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Functional factor analysis is an important dimension reduction method for functional and longitudinal data. Factor loadings give insight into patterns of variability of the observations, while latent factors provide a low-dimensional…
An arrangement of circles in which circles intersect only in angles of $\pi/2$ is called an \emph{arrangement of orthogonal circles}. We show that in the case that no two circles are nested, the intersection graph of such an arrangement is…
Orthogonality in model theory captures the idea of absence of non-trivial interactions between definable sets. We introduce a somewhat opposite notion of cohesiveness, capturing the idea of interaction among all parts of a given definable…
Conditional effects are commonly used measures for understanding how treatment effects vary across different groups, and are often used to target treatments/interventions to groups who benefit most. In this work we review existing methods…
In this paper, we focus on exploiting the group structure for large-dimensional factor models, which captures the homogeneous effects of common factors on individuals within the same group. In view of the fact that datasets in…
Multivariate orthogonal polynomials can be introduced by using a moment functional defined on the linear space of polynomials in several variables with real coefficients. We study the so-called Uvarov and Christoffel modifications obtained…
The various ways to reduce number of vectors describing condition of particles for high energy physics problems are presented. In particular decomposition of any vector with respect to the basis, consisting of any four linearly independent…
The circular orthogonal and circular symplectic ensembles are mapped onto free, non-hermitian fermion systems. As an illustration, the two-level form factors are calculated.
Blocking is often used to reduce known variability in designed experiments by collecting together homogeneous experimental units. A common modelling assumption for such experiments is that responses from units within a block are dependent.…
We generate all the Orthogonal Arrays (OAs) of a given size n and strength t as the union of a collection of OAs which belong to an inclusion-minimal set of OAs. We derive a formula for computing the (Generalized) Word Length Pattern of a…
Orthogonal polynomials on quadratic curves in the plane are studied. These include orthogonal polynomials on ellipses, parabolas, hyperbolas, and two lines. For an integral with respect to an appropriate weight function defined on any…
Block maxima methods constitute a fundamental part of the statistical toolbox in extreme value analysis. However, most of the corresponding theory is derived under the simplifying assumption that block maxima are independent observations…
We study the momentum-space 4-point correlation function of identical scalar operators in conformal field theory. Working specifically with null momenta, we show that its imaginary part admits an expansion in conformal blocks. The blocks…
The goal of this paper is to develop methods for the construction of saturated designs that include the mean, main effects and the two-factor interactions of one factor with a subset of the remaining factors. If one factor is interacting…
We introduce and analyze BPALM and A-BPALM, two multi-block proximal alternating linearized minimization algorithms using Bregman distances for solving structured nonconvex problems. The objective function is the sum of a multi-block…
We give a polynomial-time constant-factor approximation algorithm for maximum independent set for (axis-aligned) rectangles in the plane. Using a polynomial-time algorithm, the best approximation factor previously known is $O(\log\log n)$.…
We propose an algorithm, called OEM (a.k.a. orthogonalizing EM), intended for var- ious least squares problems. The first step, named active orthogonization, orthogonalizes an arbi- trary regression matrix by elaborately adding more rows.…
We describe a prescription for constructing conformal blocks in conformal field theories in any space-time dimension with arbitrary quantum numbers. Our procedure reduces the calculation of conformal blocks to constructing certain group…
We present a fundamentally different approach to orthogonal layout of data flow diagrams with ports. This is based on extending constrained stress majorization to cater for ports and flow layout. Because we are minimizing stress we are able…
Orthogonal statistical learning and double machine learning have emerged as general frameworks for two-stage statistical prediction in the presence of a nuisance component. We establish non-asymptotic bounds on the excess risk of orthogonal…