On the PIE root-structure constraint prohibiting repeated consonants

This paper confronts and resolves the problem of apparent exceptions to the constraint prohibiting the co-occurrence of identical consonants in both syllable margins of the PIE root: schematically, †… Ci … E … Ci …, where † indicates the prohibition of the root structure following it, Ci = the identical consonant, E = the ablauting vowel, and … = optional additional consonants in the syllable margins. In advancement of previous work addressing this problem — most recently exemplified in Cooper (2009), Corbeau (2013) and Weiss (2020) — it eliminates several potential exceptions to the constraint and proposes that, once a cross-linguistic absence-of-contrast principle is taken into account which determines the relation of laryngeal features (glottalization, aspiration, and voicing) to the syllable margins that contain them, no clear-cut exceptions remain

On black hole thermalization, D0 brane dynamics, and emergent spacetime

When matter falls past the horizon of a large black hole, the expectation from string theory is that the configuration thermalizes and the information in the probe is rather quickly scrambled away. The traditional view of a classical unique spacetime near a black hole horizon conflicts with this picture. The question then arises as to what spacetime does the probe actually see as it crosses a horizon, and how does the background geometry imprint its signature onto the thermal properties of the probe. In this work, we explore these questions through an extensive series of numerical simulations of D0 branes. We determine that the D0 branes quickly settle into an incompressible symmetric state -- thermalized within a few oscillations through a process driven entirely by internal non-linear dynamics. Surprisingly, thermal background fluctuations play no role in this mechanism. Signatures of the background fields in this thermal state arise either through fluxes, i.e. black hole hair; or if the probe expands to the size of the horizon -- which we see evidence of. We determine simple scaling relations for the D0 branes' equilibrium size, time to thermalize, lifetime, and temperature in terms of their number, initial energy, and the background fields. Our results are consistent with the conjecture that black holes are the fastest scramblers as seen by Matrix theory.Comment: 43 pages, 12 figures; v2: added analysis showing that results are consistent with and confirm Susskind conjecture on black hole thermalization. Added clarification about strong coupling regime. Citation adde

Glassy correlations and microstructures in randomly crosslinked homopolymer blends

We consider a microscopic model of a polymer blend that is prone to phase separation. Permanent crosslinks are introduced between randomly chosen pairs of monomers, drawn from the Deam-Edwards distribution. Thereby, not only density but also concentration fluctuations of the melt are quenched-in in the gel state, which emerges upon sufficient crosslinking. We derive a Landau expansion in terms of the order parameters for gelation and phase separation, and analyze it on the mean-field level, including Gaussian fluctuations. The mixed gel is characterized by thermal as well as time-persistent (glassy) concentration fluctuations. Whereas the former are independent of the preparation state, the latter reflect the concentration fluctuations at the instant of crosslinking, provided the mesh size is smaller than the correlation length of phase separation. The mixed gel becomes unstable to microphase separation upon lowering the temperature in the gel phase. Whereas the length scale of microphase separation is given by the mesh size, at least close to the transition, the emergent microstructure depends on the composition and compressibility of the melt. Hexagonal structures, as well as lamellae or random structures with a unique wavelength, can be energetically favorable.Comment: 19 pages, 10 figures. Submitted to the Journal of Chemical Physics (http://jcp.aip.org

Generative Sliced MMD Flows with Riesz Kernels

Maximum mean discrepancy (MMD) flows suffer from high computational costs in large scale computations. In this paper, we show that MMD flows with Riesz kernels $K(x,y) = - \|x-y\|^r$, $r \in (0,2)$ have exceptional properties which allow for their efficient computation. First, the MMD of Riesz kernels coincides with the MMD of their sliced version. As a consequence, the computation of gradients of MMDs can be performed in the one-dimensional setting. Here, for $r=1$, a simple sorting algorithm can be applied to reduce the complexity from $O(MN+N^2)$ to $O((M+N)\log(M+N))$ for two empirical measures with $M$ and $N$ support points. For the implementations we approximate the gradient of the sliced MMD by using only a finite number $P$ of slices. We show that the resulting error has complexity $O(\sqrt{d/P})$, where $d$ is the data dimension. These results enable us to train generative models by approximating MMD gradient flows by neural networks even for large scale applications. We demonstrate the efficiency of our model by image generation on MNIST, FashionMNIST and CIFAR10

A proposal for a thesaurus for web services in solar radiation

International audienceMetadata are necessary to discover, describe and exchange any type of information, resource and service at a large scale. A significant amount of effort has been made in the field of geography and environment to establish standards. Efforts still remain to address more specific domains such as renewable energies. This communication focuses on solar energy and more specifically on aspects in solar radiation that relate to geography and meteorology. A thesaurus in solar radiation is proposed for the keys elements in solar radiation namely time, space and radiation types. The importance of time-series in solar radiation is outlined and attributes of the key elements are discussed. An XML schema for encoding metadata is proposed. The exploitation of such a schema in web services is discussed. This proposal is a first attempt at establishing a thesaurus for describing data and applications in solar radiation