Machine Learning is the study of methods for programming computers to learn. Computers are applied to a wide range of tasks, and for most of these it is relatively easy for programmers to design and implement the necessary software. However, there are many tasks for which this is difficult or impossible. These can be divided into four general categories. First, there are problems for which there exist no human experts. For example, in modern automated manufacturing facilities, there is a need to predict machine failures before they occur by analyzing sensor readings. Because the machines are new, there are no human experts who can be interviewed by a programmer to provide the knowledge necessary to build a computer system. A machine learning system can study recorded data and subsequent machine failures and learn prediction rules. Second, there are problems where human experts exist, but where they are unable to explain their expertise. This is the case in many perceptual tasks, such as speech recognition, hand-writing recognition, and natural language understanding. Virtually all humans exhibit expert-level abilities on these tasks, but none of them can describe the detailed steps that they follow as they perform them. Fortunately, humans can provide machines with examples of the inputs and correct outputs for these tasks, so machine learning algorithms can learn to map the inputs to the outputs. Third, there are problems where phenomena are changing rapidly. In finance, for example, people would like to predict the future behavior of the stock market, of consumer purchases, or of exchange rates. These behaviors change frequently, so that even if a programmer could construct a good predictive computer program, it would need to be rewritten frequently. A learning program can relieve the programmer of this burden by constantly modifying and tuning a set of learned prediction rules. Fourth, there are applications that need to be customized for each computer user separately. Consider, for example, a program to filter unwanted electronic mail messages. Different users will need different filters. It is unreasonable to expect each user to program his or her own rules, and it is infeasible to provide every user with a software engineer to keep the rules up-to-date. A machine learning system can learn which mail messages the user rejects and maintain the filtering rules automatically. Machine learning addresses many of the same research questions as the fields of statistics, data mining, and psychology, but with differences of emphasis. Statistics focuses on understanding the phenomena that have generated the data, often with the goal of testing different hypotheses about those phenomena. Data mining seeks to find patterns in the data that are understandable by people. Psychological studies of human learning aspire to understand the mechanisms underlying the various learning behaviors exhibited by people (concept learning, skill acquisition, strategy change, etc.).

Machine learning

This paper describes the contents of the 2016 edition of the HITRAN molecular spectroscopic compilation. The new edition replaces the previous HITRAN edition of 2012 and its updates during the intervening years. The HITRAN molecular absorption compilation is composed of five major components: the traditional line-by-line spectroscopic parameters required for high-resolution radiative-transfer codes, infrared absorption cross-sections for molecules not yet amenable to representation in a line-by-line form, collision-induced absorption data, aerosol indices of refraction, and general tables such as partition sums that apply globally to the data. The new HITRAN is greatly extended in terms of accuracy, spectral coverage, additional absorption phenomena, added line-shape formalisms, and validity. Moreover, molecules, isotopologues, and perturbing gases have been added that address the issues of atmospheres beyond the Earth. Of considerable note, experimental IR cross-sections for almost 300 additional molecules important in different areas of atmospheric science have been added to the database. The compilation can be accessed through www.hitran.org. Most of the HITRAN data have now been cast into an underlying relational database structure that offers many advantages over the long-standing sequential text-based structure. The new structure empowers the user in many ways. It enables the incorporation of an extended set of fundamental parameters per transition, sophisticated line-shape formalisms, easy user-defined output formats, and very convenient searching, filtering, and plotting of data. A powerful application programming interface making use of structured query language (SQL) features for higher-level applications of HITRAN is also provided.

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The HITRAN 2008 molecular spectroscopic database

Initial-value ordinary differential equation solution via variable order Adams method (SIVA/DIVA) package is collection of subroutines for solution of nonstiff ordinary differential equations. There are versions for single-precision and double-precision arithmetic. Requires fewer evaluations of derivatives than other variable-order Adams predictor/ corrector methods. Option for direct integration of second-order equations makes integration of trajectory problems significantly more efficient. Written in FORTRAN 77.

Solving Ordinary Differential Equations

Numerical Initial Value Problems in Ordinary Differential Equations

This paper describes the status circa 2001, of the HITRAN compilation that comprises the public edition available through 2001. The HITRAN compilation consists of several components useful for radiative transfer calculation codes: high-resolution spectroscopic parameters of molecules in the gas phase, absorption cross-sections for molecules with very dense spectral features, aerosol refractive indices, ultraviolet line-by-line parameters and absorption cross-sections, and associated database management software. The line-by-line portion of the database contains spectroscopic parameters for 38 molecules and their isotopologues and isotopomers suitable for calculating atmospheric transmission and radiance properties. Many more molecular species are presented in the infrared cross-section data than in the previous edition, especially the chlorofluorocarbons and their replacement gases. There is now sufficient representation so that quasi-quantitative simulations can be obtained with the standard radiance codes. In addition to the description and justification of new or modified data that have been incorporated since the last edition of HITRAN (1996), future modifications are indicated for cases considered to have a significant impact on remote-sensing experiments. (C) 2003 Elsevier Ltd. All rights reserved.

The HITRAN molecular spectroscopic database: edition of 2000 including updates through 2001

The old coordinate driving procedure to find transition structures . in chemical systems is revisited. The well-known gradient criterion, =E x s 0, . which defines the stationary points of the potential energy surface PES , is reduced by one equation corresponding to one search direction. In this manner, abstract curves can be defined connecting stationary points of the PES. Starting at a given minimum, one follows a well-selected coordinate to reach the saddle of interest. Usually, but not necessarily, this coordinate will be related to the . reaction progress. The method, called reduced gradient following RGF , locally has an explicit analytical definition. We present a predictor)corrector method for tracing such curves. RGF uses the gradient and the Hessian matrix or updates of the latter at every curve point. For the purpose of testing a whole surface, the six-dimensional PES of formaldehyde, H CO, was explored by RGF 2 . using the restricted Hartree)Fock RHF method and the STO-3G basis set. Forty-nine minima and saddle points of different indices were found. At least seven stationary points representing bonded structures were detected in addition to those located using another search algorithm on the same level of theory. Further examples are the localization of the saddle for the HCN | CNH . isomerization used for steplength tests and for the ring closure of azidoazo- methine to 1 H-tetrazole. The results show that following the reduced gradient may represent a serious alternative to other methods used to locate saddle points in quantum chemistry. Q 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1087)1100, 1998

/pdf/searching-for-saddle-points-of-potential-energy-surfaces-by-52g43q0jpq.pdf

Searching for saddle points of potential energy surfaces by following a reduced gradient

This paper serves for the better understanding of the branching phenomenon of reaction paths of potential energy hypersurfaces in more than two dimensions. We apply the recently proposed reduced gradient following (RGF) method for the analysis of potential energy hypersurfaces having valley-ridge inflection (VRI) points. VRI points indicate the region of possible reaction path bifurcation. The relation between RGF and the so-called global Newton search for stationary points (Branin method) is shown. Using a 3D polynomial test surface, a whole 1D manifold of VRI points is obtained. Its relation to RGF curves, steepest descent and gradient extremals is discussed as well as the relation of the VRI manifold to bifurcation points of these curves.

Bifurcation of reaction pathways: the set of valley ridge inflection points of a simple three-dimensional potential energy surface

Some confusion regarding the properties of minimum energy paths is evident in the literature. We show that a way of steepest descent on a potential surface can be defined independently upon the choice of the coordinate systems. The result is applied to mass-weighted coordinates and their use is critically reviewed. Fukui's IRC appears to be a special case of the steepest descent path starting from a saddle point. The impossibility to define a general ascent path is illustrated and the relations of IRC to real trajectories are discussed.

/pdf/analysis-of-the-concept-of-minimum-energy-path-on-the-di11on141h.pdf

Analysis of the concept of minimum energy path on the potential energy surface of chemically reacting systems

https://www.math.uni-leipzig.de/~quapp/hcn2000.pdf

High-Temperature Infrared Measurements in the Region of the Bending Fundamental of H12C14N, H12C15N, and H13C14N

1 Guidelines in the Development of the Theory of Chemical Reactivity using the Potential Energy Surface (PES) Concept.- 1.1 The Potential Energy Surface (PES) Concept.- 1.2 The Dimensionality Problem.- 1.3 On the Definition of a Reaction Path (RP).- 1.4 The Hierarchy and Competition of Reaction Theories.- 1.5 What about the Calculation of Absolute Reaction Rates?.- 1.6 Potential Energy Calculation and Gradient Revolution.- 1.7 The "State of the Art" in Everyday Study of Chemical Reactivity.- References.- 2 Analysis of Multidimensional Potential Energy Surfaces - Stationary and Critical Points.- 2.1 Basic Definitions and Notations.- 2.2 Geometrical Properties of PES.- 2.3 Stationary Points.- 2.4 Location of Stationary Points.- 2.4.1 The Newton Process and its Modifications.- 2.4.2 Update Methods.- 2.4.3 Quasi-Newton Methods.- 2.4.4 Descent Methods.- 2.4.5 A Global Newton-like Method.- 2.5 Testing of Numerical Procedures.- 2.6 Zero Eigenvalues of the Hessian.- 2.6.1 Translational and Rotational Invariance.- 2.6.2 "True" Zero Eigenvalues: Catastrophe Points.- 2.6.3 Flat Bottoms and Double Minimum Potentials.- References.- 3 Analysis of Multidimensional Potential Energy Surfaces - Paths -.- 3.1 the Simple Valley Floor Line.- 3.2 Mathematics of Valley Floors.- 3.2.1 Gradient Extremals (GE).- 3.2.2 GE and Bifurcation Points.- 3.2..3 GE for Higher-Dimensional Cases.- 3.3 Steepest Descent Paths.- 3.4 The Independence of Steepest Descent Paths from Parameterization and Coordinate System.- 3.4.1 Parameterization.- 3.4.2 Invariance from Coordinate System.- 3.4.3 Mass-Weighted Cartesian Coordinates.- References.- 4 Quantum Chemical Pes Calculations: The Proton Transfer Reactions.- 4.1 The Problem in Visualization of PES Properties.- 4.1.1 RP Energy Profiles and Surfaces Derived from Usual PES Sections.- 4.1.2 Graphical Presentation of Three-center Problems.- 4.1.3 Interaction Surface of an Attacking Species with a Fixed Valence System.- 4.1.4 Empirically Derived Diagrams of more Complex Reactions PES.- 4.1.5 Energy Profiles from Mathematically Defined RP Calculations.- 4.1.6 Summary.- References.- 4.2 PES Properties Along the Bimolecular Single Proton Transfer.- 4.2.1 Formulation of the Reaction Mechanisms.- 4.2.2 The Proton Transfer Energy.- 4.2.3 Discussion of most Recent PES Data of Bimolecular Single Proton Transfer.- 4.2.4 Gas-Phase Results and Medium Influenced Experimental Data.- 4.2.5 Theoretical Approach to Medium Influence and the PES Concept.- 4.2.6 Proton Transfer, Transition State Theory, and Quantum Chemistry.- References.

Wolfgang Quapp

Papers

Searching for saddle points of potential energy surfaces by following a reduced gradient

Bifurcation of reaction pathways: the set of valley ridge inflection points of a simple three-dimensional potential energy surface

Analysis of the concept of minimum energy path on the potential energy surface of chemically reacting systems

High-Temperature Infrared Measurements in the Region of the Bending Fundamental of H12C14N, H12C15N, and H13C14N

Properties of Chemically Interesting Potential Energy Surfaces