We consider the problem of variable group selection for least squares regression, namely, that of selecting groups of variables for best regression performance, leveraging and adhering to a natural grouping structure within the explanatory variables. We show that this problem can be efficiently addressed by using a certain greedy style algorithm. More precisely, we propose the Group Orthogonal ...

We study schemes for interpolating functions that take values in the special orthogonal group SO(n). Our focus is on interpolation schemes obtained by embedding SO(n) in a linear space, interpolating in the linear space, and mapping the result onto SO(n) via the closest point projection. The resulting interpolants inherit both the order of accuracy and the regularity of the underlying interpola...

DRAFT VERSION The Majorana spinor is an element of a 4 dimensional real vector space. The Majorana spinor representations of the Rotation and Lorentz groups are irreducible. The spinor fields are space-time dependent spinors, solutions of the free Dirac equation. We define the Majorana-Fourier transform and relate it to the linear momentum of a spin one-half Poincare group representation. We sh...

and masculinizing effects are seen, the former being greater than the latter. The significance of these findings remains for future study.5 1 Willier, B. H., Gallagher, T. F., and Koch, F. C., Proc. Nat. Acad. Sci., 21, 625-631 (1935). 2 Willier, B. H., Gallagher, T. F., and Koch, F. C., Physiol. Zool., 10, 101-122. 3 Wolff, E., and Wolff, Em., C. R. Soc. Biol., 123, 1191-1193. 4 Wolff, E., and...

In this article we determine a generating set of rational invariants of minimal cardinality for the action of the orthogonal group O3 on the space R[x, y, z]2d of ternary forms of even degree 2d. The construction relies on two key ingredients: On one hand, the Slice Lemma allows us to reduce the problem to dermining the invariants for the action on a subspace of the finite subgroup B3 of signed...

In our previous paper [10], we established a theta correspondence between vector-valued holomorphic Siegel modular forms and cohomology with local coefficients for local symmetric spaces attached to real orthogonal groups. This correspondence is realized via theta functions associated to explicitly constructed ”special” Schwartz forms. These forms give rise to relative Lie algebra cocycles for ...

In this paper, the theory of ε-constants associated to tame finite group actions on arithmetic surfaces is used to define a Brauer group invariant μ(X , G, V ) associated to certain symplectic motives of weight one. The relationship between this invariant and w2(π) (the Galois-theoretic invariant associated to tame covers of surfaces defined by Cassou-Noguès, Erez and Taylor) is also discussed.

Learning rich and diverse representations is critical for the performance of deep convolutional neural networks (CNNs). In this paper, we consider how to use privileged information to promote inherent diversity of a single CNN model such that the model can learn better representations and offer stronger generalization ability. To this end, we propose a novel group orthogonal convolutional neura...

In much of the mathematical literature, there is talk about the (note the definite article) orthogonal group O(n, F I ) of degree n ∈ N I over a field F I . This is extremely misleading, because, given a linear space T of dimension n, one can consider the orthogonal group of any non-degenerate quadratic form Q on T . In Chapter 6 of the book Basic Algebra I [J], Jacobson denotes this orthogonal...

The orthogonal group of a quadratic space over a field has been the focus of intensive research over the past fifty years. As this article will indicate, it continues to be a source of interesting problems. Zassenhaus [17] constructed a decomposition for any element in the orthogonal group of a non-degenerate quadratic space over a field of characteristic not 2. This paper will develop the fund...