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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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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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On Boolean elements and derivations in 2-dimension linguistic lattice implication algebras
A 2-dimension linguistic lattice implication algebra (2DL-LIA) can build a bridge between logical algebra and 2-dimension fuzzy linguistic...
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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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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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A Non-injective Assouad-Type Theorem with Sharp Dimension
Lipschitz light maps, defined by Cheeger and Kleiner, are a class of non-injective “foldings” between metric spaces that preserve some geometric...
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Relative entropy dimension for countable amenable group actions
We study the topological complexities of relative entropy zero extensions acted upon by countable-infinite amenable groups. First, for a given Følner...
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A reasonable notion of dimension for singular intersection homology
M. Goresky and R. MacPherson intersection homology is also defined from the singular chain complex of a filtered space by H. King, with a key formula...
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A Note on the Global Dimension of Shifted Orders
We consider the dominant dimension of an order over a Cohen-Macaulay ring in the category of centrally Cohen-Macaulay modules. There is a canonical...
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Genericity of Homeomorphisms with Full Mean Hausdorff Dimension
It is well known that the presence of horseshoes leads to positive entropy. If our goal is to construct a continuous map with infinite entropy, we...
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Metric Mean Dimension of Free Semigroup Actions for Non-Compact Sets
In this paper, we introduce the notions of upper metric mean dimension, u -upper metric mean dimension, l -upper metric mean dimension of free...
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No dimension-free deterministic algorithm computes approximate stationarities of Lipschitzians
We consider the oracle complexity of computing an approximate stationary point of a Lipschitz function. When the function is smooth, it is well known...
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Prague Dimension of Random Graphs
The Prague dimension of graphs was introduced by Nešetřil, Pultr and Rödl in the 1970s. Proving a conjecture of Füredi and Kantor, we show that the...
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Federated Sufficient Dimension Reduction Through High-Dimensional Sparse Sliced Inverse Regression
Federated learning has become a popular tool in the big data era nowadays. It trains a centralized model based on data from different clients while...
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The residual set dimension of a generalized apollonian packing
We view space-filling circle packings as subsets of the boundary of hyperbolic space subject to symmetry conditions based on a discrete group of...
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Logarithmic Expansion, Entropy, and Dimension for Set-Valued Maps
We obtain a lower bound for the entropy of a Borel probability measure (not necessarily invariant) with respect to an upper semicontinuous set-valued...
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The Weisfeiler–Leman Dimension of Distance-Hereditary Graphs
A graph is said to be distance-hereditary if the distance function in every connected induced subgraph is the same as in the graph itself. We prove...
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Filtered deformations of commutative algebras of Krull dimension two
Let F be an algebraically closed field of positive characteristic and let R be a finitely generated F -algebra with a filtration with the property...
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Data-driven slicing for dimension reduction in regressions: A likelihood-ratio approach
To efficiently estimate the central subspace in sufficient dimension reduction, response discretization via slicing its range is one of the most used...