Machine learning phases in statistical physics

Conventionally, the study of phases in statistical mechan- ics is performed with the help of random sampling tools. Among the most powerful are Monte Carlo simulations consisting of a stochastic importance sampling over state space and evaluation of estimators for physical quantities. The ability of modern machine learning techniques to classify, identify, or in- terpret massive data sets provides a complementary paradigm to the above approach to analyze the exponentially large number of states in statistical physics. In this report, it is demonstrated by application on Ising-type models that deep learning has potential wide applications in solving many-body statis- tical physics problems. In application of supervised learning, we showed that the feed-forward neural network can identify phases and phase transitions in the ferromagnetic Ising model and the convolutional neural network (CNN) is extremely powerful in classifying T = 0 and T = ∞ phases in the Ising gauge model; In application of unsupervised learning, we illustrated that a deep auto-encoder constructed by stacked restricted Boltzmann machines (RBM) is closely related to the renormalization group (RG) method well understood in modern physics and our reconstruction of Ising spin configurations in the ferromagnetic Ising model is similar to the hand-written digits reconstruction.Statistic

Two monotonic functions involving gamma function and volume of unit ball

In present paper, we prove the monotonicity of two functions involving the gamma function $\Gamma(x)$ and relating to the $n$-dimensional volume of the unit ball $\mathbb{B}^n$ in $\mathbb{R}^n$.Comment: 7 page

Arc-swift: A Novel Transition System for Dependency Parsing

Transition-based dependency parsers often need sequences of local shift and reduce operations to produce certain attachments. Correct individual decisions hence require global information about the sentence context and mistakes cause error propagation. This paper proposes a novel transition system, arc-swift, that enables direct attachments between tokens farther apart with a single transition. This allows the parser to leverage lexical information more directly in transition decisions. Hence, arc-swift can achieve significantly better performance with a very small beam size. Our parsers reduce error by 3.7--7.6% relative to those using existing transition systems on the Penn Treebank dependency parsing task and English Universal Dependencies.Comment: Accepted at ACL 201

Galaxy growth in the concordance Λ\LambdaCDM cosmology

We use galaxy and dark halo data from the public database for the Millennium Simulation to study the growth of galaxies in the De Lucia et al. (2006) model for galaxy formation. Previous work has shown this model to reproduce many aspects of the systematic properties and the clustering of real galaxies, both in the nearby universe and at high redshift. It assumes the stellar masses of galaxies to increase through three processes, major mergers, the accretion of smaller satellite systems, and star formation. We show the relative importance of these three modes to be a strong function of stellar mass and of redshift. Galaxy growth through major mergers depends strongly on stellar mass, but only weakly on redshift. Except for massive systems, minor mergers contribute more to galaxy growth than major mergers at all redshifts and at all stellar masses. For galaxies significantly less massive than the Milky Way, star formation dominates the growth at all epochs. For galaxies significantly more massive than the Milky Way, growth through mergers is the dominant process at all epochs. At a stellar mass of $6\times 10^{10}M_\odot$, star formation dominates at $z>1$ and mergers at later times. At every stellar mass, the growth rates through star formation increase rapidly with increasing redshift. Specific star formation rates are a decreasing function of stellar mass not only at $z=0$ but also at all higher redshifts. For comparison, we carry out a similar analysis of the growth of dark matter halos. In contrast to the galaxies, growth rates depend strongly on redshift, but only weakly on mass. They agree qualitatively with analytic predictions for halo growth.Comment: 11 pages, 6 figure