Kernel-based Inference of Functions over Graphs

The study of networks has witnessed an explosive growth over the past decades with several ground-breaking methods introduced. A particularly interesting -- and prevalent in several fields of study -- problem is that of inferring a function defined over the nodes of a network. This work presents a versatile kernel-based framework for tackling this inference problem that naturally subsumes and generalizes the reconstruction approaches put forth recently by the signal processing on graphs community. Both the static and the dynamic settings are considered along with effective modeling approaches for addressing real-world problems. The herein analytical discussion is complemented by a set of numerical examples, which showcase the effectiveness of the presented techniques, as well as their merits related to state-of-the-art methods.Comment: To be published as a chapter in `Adaptive Learning Methods for Nonlinear System Modeling', Elsevier Publishing, Eds. D. Comminiello and J.C. Principe (2018). This chapter surveys recent work on kernel-based inference of functions over graphs including arXiv:1612.03615 and arXiv:1605.07174 and arXiv:1711.0930

A Novel Approach to Multimedia Ontology Engineering for Automated Reasoning over Audiovisual LOD Datasets

Multimedia reasoning, which is suitable for, among others, multimedia content analysis and high-level video scene interpretation, relies on the formal and comprehensive conceptualization of the represented knowledge domain. However, most multimedia ontologies are not exhaustive in terms of role definitions, and do not incorporate complex role inclusions and role interdependencies. In fact, most multimedia ontologies do not have a role box at all, and implement only a basic subset of the available logical constructors. Consequently, their application in multimedia reasoning is limited. To address the above issues, VidOnt, the very first multimedia ontology with SROIQ(D) expressivity and a DL-safe ruleset has been introduced for next-generation multimedia reasoning. In contrast to the common practice, the formal grounding has been set in one of the most expressive description logics, and the ontology validated with industry-leading reasoners, namely HermiT and FaCT++. This paper also presents best practices for developing multimedia ontologies, based on my ontology engineering approach

Statistical multi-moment bifurcations in random delay coupled swarms

We study the effects of discrete, randomly distributed time delays on the dynamics of a coupled system of self-propelling particles. Bifurcation analysis on a mean field approximation of the system reveals that the system possesses patterns with certain universal characteristics that depend on distinguished moments of the time delay distribution. Specifically, we show both theoretically and numerically that although bifurcations of simple patterns, such as translations, change stability only as a function of the first moment of the time delay distribution, more complex patterns arising from Hopf bifurcations depend on all of the moments

Cosmological Constant and Noncommutativity: A Newtonian point of view

We study a Newtonian cosmological model in the context of a noncommutative space. It is shown that the trajectories of a test particle undergo modifications such that it no longer satisfies the cosmological principle. For the case of a positive cosmological constant, spiral trajectories are obtained and corrections to the Hubble constant appear. It is also shown that, in the limit of a strong noncommutative parameter, the model is closely related to a particle in a G\"odel-type metric.Comment: 14 pages, 3 figures, Introduction was changed and references added. Final version accepted for publication in JMPL

The polar ring galaxy AM1934-563 revisited

We report long-slit spectroscopic observations of the dust-lane polar-ring galaxy AM1934-563 obtained with the Southern African Large Telescope (SALT) during its performance-verification phase. The observations target the spectral region of the Ha, [NII] and [SII] emission-lines, but show also deep NaI stellar absorption lines that we interpret as produced by stars in the galaxy. We derive rotation curves along the major axis of the galaxy that extend out to about 8 kpc from the center for both the gaseous and the stellar components, using the emission and absorption lines. We derive similar rotation curves along the major axis of the polar ring and point out differences between these and the ones of the main galaxy. We identify a small diffuse object visible only in Ha emission and with a low velocity dispersion as a dwarf HII galaxy and argue that it is probably metal-poor. Its velocity indicates that it is a fourth member of the galaxy group in which AM1934-563 belongs. We discuss the observations in the context of the proposal that the object is the result of a major merger and point out some observational discrepancies from this explanation. We argue that an alternative scenario that could better fit the observations may be the slow accretion of cold intergalactic gas, focused by a dense filament of galaxies in which this object is embedded (abridged).Comment: 19 pages, 13 figures, submitted to MNRAS. Some figures were bitmapped to reduce the size. Full resolution version is available from http://www.saao.ac.za/~akniazev/pub/AM1934_563.pd

Directed transport as a mechanism for protein folding in vivo

We propose a model for protein folding in vivo based on a Brownian-ratchet mechanism in the multidimensional energy landscape space. The device is able to produce directed transport taking advantage of the assumed intrinsic asymmetric properties of the proteins and employing the consumption of energy provided by an external source. Through such a directed transport phenomenon, the polypeptide finds the native state starting from any initial state in the energy landscape with great efficacy and robustness, even in the presence of different type of obstacles. This model solves Levinthal's paradox without requiring biased transition probabilities but at the expense of opening the system to an external field.Comment: 16 pages, 7 figure

On the order of BEC transition in weakly interacting gases predicted by mean-field theory

Predictions from Hartree-Fock (HF), Popov (P), Yukalov-Yukalova (YY) and $t$-matrix approximations regarding the thermodynamics from the normal to the BEC phase in weakly interacting Bose gases are considered. By analyzing the dependence of the chemical potential $\mu$ on temperature $T$ and particle density $\rho$ we show that none of them predicts a second-order phase transition as required by symmetry-breaking general considerations. In this work we find that the isothermal compressibility $\kappa_{T}$ predicted by these theories does not diverge at criticality as expected in a true second-order phase transition. Moreover the isotherms $\mu=\mu(\rho,T)$ typically exhibit a non-singled valued behavior in the vicinity of the BEC transition, a feature forbidden by general thermodynamic principles. This behavior can be avoided if a first order phase transition is appealed. The facts described above show that although these mean field approximations give correct results near zero temperature they are endowed with thermodynamic anomalies in the vicinity of the BEC transition. We address the implications of these results in the interpretation of current experiments with ultracold trapped alkali gases.Comment: 16 pages, 5 figure

The metallicity extremes of the Sagittarius dSph using SALT spectroscopy of PNe

In this work we present the first spectroscopic results obtained with the Southern African Large Telescope (SALT) telescope during its perfomance-verification phase. We find that the Sagittarius dwarf spheroidal galaxy (Sgr) Sgr contains a youngest stellar population with [O/H] -0.2 and age t>1 Gyr, and an oldest population with [O/H]=-2.0. The values are based on spectra of two planetary nebulae (PNe), using empirical abundance determinations. We calculated abundances for O, N, Ne, Ar, S, Cl, Fe, C and He. We confirm the high abundances of PN StWr2-21 with 12+log(O/H) = 8.57+/-0.02 dex. The other PN studied, BoBn1, is an extraordinary object in that the neon abundance exceeds that of oxygen. The abundances of S, Ar and Cl in BoBn1 yield the original stellar metallicity, corresponding to 12+log(O/H) = 6.72+/-0.16 dex which is 1/110 of the solar value. The actual [O/H] is much higher: third dredge-up enriched the material by a factor of ~12 in oxygen, ~240 in nitrogen and ~70 in neon. Neon as well as nitrogen and oxygen content may have been produced in the intershell of low-mass AGB stars. Well defined broad WR lines are present in the spectrum of StWr2-21 and absent in the spectrum of BoBn1. This puts the fraction of [WR]-type central PNe stars to 67% for dSph galaxies.Comment: 14 pages, 4 figures, accepted to MNRA

Ground-state dispersion and density of states from path-integral Monte Carlo. Application to the lattice polaron

A formula is derived that relates the ground-state dispersion of a many-body system with the end-to-end distribution of paths with open boundary conditions in imaginary time. The formula does not involve the energy estimator. It allows direct measurement of the ground-state dispersion by quantum Monte Carlo methods without analytical continuation or auxiliary fitting. The formula is applied to the lattice polaron problem. The exact polaron spectrum and density of states are calculated for several models in one, two, and three dimensions. In the adiabatic regime of the Holstein model, the polaron density of states deviates spectacularly from the free-particle shape.Comment: 8 pages, 9 figure