and computational intelligence and working on these topics.

Download or read book Chemical Master Equation for Large Biological Networks written by Don Kulasiri and published by Springer Nature. This book was released on 2021-09-12 with total page 231 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book highlights the theory and practical applications of the chemical master equation (CME) approach for very large biochemical networks, which provides a powerful general framework for model building in a variety of biological networks. The aim of the book is to not only highlight advanced numerical solution methods for the CME, but also reveal their potential by means of practical examples. The case studies presented are mainly from biology; however, the applications from novel methods are discussed comprehensively, underlining the interdisciplinary approach in simulation and the potential of the chemical master equation approach for modelling bionetworks. The book is a valuable guide for researchers, graduate students, and professionals alike.

Download or read book Robust Intelligence and Trust in Autonomous Systems written by Ranjeev Mittu and published by Springer. This book was released on 2016-04-07 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume explores the intersection of robust intelligence (RI) and trust in autonomous systems across multiple contexts among autonomous hybrid systems, where hybrids are arbitrary combinations of humans, machines and robots. To better understand the relationships between artificial intelligence (AI) and RI in a way that promotes trust between autonomous systems and human users, this book explores the underlying theory, mathematics, computational models, and field applications. It uniquely unifies the fields of RI and trust and frames it in a broader context, namely the effective integration of human-autonomous systems. A description of the current state of the art in RI and trust introduces the research work in this area. With this foundation, the chapters further elaborate on key research areas and gaps that are at the heart of effective human-systems integration, including workload management, human computer interfaces, team integration and performance, advanced analytics, behavior modeling, training, and, lastly, test and evaluation. Written by international leading researchers from across the field of autonomous systems research, Robust Intelligence and Trust in Autonomous Systems dedicates itself to thoroughly examining the challenges and trends of systems that exhibit RI, the fundamental implications of RI in developing trusted relationships with present and future autonomous systems, and the effective human systems integration that must result for trust to be sustained. Contributing authors: David W. Aha, Jenny Burke, Joseph Coyne, M.L. Cummings, Munjal Desai, Michael Drinkwater, Jill L. Drury, Michael W. Floyd, Fei Gao, Vladimir Gontar, Ayanna M. Howard, Mo Jamshidi, W.F. Lawless, Kapil Madathil, Ranjeev Mittu, Arezou Moussavi, Gari Palmer, Paul Robinette, Behzad Sadrfaridpour, Hamed Saeidi, Kristin E. Schaefer, Anne Selwyn, Ciara Sibley, Donald A. Sofge, Erin Solovey, Aaron Steinfeld, Barney Tannahill, Gavin Taylor, Alan R. Wagner, Yue Wang, Holly A. Yanco, Dan Zwillinger.

Download or read book Reviews in Computational Chemistry written by Abby L. Parrill and published by John Wiley & Sons. This book was released on 2018-10-25 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Reviews in Computational Chemistry series brings together leading authorities in the field to teach the newcomer and update the expert on topics centered on molecular modeling, such as computer-assisted molecular design (CAMD), quantum chemistry, molecular mechanics and dynamics, and quantitative structure-activity relationships (QSAR). This volume, like those prior to it, features chapters by experts in various fields of computational chemistry. Topics in Volume 31 include: Lattice-Boltzmann Modeling of Multicomponent Systems: An Introduction Modeling Mechanochemistry from First Principles Mapping Energy Transport Networks in Proteins The Role of Computations in Catalysis The Construction of Ab Initio Based Potential Energy Surfaces Uncertainty Quantification for Molecular Dynamics

Download or read book Weakly Connected Neural Networks written by Frank C. Hoppensteadt and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: Devoted to local and global analysis of weakly connected systems with applications to neurosciences, this book uses bifurcation theory and canonical models as the major tools of analysis. It presents a systematic and well motivated development of both weakly connected system theory and mathematical neuroscience, addressing bifurcations in neuron and brain dynamics, synaptic organisations of the brain, and the nature of neural codes. The authors present classical results together with the most recent developments in the field, making this a useful reference for researchers and graduate students in various branches of mathematical neuroscience.

Download or read book Out of Equilibrium Supra molecular Systems and Materials written by Nicolas Giuseppone and published by John Wiley & Sons. This book was released on 2021-03-30 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: A must-have resource that covers everything from out-of-equilibrium chemical systems and materials to dissipative self-assemblies Out-of-Equilibrium Supramolecular Systems and Materials presents a comprehensive overview of the synthetic approaches that use supramolecular bonds in various out-of-thermodynamic equilibrium situations. With contributions from noted experts on the topic, the text contains information on the design of dissipative self-assemblies that maintain their structures when fueled by an external source of energy. The contributors also examine molecules and nanoscale objects and materials that can produce mechanical work based on molecular machines. Additionally, the book explores non-equilibrium supramolecular polymers that can be trapped in kinetically stable states, as well as out-of-equilibrium chemical systems and oscillators that are important to understand the emergence of complex behaviors and, in particular, the origin of life. This important book: Offers comprehensive coverage of fields from design of dissipative self-assemblies to non-equilibrium supramolecular polymers Presents information on a highly emerging and interdisciplinary topic Includes contributions from internationally renowned scientists Written for chemists, physical chemists, biochemists, material scientists, Out-of-Equilibrium Supramolecular Systems and Materials is an indispensable resource written by top scientists in the field.