Comparing the hierarchy of author given tags and repository given tags in a large document archive

Folksonomies - large databases arising from collaborative tagging of items by independent users - are becoming an increasingly important way of categorizing information. In these systems users can tag items with free words, resulting in a tripartite item-tag-user network. Although there are no prescribed relations between tags, the way users think about the different categories presumably has some built in hierarchy, in which more special concepts are descendants of some more general categories. Several applications would benefit from the knowledge of this hierarchy. Here we apply a recent method to check the differences and similarities of hierarchies resulting from tags given by independent individuals and from tags given by a centrally managed repository system. The results from out method showed substantial differences between the lower part of the hierarchies, and in contrast, a relatively high similarity at the top of the hierarchies.Comment: 10 page

Extracting tag hierarchies

Tagging items with descriptive annotations or keywords is a very natural way to compress and highlight information about the properties of the given entity. Over the years several methods have been proposed for extracting a hierarchy between the tags for systems with a "flat", egalitarian organization of the tags, which is very common when the tags correspond to free words given by numerous independent people. Here we present a complete framework for automated tag hierarchy extraction based on tag occurrence statistics. Along with proposing new algorithms, we are also introducing different quality measures enabling the detailed comparison of competing approaches from different aspects. Furthermore, we set up a synthetic, computer generated benchmark providing a versatile tool for testing, with a couple of tunable parameters capable of generating a wide range of test beds. Beside the computer generated input we also use real data in our studies, including a biological example with a pre-defined hierarchy between the tags. The encouraging similarity between the pre-defined and reconstructed hierarchy, as well as the seemingly meaningful hierarchies obtained for other real systems indicate that tag hierarchy extraction is a very promising direction for further research with a great potential for practical applications.Comment: 25 pages with 21 pages of supporting information, 25 figure

Analytic properties of spherical cusp forms on GL(n)

Let $\phi$ be an $L^2$-normalized spherical vector in an everywhere unramified cuspidal automorphic representation of $\mathrm{PGL}_n$ over $\mathbb{Q}$ with Laplace eigenvalue $\lambda_{\phi}$. We establish explicit estimates for various quantities related to $\phi$ that are uniform in $\lambda_{\phi}$. This includes uniforms bounds for spherical Whittaker functions on $\mathrm{GL}_n(\mathbb{R})$, uniform bounds for the global sup-norm of $\phi$, and uniform bounds for the "essential support" of $\phi$, i.e. the region outside which it decays exponentially. The proofs combine analytic and arithmetic tools.Comment: 18 pages, LaTeX2e, submitted; v2: revised version fixing mainly (45) and its consequences; v3: revised version incorporating suggestions by the referee, e.g. Theorem 2 is now more general than before; v4: final version to appear in Journal d'Analyse Math\'ematique; v5: small corrections added in proo

The effect of quantum fluctuations in compact star observables

Astrophysical measurements regarding compact stars are just ahead of a big evolution jump, since the NICER experiment deployed on ISS on 14 June 2017. This will soon provide data that would enable the determination of compact star radius with less than 10% error. This poses new challenges for nuclear models aiming to explain the structure of super dense nuclear matter found in neutron stars. Detailed studies of the QCD phase diagram shows the importance of bosonic quantum fluctuations in the cold dense matter equation of state. Here, we using a demonstrative model to show the effect of bosonic quantum fluctuations on compact star observables such as mass, radius, and compactness. We have also calculated the difference in the value of compressibility which is caused by quantum fluctuations. The above mentioned quantities are calculated in mean field, one-loop and in high order many-loop approximation. The results show that the magnitude of these effects is ~5%, which place it into the region where forthcoming high-accuracy measurements may detect it.Comment: 6 pages 4 figues, minor corrections were adde

FRG Approach to Nuclear Matter at Extreme Conditions

Functional renormalization group (FRG) is an exact method for taking into account the effect of quantum fluctuations in the effective action of the system. The FRG method applied to effective theories of nuclear matter yields equation of state which incorporates quantum fluctuations of the fields. Using the local potential approximation (LPA) the equation of state for Walecka-type models of nuclear matter under extreme conditions could be determined. These models can be tested by solving the corresponding Tolman--Oppenheimer--Volkov (TOV) equations and investigating the properties (mass and radius) of the corresponding compact star models. Here, we present the first steps on this way, we obtained a Maxwell construction within the FRG-based framework using a Walecka-type Lagrangian.Comment: 6 pages, 3 figure

Underlying Event Studies for LHC Energies

Underlying event was originally defined by the CDF collaboration decades ago. Here we improve the original definition to extend our analysis for events with multiple-jets. We introduce a definition for surrounding rings/belts and based on this definition the jet- and surrounding-belt-excluded areas will provide a good underlying event definition. We inverstigate our definition via the multiplicity in the defined geometry. In parallel, mean transverse momenta of these areas also studied in proton-proton collisions at $\sqrt{s}=7$ TeV LHC energy.Comment: 6 pages and 4 figure

Testing a Possible Way of Geometrization of the Strong Interaction by a Kaluza-Klein Star

Geometrization of the fundamental interactions has been extensively studied during the century. The idea of introducing compactified spatial dimensions originated by Kaluza and Klein. Following their approach, several model were built representing quantum numbers (e.g. charges) as compactified space-time dimensions. Such geometrized theoretical descriptions of the fundamental interactions might lead us to get closer to the unification of the principle theories. Here, we apply a $3+1_C+1$ dimensional theory, which contains one extra compactified spatial dimension $1_C$ in connection with the flavour quantum number in Quantum Chromodynamics. Within our model the size of the $1_C$ dimension is proportional to the inverse mass-difference of the first low-mass baryon states. We used this phenomena to apply in a compact star model -- a natural laboratory for testing the theory of strong interaction and the gravitational theory in parallel. Our aim is to test the modification of the measurable macroscopical parameters of a compact Kaluza-Klein star by varying the size of the compactified extra dimension. Since larger the $R_C$ the smaller the mass difference between the first spokes of the Kaluza-Klein ladder resulting smaller-mass stars. Using the Tolman-Oppenheimer-Volkov equation, we investigate the $M$-$R$ diagram and the dependence of the maximum mass of compact stars. Besides testing the validity of our model we compare our results to the existing observational data of pulsar properties for constraints.Comment: 10 pages, 2 figure