Complex Similarity and Fluctuation Dynamics of Financial Markets on Voter Interacting Dynamic System

A financial price dynamics is developed based on the voter interacting system, in an attempt to investigate and reproduce the complex similarity and the fluctuation dynamics of financial markets. The complexity-invariance distance (CID) is applied to study the similarity of each stock pairs. A simple classification of seven real indexes and the simulated data is obtained according to the CID values for each stock pairs. The corresponding multiscale dynamical behaviors of CID values are also studied by combining CID with the multiscale method. Further, the similarity of the newest data and the historical data of the returns is investigated by a novel auto-CID analysis, and a corresponding exponent relationship is exhibited. Moveover, the cross correlation function (CCF) is applied to study the correlation of each stock pairs and the causalities of these stock pairs are investigated by the Granger causality method. Besides, the complexity and the randomness of fluctuations of returns, surrogate returns, shuffled returns and intrinsic mode functions (derived from empirical mode decomposition) are also explored at different thresholds with Lempel–Ziv complexity. The empirical study shows complex similarity and similar random property between the proposed price model and the real stock markets, which exhibits that the proposed model is feasible to some extent.

How can we assess the effects of urban environment on obesity using aggregated data?

ObjectiveThis study aimed to assess the effects of urban physical environment on individual obesity using geographically aggregated health behavior surveillance data applying a geo-imputation method.Introduction'Where we live' affects 'How we live'. Information about 'how one lives' collected from the public health surveillance data such as the Behavioral Risk Factor Surveillance System (BRFSS). Neighborhood environment surrounding individuals affects their health behavior or health status are influenced as well as their own traits. Meanwhile, geographical information of subjects recruited in the health behavior surveillance data is usually aggregated at administrative levels such as a county. Even if we do not know accurate addresses of individuals, we can allocate them to the random locations where is analogous to their real home within a locality using a geo-imputation method. In this study, we assess the association between obesity and built environment by applying random property allocation (1).MethodsData from the Korean Community Health Survey (KCHS), which is the nationwide community-based cross-sectional survey conducted by 253 community health centers in South Korea, were used (2). More than 90000 subjects recruited in the capital city Seoul from 2011 to 2014. They were selected by two-step stratified random sampling (424 administrative communities with an average area of 1.16km2 and two house types) in each 25 counties. We re-allocated them randomly on the nested locality based on their community (administrative boundaries) and hose type (land-use) using GIS program (Figure 1). Surrounding built environment elements such as fast-food markets, driving roads, public transit and road-crosse were measured within 500m buffer from randomly allocated locations as density or distance. Variables associating obesity are measured by : 1) self-reported obesity (self-reported body mass index(BMI) ≥ 25) (Figure 2), 2) perceived obesity, 3) intention to weight control. We implemented logistic regression models to estimate the effect of physical environmental factors on obesity.ResultsThe person who lives in a detached house, nearer fast food markets or with higher driving road density was more likely to be obese. Who lives in a detached house was less perceived their obesity. Who lives in a detached house, nearer fast food markets or with higher driving road density was less likely to intend to control their body weights. Association between intention to weight control and accessibility to subway station showed marginal effect.ConclusionsUrban environments influenced individual's obesity, perception, and intention to weight loss. Since we used cross-sectional survey data, we do not account cumulative environmental influence. Moreover, individuals' self-selection of more healthier places were not accounted. Even though we did not measure the environment at individuals' real address, we can measure the effects of neighborhood environment more efficiently by using random property allocation.References1. Walter SR, Rose N. Random property allocation: A novel geographic imputation procedure based on a complete geocoded address file. Spatial and spatio-temporal epidemiology. 2013;6:7-16. Epub 2013/08/27. doi: 10.1016/j.sste.2013.04.005. PubMed PMID: 23973177.2. Kim YT, Choi BY, Lee KO, Kim H, Chun JH, Kim SY, et al. Overview of Korean Community Health Survey. J Korean Med Assoc. 2012;55(1):74-83. (in Korean)

Note on Upper Density of Quasi-Random Hypergraphs

In 1964, Erdős proved that for any $\alpha > 0$, an $l$-uniform hypergraph $G$ with $n \geq n_0(\alpha, l)$ vertices and $\alpha \binom{n}{l}$ edges contains a large complete $l$-equipartite subgraph. This implies that any sufficiently large $G$ with density $\alpha > 0$ contains a large subgraph with density at least $l!/l^l$.In this note we study a similar problem for $l$-uniform hypergraphs $Q$ with a weak quasi-random property (i.e. with edges uniformly distributed over the sufficiently large subsets of vertices). We prove that any sufficiently large quasi-random $l$-uniform hypergraph $Q$ with density $\alpha > 0$ contains a large subgraph with density at least $\frac{(l-1)!}{l^{l-1}-1}$. In particular, for $l=3$, any sufficiently large such $Q$ contains a large subgraph with density at least $\frac{1}{4}$ which is the best possible lower bound.We define jumps for quasi-random sequences of $l$-graphs and our result implies that every number between 0 and $\frac{(l-1)!}{l^{l-1}-1}$ is a jump for quasi-random $l$-graphs. For $l=3$ this interval can be improved based on a recent result of Glebov, Král' and Volec. We prove that every number between [0, 0.3192) is a jump for quasi-random $3$-graphs.