Related papers: Experiments with the Census
We consider testing marginal independence versus conditional independence in a trivariate Gaussian setting. The two models are non-nested and their intersection is a union of two marginal independences. We consider two sequences of such…
The triad census is an important approach to understand local structure in network science, providing comprehensive assessments of the observed relational configurations between triples of actors in a network. However, researchers are often…
Characterization of transient intermediate or transition states is crucial for the description of biomolecular folding pathways, which is however difficult in both experiments and computer simulations. Such transient states are typically of…
We determine the asymptotic distribution of the p-rank of the sandpile groups of random bipartite graphs. We see that this depends on the ratio between the number of vertices on each side, with a threshold when the ratio between the sides…
The Thurston norm of a 3-manifold measures the complexity of surfaces representing two-dimensional homology classes. We study the possible unit balls of Thurston norms of 3-manifolds $M$ with $b_1(M) = 2$, and whose fundamental groups admit…
A few formulas and theorems for statistical structures are proved. They deal with various curvatures as well as with metric properties of the cubic form or its covariant derivative. Some of them generalize formulas and theorems known in the…
This is an intuitive survey of extrinsic and intrinsic notions of convergence of manifolds complete with pictures of key examples and a discussion of the properties associated with each notion. We begin with a description of three extrinsic…
We analyze how numerical experiments regarding elections were conducted within the computational social choice literature (focusing on papers published in the IJCAI, AAAI, and AAMAS conferences). We analyze the sizes of the studied…
We study relationships between permutation statistics and pattern-functions, counting the number of times particular patterns occur in a permutation. This allows us to write several familiar statistics as linear combinations of pattern…
A method is developed here for building differentiable three-dimensional manifolds on multicube structures. This method constructs a sequence of reference metrics that determine differentiable structures on the cubic regions that serve as…
In this paper, almost product-like Riemannian manifolds are investigated. Basic properties on tangential hypersurfaces of almost product-like Riemannian manifolds are obtained. Some examples of tangential hypersurfaces are presented. Some…
We focus on the problem of finding a good representative of a sample of random curves warped from a common pattern f. We first prove that such a problem can be moved onto a manifold framework. Then, we propose an estimation of the common…
In some applications of frequency estimation, the frequencies of multiple sinusoids are required to be estimated from sub-Nyquist sampling sequences. In this paper, we propose a novel method based on subspace techniques to estimate the…
We improve the estimates of the subgraph probabilities in a random regular graph. Using the improved results, we further improve the limiting distribution of the number of triangles in random regular graphs.
This is a first in a series of papers, devoted to the relation betwwen three-manifolds and number fields. The present paper studies first homology of finite coverings of a three-manifold with primary interest in the Thurston $b_1$…
The adaptive voter model allows for studying the interplay between homophily, the tendency of like-minded individuals to attract each other, and social influence, the tendency for connected individuals to influence each other. However, it…
The shape and orientation of data clouds reflect variability in observations that can confound pattern recognition systems. Subspace methods, utilizing Grassmann manifolds, have been a great aid in dealing with such variability. However,…
This paper is about how we study statistical methods. As an example, it uses the random regressions model, in which the intercept and slope of cluster-specific regression lines are modeled as a bivariate random effect. Maximizing this…
A 3-dimensional Riemannian manifold equipped with a tensor structure of type $(1,1)$, whose fourth power is the identity, is considered. This structure acts as an isometry with respect to the metric. A Riemannian almost product manifold…
Multivariate normal mixtures provide a flexible method of fitting high-dimensional data. It is shown that their topography, in the sense of their key features as a density, can be analyzed rigorously in lower dimensions by use of a…