Classifies -injective maps between non-compact surfaces.
problem Characterizing maps with injective fundamental groups.
method Proper homotopy classification of maps.
result All -injective proper maps are classified.
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48 results for “classifying maps”
The classifying spaces of cobordisms of singular maps have two fairly different constructions. We expose a homotopy theoretical connection between them. As a corollary we show that the classifying spaces in some cases have a simple product structure.
Classifies manifolds with dense conjugacy classes in their mapping class groups.
problem Classifying manifolds based on conjugacy classes in their mapping class groups.
method Analyzing connected orientable 2-manifolds and their mapping class groups.
result Mapping class groups of certain manifolds have dense conjugacy classes.
Maps between classifying spaces for certain groups are studied, with rational cohomology results.
problem Analyzing maps between classifying spaces for specific groups.
method Study of maps between null-components of homomorphism and based map spaces.
result Surjectivity of map in rational cohomology for certain groups, and non-surjectivity for others.
Translation surfaces in Heisenberg group classified by Gauss map determinant.
problem Classifying translation surfaces with zero intrinsic curvature in Heisenberg group.
method Constructed surfaces as product of planar curves, classified by Gauss map determinant.
result Surfaces with vanishing intrinsic curvature identified.
Classifies surfaces for pure mapping class groups with automatic continuity.
problem Determining surfaces for which pure mapping class groups have automatic continuity.
method Completely classified orientable infinite-type surfaces and specific cases of surfaces with finite ends.
result Classification of surfaces for automatic continuity of pure mapping class groups.
Classifies low energy maps from curved surfaces into spheres.
problem Classifying maps from surfaces of constant curvature into spheres.
method Analyzes maps with low energy and degree ±1, focusing on bubble configurations.
result Maps are quantitively close to a bubble configuration with specific radii.
Method uses aggregate crop statistics to improve satellite-based crop type mapping.
problem Limited field-level crop labels for training satellite-based maps.
method Corrects classifier by accounting for shifts in crop type composition and feature means.
result Substantial improvements in overall classification accuracy, reducing misclassifications by 21.9% on average.
Classifies mapping tori of specific groups, generalizing known results.
problem Classifying mapping tori of specific groups.
method Using Hopf-type properties and Poincaré Duality groups.
result Generalizes and provides new proofs for fibered 3-manifolds.
Homomorphisms between pure mapping class groups are classified for certain genus surfaces.
problem Classifying homomorphisms between pure mapping class groups for specific genus surfaces.
method Proving every multitwist-preserving map is induced by a multi-embedding, then applying to classify homomorphisms.
result All homomorphisms between pure mapping class groups for and are classified.
Currently available methods for extracting saliency maps identify parts of the input which are the most important to a specific fixed classifier. We show that this strong dependence on a given classifier hinders their performance. To address this problem, we propose classifier-agnostic saliency map extraction, which fi…
The paper classifies homomorphisms between braid groups and mapping class groups.
problem Classifying homomorphisms between braid groups and mapping class groups.
method Analyzing specific cases and using surface bundles over configuration spaces.
result Sharp classification of homomorphisms, showing cyclic or standard representations.
Classifies non-linear Fredholm maps linking to stable homotopy groups of spheres.
problem Classifying non-linear proper Fredholm maps between Hilbert spaces.
method Using stable homotopy groups of spheres to classify maps up to proper homotopy.
result Determines the non-trivial kernel of the map from stable homotopy groups to non-linear proper Fredholm maps.
We give an explicit simple construction for classifying spaces of maps obtained as hyperplane projections of immersions. We prove structure theorems for these classifying spaces.
Active learning reduces simulation needs for high-fidelity mobility maps.
problem Efficiently training machine learning classifiers for high-fidelity mobility maps.
method Active learning based on PAC learning theory to reduce simulation needs.
result Our sampling algorithm trains neural networks with higher accuracy using less than half the number of simulations.
Semi-Equivelar maps are generalizations of Archimedean solids to the surfaces other than 2-sphere. In earlier work a complete classification of semi-equivelar map of type on the surface of Euler characteristic -1 was given. In the meantime Karabas an Nedela classified vertex transitive semi-equivelar maps on…
We classify all tight holomorphic maps between Hermitian symmetric spaces of non-compact type.
This paper classifies semi-equivelar maps on a special surface.
problem Classifying semi-equivelar maps on a surface of Euler genus 3.
method Analyzing cyclic face sequences and presenting complete map types.
result Complete list of semi-equivelar maps on a surface of Euler characteristic -1.
The proper geometric dimension of the mapping class group of an orientable surface with puncturesmath.GT
Study shows mapping class group dimension for surfaces with punctures.
problem Determining the geometric dimension of mapping class groups of surfaces with punctures.
method Proved cocompact classifying space for proper actions with dimension equal to virtual cohomological dimension.
result Proper geometric dimension of mapping class groups of orientable surfaces with punctures.
Study of pure mapping class groups on infinite graphs.
problem Classifying graphs with specific mapping class groups.
method Completely classified graphs with pure mapping class groups.
result Established semidirect product decomposition and computed first integral cohomology.
Classifies 2-uniform maps on torus with formulas and asymptotic bounds.
problem Classifying 2-uniform maps on torus.
method Classification through arithmetic functions and asymptotic analysis.
result Explicit formulas and asymptotic bounds for 2-uniform maps on torus.
The study classifies homomorphisms from mapping class groups using finite subgroups.
problem Classifying homomorphisms from mapping class groups.
method Using finite subgroups to classify homomorphisms.
result Only finitely many mapping class groups have non-trivial homomorphisms into Homeo(S^n) for any n.
Dimensionality reduction (DR) is often used as a preprocessing step in classification, but usually one first fixes the DR mapping, possibly using label information, and then learns a classifier (a filter approach). Best performance would be obtained by optimizing the classification error jointly over DR mapping and cla…
Classifies homomorphisms from braid groups to mapping class groups of nonorientable surfaces.
problem Classifying homomorphisms from braid groups to mapping class groups of nonorientable surfaces.
method Classifies homomorphisms based on the properties of Dehn twists and crosscap transpositions.
result Every homomorphism is either cyclic or maps generators to distinct Dehn twists or crosscap transpositions.
Narasihman and Ramanan proved that an arbitrary connection in a vector bundle over a base space B can be obtained as the pull-back (via a correctly chosen classifying map from B into the appropriate Grassmannian) of the universal connection in the universal bundle over the Grassmannian. The purpose of this paper is to …
We define generalized distance-squared mappings, and we concentrate on the plane to plane case. We classify generalized distance-squared mappings of the plane into the plane in a recognizable way.
Tight maps was introduced along tight homomorphisms by Burger, Iozzi and Wienhard with aims towards maximal representations. In this paper we classify tight maps into classical Hermitian symmetric spaces and give a partial result for the exceptional spaces.
On existence, uniqueness and scalability of adversarial robustness measures for AI classifiersstat.ML
Mathematical conditions and practical computations for adversarial robustness measures are established.
problem Existence, uniqueness, and scalability of adversarial robustness measures for AI classifiers.
method Formulated and proven mathematical conditions for existence, uniqueness, and explicit analytical computation of minimal adversarial paths and distances. Practical computation demonstrated on various AI tools and synthetic benchmarks.
result Explicit mathematical conditions and practical computations for adversarial robustness measures are established.
This paper classifies regular maps with Euler characteristic -p^4 for a prime p≥5.
problem Classify regular maps on surfaces with Euler characteristic -p^4.
method Use inductive method and properties of Sylow p-subgroups to classify.
result Closed surfaces with Euler characteristic -p^4 support no regular maps if p∉{2,3,5,7,13}.
Cobordisms of singular mapsmath.GT
Szűcs introduced cobordism of singular maps to compute groups of immersions and embeddings.
problem Computing cobordism groups of immersions and embeddings in dimensions where classical theory fails.
method Investigation of classifying spaces constructed by Szűcs and Rimányi.
result Collection and organization of results towards computation of cobordism groups of singular maps.
In this paper we consider convex improper affine maps of the 3-dimensional affine space and classify their singularities. The main tool developed is a generating family with properties that closely resembles the area function for non-convex improper affine maps.
Improving the performance of classifiers is the realm of feature mapping, prototype selection, and kernel function transformations; these techniques aim for reducing the complexity, and also, improving the accuracy of models. In particular, our objective is to combine them to transform data's shape into another more co…
Every surface bundle with genus fiber has a canonical Heegaard splitting of genus . We classify the mapping class groups of such Heegaard splittings in the case when the surface bundle has a sufficiently complicated monodromy map.
Classifies low-energy harmonic maps from curved surfaces to spheres.
problem Classifying harmonic maps from curved surfaces to spheres under low energy conditions.
method Classifies maps via bubble scales and centers, focusing on degree-one maps as α approaches 1.
result Degree-one -harmonic maps blow a bubble based at a critical point of a function , which is the sum of squares of holomorphic one-forms.
Classifies representations up to dimension 3g-3 for surface mapping class groups.
problem Classifying representations of mapping class groups up to a certain dimension.
method Direct sum of a 2g or 2g+1 dimensional representation and a trivial one.
result Any representation up to dimension 3g-3 is a direct sum of a 2g or 2g+1 dimensional representation and a trivial one.
Classifies hypersurfaces preserving Gauss map with two conditions.
problem Classify nonflat hypersurfaces preserving the Gauss map.
method Analyzes conditions for hypersurfaces to preserve the Gauss map.
result Hypersurfaces must be Kaehler.
The performance of the Self-Organizing Map (SOM) algorithm is dependent on the initial weights of the map. The different initialization methods can broadly be classified into random and data analysis based initialization approach. In this paper, the performance of random initialization (RI) approach is compared to that…
We show that the mapping class group of a closed surface admits a cocompact classifying space for proper actions of dimension equal to its virtual cohomological dimension.
Neural networks can separate non-separable data using feature maps.
problem Non-separable data in neural networks.
method Characterization of feedforward neural networks and use of feature maps.
result ReLU neural networks can separate concentric data.
Study Farrell cohomology for non-orientable surfaces, classifying subgroup conjugacy.
problem Determine the -primary component of Farrell cohomology for non-orientable surfaces.
method Classify subgroups of order using topological equivalence adapted to surfaces with marked points.
result Determine the -primary component of Farrell cohomology for non-orientable surfaces.
We show that the natural map from the mapping class groups of surfaces to the automorphism groups of free groups, induces an infinite loop map on the classifying spaces of the stable groups after plus construction. The proof uses automorphisms of free groups with boundaries which play the role of mapping class groups o…
Holomorphic maps between configuration spaces are classified, resolving quartic and elliptic curve problems.
problem Classifying holomorphic maps between configuration spaces.
method Using braid groups, elliptic curves, and complex analysis, the authors classify maps and families of elliptic curves.
result The only non-trivial, non-identity holomorphic maps are the resolving quartic map and a map from elliptic curves.
In this work, we study the pseudo-Riemannian submanifolds of a pseudo-sphere with 1-type pseudo-spherical Gauss map. First, we classify the Lorentzian surfaces in a 4-dimensional pseudo-sphere with index s, , and having harmonic pseudo-spherical Gauss map. Then we give a characterization the…
Study contact structures on lens spaces, classifying rational knots.
problem Classify rational knots in lens spaces.
method One-parametric convex surface theory to classify Legendrian and transverse rational unknots.
result Determine the contact mapping class group of lens spaces.
timeXplain bridges AI and time series, making predictions understandable.
problem Making time series classifier predictions interpretable.
method Developed a framework that combines time series data with model-agnostic explainers.
result timeXplain improves the interpretability of time series classifiers.
In this paper, we study the local properties of the moduli space of a polarized Calabi-Yau manifold. Let be a neighborhood of the moduli space. Then we know the universal covering space of is a smooth manifold. Suppose is the classifying space of a polarized Calabi-Yau manifold with the automorphism gro…
One-Class Classification (OCC) has been prime concern for researchers and effectively employed in various disciplines. But, traditional methods based one-class classifiers are very time consuming due to its iterative process and various parameters tuning. In this paper, we present six OCC methods based on extreme learn…
Spherical quadrilaterals classified based on geometric properties.
problem Classifying spherical quadrilaterals up to isometry.
method Developing map and condition of genericity.
result Space of quadrilaterals with prescribed angles consists of finitely many open curves.