We offer open-source code for a fundamental industry classification.
problem Creating accurate industry classifications from public data.
method Developed open-source code with modules for data handling.
result Improved trading signals through various industry classifications.
Homotopy classification for certain 4-manifolds with dihedral fundamental groups.
problem Classifying the homotopy types of specific 4-manifolds with dihedral fundamental groups.
method Using quadratic 2-type and combining with results from Hambleton-Kreck and Bauer.
result Homotopy types of finite oriented Poincaré 4-complexes are determined by their quadratic 2-type when fundamental group is dihedral.
New classification for 4-manifolds with specific fundamental groups.
problem Classifying 4-manifolds with fundamental group Z/ptimesZ. method Using quadratic 2-type and intersection form, along with generalizations to infinite groups.
result Homotopy type determined by quadratic 2-type and Z/p-valued intersection form. New classification of nonorientable 4-manifolds with specific fundamental groups.
problem Classifying nonorientable 4-manifolds with cyclic fundamental groups.
method Simple cut-and-paste construction, using results from Hambleton-Kreck-Teichner and Khan.
result Plausible classification of a large set of nonorientable 4-manifolds with cyclic fundamental groups of order 2p.
Classifies 2-stratifolds with fundamental group Z.
problem Classifying 2-stratifolds with specific fundamental groups.
method Using bicoloured labelled graphs and algorithms.
result Efficient algorithm to determine fundamental group Z.
Classification of 4-manifolds with finite fundamental groups using stable homeomorphism criteria.
problem Classifying 4-manifolds with finite fundamental groups.
method Using stable homeomorphism criteria based on quadratic 2-types and Kirby-Siebenmann invariant.
result Two 4-manifolds are CP2-stably homeomorphic if and only if their quadratic 2-types are stably isomorphic and their Kirby-Siebenmann invariant agrees. The paper classifies 4-manifolds based on their fundamental groups and orientation characters.
problem Classifying 4-manifolds with specific fundamental groups and orientation characters.
method Developed a criterion for groups and homomorphisms to classify 4-manifolds up to homotopy equivalence.
result Closed 4-manifolds with specified fundamental groups and orientation characters are classified by their quadratic 2-types.
A classification of partially hyperbolic diffeomorphisms on 3-dimensional manifolds with (virtually) solvable fundamental group is obtained. If such a diffeomorphism does not admit a periodic attracting or repelling two-dimensional torus, it is dynamically coherent and leaf conjugate to a known algebraic example. This …
Paper classifies special Euclidean hypersurfaces with specific geometric properties.
problem Classifying Euclidean hypersurfaces with semi-parallel Moebius second fundamental form.
method Complete classification of hypersurfaces with three distinct principal curvatures.
result Classification of Euclidean umbilic-free hypersurfaces with semi-parallel Moebius second fundamental form.
We give a diffeomorphism classification of pinched negatively curved manifolds with amenable fundamental groups, namely, they are precisely the Möbius band, and the products of a line with the total spaces of flat vector bundles over closed infranilmanifolds.
Classifies curves on a punctured Klein bottle, providing a counterexample to a loop conjecture.
problem Classifying curves on a punctured Klein bottle and addressing the simple loop conjecture.
method Explicit description of the mapping class group and classification of fundamental group elements.
result Provides a counterexample to the simple loop conjecture for Klein bottle representations.
Paper shows adversarial classification algorithms are inherently more sensitive to data manipulation.
problem Inadequate provable guarantees for machine learning performance, especially in unreliable data environments.
method Formal analysis of binary classification algorithms' sensitivity to adversarial manipulation.
result Fundamental tradeoff curve between accuracy and sensitivity is determined by data statistics, not algorithm tuning.
Develops algorithms for constructing statistical industry classifications.
problem Creating accurate industry classifications for quantitative trading.
method Combines clustering algorithms with correlation analysis to improve fundamental industry classifications.
result Shows that clustering methods improve off-the-shelf industry classifications.
This paper classifies fundamental groups of perforated surfaces.
problem Classifying the fundamental groups of perforated surfaces.
method Using the classification theorem for surfaces and covering spaces.
result Fundamental groups of perforated surfaces are large and not Hopfian.
The paper classifies 2D complete Lagrangian self-expanders in complex 2-space.
problem Classifying complete Lagrangian self-expanders in complex 2-space.
method Obtained a classification theorem.
result A classification of 2D complete Lagrangian self-expanders with constant squared norm of the second fundamental form.
Classifies 4-manifolds with specific properties and fundamental group.
problem Classifying 4-manifolds with fundamental group Z and boundary. method Topological and smooth classification methods, including Hermitian forms and 2-handlebody constructions. result Every Hermitian form over Z[t±1] arises as the equivariant intersection form of exotic smooth 4-manifolds. In this paper we first state the classification of the prolongations of complex free fundamental graded Lie algebras. Next we introduce the notion of free pseudo-product fundamental graded Lie algebras and study the prolongations of complex free pseudo-product fundamental graded Lie algebras. Furthermore we investigate…
The paper classifies 2D complete λ-surfaces in 3D space.
problem Classifying complete λ-surfaces in R3. method Complete classification of 2D complete λ-surfaces with constant squared norm of the second fundamental form. result A complete classification for 2-dimensional complete λ-surfaces in Euclidean space R3 with constant squared norm of the second fundamental form. Study on spheres in simply-connected 4-manifolds with abelian complements.
problem Classifying locally flat spheres in simply-connected 4-manifolds.
method Focus on complements with abelian fundamental groups.
result New classifications of spheres in specific 4-manifolds.
The paper classifies hypersurfaces with constant weighted mean curvature.
problem Characterizing and classifying hypersurfaces with specific curvature properties.
method Using intrinsic properties of the second fundamental form and analyzing weighted volume and growth.
result Characterization of hyperplanes and generalized round cylinders.
We study closed, oriented 4-manifolds whose fundamental group is that of a closed, oriented, aspherical 3-manifold. We show that two such 4-manifolds are stably diffeomorphic if and only if they have the same w_2-type and their equivariant intersection forms are stably isometric. We also find explicit algebraic invaria…
New classification and realization results for 3D and higher PD complexes with highly connected covers.
problem Classifying and realizing PD complexes with (n−2)-connected universal cover. method Using fundamental group, orientation class, and homology class, proving classification, realization, and splitting results.
result Triple (G,ω,μ) can be realized by a PDn-complex with (n−2)-connected universal cover if and only if certain conditions are met. Extends knotted defect classification to bounded domains using handlebodies.
problem Classifying knotted defects in bounded domains.
method Using continuous maps and monodromies around meridional loops, global defects are described in terms of planar diagrams.
result Classification scheme for defects in handlebodies.
New method classifies spin 4-manifolds using Kervaire-Milnor invariant.
problem Classifying spin 4-manifolds up to stabilisation.
method Using Kervaire-Milnor invariant to compute Arf invariants and classify.
result New stable classification of spin 4-manifolds with 2-dimensional fundamental groups.
Estimating data limits easier than building algorithms to achieve them.
problem Achieving the fundamental limits of data processing.
method Case studies on binary classification, data compression, and prediction.
result Estimators of limits can be constructed with fewer samples than explicit algorithms to achieve limits.
Classifies special Lie algebras with semisimple types.
problem Classifying Lie algebras of semisimple type.
method Introduced conformal pseudo-subriemannian fundamental graded Lie algebras and provided their classification.
result Classification of conformal pseudo-subriemannian fundamental graded Lie algebras of semisimple type and their prolongations.
The study classifies complete Lagrangian self-shrinkers in 4D space.
problem Classifying complete Lagrangian self-shrinkers in 4D space.
method Complete classification of 2D complete Lagrangian self-shrinkers with constant squared norm of the second fundamental form.
result A complete classification for 2-dimensional complete Lagrangian self-shrinkers in R4 with constant squared norm of the second fundamental form. In this paper, an explicit classification result for certain 5-manifolds with fundamental group Z/2 is obtained. These manifolds include total spaces of circle bundles over simply-connected 4-manifolds.
Study finds all conformal minimal immersions of 2-spheres in a complex Grassmann manifold with parallel second fundamental form.
problem Classifying conformal minimal immersions with parallel second fundamental form.
method Analyzing immersions in complex Grassmann manifold G(2,N;C). result Determined all conformal minimal immersions of 2-spheres with parallel second fundamental form.
We present a detailed description of a fundamental group algorithm based on Forman's combinatorial version of Morse theory. We use this algorithm in a classification problem of prime knots up to 14 crossings.
The complete local classification and geometric description of n-dimensional submanifolds F with recurrent nonparallel second fundamental form in the spaces of constant curvature M(c) are obtained in this article.
k-hop GNNs improve GNNs' ability to identify graph properties.
problem GNNs' limitations in identifying fundamental graph properties.
method Proposes k-hop GNNs that aggregate information from a node's k-hop neighborhood.
result k-hop GNNs can identify fundamental graph properties.
We describe the quasi-isometric classification of fundamental groups of irreducible non-geometric 3-manifolds which do not have "too many" arithmetic hyperbolic geometric components, thus completing the quasi-isometric classification of 3--manifold groups in all but a few exceptional cases.
We show the existence of isometric (or Ford) fundamental regions for a large class of subgroups of the isometry group of any rank one Riemannian symmetric space of noncompact type. The proof does not use the classification of symmetric spaces. All hitherto known existence results of isometric fundamental regions and do…
Closed oriented 4-manifolds with the same geometrically 2-dimensional fundamental group (satisfying certain properties) are classified up to s-cobordism by their w2-type, equivariant intersection form and the Kirby-Siebenmann invariant. As an application, we obtain a complete homeomorphism classification of closed…
4-manifolds with specific groups have unique homotopy types.
problem Classifying 4-manifolds with finite abelian 2-generator fundamental groups.
method Showed homotopy type is determined by quadratic 2-type.
result Homotopy type of 4-manifolds is determined by their quadratic 2-type.
A new sector classification method outperforms existing ones in risk-adjusted returns.
problem Subjective sector classification heuristics like GICS and NAICS are not optimal.
method Learned sector classification using hierarchical clustering and reIndexer evaluation tool.
result 17-sector learned sector universe outperforms GICS and NAICS in backtests.
This paper is concerned with fixed-point free S1-actions (smooth or locally linear) on orientable 4-manifolds. We show that the fundamental group plays a predominant role in the equivariant classification of such 4-manifolds. In particular, it is shown that for any finitely presented group with infinite center, ther…
The paper classifies homotopy ribbon discs with specific groups.
problem Classifying homotopy ribbon discs with given fundamental groups.
method Using geometric and algebraic properties of groups, particularly Farrell-Jones conjecture.
result Classification of homotopy ribbon discs for specific knot groups and Baumslag-Solitar groups.
The goal of these lectures is to give an introduction to the study of the fundamental group of a Klein surface. We start by reviewing the topological classification of Klein surfaces and by explaining the relation with real algebraic curves. Then we introduce the fundamental group of a Klein surface and present its mai…
We give a sufficient and necessary condition of the fundamental group homomorphism of a map between manifolds to induce homology equivalences. Moreover, a classification of one-sided h-cobordism of manifolds up to diffeomorphisms is obtained, based on Quillen's plus construction with Whitehead torsions.
Local probabilistic models simplify Bayesian classification for complex data.
problem Complex real-world data requires simpler models than global ones.
method Establish local probabilistic models for local regions, relaxing global assumptions.
result Local probabilistic models improve classification accuracy on real-world datasets.
Classifies Spin(7) structures on compact 8-manifolds with abelian fundamental group.
problem Classifying Spin(7) structures on compact 8-manifolds.
method Obstruction theory applied to Spin(7) structures on compact 8-manifolds with abelian fundamental group.
result Compact Riemannian 8-manifolds with holonomy Spin(7) have exactly two Spin(7) structures extending the induced G2 structure on the boundary.
We present a classification of fake lens spaces of dimension greater or equal to 5 which have as fundamental group the cyclic group of order N = 2^K, in that we extend the results of Wall and others in the case N=2.
Scores measure certainty and doubt in classification predictions.
problem Quantitative uncertainty assessment in classification problems.
method Intuitive scores in Bayesian and frequentist frameworks.
result Measures assess and compare prediction quality and uncertainty.
This paper gives new and elementary combinatorial topological proofs of the classification of unoriented and oriented rational knots and links. These proofs are based on the known classification of alternating knots through flyping, and the calculus of continued fractions. We characterize the class of strongly invertib…
Classification of groups as symmetries of infinite translation surfaces.
problem Classifying groups as isometry groups of translation surfaces.
method Adapting ideas from hyperbolic surfaces to translation surfaces.
result Every countable subgroup of GL+(2,ℝ) can be realized as the Veech group of a translation surface.
Classifies stable diffeomorphism of spin 4-manifolds with specific fundamental groups.
problem Classifying stable diffeomorphism of spin 4-manifolds with given fundamental groups.
method Formulated conjectural relationships between algebraic invariants and obstructions, proved for specific groups.
result Proved conjectures for specific fundamental groups, providing complete algebraic stable classification.