Limit theorems for the maximal path weight in a directed graph on the line with random weights of edges

We consider the infinite directed graph with vertices the set of integers ...,-2,-1,0,1,2,... . Let v be a random variable taking either finite values or value "minus infinity". Consider random weights v(j,k), indexed by pairs (j,k) of integers with j<k, and assume that they are i.i.d. copies of v. The set of edges of the graph is the set (j,k), j<k. A path in the graph from vertex j to vertex k, j<k, is a finite sequence of edges (j(0), j(1)), (j(1), j(2)), ..., (j(m-1), j(m)) with j(0)=j and j(m)=j; the weight of this path is taken to be the sum v(j(0),j(1))+v(j(1),j(2))+...+v(j(m-1),j(m)) of the weights of its edges. Let w(0,n) be the maximal weight of all paths from 0 to n. We study the asymptotic behaviour of the sequence w(0,n), n=1, 2, ..., as n tends to infinity, under the assumptions that P(v>0)>0, the conditional distribution of v, given v>0, is not degenerate, and that E exp(Cv) is finite, for some C>0. We derive local limit theorems in the normal and moderate large deviations regimes in the case where v has an arithmetic distribution. We also derive an integro-local theorem in the case where v has a non-lattice distribution.Comment: 16 pages, 1 figur

Power management optimisation for hybrid electric systems using reinforcement learning and adaptive dynamic programming

This paper presents an online learning scheme based on reinforcement learning and adaptive dynamic programming for the power management of hybrid electric systems. Current methods for power management are conservative and unable to fully account for variations in the system due to changes in the health and operational conditions. These conservative schemes result in less efficient use of available power sources, increasing the overall system costs and heightening the risk of failure due to the variations. The proposed scheme is able to compensate for modelling uncertainties and the gradual system variations by adapting its performance function using the observed system measurements as reinforcement signals. The reinforcement signals are nonlinear and consequently neural networks are employed in the implementation of the scheme. Simulation results for the power management of an autonomous hybrid system show improved system performance using the proposed scheme as compared with a conventional offline dynamic programming approach

The generating functions of stirling numbers of the second kind derived probabilistically

Stirling numbers of the second kind, S(n, r), denote the number of partitions of a finite set of size n into r disjoint nonempty subsets. The aim of this short article is to shed some light on the generating functions of these numbers by deriving them probabilistically. We do this by linking them to Markov chains related to the classical coupon collector problem; coupons are collected in discrete time (ordinary generating function) or in continuous time (exponential generating function). We also review the shortest possible combinatorial derivations of these generating functions

Stellar Populations in Compact Galaxy Groups: a Multi-Wavelength Study of HCGs 16, 22, and 42, their Star Clusters and Dwarf Galaxies

We present a multi-wavelength analysis of three compact galaxy groups, HCGs 16, 22, and 42, which describe a sequence in terms of gas richness, from space- (Swift, HST, Spitzer) and ground-based (LCO, CTIO) imaging and spectroscopy. We study various signs of past interactions including a faint, dusty tidal feature about HCG 16A, which we tentatively age-date at <1 Gyr. This represents the possible detection of a tidal feature at the end of its phase of optical observability. Our HST images also resolve what were thought to be double nuclei in HCG 16C and D into multiple, distinct sources, likely to be star clusters. Beyond our phenomenological treatment, we focus primarily on contrasting the stellar populations across these three groups. The star clusters show a remarkable intermediate-age population in HCG 22, and identify the time at which star formation was quenched in HCG 42. We also search for dwarf galaxies at accordant redshifts. The inclusion of 33 members and 27 'associates' (possible members) radically changes group dynamical masses, which in turn may affect previous evolutionary classifications. The extended membership paints a picture of relative isolation in HCGs 16 and 22, but shows HCG 42 to be part of a larger structure, following a dichotomy expected from recent studies. We conclude that (a) star cluster populations provide an excellent metric of evolutionary state, as they can age-date the past epochs of star formation; and (b) the extended dwarf galaxy population must be considered in assessing the dynamical state of a compact group.Comment: 29 pages, 13 figures. Accepted for publication in The Astrophysical Journa

The SAMI Galaxy Survey: Unveiling the nature of kinematically offset active galactic nuclei

We have observed two kinematically offset active galactic nuclei (AGN), whose ionised gas is at a different line-of-sight velocity to their host galaxies, with the SAMI integral field spectrograph (IFS). One of the galaxies shows gas kinematics very different to the stellar kinematics, indicating a recent merger or accretion event. We demonstrate that the star formation associated with this event was triggered within the last 100 Myr. The other galaxy shows simple disc rotation in both gas and stellar kinematics, aligned with each other, but in the central region has signatures of an outflow driven by the AGN. Other than the outflow, neither galaxy shows any discontinuity in the ionised gas kinematics at the galaxy's centre. We conclude that in these two cases there is no direct evidence of the AGN being in a supermassive black hole binary system. Our study demonstrates that selecting kinematically offset AGN from single-fibre spectroscopy provides, by definition, samples of kinematically peculiar objects, but IFS or other data are required to determine their true nature.Comment: MNRAS accepted. 14 pages, 11 figure

Enhancing shopping experiences in smart retailing

The retailing market has undergone a paradigm-shift in the last decades, departing from its traditional form of shopping in brick-and-mortar stores towards online shopping and the establishment of shopping malls. As a result, “small” independent retailers operating in urban environments have suffered a substantial reduction of their turnover. This situation could be presumably reversed if retailers were to establish business “alliances” targeting economies of scale and engage themselves in providing innovative digital services. The SMARTBUY ecosystem realizes the concept of a “distributed shopping mall”, which allows retailers to join forces and unite in a large commercial coalition that generates added value for both retailers and customers. Along this line, the SMARTBUY ecosystem offers several novel features: (i) inventory management of centralized products and services, (ii) geo-located marketing of products and services, (iii) location-based search for products offered by neighboring retailers, and (iv) personalized recommendations for purchasing products derived by an innovative recommendation system. SMARTBUY materializes a blended retailing paradigm which combines the benefits of online shopping with the attractiveness of traditional shopping in brick-and-mortar stores. This article provides an overview of the main architectural components and functional aspects of the SMARTBUY ecosystem. Then, it reports the main findings derived from a 12&nbsp;months-long pilot execution of SMARTBUY across four European cities and discusses the key technology acceptance factors when deploying alike business alliances

The SAMI Galaxy Survey: Gas Streaming and Dynamical M/L in Rotationally Supported Systems

Line-of-sight velocities of gas and stars can constrain dark matter (DM) within rotationally supported galaxies if they trace circular orbits extensively. Photometric asymmetries may signify non-circular motions, requiring spectra with dense spatial coverage. Our integral-field spectroscopy of 178 galaxies spanned the mass range of the SAMI Galaxy Survey. We derived circular speed curves (CSCs) of gas and stars from non-parametric Diskfit fits out to $r\sim2r_e$. For 12/14 with measured H I profiles, ionized gas and H I maximum velocities agreed. We fitted mass-follows-light models to 163 galaxies by approximating the radial starlight profile as nested, very flattened mass homeoids viewed as a S\'ersic form. Fitting broad-band SEDs to SDSS images gave median stellar mass/light 1.7 assuming a Kroupa IMF vs. 2.6 dynamically. Two-thirds of the dynamical mass/light measures were consistent with star+remnant IMFs. One-fifth required upscaled starlight to fit, hence comparable mass of unobserved baryons and/or DM distributed similarly across the SAMI aperture that came to dominate motions as the starlight CSC declined rapidly. The rest had mass distributed differently from starlight. Subtracting fits of S\'ersic profiles to 13 VIKING Z-band images revealed residual weak bars. Near the bar PA, we assessed m = 2 streaming velocities, and found deviations usually <30 km/s from the CSC; three showed no deviation. Thus, asymmetries rarely influenced our CSCs despite co-located shock-indicating, emission-line flux ratios in more than 2/3.Comment: 21 pages, 15 figures. Accepted to MNRA