Congruence conditions, parcels, and Tutte polynomials of graphs and matroids

Let $G$ be a matrix and $M(G)$ be the matroid defined by linear dependence on the set $E$ of column vectors of $G.$ Roughly speaking, a parcel is a subset of pairs $(f,g)$ of functions defined on $E$ to an Abelian group $A$ satisfying a coboundary condition (that $f-g$ is a flow over $A$ relative to $G$) and a congruence condition (that the size of the supports of $f$ and $g$ satisfy some congruence condition modulo an integer). We prove several theorems of the form: a linear combination of sizes of parcels, with coefficients roots of unity, equals an evaluation of the Tutte polynomial of $M(G)$ at a point $(\lambda-1,x-1)$ on the complex hyperbola $(\lambda - 1)(x-1) = |A|.

Effect of Ground Motion Characteristics on the Seismic Response of Torsionally Coupled Elastic Systems

This study presents a systematic investigation of the effects of ground motion characteristics, especially its multi-directional character, on the response of torsionally coupled elastic structural systems. The ground motion model is probabilistic and is founded on the assumption of the existence of ground motion principal directions. The structural systems considered are single-story and multi-story elastic shear beam models with stiffness eccentricity.National Science Foundation Grants ENV 77-07190 and PFR 80-0258

Discussion of "Feature Matching in Time Series Modeling" by Y. Xia and H. Tong

Discussion of "Feature Matching in Time Series Modeling" by Y. Xia and H. Tong [arXiv:1104.3073]Comment: Published in at http://dx.doi.org/10.1214/11-STS345B the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

On practical design for joint distributed source and network coding

This paper considers the problem of communicating correlated information from multiple source nodes over a network of noiseless channels to multiple destination nodes, where each destination node wants to recover all sources. The problem involves a joint consideration of distributed compression and network information relaying. Although the optimal rate region has been theoretically characterized, it was not clear how to design practical communication schemes with low complexity. This work provides a partial solution to this problem by proposing a low-complexity scheme for the special case with two sources whose correlation is characterized by a binary symmetric channel. Our scheme is based on a careful combination of linear syndrome-based Slepian-Wolf coding and random linear mixing (network coding). It is in general suboptimal; however, its low complexity and robustness to network dynamics make it suitable for practical implementation

Exploring universal patterns in human home-work commuting from mobile phone data

Home-work commuting has always attracted significant research attention because of its impact on human mobility. One of the key assumptions in this domain of study is the universal uniformity of commute times. However, a true comparison of commute patterns has often been hindered by the intrinsic differences in data collection methods, which make observation from different countries potentially biased and unreliable. In the present work, we approach this problem through the use of mobile phone call detail records (CDRs), which offers a consistent method for investigating mobility patterns in wholly different parts of the world. We apply our analysis to a broad range of datasets, at both the country and city scale. Additionally, we compare these results with those obtained from vehicle GPS traces in Milan. While different regions have some unique commute time characteristics, we show that the home-work time distributions and average values within a single region are indeed largely independent of commute distance or country (Portugal, Ivory Coast, and Boston)--despite substantial spatial and infrastructural differences. Furthermore, a comparative analysis demonstrates that such distance-independence holds true only if we consider multimodal commute behaviors--as consistent with previous studies. In car-only (Milan GPS traces) and car-heavy (Saudi Arabia) commute datasets, we see that commute time is indeed influenced by commute distance