Atom-Density Representations for Machine Learning

The applications of machine learning techniques to chemistry and materials science become more numerous by the day. The main challenge is to devise representations of atomic systems that are at the same time complete and concise, so as to reduce the number of reference calculations that are needed to predict the properties of different types of materials reliably. This has led to a proliferation of alternative ways to convert an atomic structure into an input for a machine-learning model. We introduce an abstract definition of chemical environments that is based on a smoothed atomic density, using a bra-ket notation to emphasize basis set independence and to highlight the connections with some popular choices of representations for describing atomic systems. The correlations between the spatial distribution of atoms and their chemical identities are computed as inner products between these feature kets, which can be given an explicit representation in terms of the expansion of the atom density on orthogonal basis functions, that is equivalent to the smooth overlap of atomic positions (SOAP) power spectrum, but also in real space, corresponding to $n$-body correlations of the atom density. This formalism lays the foundations for a more systematic tuning of the behavior of the representations, by introducing operators that represent the correlations between structure, composition, and the target properties. It provides a unifying picture of recent developments in the field and indicates a way forward towards more effective and computationally affordable machine-learning schemes for molecules and materials

Feature Optimization for Atomistic Machine Learning Yields A Data-Driven Construction of the Periodic Table of the Elements

Machine-learning of atomic-scale properties amounts to extracting correlations between structure, composition and the quantity that one wants to predict. Representing the input structure in a way that best reflects such correlations makes it possible to improve the accuracy of the model for a given amount of reference data. When using a description of the structures that is transparent and well-principled, optimizing the representation might reveal insights into the chemistry of the data set. Here we show how one can generalize the SOAP kernel to introduce a distance-dependent weight that accounts for the multi-scale nature of the interactions, and a description of correlations between chemical species. We show that this improves substantially the performance of ML models of molecular and materials stability, while making it easier to work with complex, multi-component systems and to extend SOAP to coarse-grained intermolecular potentials. The element correlations that give the best performing model show striking similarities with the conventional periodic table of the elements, providing an inspiring example of how machine learning can rediscover, and generalize, intuitive concepts that constitute the foundations of chemistry.Comment: 9 pages, 4 figure

Fast and Accurate Uncertainty Estimation in Chemical Machine Learning

We present a scheme to obtain an inexpensive and reliable estimate of the uncertainty associated with the predictions of a machine-learning model of atomic and molecular properties. The scheme is based on resampling, with multiple models being generated based on sub-sampling of the same training data. The accuracy of the uncertainty prediction can be benchmarked by maximum likelihood estimation, which can also be used to correct for correlations between resampled models, and to improve the performance of the uncertainty estimation by a cross-validation procedure. In the case of sparse Gaussian Process Regression models, this resampled estimator can be evaluated at negligible cost. We demonstrate the reliability of these estimates for the prediction of molecular energetics, and for the estimation of nuclear chemical shieldings in molecular crystals. Extension to estimate the uncertainty in energy differences, forces, or other correlated predictions is straightforward. This method can be easily applied to other machine learning schemes, and will be beneficial to make data-driven predictions more reliable, and to facilitate training-set optimization and active-learning strategies

Atomic-scale representation and statistical learning of tensorial properties

This chapter discusses the importance of incorporating three-dimensional symmetries in the context of statistical learning models geared towards the interpolation of the tensorial properties of atomic-scale structures. We focus on Gaussian process regression, and in particular on the construction of structural representations, and the associated kernel functions, that are endowed with the geometric covariance properties compatible with those of the learning targets. We summarize the general formulation of such a symmetry-adapted Gaussian process regression model, and how it can be implemented based on a scheme that generalizes the popular smooth overlap of atomic positions representation. We give examples of the performance of this framework when learning the polarizability and the ground-state electron density of a molecule

Understanding Kant’s architectonic method in the critique of pure reason and its role in the work of Gilles Deleuze

How we read Kant's Critique of Pure Reason has a huge influence on how convincing we find the parts of which it is composed. This thesis will argue that by taking its arguments and concepts in isolation we neglect the unifying architectonic method that Kant employed. Understanding this text as a response to a single problem, that of the possibility of synthetic a priori judgement, will allow us to evaluate it more fully. We will explore Kant's attempts to relate the a priori and the synthetic in the Introduction, Metaphysical Deduction and Analytic of Principles of the Critique of Pure Reason. Having developed this reading at length we will be able to reassess Kant's relation to the work of Gilles Deleuze. Deleuze's critique of Kant and his tendency to make selective use of his work has so far characterised their relations. However, by reading Kant's Critique of Pure Reason in terms of its unifying method we will open up a new means of relating these two thinkers. Whilst Deleuze rejects many key Kantian concerns and concepts he embraces his methodological concern with the ability of problems to unify our thought. The problem-setting and forms of argument that emerge within Kant's architectonic method will be related to Deleuze's account of experience. This thesis will contribute to both Kant and Deleuze studies on the basis of the reading of the Critique of Pure Reason it will present. By showing how Kant's text is to be read as a whole we will be able to challenge the conclusion that the arguments he makes ultimately rely upon a notion of 'subjective origin'. The problem of accounting for 'the actual' through its relation to 'the virtual' in Deleuze's thought will be re-assessed on the basis of his newly established relation with Kant. Understanding Kant's method in the Critique of Pure Reason will be shown to strengthen both his own account of experience and that offered by Deleuze

EL DISEÑO COMO TERAPIA: FACILITANDO LA VIDA DE LAS PERSONAS CON LA ENFERMEDAD DE ALZHEIMER A TRAVÉS DEL DISEÑO AMBIENTAL

The aim of this research was to combine research methods with the architectural design process in order to put forward a current and relevant proposal for a supportive environment for people with Alzheimer's disease, their family and carers. A review of the literature identified the environmental design features considered most relevant to the topic. Visits to and analysis of three 'exemplary' London-based dementia facilities revealed further design issues first-hand, whilst testing how successfully the features identified in the literature review are integrated into these designs. User preferences were identified through first-hand conversations with patients' relatives and nursing staff and by consulting conversation threads in Alzheimer's forums.El objetivo de esta investigación fue la de combinar los métodos de investigación con el proceso de diseño arquitectónico con el fin de presentar una propuesta actualizada y relevante para un ambiente de apoyo para las personas con enfermedad de Alzheimer, sus familiares y cuidadores. Una revisión de la literatura identificó las características de diseño del medio ambiente consideradas más relevantes para el tema. Visitas y análisis de tres instalaciones “ejemplares” para demencia con sede en Londres reveló cuestiones adicionales de diseño de primera mano, mientras que las pruebas con éxito como las características identificadas en la revisión de la literatura, se integran en estos diseños. Preferencias de los usuarios fueron identificados a través de conversaciones directas con familiares de los pacientes y el personal de enfermería y consultando temas de conversación en los foros de Alzheimer

Boltzmann-conserving classical dynamics in quantum time-correlation functions: "Matsubara dynamics".

We show that a single change in the derivation of the linearized semiclassical-initial value representation (LSC-IVR or "classical Wigner approximation") results in a classical dynamics which conserves the quantum Boltzmann distribution. We rederive the (standard) LSC-IVR approach by writing the (exact) quantum time-correlation function in terms of the normal modes of a free ring-polymer (i.e., a discrete imaginary-time Feynman path), taking the limit that the number of polymer beads N → ∞, such that the lowest normal-mode frequencies take their "Matsubara" values. The change we propose is to truncate the quantum Liouvillian, not explicitly in powers of ħ(2) at ħ(0) (which gives back the standard LSC-IVR approximation), but in the normal-mode derivatives corresponding to the lowest Matsubara frequencies. The resulting "Matsubara" dynamics is inherently classical (since all terms O(ħ(2)) disappear from the Matsubara Liouvillian in the limit N → ∞) and conserves the quantum Boltzmann distribution because the Matsubara Hamiltonian is symmetric with respect to imaginary-time translation. Numerical tests show that the Matsubara approximation to the quantum time-correlation function converges with respect to the number of modes and gives better agreement than LSC-IVR with the exact quantum result. Matsubara dynamics is too computationally expensive to be applied to complex systems, but its further approximation may lead to practical methods.T.J.H.H., M.J.W., and S.C.A. acknowledge funding from the U.K. Engineering and Physical Sciences Research Council. A.M. acknowledges the European Lifelong Learning Programme (LLP) for an Erasmus student placement scholarship. T.J.H.H. also acknowledges a Research Fellowship from Jesus College, Cambridge and helpful discussions with Dr. Adam Harper.This is the author accepted manuscript. The final version is available from AIP via http://dx.doi.org/10.1063/1.491631

Machine-learning of atomic-scale properties based on physical principles

We briefly summarize the kernel regression approach, as used recently in materials modelling, to fitting functions, particularly potential energy surfaces, and highlight how the linear algebra framework can be used to both predict and train from linear functionals of the potential energy, such as the total energy and atomic forces. We then give a detailed account of the Smooth Overlap of Atomic Positions (SOAP) representation and kernel, showing how it arises from an abstract representation of smooth atomic densities, and how it is related to several popular density-based representations of atomic structure. We also discuss recent generalisations that allow fine control of correlations between different atomic species, prediction and fitting of tensorial properties, and also how to construct structural kernels---applicable to comparing entire molecules or periodic systems---that go beyond an additive combination of local environments

The effects of amoebic dysentery as encountered in British troops from 1942 to 1946

1. Amoebic Dysentery has constituted a considerable problem during the War. 2. Large numbers of British troops suffered from Amoebic Dysentery for the fist time in 1942 in Bengal. Most of the patients were recent arrivals in India. 815 cases were treated in eight months in a Hospital in Calcutta in 1942. 3. The incidence of Amoebic Dysentery was greater than that of Bacillary Dysentery among British troops treated in Calcutta in 1942. 4. There was a marked rise in the incidence of Amoebic Dysentery at the time of the Monsoon, favouring a water borne spread. Bacillary Dysentery showed a similar rise in the Monsoon period. 5. The immediate mortality from fresh infections with Amoebic Dysentery was low. 6. Emetine Hydrochloride injections and Carbarsone were administered as routine treatment in 1942. The period of observation of cases following treatment was unduly short. The form of treatment and the short period of observation were dicta /ted by conditions at the time. Relapses occurred following this treatment and the proved relapse figure of 5% within eight months is a minimal one. Carbarsone appeared to be of value in eradicating Entamoeba Histolytica cysts. Kurchi Bismuth Iodide was valueless as an Amoebicidal agent and was of symptomatic use in relieving diarrhoea only. 7. Fifty chronic cases of Amoebiasis were treated in 1943 as the Hospital had become e Centre for the treatment of Chronic Amoebic Dysentery. All the cases had recieved repeated courses of Emetine injections and it is postulated that they had experienced relief from this treatment but had never been cured. The unsatisfactory nature of treatment by Emine injections and Carbarsone alone was thus displayed again. 8. Chronic Amoebic Dysentery leads to a state of invalidism with mentalapathy, intermittent diarrhoea, weaknes gross loss of weight and abdominal pain. 9. Sigmoidoscopy is an excellent method of assessing progress in Chronic Ameóbiasis but stool examinations are even more important in diagnosis. Thus 85% of cases in which the stools were positive showed Sigmoidoscopic lesions. It was interesting to observe the disappearance of ulcers in three weeks in some cases of Chronic Amoebiasis while other ulcers showed no response following Emetine Bismuth Iodide and Chiniofon. Sigmoidoscopy is a good test of cure but stool examination is even more reliable. 10. Emetine Bismuth Iodide was a drug of low toxicity in that the pulse and blood pressure were not affected following treatment. . 11. Emetine Bismuth Iodide and Chiniofon alone cured only 42% of fifty chronic cases. This consitituted an advance in that the patients had not been cured by Emetine injections The result was nevertheless disappointing. 12. 125 of the cases relapsed during observation over a period of one month, thus emphasising the importance of an adequate period of surveillance. 13. The lack of response to Emetine Bismuth Iodide and Chiniofon or Yatren was apparent to various workers when chronic refractory cases from the India and Burma Theatres returned to the United Kingdom. 14. Failure of previous methods of treatment give rise to speculation on the causes of chronicity. 15. Hargreaves contended that secondary infection was responsible for the failure of Chronic Amoebiasis to respond to treatment by Amoebici dal drugs. He therefore advocated a preliminary course of Penicillin and Sulpha-suxidine in all such cases. A few cases were personally treated in this way in the United Kingdom. Three cases of Chronic Colonic Amoebiasis have progressed well to date and are still under observation. A Haemolytic Streptococcus was cultured from the Amoebic ulcers of one case. 16. Perusal of the researches of various workers corroborate the importance of secondary infection in Amoebic Dysentery. It is considered that this is the most important factor from the therapeutic point of view. Cultures from Amoebic ulcers on Desoxycholate and bloodfiger media from a large number of Chronic cases would enable t e frequency of occurrence of some of the various secondary organisms to be assessed. 17. An adequate period of surveillance after treatment of Amoebic Dysentery is essential. Observation for three months at least is suggested as fifty chronic cases treated in 1943 averaged two and a half months between recurrences of symptoms. 18. After witnessing the effects of this disease for four years, one feels that no treatment, however prolonged, can be too thorough in the eradication of the infection