Double-Trace Flows and the Swampland

We explore the idea that large $N$, non-supersymmetric conformal field theories with a parametrically large gap to higher spin single-trace operators may be obtained as infrared fixed points of relevant double-trace deformations of superconformal field theories. After recalling the AdS interpretation and some potential pathologies of such flows, we introduce a concrete example that appears to avoid them: the ABJM theory at finite $k$, deformed by $\int\!{\cal O}^2$, where ${\cal O}$ is the superconformal primary in the stress-tensor multiplet. We address its relation to recent conjectures based on weak gravity bounds, and discuss the prospects for a wider class of similarly viable flows. Next, we proceed to analyze the spectrum and correlation functions of the putative IR CFT, to leading non-trivial order in $1/N$. This includes analytic computations of the change under double-trace flow of connected four-point functions of ABJM superconformal primaries; and of the IR anomalous dimensions of infinite classes of double-trace composite operators. These would be the first analytic results for anomalous dimensions of finite-spin composite operators in any large $N$ CFT$_3$ with an Einstein gravity dual.Comment: 25+13 pages. v2: refs added, minor clarification

Reinterpreting the development of extensive air showers initiated by nuclei and photons

Ultra-high energy cosmic rays (UHECRs) interacting with the atmosphere generate extensive air showers (EAS) of secondary particles. The depth corresponding to the maximum development of the shower, \Xmax, is a well-known observable for determining the nature of the primary cosmic ray which initiated the cascade process. In this paper, we present an empirical model to describe the distribution of \Xmax for EAS initiated by nuclei, in the energy range from $10^{17}$ eV up to $10^{21}$ eV, and by photons, in the energy range from $10^{17}$ eV up to $10^{19.6}$ eV. Our model adopts the generalized Gumbel distribution motivated by the relationship between the generalized Gumbel statistics and the distribution of the sum of non-identically distributed variables in dissipative stochastic systems. We provide an analytical expression for describing the \Xmax distribution for photons and for nuclei, and for their first two statistical moments, namely \langle \Xmax\rangle and \sigma^{2}(\Xmax). The impact of the hadronic interaction model is investigated in detail, even in the case of the most up-to-date models accounting for LHC observations. We also briefly discuss the differences with a more classical approach and an application to the experimental data based on information theory.Comment: 21 pages, 4 tables, 8 figure

Maximal Sensitive Dependence and the Optimal Path to Epidemic Extinction

Extinction of an epidemic or a species is a rare event that occurs due to a large, rare stochastic fluctuation. Although the extinction process is dynamically unstable, it follows an optimal path that maximizes the probability of extinction. We show that the optimal path is also directly related to the finite-time Lyapunov exponents of the underlying dynamical system in that the optimal path displays maximum sensitivity to initial conditions. We consider several stochastic epidemic models, and examine the extinction process in a dynamical systems framework. Using the dynamics of the finite-time Lyapunov exponents as a constructive tool, we demonstrate that the dynamical systems viewpoint of extinction evolves naturally toward the optimal path.Comment: 21 pages, 5 figures, Final revision to appear in Bulletin of Mathematical Biolog

Microstructure and properties of welds between 5754 Al alloys and AZ31 Mg alloys using a Yb:YAG laser

The authors wish to thank Mr. Henri ANDRZEJEWSKI for his technical assistance in laser experiments. The authors wish to place their sincere thanks to Professor Philippe BOURNOT and Dr. Eric VALERIO for helpful discussions.Dissimilar laser beam welding between A5754 Al alloy and AZ31 Mg alloy with the plate thickness of 2 mm was investigated. Complex flow pattern characterized by a large volume of intermetallic compounds Al12Mg17 and Al3Mg2 is formed in the fusion zone. Microhardness measurement of the dissimilar welds presents an uneven distribution due to the complicated microstructure of the weld, and the maximum value of microhardness in the fusion zone is much higher than of the base materials

Investigating CXOU J163802.6-471358: a new pulsar wind nebula in the Norma region?

We present the first analysis of the extended source CXOU J163802.6--471358, which was discovered serendipitously during the {\em Chandra} X-ray survey of the Norma region of the Galactic spiral arms. The X-ray source exhibits a cometary appearance with a point source and an extended tail region. The complete source spectrum is fitted well with an absorbed power law model and jointly fitting the {\em Chandra} spectrum of the full source with one obtained from an archived {\em XMM-Newton} observation results in best fit parameters $N_{\rm H}$ $=1.5^{+0.7}_{-0.5}\times10^{23} \text{cm}{^{-2}}$ and $\Gamma=1.1^{+0.7}_{-0.6}$ (90$$ confidence uncertainties). The unabsorbed luminosity of the full source is then $L_X\sim 4.8\times10^{33}d_{10}^2$ergs s$^{-1}$ with $d_{10}=d/10$kpc, where a distance of 10 kpc is a lower bound inferred from the large column density. The radio counterpart found for the source using data from the Molonglo Galactic Plane Survey epoch-2 (MGPS-2) shows an elongated tail offset from the X-ray emission. No infrared counterpart was found. The results are consistent with the source being a previously unknown pulsar driving a bow shock through the ambient medium

Double-Trace Deformations of Conformal Correlations

Large $N$ conformal field theories often admit unitary renormalization group flows triggered by double-trace deformations. We compute the change in scalar four-point functions under double-trace flow, to leading order in $1/N$. This has a simple dual in AdS, where the flow is implemented by a change of boundary conditions, and provides a physical interpretation of single-valued conformal partial waves. We extract the change in the conformal dimensions and three-point coefficients of infinite families of double-trace composite operators. Some of these quantities are found to be sign-definite under double-trace flow. As an application, we derive anomalous dimensions of spinning double-trace operators comprised of non-singlet constituents in the $O(N)$ vector model.Comment: 29+15 pages. v2: typo corrected, minor changes in Appendix

Building more accurate decision trees with the additive tree.

The expansion of machine learning to high-stakes application domains such as medicine, finance, and criminal justice, where making informed decisions requires clear understanding of the model, has increased the interest in interpretable machine learning. The widely used Classification and Regression Trees (CART) have played a major role in health sciences, due to their simple and intuitive explanation of predictions. Ensemble methods like gradient boosting can improve the accuracy of decision trees, but at the expense of the interpretability of the generated model. Additive models, such as those produced by gradient boosting, and full interaction models, such as CART, have been investigated largely in isolation. We show that these models exist along a spectrum, revealing previously unseen connections between these approaches. This paper introduces a rigorous formalization for the additive tree, an empirically validated learning technique for creating a single decision tree, and shows that this method can produce models equivalent to CART or gradient boosted stumps at the extremes by varying a single parameter. Although the additive tree is designed primarily to provide both the model interpretability and predictive performance needed for high-stakes applications like medicine, it also can produce decision trees represented by hybrid models between CART and boosted stumps that can outperform either of these approaches