Unevenness of Loop Location in Complex Networks

The loop structure plays an important role in many aspects of complex networks and attracts much attention. Among the previous works, Bianconi et al find that real networks often have fewer short loops as compared to random models. In this paper, we focus on the uneven location of loops which makes some parts of the network rich while some other parts sparse in loops. We propose a node removing process to analyze the unevenness and find rich loop cores can exist in many real networks such as neural networks and food web networks. Finally, an index is presented to quantify the unevenness of loop location in complex networks.Comment: 7 pages, 6 figure

Stationarity and geometric ergodicity of a class of nonlinear ARCH models

A class of nonlinear ARCH processes is introduced and studied. The existence of a strictly stationary and $\beta$-mixing solution is established under a mild assumption on the density of the underlying independent process. We give sufficient conditions for the existence of moments. The analysis relies on Markov chain theory. The model generalizes some important features of standard ARCH models and is amenable to further analysis.Comment: Published at http://dx.doi.org/10.1214/105051606000000565 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Monolayer Self-Assembly of Monodisperse Nanocrystals at The Liquid-Air Interface

The study of nanocrystals (NCs) self-assembly into monolayers have attracted significant interests, due to wide applications in sensors, catalysts, nanodevices and pattern transfer. Liquid-air interface self-assembly (LAISA) is a useful technique used for the monolayer fabrication. In this capstone project, a library of NCs is built for LAISA and binary superlattice study. Monodisperse iron oxide, gold and gadolinium fluoride NCs of various sizes were synthesized by modifying reported methods.9,10,20 The obtained NCs were characterized by TEM, SAXS, DLS and TGA, revealing their geometry, size and surface chemistry. The second part of this project is optimizing conditions of LAISA. Significant variables, including evaporation rate, NCs geometry, and ambient environment were isolated and studied for different building blocks. Centimeter-scale NCs monolayers with long-range order were obtained by using optimized conditions of LAISA. The binary superlattice system of spherical NCs was also investigated during this project with optimized LAISA. A 1:2 number ratio of iron oxide to gold NCs was used to fabricate binary superlattice monolayers by LAISA. The structure was revealed with TEM. However, future work is needed to investigate other size ratio and number ratio of two different kinds of NCs, and their effects on 2D structures

N∗(1520)N^* (1520) transition form factors from dispersion theory

The electromagnetic transition form factors (TFFs) of the nucleon provide important information on the internal structure of hadrons. A model-independent dispersive calculation of the electromagnetic TFFs $N^{*}(1520)\to N$ at low energies is presented. Taking pion rescattering into consideration, we derived dispersive relations for the $N^{*}(1520)\to N$ TFFs that relate space-like and time-like regions from the first principles. Based on the space-like data from JLab and hadronic data measured by HADES, we make predictions for TFFs in the time-like region. Our predictions can be tested in future experiments (e.g. HADES).Comment: Conference Proceedings for meson 23. The conference proceedings will be published as a special issue of EPJ Web of Conference

Spectral coarse graining for random walk in bipartite networks

Many real-world networks display a natural bipartite structure, while analyzing or visualizing large bipartite networks is one of the most challenges. As a result, it is necessary to reduce the complexity of large bipartite systems and preserve the functionality at the same time. We observe, however, the existing coarse graining methods for binary networks fail to work in the bipartite networks. In this paper, we use the spectral analysis to design a coarse graining scheme specifically for bipartite networks and keep their random walk properties unchanged. Numerical analysis on artificial and real-world bipartite networks indicates that our coarse graining scheme could obtain much smaller networks from large ones, keeping most of the relevant spectral properties. Finally, we further validate the coarse graining method by directly comparing the mean first passage time between the original network and the reduced one.Comment: 7 pages, 3 figure

Short-duration lensing events: I. wide-orbit planets? free-floating low-mass objects? or high-velocity stars?

Short duration lensing events tend to be generated by low-mass lenses or by lenses with high transverse velocities. Furthermore, for any given lens mass and speed, events of short duration are preferentially caused by nearby lenses (mesolenses) that can be studied in detail, or else by lenses so close to the source star that finite-source-size effects may be detected, yielding information about both the Einstein ring radius and the surface of the lensed star. Planets causing short-duration events may be in orbits with any orientation, and may have semimajor axes smaller than an AU, or they may reach the outer limits of their planetary systems, in the region corresponding to the Solar System's Oort Cloud. They can have masses larger than Jupiter's or smaller than Pluto's. Lensing therefore has a unique potential to expand our understanding of planetary systems. A particular advantage of lensing is that it can provide precision measurements of system parameters, including the masses of and projected separation between star and planet. We demonstrate how the parameters can be extracted and show that a great deal can be learned. For example, it is remarkable that the gravitational mass of nearby free-floating planet-mass lenses can be measured by complementing observations of a photometric event with deep images that detect the planet itself. A fraction of short events may be caused by high-velocity stars located within a kpc. Many high-velocity lenses are likely to be neutron stars that received large natal kicks. Other high-speed stars may be members of the halo population. Still others may be hypervelocity stars that have been ejected from the Galactic Center, or runaway stars escaped from close binaries, possibly including the progenitor binaries of Type Ia supernovae.Comment: 17 pages; 2 figures; submitted to ApJ 3 July 200