1,697 research outputs found
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
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