Related papers: The classification of 7- and 8-dimensional natural…
Sufficient dimension reduction methods often require stringent conditions on the joint distribution of the predictor, or, when such conditions are not satisfied, rely on marginal transformation or reweighting to fulfill them approximately.…
Modeling data as being sampled from a union of independent subspaces has been widely applied to a number of real world applications. However, dimensionality reduction approaches that theoretically preserve this independence assumption have…
This paper is the first of a 3-part series that classifies the 5-dimensional Thurston geometries. The present paper (part 1 of 3) summarizes the general classification, giving the full list, an outline of the method, and some illustrative…
Recent decades have seen the discovery of numerous complex materials. At the root of the complexity underlying many of these materials lies a large number of possible contending atomic- and larger-scale configurations and the intricate…
Four-dimensional spacetime, together with a natural generalisation to extra dimensions, is obtained through an analysis of the structures and symmetries deriving from possible arithmetic expressions for one-dimensional time. On taking the…
Several approaches were proposed to describe the geomorphology of drainage networks and the abiotic/biotic factors determining their morphology. There is an intrinsic complexity of the explicit qualification of the morphological variations…
A classification of all four-dimensional power-commutative real division algebras is given. It is shown that every four-dimensional power-commutative real division algebra is an isotope of a particular kind of a quadratic division algebra.…
The aim of this paper is to classify Ricci soliton metrics on $7$-dimensional nilpotent Lie groups. It can be considered as a continuation of our paper in [Transformation Groups, Volume 17, Number 3 (2012), 639--656]. To this end, we use…
Random projection is widely used as a method of dimension reduction. In recent years, its combination with standard techniques of regression and classification has been explored. Here we examine its use with principal component analysis…
The joint optimization of the reconstruction and classification error is a hard non convex problem, especially when a non linear mapping is utilized. In order to overcome this obstacle, a novel optimization strategy is proposed, in which a…
On the long-established classification problems in general relativity we take a novel perspective by adopting fruitful techniques from machine learning and modern data-science. In particular, we model Petrov's classification of spacetimes,…
In this article, we develop and investigate a new classifier based on features extracted using spatial depth. Our construction is based on fitting a generalized additive model to the posterior probabilities of the different competing…
Two-dimensional real hyporeductive triple algebras (h.t.a.) are investigated. A classification of such algebras is presented. As a consequence, a classification of two-dimensional real Lie triple algebras (i.e. generalized Lie triple…
In this work we are interested in the general problem of the determination of the normed division algebras. Our fundamental results are obtained in the particular subclass of those 8-dimensional quadratic flexible real division algebras. We…
We classify orbifold geometries which can be interpreted as moduli spaces of four-dimensional $\mathcal{N}\geq 3$ superconformal field theories up to rank 2 (complex dimension 6). The large majority of the geometries we find correspond to…
We argue that there are two distinct classes of type I compactification to four dimensions on any space. These two classes are distinguished in a mysterious way by the presence (or absence) of a discrete 6-form potential. In simple…
In this paper, we discuss the self-shrinking systems in higher codimensional spaces. We mainly obtain several Bernstein type results and a sharp growth estimate.
In this paper we examine various properties/constructions which are known for reductive groups and we do some experiments to see to what extent they generalize to symmetric spaces.
We study gauge theories which are associated with classical vacua of perturbative Type II string theory that allows for a conformal field theory description. We show that even if we compactify seven spatial dimensions (allowing for one…
Experimental life sciences like biology or chemistry have seen in the recent decades an explosion of the data available from experiments. Laboratory instruments become more and more complex and report hundreds or thousands measurements for…