Related papers: Deformed dimensional reduction

Following an insight of Kontsevich, we prove that the quotient of Voevodsky's category of geometric mixed motives DM by the endofunctor -Q(1)[2] embeds fully-faithfully into Kontsevich's category of noncommutative mixed motives KMM. We show…

This note provides a short guide to dimensional analysis in Lorentzian and general relativity and in differential geometry. It tries to revive Dorgelo and Schouten's notion of 'intrinsic' or 'absolute' dimension of a tensorial quantity. The…

In 2011, Kilmer and Martin proposed tensor singular value decomposition (T-SVD) for third order tensors. Since then, T-SVD has applications in low rank tensor approximation, tensor recovery, multi-view clustering, multi-view feature…

We study the approaches to two-dimensional integrable field theories via a six-dimensional(6D) holomorphic Chern-Simons theory defined on twistor space. Under symmetry reduction, it reduces to a four-dimensional Chern-Simons theory, while…

Dynamic mode decomposition (DMD) is a recently developed tool for the analysis of the behavior of complex dynamical systems. In this paper, we will propose an extension of DMD that exploits low-rank tensor decompositions of potentially…

We construct and study Donaldson-Thomas invariants counting orthogonal and symplectic objects in linear categories, which are a generalization of the usual Donaldson-Thomas invariants from the structure groups $\mathrm{GL} (n)$ to the…

We show that the reduced motive of a smooth affine quadric is invertible as an object of the triangulated category of motives DM(k, ZZ[1/e]) (where k is a perfect field of exponential characteristic e). We also establish a motivic version…

Dimensionality reduction is a popular preprocessing and a widely used tool in data mining. Transparency, which is usually achieved by means of explanations, is nowadays a widely accepted and crucial requirement of machine learning based…

A novel general framework is proposed in this paper for dimension reduction in regression to fill the gap between linear and fully nonlinear dimension reduction. The main idea is to transform first each of the raw predictors monotonically,…

Integrable systems in low dimensions, constructed through the symmetry reduction method, are studied using phase portrait and variable separation techniques. In particular, invariant quantities and explicit periodic solutions are…

Combinatorial aspects of multivariate diagonal invariants of the symmetric group are studied. As a consequence it is proved the existence of a multivariate extension of the classical Robinson-Schensted correspondence. Further byproduct are…

It is conjectured that the dual variety of every smooth nonlinear subvariety of dimension $> \frac{2N}{3}$ in projective $N$-space is a hypersurface, an expectation known as the duality defect conjecture. This would follow from the truth of…

A version of the Bondal-Orlov conjecture, proved by Bridgeland, states that if $X$ and $Y$ are smooth complex projective threefolds linked by a flop, then they are derived equivalent. Van den Bergh gave a new proof of Bridgeland's theorem…

In this paper we produce further specification of the geometric and algebraic properties of the earlier introduced superdimensional dual-covariant field theory (SFT) in a N-dimensional manifold [1] as an approach to a unified field theory…

We describe the dimensional reduction of the IIB B-fields in F-theory using a conjectured description of normalizable B-fields in terms of perverse sheaves. Computations are facilitated using the Decomposition Theorem. Many of our…

We offer a short and elementary proof that, for a Z-set A in a finite-dimensional ANR Y, dimA<dimY. This result is relevant to the study of group boundaries. The original proof by Bestvina and Mess relied on cohomological dimension theory.

This is a tutorial and survey paper on various methods for Sufficient Dimension Reduction (SDR). We cover these methods with both statistical high-dimensional regression perspective and machine learning approach for dimensionality…

Using the theory of framed correspondences developed by Voevodsky, we introduce and study framed motives of algebraic varieties. They are the major computational tool for constructing an explicit quasi-fibrant motivic replacement of the…

We unify the discrete Fourier transform (DFT), discrete cosine transform (DCT), Walsh-Hadamard, Haar wavelet, Karhunen-Lo\`eve transform, and several others along with their continuous counterparts (Fourier transform, Fourier series,…

We investigate the critical behavior of disordered systems transversely driven at a uniform and steady velocity. An intuitive argument predicts that the long-distance physics of $D$-dimensional driven disordered systems at zero temperature…