On Some implications of the Poisson relation

The potentialities of the so-called 'Poisson relation', which holds for uniformly magnetized bodies of constant density, for showing the connections between the gravitational and the magnetic fields of such bodies are considered. In particular, it is seen that the same characteristic ratios occur among the components of the magnetic field intensity and the components of the gradient tensors of the two fields, both locally and non-locally. It is also shown that along the magnetization axis of the body the gradient tensor of the magnetic field displays a 'tidal' structure.     

Hypotheses for earthquake occurrences

Very little work has been done in generating alternatives to the Poisson process model. The work reported here deals with alternatives to the Poisson process model for the earthquakes and checks them using empirical data and the statistical hypothesis testing apparatus. The strategy used here for generating hypotheses is to compound the Poisson process. The parameter of the Poisson process is replaced by a random variable having prescribed density function. The density functions used are gamma, chi and extended (gamma/chi). The original distribution is then averaged out with respect to these density functions. For the compound Poisson processes the waiting time distributions for the future events are derived. As the parameters for the various statistical models for earthquake occurrences are not known, the problem is basically of composite hypothesis testing. One way of designing a test is to estimate these parameters and use them as true values. Momentmatching is used here to estimate the parameters. The results of hypothesis testing using data from Hindukush and North East India are presented.     

A Statistical Analysis of Trends for Warm and Cold Spells in Uppsala by Means of Counts

Statistical studies of extremes are of interest in the climatic sciences, in particular trends of periods of unusually warm or cold weather, which could be labelled warm and cold spells, respectively. We study the yearly number of spells in Uppsala, Sweden which from a data‐analytic point of view truly are counts, and employ theory and methods from the field of regression models for counts. A possible trend for the period 1840–2012 was investigated. The trend for warm spells is positive and demonstrated to be larger in magnitude compared with the one for cold spells, and is found to be statistically significant. The methodology could be extended to analyse other climate indicators.     

一类广义Hamilton系统的辛格式

通过引人泊松括号，分析了无限维Hamilton的性质，并将其推广到广义Hamilton系统，且从理论和实用角度讨论了这类广义Hamilton系统的辛格式构造问题，从而为辛几何算法在一般的时间发展方程的数值求解提供新的具体途径。     

Strip Transect Sampling to Estimate Object Abundance in Homogeneous and Non-homogeneous Poisson Fields: a Simulation Study of the Effects of Changing Transect Width and Number

This paper investigates the use of strip transect sampling to estimate object abundance when the underlying spatial distribution is assumed to be Poisson. A design-based rather than model-based approach to estimation is investigated through computer simulation, with both homogeneous and non-homogeneous fields representing individual realizations of spatial point processes being considered. Of particular interest are the effects of changing the number of transects and transect width (or alternatively, coverage percent or fraction) on the quality of the estimate. A specific application to the characterization of unexploded ordnance (UXO) in the subsurface at former military firing ranges is discussed. The results may be extended to the investigation of outcrop characteristics as well as subsurface geological features.     

Specifying a joint space- and time-lag using a bivariate Poisson distribution

Separate space- or time-lags have been considered regularly in data analyses; as space–time models are more recently being studied extensively in data analytic fashion, joint estimation of both lags has to be considered explicitly. This paper addresses this issue, taking into special consideration parametric parsimony together with specification richness; use of the bivariate Poisson frequency distribution is advocated and applied to an empirical case. The relation of this approach to random effects specifications is investigated. Data for Belgian regional products constitute the empirical case study.

Spatiotemporal correlation in WebGIS group-user intensive access patterns

Group-user intensive access to WebGIS exhibits spatiotemporal behaviour patterns with aggregation features and regularity distributions when geospatial data are accessed repeatedly over time and aggregated in certain spatial areas. We argue that these observable group-user access patterns provide a foundation for improved optimization of WebGIS so that it can respond to volume intensive requests with a higher quality of service and improve performance. Subsequently, a measure of access popularity distribution must precisely reflect the access aggregation and regularity features found in group-user intensive access. In our research, we considered both the temporal distribution characteristics and spatial correlation in the access popularity of tiled geospatial data (tiles). Based on the observation that group-user access follows a Zipf-like law, we built a tile-access popularity distribution based on time-sequence, to express the access aggregation of group-users with heavy-tailed characteristics. Considering the spatial locality of user-browsed tiles, we built a quantitative expression for the correlation between tile-access popularities and the distances to hotspot tiles, reflecting the attenuation of tile-access popularity to distance. Moreover, given the geographical spatial dependency and scale attribute of tiles, and the time-sequence of tile-access popularity, we built a Poisson regression model to express the degree of correlation among the accesses to adjacent tiles at different scales, reflecting the spatiotemporal correlation in tile access patterns. Experiments verify the accuracy of our Poisson regression model, which we then applied to a cluster-based cache-prefetching scenario. The results show that our model successfully reflects the spatiotemporal aggregation features of group-user intensive access and group-user behaviour patterns in WebGIS. The refined mathematical method in our model represents a time-sequence distribution of intensive access to tiles and the spatial aggregation and correlation in access to tiles at different scales, quantitatively expressing group-user spatiotemporal behaviour patterns with aggregation features and a regular distribution. Our proposed model provides a precise and empirical basis for performance-optimization strategies in WebGIS services, such as planning computing resource allocation and utilization, distributed storage of geospatial data, and providing distributed services so as to respond rapidly to geospatial data requests, thus addressing the challenges of volume-intensive user access.     

2022年1月8日青海门源6.9级地震的震源区结构特征和b值意义初探

2022年1月8日1时45分青海省门源县发生M_S6.9地震.本文基于青藏高原东北缘水平分辨率为0.3°的地震层析成像结果,获取了震源周边区域的地壳浅部构造信息,包括波速、泊松比以及估计的裂隙密度和饱和率的空间分布.结果表明:此次门源M_S6.9地震发生在P波和S波波速剧烈变化的区域,靠近高速体的边缘.泊松比和饱和率同样都显示,门源M_S6.9地震发生在高低值变化的过渡区.地震活动参数分析显示,震前冷龙岭断裂带的震源周边区域显示出了低b值、较低的a值和高a/b值的特征,与龙门山—岷山构造带强震之前的情况类似.裂隙密度在冷龙岭断裂两侧呈现出显著差异,北侧高于南侧,这可能是震后现场科考发现的断裂带地表破裂北侧高于南侧的构造成因.     

Statistical analysis and long-term prediction of seismicity for linear zones

The model of the Poisson point process is too vague for earthquake locations in space and time: earthquakes tend to cluster in middle distances and to repulse in large ones. The Poisson point model with variable density makes it possible to describe the tendency for clustering but does not reveal the periodicity of clusters. The author proposes the point-process model where locations of points are determined not by densities of point distribution, but by densities of interpoint differences distribution. In the model, a latent periodicity is revealed and used for prediction of a point process. In 1983, the point-process model prediction was made for the Kuril Islands for 1983–1987 and two signs of danger in time and location were determined. Then they were confirmed by strong earth-quakes. In 1989, a similar prediction was made for North Armenia. The Spitak earthquake in 1988 is clearly seen from the data of previous earthquakes.     

Risk assessment for the Yucca Mountain high-level nuclear waste repository site: Estimation of volcanic disruption

In this article, we model the volcanism near the proposed nuclear waste repository at Yucca Mountain, Nevada, U.S.A. by estimating the instantaneous recurrence rate using a nonhomogeneous Poisson process with Weibull intensity and by using a homogeneous Poisson process to predict future eruptions. We then quantify the probability that any single eruption is disruptive in terms of a (prior) probability distribution, since not every eruption would result in disruption of the repository. Bayesian analysis is performed to evaluate the volcanic risk. Based on the Quaternary data, a 90% confidence interval for the instantaneous recurrence rate near the Yucca Mountain site is (1.85×10^–6/yr, 1.26×10^–5/yr). Also, using-these confidence bounds, the corresponding 90% confidence interval for the risk (probability of at least one disruptive eruption) for an isolation time of 10⁴ years is (1.0×10^–3, 6.7×10^–3), if it is assumed that the intensity remains constant during the projected time frame.