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Rouquier dimension is Krull dimension for normal toric varieties
We prove that for any normal toric variety, the Rouquier dimension of its bounded derived category of coherent sheaves is equal to its Krull...
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A note on sufficient dimension reduction with post dimension reduction statistical inference
Sufficient dimension reduction is a widely used tool to extract core information hidden in high-dimensional data for classifying, clustering, and...
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Dimension by Dimension Finite Volume HWENO Method for Hyperbolic Conservation Laws
In this paper, we propose a finite volume Hermite weighted essentially non-oscillatory (HWENO) method based on the dimension by dimension framework...
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Metric dimension and strong metric dimension in annihilator-ideal graphs
Let R be a commutative ring with identity and A ( R ) be the set of ideals with non-zero annihilator. The annihilator-ideal graph of R is defined as the...
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Dimension of non-summand submodules
We introduce and study the concept of essential Krull dimension as dual of small Krull dimension of a module, which are defined in the same vein as...
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Universal scaling in real dimension
The concept of universality has shaped our understanding of many-body physics, but is mostly limited to homogenous systems. Here, we present a study...
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Mean dimension of continuous cellular automata
We investigate the mean dimension of a cellular automaton (CA for short) with a compact non-discrete space of states. A formula for the mean...
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Dark dimension gravitons as dark matter
We consider cosmological aspects of the Dark Dimension (a mesoscopic dimension of micron scale), which has recently been proposed as the unique...
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Supervised dimension reduction for functional time series
Functional time series model has been the subject of the most research in recent years, and since functional data is infinite dimensional, dimension...
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Die vierte Dimension
Wir beschreiben einen vierdimensionalen Ort, das heißt, einen Teil eines vierdimensionalen Raums, der von einem Hyperwürfel eingeschlossen ist....
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The shift-dimension of multipersistence modules
We present the shift-dimension of multipersistence modules and investigate its algebraic properties. This gives rise to a new invariant of...
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Polynomial growth and asymptotic dimension
Bonamy et al. [4] showed that graphs of polynomial growth have finite asymptotic dimension. We refine their result showing that a graph of polynomial...
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Metric Mean Dimension via Preimage Structures
The preimage entropy provides a quantitative estimate of how “invertible” a system is. Once there are several examples where the preimage entropy is...
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On the dynamic asymptotic dimension of étale groupoids
We investigate the dynamic asymptotic dimension for étale groupoids introduced by Guentner, Willett and Yu. In particular, we establish several...
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Scaling Dimension
Conceptual Scaling is a useful standard tool in Formal Concept Analysis and beyond. Its mathematical theory, as elaborated in the last chapter of the...
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Maximizing adjusted covariance: new supervised dimension reduction for classification
This study proposes a new linear dimension reduction technique called Maximizing Adjusted Covariance (MAC), which is suitable for supervised...
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Dimension theory of Lüroth digits
We investigate the relative growth properties of the Lüroth digits and establish the Hausdorff dimension of exceptional sets of points with a given...
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Regression with Variable Dimension Covariates
Regression is one of the most fundamental statistical inference problems. A broad definition of regression problems is as estimation of the...
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Dimension of a Graph
In 1965, a distinguished group of mathematicians consisting of Paul Erdős, Frank Harary, and William Thomas Tutte created a notion of the dimension...