β models for random hypergraphs with a given degree sequence

We introduce the beta model for random hypergraphs in order to represent the occurrence of multi-way interactions among agents in a social network. This model builds upon and generalizes the well-studied beta model for random graphs, which instead only considers pairwise interactions. We provide two algorithms for fitting the model parameters, IPS (iterative proportional scaling) and fixed point algorithm, prove that both algorithms converge if maximum likelihood estimator (MLE) exists, and provide algorithmic and geometric ways of dealing the issue of MLE existence

Differentially Private Model Selection with Penalized and Constrained Likelihood

In statistical disclosure control, the goal of data analysis is twofold: The released information must provide accurate and useful statistics about the underlying population of interest, while minimizing the potential for an individual record to be identified. In recent years, the notion of differential privacy has received much attention in theoretical computer science, machine learning, and statistics. It provides a rigorous and strong notion of protection for individuals' sensitive information. A fundamental question is how to incorporate differential privacy into traditional statistical inference procedures. In this paper we study model selection in multivariate linear regression under the constraint of differential privacy. We show that model selection procedures based on penalized least squares or likelihood can be made differentially private by a combination of regularization and randomization, and propose two algorithms to do so. We show that our private procedures are consistent under essentially the same conditions as the corresponding non-private procedures. We also find that under differential privacy, the procedure becomes more sensitive to the tuning parameters. We illustrate and evaluate our method using simulation studies and two real data examples

Decrease in the orbital period of dwarf nova OY Carinae

We have measured the orbital light curve of dwarf nova OY Carinae on 8 separate occasions between 1997 September and 2005 December. The measurements were made in white light using CCD photometers on the Mt Canopus 1 m telescope. The time of eclipse in 2005 December was 168 +- 5 s earlier than that predicted by the Wood et al.(1989) ephemeris. Using the times of eclipse from our measurements and the compilation of published measurements by Pratt et al (1999) we find that the observational data are inconsistent with a constant period and indicate that the orbital period is decreasing by 5+-1 X 10^-12 s/s. This is too fast to be explained by gravitational radiation emission. It is possible that the change is cyclic with a period greater than about 80 years. This is much longer than typical magnetic activity cycles and may be due to the presence of a third object in the system. Preliminary estimates suggest that this is a brown dwarf with mass about 0.016 Msun and orbital radius >= 17 AU.Comment: 4 pages 2 figures. MNRAS submitted Final proofread version. Discussion modified with figure showing fits and residuals to models, statistical significance of fits added and minor typographical edit

Sharing Social Network Data: Differentially Private Estimation of Exponential-Family Random Graph Models

Motivated by a real-life problem of sharing social network data that contain sensitive personal information, we propose a novel approach to release and analyze synthetic graphs in order to protect privacy of individual relationships captured by the social network while maintaining the validity of statistical results. A case study using a version of the Enron e-mail corpus dataset demonstrates the application and usefulness of the proposed techniques in solving the challenging problem of maintaining privacy \emph{and} supporting open access to network data to ensure reproducibility of existing studies and discovering new scientific insights that can be obtained by analyzing such data. We use a simple yet effective randomized response mechanism to generate synthetic networks under $\epsilon$-edge differential privacy, and then use likelihood based inference for missing data and Markov chain Monte Carlo techniques to fit exponential-family random graph models to the generated synthetic networks.Comment: Updated, 39 page

Gravitational and electromagnetic fields of a charged tachyon

An axially symmetric exact solution of the Einstein-Maxwell equations is obtained and is interpreted to give the gravitational and electromagnetic fields of a charged tachyon. Switching off the charge parameter yields the solution for the uncharged tachyon which was earlier obtained by Vaidya. The null surfaces for the charged tachyon are discussed.Comment: 8 pages, LaTex, To appear in Pramana- J. Physic

Statistical Inference in a Directed Network Model with Covariates

Networks are often characterized by node heterogeneity for which nodes exhibit different degrees of interaction and link homophily for which nodes sharing common features tend to associate with each other. In this paper, we propose a new directed network model to capture the former via node-specific parametrization and the latter by incorporating covariates. In particular, this model quantifies the extent of heterogeneity in terms of outgoingness and incomingness of each node by different parameters, thus allowing the number of heterogeneity parameters to be twice the number of nodes. We study the maximum likelihood estimation of the model and establish the uniform consistency and asymptotic normality of the resulting estimators. Numerical studies demonstrate our theoretical findings and a data analysis confirms the usefulness of our model.Comment: 29 pages. minor revisio

Geometry of Goodness-of-Fit Testing in High Dimensional Low Sample Size Modelling

We introduce a new approach to goodness-of-fit testing in the high dimensional, sparse extended multinomial context. The paper takes a computational information geometric approach, extending classical higher order asymptotic theory. We show why the Wald – equivalently, the Pearson X2 and score statistics – are unworkable in this context, but that the deviance has a simple, accurate and tractable sampling distribution even for moderate sample sizes. Issues of uniformity of asymptotic approximations across model space are discussed. A variety of important applications and extensions are noted

The interplay of microscopic and mesoscopic structure in complex networks

Not all nodes in a network are created equal. Differences and similarities exist at both individual node and group levels. Disentangling single node from group properties is crucial for network modeling and structural inference. Based on unbiased generative probabilistic exponential random graph models and employing distributive message passing techniques, we present an efficient algorithm that allows one to separate the contributions of individual nodes and groups of nodes to the network structure. This leads to improved detection accuracy of latent class structure in real world data sets compared to models that focus on group structure alone. Furthermore, the inclusion of hitherto neglected group specific effects in models used to assess the statistical significance of small subgraph (motif) distributions in networks may be sufficient to explain most of the observed statistics. We show the predictive power of such generative models in forecasting putative gene-disease associations in the Online Mendelian Inheritance in Man (OMIM) database. The approach is suitable for both directed and undirected uni-partite as well as for bipartite networks

Design and Performance of SiPM-Based Readout of PbF\u3csub\u3e2\u3c/sub\u3e Crystals for High-Rate, Precision Timing Applications

We have developed a custom amplifier board coupled to a large-format 16-channel Hamamatsu silicon photomultiplier device for use as the light sensor for the electromagnetic calorimeters in the Muon g - 2 experiment at Fermilab. The calorimeter absorber is an array of lead-fluoride crystals, which produces short-duration Cherenkov light. The detector sits in the high magnetic field of the muon storage ring. The SiPMs selected, and their accompanying custom electronics, must preserve the short pulse shape, have high quantum efficiency, be non-magnetic, exhibit gain stability under varying rate conditions, and cover a fairly large fraction of the crystal exit surface area. We describe an optimized design that employs the new-generation of thru-silicon via devices. The performance is documented in a series of bench and beam tests

Studies of an array of PbF2 Cherenkov crystals with large-area SiPM readout

The electromagnetic calorimeter for the new muon (g-2) experiment at Fermilab will consist of arrays of PbF2 Cherenkov crystals read out by large-area silicon photo-multiplier (SiPM) sensors. We report here on measurements and simulations using 2.0 -- 4.5 GeV electrons with a 28-element prototype array. All data were obtained using fast waveform digitizers to accurately capture signal pulse shapes versus energy, impact position, angle, and crystal wrapping. The SiPMs were gain matched using a laser-based calibration system, which also provided a stabilization procedure that allowed gain correction to a level of 1e-4 per hour. After accounting for longitudinal fluctuation losses, those crystals wrapped in a white, diffusive wrapping exhibited an energy resolution sigma/E of (3.4 +- 0.1) % per sqrt(E/GeV), while those wrapped in a black, absorptive wrapping had (4.6 +- 0.3) % per sqrt(E/GeV). The white-wrapped crystals---having nearly twice the total light collection---display a generally wider and impact-position-dependent pulse shape owing to the dynamics of the light propagation, in comparison to the black-wrapped crystals, which have a narrower pulse shape that is insensitive to impact position.Comment: 14 pages, 19 figures, accepted to Nucl.Instrum.Meth. A. In v2, edited Figures 14,15, and 17 for clarity, improved explanation of energy resolution systematics, added reference to SiP