Exact solution of mean geodesic distance for Vicsek fractals

The Vicsek fractals are one of the most interesting classes of fractals and the study of their structural properties is important. In this paper, the exact formula for the mean geodesic distance of Vicsek fractals is found. The quantity is computed precisely through the recurrence relations derived from the self-similar structure of the fractals considered. The obtained exact solution exhibits that the mean geodesic distance approximately increases as an exponential function of the number of nodes, with the exponent equal to the reciprocal of the fractal dimension. The closed-form solution is confirmed by extensive numerical calculations.Comment: 4 pages, 3 figure

Characterizing Some Gaia Alerts with LAMOST and SDSS

Gaia is regularly producing Alerts on objects where photometric variability has been detected. The physical nature of these objects has often to be determined with the complementary observations from ground-based facilities. We have compared the list of Gaia Alerts (until 20181101) with archival LAMOST and SDSS spectroscopic data. The date of the ground-based observation rarely corresponds to the date of the Alert, but this allows at least the identification of the source if it is persistent, or the host galaxy if the object was only transient like a supernova. A list of Gaia Nuclear Transients from Kostrzewa-Rutkowska et al. (2018) has been included in this search also. We found 26 Gaia Alerts with spectra in LAMOST+SDSS labelled as stars (12 with multi-epoch spectra). A majority of them are CVs. Similarly 206 Gaia Alerts have associated spectra labelled as galaxies (49 with multi-epoch spectra). Those spectra were generally obtained on a date different from the Alert date, are mostly emission-line galaxies, leading to the suspicion that most of the Alerts were due to a SN. As for the GNT list, we found 55 associated spectra labelled as galaxies (13 with multi-epoch spectra). In two galaxies, Gaia17aal and GNTJ170213+2543, was the date of the spectroscopic observation close enough to the Alert date: we find a trace of the SN itself in their LAMOST spectrum, both classified here as a type Ia SN. The GNT sample has a higher proportion of AGNs, suggesting that some of the detected variations are also due to the AGN itself. Similar for Quasars, we found 30 Gaia Alerts but 68 GNT cases have single epoch quasar spectra, while 12 plus 23 have multi-epoch spectra. For ten out of these 35, their multi-epoch spectra show appearance or disappearance of the broad Balmer lines and also variations in the continuum, qualifying them as "Changing Look Quasars".Comment: Accepted for publication in APSS, 14 pages, 8 figures, 2 table

State-of-the-art on research and applications of machine learning in the building life cycle

Fueled by big data, powerful and affordable computing resources, and advanced algorithms, machine learning has been explored and applied to buildings research for the past decades and has demonstrated its potential to enhance building performance. This study systematically surveyed how machine learning has been applied at different stages of building life cycle. By conducting a literature search on the Web of Knowledge platform, we found 9579 papers in this field and selected 153 papers for an in-depth review. The number of published papers is increasing year by year, with a focus on building design, operation, and control. However, no study was found using machine learning in building commissioning. There are successful pilot studies on fault detection and diagnosis of HVAC equipment and systems, load prediction, energy baseline estimate, load shape clustering, occupancy prediction, and learning occupant behaviors and energy use patterns. None of the existing studies were adopted broadly by the building industry, due to common challenges including (1) lack of large scale labeled data to train and validate the model, (2) lack of model transferability, which limits a model trained with one data-rich building to be used in another building with limited data, (3) lack of strong justification of costs and benefits of deploying machine learning, and (4) the performance might not be reliable and robust for the stated goals, as the method might work for some buildings but could not be generalized to others. Findings from the study can inform future machine learning research to improve occupant comfort, energy efficiency, demand flexibility, and resilience of buildings, as well as to inspire young researchers in the field to explore multidisciplinary approaches that integrate building science, computing science, data science, and social science

Surface Impedance and Bulk Band Geometric Phases in One-Dimensional Systems

Surface impedance is an important concept in classical wave systems such as photonic crystals (PCs). For example, the condition of an interface state formation in the interfacial region of two different one-dimensional PCs is simply Z_SL +Z_SR=0, where Z_SL (Z_SR)is the surface impedance of the semi-infinite PC on the left- (right-) hand side of the interface. Here, we also show a rigorous relation between the surface impedance of a one-dimensional PC and its bulk properties through the geometrical (Zak) phases of the bulk bands, which can be used to determine the existence or non-existence of interface states at the interface of the two PCs in a particular band gap. Our results hold for any PCs with inversion symmetry, independent of the frequency of the gap and the symmetry point where the gap lies in the Brillouin Zone. Our results provide new insights on the relationship between surface scattering properties, the bulk band properties and the formation of interface states, which in turn can enable the design of systems with interface states in a rational manner

Evolving small-world networks with geographical attachment preference

We introduce a minimal extended evolving model for small-world networks which is controlled by a parameter. In this model the network growth is determined by the attachment of new nodes to already existing nodes that are geographically close. We analyze several topological properties for our model both analytically and by numerical simulations. The resulting network shows some important characteristics of real-life networks such as the small-world effect and a high clustering.Comment: 11 pages, 4 figure