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We propose a fully nonlinear framework to construct consistency relations for testing generic cosmological scenarios using the evolution of large scale structure. It is based on the covariant approach in combination with a frame that is…
It has been proposed that complex populations, such as those that arise in genomics studies, may exhibit dependencies among observations as well as among variables. This gives rise to the challenging problem of analyzing unreplicated…
This paper is the first in a series. The main goal of the series is to present a geometric construction of certain remarkable tensor categories arising from quantum groups coresponding to the value of deformation parameter $q$ equal to a…
Standard penalized methods of variable selection and parameter estimation rely on the magnitude of coefficient estimates to decide which variables to include in the final model. However, coefficient estimates are unreliable when the design…
A series of works has established rewriting as an essential tool in order to prove coherence properties of algebraic structures, such as MacLane's coherence theorem for monoidal categories, based on the observation that, under reasonable…
A projection space is a collection of spaces interrelated by the combinatorics of projection onto tensor factors in a symmetric monoidal background category. Examples include classical configuration spaces, orbit configuration spaces, the…
Many applications benefit from theory relevant to the identification of variables having large correlations or partial correlations in high dimension. Recently there has been progress in the ultra-high dimensional setting when the sample…
This paper establishes a metric framework for Spencer complexes based on the geometric theory of compatible pairs $(D,\lambda)$ in principal bundle constraint systems, solving fundamental technical problems in computing Spencer cohomology…
We introduce a method for aggregating many least squares estimator so that the resulting estimate has two properties: sparsity and structure. That is, only a few candidate covariates are used in the resulting model, and the selected…
We introduce a transport cohomological framework for categorical filtrations. Given a contravariant filtration $F:\mathcal T^{op}\to\mathbf{Prob}$ on a small category \(\mathcal T\), conditional expectation induces transport operators…
Estimation of covariance matrices is a fundamental problem in multivariate statistics. Recently, growing efforts have focused on incorporating covariate effects into these matrices, facilitating subject-specific estimation. Despite these…
A co-valuation is, essentially, a minimal finite cover. We introduce a logic based on co-valuations, which play the role of valuations of free variables in classical first-order logic, and show that the fundamental tools of model theory --…
Real-world learning tasks often encounter uncertainty due to covariate shift and noisy or inconsistent labels. However, existing robust learning methods merge these effects into a single distributional uncertainty set. In this work, we…
Quantifying the complexity of systems consisting of many interacting parts has been an important challenge in the field of complex systems in both abstract and applied contexts. One approach, the complexity profile, is a measure of the…
For a connected regular scheme X, flat and of finite type over Spec(Z), we construct a reciprocity homomorphism \rho_X: C_X --> \pi_1^\ab(X), which is surjective and whose kernel is the connected component of the identity. The (topological)…
Regression analysis is commonly conducted in survey sampling. However, existing methods fail when the relationships vary across different areas or domains. In this paper, we propose a unified framework to study the group-wise covariate…
One of the key aspects in component-based design is specifying the software architecture that characterizes the topology and the permissible interactions of the components of a system. To achieve well-founded design there is need to address…
We study low-rank matrix regression in settings where matrix-valued predictors and scalar responses are observed across multiple individuals. Rather than assuming a fully homogeneous coefficient matrices across individuals, we accommodate…
The purpose of this article is to give an interpretation of real projective structures and associated cohomology classes in terms of connections, sections, etc. satisfying elliptic partial differential equations in the spirit of Hodge…
We define a $\mathbb{Z}_2$-valued invariant for transversely-intersecting coassociative $4$-folds equipped with spin structures. Our main result shows this invariant provides an obstruction to separating two such coassociatives through a…