Phase space sampling and operator confidence with generative adversarial networks

We demonstrate that a generative adversarial network can be trained to produce Ising model configurations in distinct regions of phase space. In training a generative adversarial network, the discriminator neural network becomes very good a discerning examples from the training set and examples from the testing set. We demonstrate that this ability can be used as an anomaly detector, producing estimations of operator values along with a confidence in the prediction

Deep neural networks for direct, featureless learning through observation: the case of 2d spin models

We demonstrate the capability of a convolutional deep neural network in predicting the nearest-neighbor energy of the 4x4 Ising model. Using its success at this task, we motivate the study of the larger 8x8 Ising model, showing that the deep neural network can learn the nearest-neighbor Ising Hamiltonian after only seeing a vanishingly small fraction of configuration space. Additionally, we show that the neural network has learned both the energy and magnetization operators with sufficient accuracy to replicate the low-temperature Ising phase transition. We then demonstrate the ability of the neural network to learn other spin models, teaching the convolutional deep neural network to accurately predict the long-range interaction of a screened Coulomb Hamiltonian, a sinusoidally attenuated screened Coulomb Hamiltonian, and a modified Potts model Hamiltonian. In the case of the long-range interaction, we demonstrate the ability of the neural network to recover the phase transition with equivalent accuracy to the numerically exact method. Furthermore, in the case of the long-range interaction, the benefits of the neural network become apparent; it is able to make predictions with a high degree of accuracy, and do so 1600 times faster than a CUDA-optimized exact calculation. Additionally, we demonstrate how the neural network succeeds at these tasks by looking at the weights learned in a simplified demonstration

Sampling algorithms for validation of supervised learning models for Ising-like systems

In this paper, we build and explore supervised learning models of ferromagnetic system behavior, using Monte-Carlo sampling of the spin configuration space generated by the 2D Ising model. Given the enormous size of the space of all possible Ising model realizations, the question arises as to how to choose a reasonable number of samples that will form physically meaningful and non-intersecting training and testing datasets. Here, we propose a sampling technique called ID-MH that uses the Metropolis-Hastings algorithm creating Markov process across energy levels within the predefined configuration subspace. We show that application of this method retains phase transitions in both training and testing datasets and serves the purpose of validation of a machine learning algorithm. For larger lattice dimensions, ID-MH is not feasible as it requires knowledge of the complete configuration space. As such, we develop a new "block-ID" sampling strategy: it decomposes the given structure into square blocks with lattice dimension no greater than 5 and uses ID-MH sampling of candidate blocks. Further comparison of the performance of commonly used machine learning methods such as random forests, decision trees, k nearest neighbors and artificial neural networks shows that the PCA-based Decision Tree regressor is the most accurate predictor of magnetizations of the Ising model. For energies, however, the accuracy of prediction is not satisfactory, highlighting the need to consider more algorithmically complex methods (e.g., deep learning).Comment: 43 pages and 16 figure

A note on the metallization of compressed liquid hydrogen

We examine the molecular-atomic transition in liquid hydrogen as it relates to metallization. Pair potentials are obtained from first principles molecular dynamics and compared with potentials derived from quadratic response. The results provide insight into the nature of covalent bonding under extreme conditions. Based on this analysis, we construct a schematic dissociation-metallization phase diagram and suggest experimental approaches that should significantly reduce the pressures necessary for the realization of the elusive metallic phase of hydrogen.Comment: 11 pages, 4 figure

Unjust enrichment, leapfrogging, and a defence of entitlement

A definitive version is available online on a current, full text basis on the Westlaw database - http://www.westlaw.comThis article argues that a defence of entitlement should be recognized in the law of unjust enrichment, consistently with the case law and sound principle, and in mutual support of a rule against leapfrogging. In so doing, this article also explores the relationship between unjust enrichment and contract

The Common Ground of Law and Anarchism

This is the the final version.Available from Springer via the DOI in this recordAnarchism often sets itself against the law. However, the alternative vision advanced by anarchism faces theoretical problems. Further, case studies of anarchist communities reveal practical difficulties, and resort to the very behaviour for which anarchism criticises the law. Nevertheless, the values inherent in law are strongly aligned with those championed by anarchism. Ultimately, law and anarchism need not be antithetical; they can be mutually helpful

Necessity and Murder

This is the author accepted manuscript. The final version is available from SAGE Publications via the DOI in this recordThis article argues that there is an alternative and hitherto unarticulated defence of necessity latent in the case law which could be a defence to murder. The defence can be formulated as follows: if a group of two or more people are virtually certain to suffer death imminently and together, from the same cause, but one or more could be saved only by killing a particular person in that group, then such killing would be lawful. (The killer does not have to be one of the group.) Formulating the defence this way also reveals its underlying justification: if all life is otherwise going to be lost anyway, it is better to save at least some of that life. This article begins by showing how this proposed defence of necessity is consistent with the leading cases and prominent real-life situations. It then differentiates the proposed defence from a defence of lesser evil necessity