Categorifies Hopf fibration using category theory.
problem Describing Hopf fibration using category theory.
method Using small categories to classify spaces and describe the Hopf map.
result Realizes Hopf map as a functor between classifying spaces.
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A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
169,291 papers · 148 categories
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48 results for “small categories”
We generalize the notion of a small sheaf of sets over a topological space or manifold to define the notion of a small stack of groupoids over an étale topological or differentiable stack. We then provide a construction analogous to the étalé space construction in this context, establishing an equivalence of 2-categori…
Survey of techniques for learning with small samples in big data.
problem Learning from limited data in big data environments.
method Divided into concept learning and experience learning.
result Clarifies the rationality of SSL and its relationship with human learning.
The paper classifies virtual knot polynomials and trivalent graph invariants using skein theory.
problem Classifying virtual knot polynomials and trivalent graph invariants with specific conditions.
method Skein-theoretic techniques applied to classify invariants with smallness conditions.
result Classification of all non-trivial invariants of trivalent graphs and skein theories of virtual tangles.
Pareto index induced from the scale of companiesphysics.soc-ph
Employing profits data of Japanese companies in 2002 and 2003, we confirm that Pareto's law and the Pareto index are derived from the law of detailed balance and Gibrat's law. The last two laws are observed beyond the region where Pareto's law holds. By classifying companies into job categories, we find that companies …
We prove that manifolds of Lusternik-Schnirelmann category 2 necessarily have free fundamental group. We thus settle a 1992 conjecture of Gomez-Larranaga and Gonzalez-Acuna, by generalizing their result in dimension 3, to all higher dimensions. We also obtain some general results on the relations between the fundamenta…
We prove that manifolds of Lusternik-Schnirelmann category 2 necessarily have free fundamental group. We thus settle a 1992 conjecture of Gomez-Larranaga and Gonzalez-Acuna, by generalizing their result in dimension 3, to all higher dimensions. We examine its ramifications in systolic topology, and provide a sufficient…
Dimension zero at all scalesmath.MG
We consider the notion of dimension in four categories: the category of (unbounded) separable metric spaces and (metrically proper) Lipschitz maps, and the category of (unbounded) separable metric spaces and (metrically proper) uniform maps. A unified treatment is given to the large scale dimension and the small scale …
The category of small covariant functors from simplicial sets to simplicial sets supports the projective model structure. In this paper we construct various localizations of the projective model structure and also give a variant for functors from simplicial sets to spectra. We apply these model categories in the study …
In this paper we analyze supergeometric locally covariant quantum field theories. We develop suitable categories SLoc of super-Cartan supermanifolds, which generalize Lorentz manifolds in ordinary quantum field theory, and show that, starting from a few representation theoretic and geometric data, one can construct a f…
Study projective representations from non-semisimple TQFTs on surfaces.
problem Understanding projective representations of mapping class groups from non-semisimple TQFTs.
method Construct 3D TQFTs using non-semisimple modular categories and analyze projective representations of mapping class groups.
result Projective representations from non-semisimple TQFTs are equivalent to those obtained by Lyubashenko.
The study finds multiple solutions for constant Q-curvature metrics.
problem Finding multiple metrics with constant Q-curvature.
method Proving subcritical equations have at least Cat(M) positive solutions.
result Proves existence of at least Cat(M) metrics with constant Q-curvature.
Unsupervised learning on imbalanced data is challenging because, when given imbalanced data, current model is often dominated by the major category and ignores the categories with small amount of data. We develop a latent variable model that can cope with imbalanced data by dividing the latent space into a shared space…
Paper proposes CIV estimator for categorical instruments in small sample settings.
problem Estimation with categorical instruments in settings with few observations per category.
method CIV estimator leveraging regularization assumption for latent categorical variable.
result CIV estimator is asymptotically normal, efficient, and semiparametrically efficient under homoskedasticity.
Homological mirror symmetry proved for symmetric squares of punctured spheres.
problem Proving homological mirror symmetry for symmetric squares of punctured spheres.
method Constructed quasi-equivalences between wrapped Fukaya categories and derived categories of coherent sheaves, using categorical resolutions and localisation.
result Wrapped Fukaya category of symmetric square quasi-equivalent to coherent sheaves on a singular surface.
Robotic clothing manipulation improved with fashion image analysis techniques.
problem Automated identification of clothing categories and landmarks for robotic tasks.
method Training data augmentation methods and rotation invariant convolutions.
result Our approach outperforms state-of-the-art models on unseen datasets.
We construct link invariants using the subfactor planar algebras, and use these to prove new identities relating certain specializations of colored Jones polynomials to specializations of other quantum knot polynomials. These identities can also be explained by coincidences between small modular categories inv…
The study finds conditions for nonmaximal topological complexity of manifolds with abelian fundamental groups.
problem Conditions for nonmaximal topological complexity of manifolds with abelian fundamental groups.
method Analyzes conditions and examples to generalize results on topological complexity and Lusternik-Schnirelmann category.
result Generalizes results on topological complexity and Lusternik-Schnirelmann category for manifolds with abelian fundamental groups.
New method tackles instance segmentation on 3D point clouds with improved metrics.
problem Evaluation metrics are affected by small regions containing few instances.
method Proposes a new method with O(Np) space complexity that learns embeddings for clusters of instances.
result Achieves state-of-the-art performance using both existing and proposed metrics.
Unified framework connects deformation theory and derived categories for multiparameter persistence.
problem Algebraic complexity of multiparameter persistence modules hinders classification, stability, and interpretability.
method Combines deformation theory and derived categories to study multiparameter persistence geometrically.
result Unified conjecture relating interleaving distance to derived convolution metrics established.
Calculates Dehn twist actions on conformal blocks for modular categories.
problem Order of Dehn twists on spaces of conformal blocks.
method Quantum representations of mapping class groups, ribbon twists, monoidal powers.
result Order of Dehn twists generalizes previous results for small quantum group.
New quantum invariants derived from unrolled quantum groups match existing Hennings invariants.
problem Constructing non-semisimple quantum invariants for 3-manifolds.
method Using unrolled quantum groups at odd roots of unity and small quantum groups.
result Renormalized Hennings invariants coincide with new quantum invariants.
Big data comes in various ways, types, shapes, forms and sizes. Indeed, almost all areas of science, technology, medicine, public health, economics, business, linguistics and social science are bombarded by ever increasing flows of data begging to analyzed efficiently and effectively. In this paper, we propose a rough …
Automatic selection of eye tracking variables in visual categorization in adults and infantsq-bio.QM
Automated method selects eye tracking variables for categorization tasks.
problem Limited duration of infant cooperation and biases in handpicked eye tracking variables.
method Automated selection of eye tracking variables using statistical techniques.
result Same eye tracking variables classify category learners from non-learners in adults and infants with high accuracy.
Diffusion in a linear potential in the presence of position-dependent killing is used to mimic a default process. Different assumptions regarding transport coefficients, initial conditions, and elasticity of the killing measure lead to diverse models of bankruptcy. One "stylized fact" is fundamental for our considerati…
We use the Heegaard-Floer homology correction terms defined by Ozsváth--Szabó to formulate a new obstruction for a knot to be of finite order in the smooth concordance group. This obstruction bears a formal resemblance to that of Casson and Gordon but is sensitive to the difference between the smooth versus topological…
Proposes IFCDA framework to improve cross-domain adaptation.
problem Negative transfer and difficulty in handling category-irrelevant losses in DA.
method Importance filtered mechanism to generate filtered soft labels, combined with graph-based label propagation.
result Significantly improves performance in both Closed-Set and Open-Set DA scenarios.
New bounds on triangulations of manifolds with non-free fundamental groups.
problem Finding lower bounds on the number of vertices in PL-triangulations of manifolds.
method Using fundamental group structure and Lusternik-Schnirelmann category theory.
result Every PL-triangulation of a -dimensional manifold with non-free fundamental group has at least vertices.
Kan extensions help in data science extrapolation and learning.
problem Generalizing functions over larger sets in data science.
method Kan extensions in category theory applied to data science problems.
result Kan extensions can be used to derive classification and clustering algorithms.
Our main objective is to demonstrate how homological perturbation theory (HPT) results over the last 40 years immediately or with little extra work give some of the Koszul duality results that have appeared in the last decade. Higher homotopies typically arise when a huge object, e. g. a chain complex defining various …
Study examines Indian equity mutual funds' investment style and risk-shifting.
problem Understanding how Indian equity mutual funds' investment styles affect their returns.
method Estimating size and style beta coefficients, identifying breakpoints, analyzing investment styles, and assessing risk-shifting intensity.
result Funds can enhance returns by shifting to high-return styles like Small Value and Small Blend.
The paper disproves a conjecture about satellite maps not inducing homomorphisms.
problem Satellite maps and their impact on knot concordance groups.
method Casson-Gordon signatures and -solvable filtration analysis.
result Examples of satellite maps that act like homomorphisms but do not induce them.
Studies amenable category's monotonicity and its relation to topological complexity.
problem Monotonicity of amenable category for degree-one maps.
method Uses amenable covers and compares with topological complexity.
result Establishes a relation between amenable category and topological complexity.
Formal Contact Categoriesmath.GT
To each oriented surface S, we associate a differential graded category Ko(S). The homotopy category Ho(Ko(S)) is a triangulated category which satisfies properties akin to those of the contact categories studied by K. Honda. These categories are also related to the algebraic contact categories of Y. Tian and to the bo…
Study extends cognitive modeling to natural images, revealing the importance of image representation.
problem Extending cognitive modeling to natural images and understanding human categorization.
method Conducted a large-scale study with over 500,000 human judgments. Used deep and shallow machine learning methods to represent images. Applied psychological models of categorization to natural images.
result Simple models with abstract prototypes outperform complex exemplar accounts when using expressive, data-driven image representations.
Deep Learning model diagnoses four lymphoma categories with high accuracy.
problem Automated detection of lymphoma categories using digital pathology images.
method Convolutional neural network algorithm trained on 128 cases of lymph node images.
result Excellent diagnostic accuracy (95% image-by-image, 10% set-by-set).
Innovative 2-categories create 4-manifold invariants.
problem Constructing invariants for 4-manifolds.
method Semisimple 2-categories, fusion 2-categories, and state-sum construction.
result Construct a state-sum invariant for 4-manifolds.
New geometric structures in tangent categories.
problem Defining affine structures in tangent categories.
method Structural differential geometry, axiomatization of tangent categories, flat torsion-free connections.
result Affine objects form a tangent category and provide new characterizations of flat torsion-free connections.
Formulates a new connection between topological and geometric categories.
problem No specific problem stated; focuses on category formulation.
method Formulates a connection between a topological and geometric category.
result Provides a more precise and improved version of a previous proposal.
Quandle Cocycle Quiversmath.GT
New graph-based invariants from quandle cocycles.
problem Defining new link invariants from quandle cocycles.
method Integrating quandle cocycle information into quandle coloring quivers to create weighted directed graphs.
result Definition of new link invariants including a 2-variable polynomial.
Extends monetary value measures to probability spaces.
problem No specific problem stated; generalization of monetary value measures.
method Extends category from hi to Prob.
result Generalized monetary value measures to probability spaces.
Survivorship Bias in Emerging Market Small-Cap Indices: Evidence from India's NIFTY Smallcap 250q-fin.ST
Study shows survivorship bias inflates returns in India's small-cap index.
problem Survivorship bias in emerging market small-cap indices.
method Reconstructing historical index composition through market capitalization ranking and comparing equal-weight portfolios of current constituents versus all historical members.
result Survivor-only backtesting overstates returns by 4.94 percentage points and Sharpe ratios by 0.097.
A groupoid is a small category in which each morphism has an inverse. A topological groupoid is a groupoid in which both sets of objects and morphisms have topologies such that all groupoid structure maps are continuous. The notion of monodromy groupoid of a topological groupoid generalises those of fundamental groupoi…
Zero-shot audio classification using class label embeddings.
problem Classifying audio without labeled data.
method Bilinear model with audio feature embeddings and class label embeddings.
result Achieved accuracy up to 39.7% for natural audio categories.
Generalizes Morse theory to n-categories using critical points and moduli spaces.
problem Constructing n-categories from Morse theory.
method Extending Cohen & Jones & Segal's flow category to n-categories by Morse theory on critical points and moduli spaces.
result The resulting structure is an 'almost strict' n-category.
A new TQFT is conjectured to extend Reshetikhin-Turaev TQFT.
problem Extending TQFT to lower dimensions.
method Defining a symmetric monoidal (4,3)-category with duals from enriched multi-fusion categories.
result A conjectured extension of 1-2-3-dimensional TQFT to dimension zero.
Survey on decorated marked surfaces for Calabi-Yau categories.
problem Understanding Calabi-Yau categories and related structures.
method Introducing decorations on marked surfaces to study various categories.
result Exploration of Calabi-Yau-2 and 3 categories, braid groups, quadratic differentials, and stability conditions.
The paper defines new TQFTs from non-semisimple categories and proves spherical categories are chromatic.
problem Defining non-compact TQFTs from non-semisimple categories.
method Introducing admissible skein modules, chromatic categories, and using Juhász's cobordism presentation.
result Non-compact (2+1)-TQFTs can be defined from chromatic categories, extending Turaev-Viro TQFTs.