Heat kernel transform for nilmanifolds associated to the Heisenberg group

We study the heat kernel transform on a nilmanifold $M$ of the Heisenberg group. We show that the image of $L^2(M)$ under this transform is a direct sum of weighted Bergman spaces which are related to twisted Bergman and Hermite-Bergman spaces.Comment: Revised version; to appear in Revista Mathematica Iberoamericana, 28

Stochastic Block Transition Models for Dynamic Networks

There has been great interest in recent years on statistical models for dynamic networks. In this paper, I propose a stochastic block transition model (SBTM) for dynamic networks that is inspired by the well-known stochastic block model (SBM) for static networks and previous dynamic extensions of the SBM. Unlike most existing dynamic network models, it does not make a hidden Markov assumption on the edge-level dynamics, allowing the presence or absence of edges to directly influence future edge probabilities while retaining the interpretability of the SBM. I derive an approximate inference procedure for the SBTM and demonstrate that it is significantly better at reproducing durations of edges in real social network data.Comment: To appear in proceedings of AISTATS 201

Variations in radiocarbon ages of various organic fractions in core sediments from Erhai Lake, SW China

Radiocarbon dating was performed for the extracted organic fractions (cellulose-rich and humic acid fractions of plant fragment; fulvic acid, humic acid and humin fractions of humus substance) and shell from core sediments of the Erhai Lake, SW China. The C-14 dating results reveal that there are considerable differences, but there apparently is a humic acid less than or equal to humin < fulvic acid fraction sequence of C-14 age increase. The variability in radiocarbon ages of organic fraction of lake sediment suggests that special caution is necessary when radiocarbon ages of bulk sediments are used. The linear correlation between C-14 age of allochthonous terrestrial macrofossil (plant fragment and shell) and depth indicates roughly a constant sedimentation rate of ca. 0.7 rum yr(-1) in central Erhai Lake since 4500 yr BP. The C-14 ages of the autochthonous humic acid fraction are 210similar to4800 yr shift from "the true C-14 age" obtained by interpolating the corresponding horizontal level to the above C-14 age-depth correlation. Such age difference may be alternatively attributed to a uniform reservoir effect (most likely ca. 300 yr). The period with large C-14 age shift synchronizes with the period of changes in (delta(13)C and ARM intensity and ARM/susceptibility values

Narrow double-peaked emission lines of SDSS J131642.90+175332.5: signature of a single or a binary AGN in a merger, jet-cloud interaction, or unusual narrow-line region geometry

We present an analysis of the active galaxy SDSS J131642.90+175332.5, which is remarkable because all of its narrow emission lines are double-peaked, and because it additionally shows an extra broad component (FHWM ~ 1400 km/s) in most of its forbidden lines, peaking in between the two narrow systems. The peaks of the two narrow systems are separated by 400--500 km/s in velocity space. The spectral characteristics of double-peaked [O III] emission have previously been interpreted as a signature of dual or binary active galactic nuclei (AGNs), among other models. In the context of the binary scenario, SDSS J131642.90+175332.5 is a particularly good candidate because not just one line but all of its emission lines are double-peaked. However, we also discuss a number of other scenarios which can potentially account for double-peaked narrow emission lines, including projection effects, a two-sided outflow, jet-cloud interactions, special narrow-line region (NLR) geometries (disks, bars, or inner spirals), and a galaxy merger with only one AGN illuminating two NLRs. We argue that the similarity of the emission-line ratios in both systems, and the presence of the very unusual broad component at intermediate velocity, makes a close pair of unrelated AGNs unlikely, and rather argues for processes in a single galaxy or merger. We describe future observations which can distinguish between these remaining possibilities.Comment: ApJ Letters, 705, L20-L24, 2009 (November 1 issue); incl. 2 colour figure

Discontinuous resistance change and domain wall scattering in patterned NiFe wires with a nanoconstriction

A nonlinear current-voltage (I-V) characteristic was observed in patterned NiFe wires with a central "bow-tie" point contact constriction. By passing a dc current through the wire, a sharp resistance drop was obtained for current densities in the range of 1.1-1.4 x 10(7) A/cm(2). This is attributed to current-induced domain wall drag, resulting in displacement of a domain wall away from the constriction. A maximum current-induced resistance change of 0.079% was obtained for a 100-nm constriction, which is comparable with the magnetoresistance due to domain wall scattering in NiFe

Personalized Degrees: Effects on Link Formation in Dynamic Networks from an Egocentric Perspective

Understanding mechanisms driving link formation in dynamic social networks is a long-standing problem that has implications to understanding social structure as well as link prediction and recommendation. Social networks exhibit a high degree of transitivity, which explains the successes of common neighbor-based methods for link prediction. In this paper, we examine mechanisms behind link formation from the perspective of an ego node. We introduce the notion of personalized degree for each neighbor node of the ego, which is the number of other neighbors a particular neighbor is connected to. From empirical analyses on four on-line social network datasets, we find that neighbors with higher personalized degree are more likely to lead to new link formations when they serve as common neighbors with other nodes, both in undirected and directed settings. This is complementary to the finding of Adamic and Adar that neighbor nodes with higher (global) degree are less likely to lead to new link formations. Furthermore, on directed networks, we find that personalized out-degree has a stronger effect on link formation than personalized in-degree, whereas global in-degree has a stronger effect than global out-degree. We validate our empirical findings through several link recommendation experiments and observe that incorporating both personalized and global degree into link recommendation greatly improves accuracy.Comment: To appear at the 10th International Workshop on Modeling Social Media co-located with the Web Conference 201