Counting all cubes in {0,1,...,n}^3

In this paper we describe a procedure of calculating the number cubes that have coordinates in the set {0,1,...,n}. We adapt the code that appeared in [11] developed to calculate the number of regular tetrahedra with coordinates in the set {0,1,...,n}. The idea is based on the theoretical results obtained in [13]. We extend then the sequence A098928 in the Online Encyclopedia of Integer Sequences to the first one hundred terms.Comment: 24 pages, 5 figure

Spherical electro-vacuum black holes with resonant, scalar QQ-hair

The asymptotically flat, spherical, electro-vacuum black holes (BHs) are shown to support static, spherical configurations of a gauged, self-interacting, scalar field, minimally coupled to the geometry. Considering a $Q$-ball type potential for the scalar field, we dub these configurations $Q$-clouds, in the test field approximation. The clouds exist under a resonance condition, at the threshold of (charged) superradiance. This is similar to the stationary clouds supported by Kerr BHs, which exist for a synchronisation condition, at the threshold of (rotational) superradiance. In contrast with the rotating case, however, $Q$-clouds require the scalar field to be massive and self-interacting; no similar clouds exist for massive but free scalar fields. First, considering a decoupling limit, we construct $Q$-clouds around Schwarzschild and Reissner-Nordstr\"om BHs, showing there is always a mass gap. Then, we make the $Q$-clouds backreact, and construct fully non-linear solutions of the Einstein-Maxwell-gauged scalar system describing spherical, charged BHs with resonant, scalar $Q$-hair. Amongst other properties, we observe there is non-uniqueness of charged BHs in this model and the $Q$-hairy BHs can be entropically preferred over Reissner-Nordstr\"om, for the same charge to mass ratio; some $Q$-hairy BH solutions can be overcharged. We also discuss how some well known no-hair theorems in the literature, applying to electro-vacuum plus minimally coupled scalar fields, are circumvented by this new type of BHs.Comment: 18 pages, 5 figures; v2. typos corrected, matches published versio

Expolring Architectures for CNN-Based Word Spotting

The goal in word spotting is to retrieve parts of document images which are relevant with respect to a certain user-defined query. The recent past has seen attribute-based Convolutional Neural Networks take over this field of research. As is common for other fields of computer vision, the CNNs used for this task are already considerably deep. The question that arises, however, is: How complex does a CNN have to be for word spotting? Are increasingly deeper models giving increasingly bet- ter results or does performance behave asymptotically for these architectures? On the other hand, can similar results be obtained with a much smaller CNN? The goal of this paper is to give an answer to these questions. Therefore, the recently successful TPP- PHOCNet will be compared to a Residual Network, a Densely Connected Convolutional Network and a LeNet architecture empirically. As will be seen in the evaluation, a complex model can be beneficial for word spotting on harder tasks such as the IAM Offline Database but gives no advantage for easier benchmarks such as the George Washington Database

Irisin evokes bradycardia by activating cardiac-projecting neurons of nucleus ambiguus.

Irisin is a newly identified hormone induced in muscle and adipose tissues by physical activity. This protein and its encoding gene have been identified in the brain; in addition, the precursor for irisin, FNDC5, can cross the blood-brain barrier. The fact that irisin is secreted during exercise together with the lower resting heart rate in athletes prompted us to investigate the effect of irisin on cardiac-projecting vagal neurons of nucleus ambiguus, a key regulatory site of heart rate. In vitro experiments in cultured nucleus ambiguus neurons indicate that irisin activates these neurons, inducing an increase in cytosolic Ca(2+) concentration and neuronal depolarization. In vivo microinjection of irisin into the nucleus ambiguus promotes bradycardia in conscious rats. Our study is the first to report the effects of irisin on the neurons controlling the cardiac vagal tone and to link a myokine to a cardioprotective role, by modulating central cardiovascular regulation

Stable black hole solutions with non-Abelian fields

We construct finite mass, asymptotically flat black hole solutions in d=4 Einstein-Yang-Mills theory augmented with higher order curvature terms of the gauge field. They possess non-Abelian hair in addition to Coulomb electric charge, and, below some non-zero critical temperature, they are thermodynamically preferred over the Reissner-Nordstrom solution. Our results indicate the existence of hairy non-Abelian black holes which are stable under linear, spherically symmetric perturbations.Comment: 8 pages, 3 figure

Asymptotically flat, stable black hole solutions in Einstein--Yang-Mills--Chern-Simons theory

We construct finite mass, asymptotically flat black hole solutions in d=5 Einstein--Yang-Mills--Chern-Simons theory. Our results indicate the existence of a second order phase transition between Reissner-Nordstrom solutions and the non-Abelian black holes which generically are thermodynamically preferred. Some of the non-Abelian configurations are also stable under linear, spherically symmetric perturbations. In addition a solution in closed form describing an extremal black hole with non-Abelian hair is found for a special value of the Chern-Simons coupling constant.Comment: 9 pages, 3 figure