All scale-free networks are sparse

We study the realizability of scale free-networks with a given degree sequence, showing that the fraction of realizable sequences undergoes two first-order transitions at the values 0 and 2 of the power-law exponent. We substantiate this finding by analytical reasoning and by a numerical method, proposed here, based on extreme value arguments, which can be applied to any given degree distribution. Our results reveal a fundamental reason why large scale-free networks without constraints on minimum and maximum degree must be sparse.Comment: 4 pages, 2 figure

Collecting Diverse Natural Language Inference Problems for Sentence Representation Evaluation

We present a large-scale collection of diverse natural language inference (NLI) datasets that help provide insight into how well a sentence representation captures distinct types of reasoning. The collection results from recasting 13 existing datasets from 7 semantic phenomena into a common NLI structure, resulting in over half a million labeled context-hypothesis pairs in total. We refer to our collection as the DNC: Diverse Natural Language Inference Collection. The DNC is available online at https://www.decomp.net, and will grow over time as additional resources are recast and added from novel sources.Comment: To be presented at EMNLP 2018. 15 page

Self-Completeness and the Generalized Uncertainty Principle

The generalized uncertainty principle discloses a self-complete characteristic of gravity, namely the possibility of masking any curvature singularity behind an event horizon as a result of matter compression at the Planck scale. In this paper we extend the above reasoning in order to overcome some current limitations to the framework, including the absence of a consistent metric describing such Planck-scale black holes. We implement a minimum-size black hole in terms of the extremal configuration of a neutral non-rotating metric, which we derived by mimicking the effects of the generalized uncertainty principle via a short scale modified version of Einstein gravity. In such a way, we find a self-consistent scenario that reconciles the self-complete character of gravity and the generalized uncertainty principle.Comment: 20 pages, 6 figures, v2: additional references, version in press on JHE

Effects of supersymmetric threshold corrections on the Yukawa matrix unification

We present an updated analysis of the Yukawa matrix unification within the renormalizable Minimal Supersymmetric Standard Model. It is assumed that the soft terms are non-universal but flavour-diagonal in the super-CKM basis at the GUT scale. Trilinear Higgs-squark-squark A-terms can generate large threshold corrections to the Yukawa matrix $\mathbf{Y}^d$ at the superpartner decoupling scale. In effect, the SU(5) boundary condition $\mathbf{Y}^d=\mathbf{Y}^{e\,T}$ at the GUT scale can be satisfied. However, such large trilinear terms make the usual Higgs vacuum metastable (though long-lived). We broaden previous studies by including results from the first LHC phase, notably the measurement of the Higgs particle mass, as well as a quantitative investigation of flavour observables.Comment: 19 pages, 9 figures, 3 tables; journal version: updated numerical results after finding a bug in the software, their meaning and reasoning in the article remain the same; added scatter plots of scanned points; The European Physical Journal C, Volume 75, Issue 2 (February 2015