Statistics of spatial averages and optimal averaging in the presence of missing data

We consider statistics of spatial averages estimated by weighting observations over an arbitrary spatial domain using identical and independent measuring devices, and derive an account of bias and variance in the presence of missing observations. We test the model relative to simulations, and the approximations for bias and variance with missing data are shown to compare well even when the probability of missing data is large. Previous authors have examined optimal averaging strategies for minimizing bias, variance and mean squared error of the spatial average, and we extend the analysis to the case of missing observations. Minimizing variance mainly requires higher weights where local variance and covariance is small, whereas minimizing bias requires higher weights where the field is closer to the true spatial average. Missing data increases variance and contributes to bias, and reducing both effects involves emphasizing locations with mean value nearer to the spatial average. The framework is applied to study spatially averaged rainfall over India. We use our model to estimate standard error in all-India rainfall as the combined effect of measurement uncertainty and bias, when weights are chosen so as to yield minimum mean squared error

Miniaturized Circular-Waveguide Probe Antennas Using Metamaterial Liners

This work presents the radiation performance of open-ended circular-waveguide probe antennas that have been miniaturized by the introduction of thin metamaterial liners. The liners introduce an HE$_{11}$ mode well below the natural cutoff frequency, which provides substantial gain improvements over a similarly sized waveguide probe. A new feeding arrangement employing a shielded-loop source embedded inside the miniaturized waveguide is developed to efficiently excite the HE$_{11}$ mode and avoid the excitation of other modes across the frequency reduced band while maintaining the antenna's compactness. A metamaterial-lined circular-waveguide probe antenna operating over 42% below its natural cutoff frequency is designed to provide a radiation efficiency of up to 28.8%. A simple, printed-circuit implementation of the metamaterial liner based on inductively loaded wires is proposed and its dispersion features are discussed.Comment: The manuscript has been revised for publication as a 6 page communication in the IEEE Transactions on Antennas and Propagation. This included a reduction of material in the theory section, removal of all discussion on anisotropic theory, and introduction of a novel excitation sourc

Infinities of stable periodic orbits in systems of coupled oscillators

We consider the dynamical behavior of coupled oscillators with robust heteroclinic cycles between saddles that may be periodic or chaotic. We differentiate attracting cycles into types that we call phase resetting and free running depending on whether the cycle approaches a given saddle along one or many trajectories. At loss of stability of attracting cycling, we show in a phase-resetting example the existence of an infinite family of stable periodic orbits that accumulate on the cycling, whereas for a free-running example loss of stability of the cycling gives rise to a single quasiperiodic or chaotic attractor

The Complete Jamming Landscape of Confined Hard Discs

An exact description of the complete jamming landscape is developed for a system of hard discs of diameter $\sigma$, confined between two lines separated by a distance $1+\sqrt{3/4} < H/\sigma < 2$. By considering all possible local packing arrangements, the generalized ensemble partition function of jammed states is obtained using the transfer matrix method, which allows us to calculate the configurational entropy and the equation of state for the packings. Exploring the relationship between structural order and packing density, we find that the geometric frustration between local packing environments plays an important role in determining the density distribution of jammed states and that structural "randomness" is a non-monotonic function of packing density. Molecular dynamics simulations show that the properties of the equilibrium liquid are closely related to those of the landscape.Comment: 5 Pages, 4 figure

Convergent estimators of variance of a spatial mean in the presence of missing observations

In the geosciences, a recurring problem is one of estimating spatial means of a physical field using weighted averages of point observations. An important variant is when individual observations are counted with some probability less than one. This can occur in different contexts: from missing data to estimating the statistics across subsamples. In such situations, the spatial mean is a ratio of random variables, whose statistics involve approximate estimators derived through series expansion. The present paper considers truncated estimators of variance of the spatial mean and their general structure in the presence of missing data. To all orders, the variance estimator depends only on the first and second moments of the underlying field, and convergence requires these moments to be finite. Furthermore, convergence occurs if either the probability of counting individual observations is larger than 1/2 or the number of point observations is large. In case the point observations are weighted uniformly, the estimators are easily found using combinatorics and involve Stirling numbers of the second kind

Influence of Personal Preferences on Link Dynamics in Social Networks

We study a unique network dataset including periodic surveys and electronic logs of dyadic contacts via smartphones. The participants were a sample of freshmen entering university in the Fall 2011. Their opinions on a variety of political and social issues and lists of activities on campus were regularly recorded at the beginning and end of each semester for the first three years of study. We identify a behavioral network defined by call and text data, and a cognitive network based on friendship nominations in ego-network surveys. Both networks are limited to study participants. Since a wide range of attributes on each node were collected in self-reports, we refer to these networks as attribute-rich networks. We study whether student preferences for certain attributes of friends can predict formation and dissolution of edges in both networks. We introduce a method for computing student preferences for different attributes which we use to predict link formation and dissolution. We then rank these attributes according to their importance for making predictions. We find that personal preferences, in particular political views, and preferences for common activities help predict link formation and dissolution in both the behavioral and cognitive networks.Comment: 12 page