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ChemML : A machine learning and informatics program package for the analysis, mining, and modeling of chemical and materials data
ChemML is an open machine learning (ML) and informatics program suite that is designed to support and advance the data-driven research paradigm that is currently emerging in the chemical and materials domain. ChemML allows its users to perform various data science tasks and execute ML workflows that are adapted specifically for the chemical and materials context. Key features are automation, general-purpose utility, versatility, and user-friendliness in order to make the application of modern data science a viable and widely accessible proposition in the broader chemistry and materials community. Finally, ChemML is also designed to facilitate methodological innovation, and it is one of the cornerstones of the software ecosystem for data-driven in silico research.
Diffusion Monte Carlo approaches for studying nuclear quantum effects in fluxional molecules
Abstract Diffusion quantum Monte Carlo (DMC) provides a powerful approach for obtaining the ground state energy and wave function of molecules, ions, and molecular clusters. The approach is uniquely well suited for studies of fluxional molecules, which undergo large amplitude vibrational motions even in their ground state. In contrast to the electronic structure problem, where the wave function must be antisymmetric with respect to exchange of any pair of electrons, the wave function for the ground vibrational state is nodeless. This greatly simplifies the application of DMC for vibrational problems. Because there is not a single potential function that can be used to describe the intramolecular and intermolecular interactions in all molecular systems, most methods that are used to describe nuclear quantum effects rely on a carefully chosen zero‐order description of the molecular vibrations. In contrast, DMC calculations can be performed in Cartesian coordinates, making the DMC algorithm easily transferable between different chemical systems. In this contribution, the theory that underlies DMC will be discussed along with important considerations for performing DMC calculations. Extensions for evaluating vibrationally excited states and molecular properties are also discussed. Insights that can be obtained from DMC calculations are illustrated in the context of the protonated water clusters. This article is categorized under: Molecular and Statistical Mechanics > Molecular Dynamics and Monte‐Carlo Methods Theoretical and Physical Chemistry > Spectroscopy
Improving the five-point bootstrap
We present a new algorithm for the numerical evaluation of five-point conformal blocks in d-dimensions, greatly improving the efficiency of their computation. To do this we use an appropriate ansatz for the blocks as a series expansion in radial coordinates, derive a set of recursion relations for the unknown coefficients in the ansatz, and evaluate the series using a Padé approximant to accelerate its convergence. We then study the 〈σσϵσσ〉 correlator in the 3d critical Ising model by truncating the operator product expansion (OPE) and only including operators with conformal dimension below a cutoff ∆ ⩽ ∆cutoff. We approximate the contributions of the operators above the cutoff by the corresponding contributions in a suitable disconnected five-point correlator. Using this approach, we compute a number of OPE coefficients with greater accuracy than previous methods.
Physics-preserving enriched Galerkin method for a fully-coupled thermo-poroelasticity model
This paper proposes a new numerical method for a fully-coupled, quasi-static thermo-poroelasticity model in a unified enriched Galerkin (EG) method framework. In our method, the mechanics sub-problem is solved using a locking-free EG method, and the flow and heat sub-problems are solved using a locally-conservative EG method. The proposed method offers mass and energy conservation properties with much lower costs than other methods with the same properties, including discontinuous Galerkin methods and mixed finite element methods. The well-posedness and optimal a priori error estimates are carefully derived. Here, several numerical tests confirm the theoretical optimal convergence rates and the mass and energy conservation properties of the new method.
A theory of mechanical stress-induced H2O2 signaling waveforms in Planta
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Learning black- and gray-box chemotactic PDEs/closures from agent based Monte Carlo simulation data
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Properties of Existentially Closed Companions
Necessary and sufficient conditions are stated for an arbitrary theory to be an elementary theory for a class of its existentially closed models. Conditions are given under which some existentially closed model simultaneously realizes one maximal existential type and omits another. We also prove a theorem on a prime existentially closed model over a maximal existential type. Considerable complexity of existentially closed structures and their theories was noted by A. Macintyre. Therefore, the examples of existentially closed companions having any finite or countable number of pairwise non elementarily equivalent existentially closed models constructed here are of interest.
Conjugacy Analysis of the Finite-Difference Equations of the Method of Characteristics on the Basis of a Linear-Algebraic Formulation
A linear-algebraic form of the equations of the method of characteristics, which is used to approximate the neutron transport equation, is obtained. It is shown on the basis of the obtained linear-algebraic form that the discrete form of the conjugate equation differs from the algebraically discrete problem constructed by linear-algebraic transformations of the discrete form of the normal problem. The reason for the discrepancy lies in the approximation of the volumes of the spatial cells in covering the working region by a network of characteristics. It is shown by means of test calculations that when the network of characteristics is refined the solution of the conjugate transport equation converges to the solution of the algebraically conjugate problem.
Solvability of Parametric Inverse Problem for Parabolic Equation
We establish the solvability of a parametric inverse problem for an n-dimensional parabolic equation. We obtain sufficient conditions for the existence and uniqueness of a solution.
Solvability of Nonlinear Inverse Problem for Hyperbolic Equation
We consider the nonlinear inverse problem for a second order hyperbolic equation with unknown coefficient depending on the time. We establish the existence and uniqueness of regular solutions which are used for constructing a soltuion to the inverse problem under consideration.
A Method of Parametric Solution of Convolution Equations
A method of moments is developed for the parametric form the solution of convolution equations of the first kind. Two models, the gamma model and the shifted gamma model, are studied in details and a non-parametric approach based on regularization is presented.
Sharp Inequalities for Seminorms Defined on Spaces of Periodic Functions
We present a polynomial approximation method for realizing modified Landau–Kolmogorov type inequalities with small order derivatives. Bibliography: 6 titles.
Explicitly Solvable Models of Redistribution of the Conflict Space
We analyze a class of explicitly solvable models for the problems of redistribution of the conflict space between two alternative opponents. The existence of equilibrium state is proved for a complex nonlinear system whose time evolution is generated by the conflict interaction between its components. Explicit formulas are obtained for the limit compromise distributions in terms of the densities of probability measures. We consider a number of specific model examples of the dynamics of redistribution of the conflict territory and formation of an equilibrium (compromise) distribution of the space. We propose an interpretation of the results for the case of social and territorial conflicts.
Notes on the Codimension One Conjecture in the Operator Corona Theorem
Answering a question of S. R. Treil (2004), for every δ, 0 < δ < 1, we construct examples of contractions whose characteristic function F ∈ H{sup ∞}(ε →ε{sub ∗}) satisfies the conditions ‖F(z)x‖ ≥ δ‖x‖ and dim ε{sub ∗} ⊝ F(z)ε = 1 for every z ∈ 𝔻, x ∈ ε, but is not left invertible. In addition, we show that the condition where is the trace class of operators, which is sufficient for the left invertibility of an operatorvalued function F satisfying the estimate ‖F(z)x‖ ≥ δ‖x‖ for every z ∈ 𝔻, x ∈ ε, with some δ > 0 (Treil, 2004), is necessary for the left invertibility of an inner function F such that dim ε{sub ∗} ⊝ F(z)ε < ∞ for some z ∈ 𝔻.
On the Rate of Convergence in the Strong Law of Large Numbers for Nonnegative Random Variables
The rate of convergence in the strong law of large numbers for sequences of nonnegative random variables is studied without the independence assumption. Conditions for which an analog of the Baum–Katz theorem holds are obtained.
Quasielliptic Operators and Equations Not Solvable with Respect to the Higher Order Derivative
We consider a class of quasielliptic operators in R{sup n} and establish the isomorphism property in special weighted Sobolev spaces. In more general weighted spaces, we obtain the unique solvability conditions for quasielliptic equations and prove estimates for solutions. Based on the obtained results, we study the solvability of the initial problem for equations that are not solvable with respect to the higher order derivative.