Logistic regression and neural networks reinterpreted using Dempster-Shafer theory.
problem Lack of evidence and conflicting evidence in classification problems.
method Reinterpretation of classifiers as mass functions and aggregation by Dempster's rule.
result Mass functions provide more informative decision-making than probabilities.
Fault detection in IoT nodes using Dempster-Shafer Theory of Evidence.
problem Fault detection in sensor nodes in IoT applications.
method Dempster-Shafer Theory of Evidence for sensor data fusion.
result Competent accuracy for fault detection in both benchmark and laboratory data sets.
Rule-based classifiers quantify uncertainty using Bernoulli random variables.
problem Quantifying the uncertainty of precision estimates for rule-based text classifiers.
method Treat partitions of sub-strings as Bernoulli random variables, compare means using statistical tests, and combine classifiers using Dempster-Shafer theory.
result The approach can be used to combine binary classifiers into a multi-label classifier.
A novel ensemble classifier improves vibration-based quality monitoring accuracy.
problem Developing high accuracy classification methods for general datasets.
method Dempster-Shafer theory of evidence with three remedies for conflicting evidences.
result The proposed ensemble classifier outperforms state-of-the-art fusion techniques.
A fuzzy expert system selects stocks for BSE using AI techniques.
problem Selecting stocks for investment allocation is challenging due to many influencing factors.
method Dempster-Shafer (DS) evidence theory for rule base generation, portfolio optimization model with ACO algorithm.
result The model's performance is satisfactory for short-term investment.
A method to simplify complex high-dimensional data visualization.
problem Difficult interpretation of linear projections in high-dimensional data.
method Decomposition of linear projections into axis-aligned projections using Dempster-Shafer theory.
result Linear projections can be effectively represented by a sparse set of axis-aligned projections, revealing more intuitive insights.
The paper proposes a method to calibrate evidential clustering using bootstrapped finite mixture models.
problem Representing uncertainty in cluster membership using Dempster-Shafer mass functions.
method Constructing Dempster-Shafer mass functions by bootstrapping finite mixture models, computing confidence intervals, and calibrating the evidential partition.
result The proposed method calibrates the evidential partition such that the belief and plausibility degrees approximate the true probabilities with high confidence.
NN-EVCLUS uses neural networks to cluster data with uncertainty.
problem Clustering data with uncertainty and handling outliers.
method NN-EVCLUS learns a neural network to map attributes to mass functions, minimizing discrepancy between dissimilarities and conflict.
result NN-EVCLUS outperforms existing methods in clustering tasks.
A method for consensus prediction from probabilistic classifier outputs.
problem Combining probabilistic classifier outputs without prior information.
method Iteratively updating predictions based on classifier diversity and convergence.
result Consensus predictions converge to a decision based on classifier outputs' correspondence.
Discrete Morse-Bott theory on CW complexes generalizes Forman's theory.
problem No specific problem stated; focuses on theory development.
method Derived a discrete Morse-Bott theory on CW complexes.
result Discrete Morse-Bott theory is a generalization of Forman's theory.
The paper connects function theory, dynamics, and ergodic theory via Thurston's theory.
problem Function theory on Teichmüller space and dynamics of mapping class groups.
method Utilizes Thurston's theory and Sullivan's theory on discrete subgroups of hyperbolic space.
result Establishes connections between function theory, dynamics, and ergodic theory.
Survey of Floer theories and their connections.
problem None explicitly stated; focuses on surveying theories.
method None explicitly stated; focuses on surveying theories.
result None explicitly stated; focuses on surveying theories.
New classes from 4D gauge theories.
problem Constructing characteristic classes for 4-manifold bundles.
method Using SO(3)-Yang-Mills theory and Seiberg-Witten theory for families. result Characteristic classes of 4-manifold bundles constructed.
Lectures on topological field theories and differential cohomology.
problem Exploring topological field theories and their connections to differential cohomology.
method Introduction to topological field theory and generalized Abelian gauge theories.
result Explains the relationship between topological field theories and differential cohomology.
New theory couples Chern-Simons to matter, topological.
problem Developing a new topological theory in 3D.
method Coupling Chern-Simons to matter, using transverse holomorphic foliation.
result The theory is equivalent to an N=2 supersymmetric Chern-Simons matter theory.
The paper defines strong emergence in field theories and proves it exists between certain theories.
problem Defining and proving the existence of strong emergence phenomena between field theories.
method Formal definition and sufficient conditions for emergence, proving existence in Euclidean background.
result Strong emergence exists between certain parameterized Lagrangian field theories.
Topological string theory derived from string geometry for non-perturbative effects.
problem Deriving non-perturbative effects in string theory.
method Formulating topological string geometry theory and deriving the partition function from fluctuations around a classical solution.
result Perturbative partition function of topological string theory derived.
New cohomology theory for Lie 2-algebras extends classical theory.
problem Classical cohomology theory limitations for Lie 2-algebras.
method Introduced a new cohomology theory for Lie 2-algebras.
result Second cohomology group classifies extensions of Lie 2-algebras.
Researchers solve M-theory's gauge enhancement problem using advanced homotopy theory.
problem Lift nonabelian gauge fields from D-branes to M-theory.
method Universal constructions in super homotopy theory, focusing on the cyclification adjunction and fiberwise stabilization.
result Gauge enhancement in M-theory is explained by lifting against the fiberwise stabilization of the unit of the cyclification adjunction.
Unified Higgs bundle vacua from M-theory on Spin(7) spaces.
problem Unifying Higgs bundle vacua from different string compactifications.
method Developed formalism for M-theory on local Spin(7) spaces and constructed explicit solutions.
result Unified 3D effective field theory from 4D M- and F-theory vacua.
This is the first paper in a series introducing a generalized Fredholm theory in a new class of smooth spaces called polyfolds. The theory will be illustrated in upcoming papers by applications to Floer Theory, Gromov-Witten Theory and Symplectic Field Theory.
Researchers find new G2-conifolds in M-theory with potential field theory duals.
problem Exploring the field theory interpretation of M-theory G2-conifolds. method Constructing G2-holonomy orbifolds from circle bundles over Calabi-Yau cones. result Many UV perturbative gauge theories have an infrared dual described by smooth G2-holonomy backgrounds in M-theory. We survey three different ways in which K-theory in all its forms enters quantum field theory. In Part 1 we give a general argument which relates topological field theory in codimension two with twisted K-theory, and we illustrate with some finite models. Part 2 is a review of pfaffians of Dirac operators, anomalies, a…
New theory captures framing anomaly in gauge theory.
problem Capturing framing anomaly in gauge theory.
method Constructs a relative Crane-Yetter theory from non-semisimple data.
result Establishes invertibility property for the theory.
Researchers compute K-theory for cohomogeneity-one actions.
problem Computing equivariant K-theory for cohomogeneity-one actions.
method Equivariant homotopy theory, representation theory, Lie theory.
result Derived generators and relations for K-theory ring.
Distributivity in algebraic structures appeared in many contexts such as in quasigroup theory, semigroup theory and algebraic knot theory. In this paper we give a survey of distributivity in quasigroup theory and in quandle theory.
Survey on algebraic K- and L-theory conjecture.
problem Algebraic K- and L-theory of groups rings.
method Not specified in the abstract, likely involves algebraic and geometric approaches.
result Applications to algebra, geometry, group theory, and topology.
Study pin manifolds using Clifford linear Dirac operator and KO-theory.
problem Index theory on Pin manifolds.
method Clifford linear Dirac operator and differential KO-theory.
result Systematic treatment of index theory on Pin manifolds.
Main mathematical applications of Frobenius manifolds are in the theory of Gromov - Witten invariants, in singularity theory, in differential geometry of the orbit spaces of reflection groups and of their extensions, in the hamiltonian theory of integrable hierarchies. The theory of Frobenius manifolds establishes rema…
String theory connects lattice models, links, and geometric Langlands.
problem Connecting lattice models, links, and geometric Langlands.
method T-duality and worldvolume theories in string theory.
result Unified understanding of various mathematical concepts.
In this paper, we construct a new homology theory for semi-groups satisfying the self distributivity axiom or the idempotency axiom. Next, we consider the geometric realization corresponding to the homology theory. We continue with the comparison of this homology theory with one term and two term (rack) homology theori…
Quantum field theory uses Lorentzian bordisms to describe time evolution.
problem Describing the time evolution of quantum field theories.
method Defines a functorial field theory on Lorentzian bordism pseudo-category.
result Lorentzian bordisms naturally arise in algebraic quantum field theory.
Recent work connects Thompson's groups to knot theory.
problem Understanding knots and links through Thompson's groups.
method Review of recent research on Thompson group representations.
result Recent developments link Thompson's groups to knot theory.
This thesis proposes a global geometric formulation of Extended Field Theories.
problem Global understanding of Extended Field Theories remains an open problem.
method Introducing an atlas for the principal infinity-bundle, unifying metric and higher gauge field.
result Global abelian T-duality and Poisson-Lie T-duality are automatically recovered.
The paper quantizes hybrid topological-holomorphic field theories on RmimesCn.
problem Quantizing hybrid topological-holomorphic field theories rigorously.
method Constructing perturbative, one-loop quantizations on RmimesCn. result The one-loop obstruction to quantization vanishes when m≥1. This is the revised version of the second paper in a series introducing a generalized Fredholm theory in a new class of smooth spaces called polyfolds. The theory will be illustrated in upcoming papers by applications to Floer Theory, Gromov-Witten Theory and Symplectic Field Theory. Some proofs have been improved and …
3D dual field theories for Virasoro minimal models constructed using Seifert fiber spaces.
problem Constructing 3D dual field theories for Virasoro minimal models.
method 3D-3D correspondence and Seifert fiber spaces.
result 3D dual field theories constructed for Virasoro minimal models.
Cohomotopy theory predicts M-theory anomaly cancellation on 8-manifolds.
problem Anomaly cancellation in M-theory on 8-manifolds.
method Using J-twisted Cohomotopy theory, we prove anomaly cancellation conditions.
result Cohomotopy theory implies specific anomaly cancellation conditions in M-theory.
The paper extends Alexander and Markov theories to generalized knot theories.
problem Defining Alexander and Markov theories for generalized knot theories.
method Extending existing theories to new knot types.
result Alexander and Markov theories can be applied to generalized knot theories.
We show that Chern-Simons gauge theory with appropriate cutoffs is equivalent, term by term in perturbation theory, to a Fermionic theory with a nonlocal interaction term. When an additional cutoff is placed on the Fermi fields, this Fermionic theory gives rise to a convergent perturbation expansion. This leads us to c…
We find canonical gauges for higher gauge theories in 2- and 3-gauge theories.
problem Finding good gauges for connections in higher gauge theories.
method Defined Coulomb gauges for 2- and 3-connections in strict 2- and 3-gauge theories.
result Coulomb gauges are essentially unique and linear in critical dimensions.
Abstract: Linking field theory to Floer theory via regularization.
problem Finding periodic solutions of Hamilton's equation.
method Regularization scheme for polysymplectic formalism linking Euclidean field theory to hyperkähler Floer theory.
result Proved a cuplength estimate.
Unified treatment of gauge theories and Yang-Mills theory duality.
problem Unified treatment of gauge theories and Yang-Mills theory duality.
method Cohomological localization techniques and Atiyah-Singer index theorem.
result Unified framework and simplified derivations of localization formulas.
New theory connects string theory to swampland distance conjecture.
problem Connecting string theory to swampland distance conjecture.
method Deformations of the heterotic superpotential, treating separately for large fluxes or large distances, integrating out fields to obtain a new field theory.
result New holomorphic theory defined, connects to swampland distance conjecture.
Identifies all perturbative vacua in bosonic string theory.
problem Identifying all perturbative vacua in bosonic string theory.
method Completely identified perturbative vacua through string fluctuations.
result Derivation of path-integrals up to any order from fluctuations.
Explores polyfold and Fredholm theory for complex mathematical structures.
problem None explicitly stated; focuses on theory.
method Theoretical development and reference.
result Theoretical advancements in polyfold and Fredholm theory.
Anomaly in free fermion theory revealed in functorial field theory.
problem Chiral anomaly in the free fermion theory.
method Detailed construction of anomaly theory as a functor.
result The anomaly theory assigns elements of complex line to manifolds.
In this short note we show how Dubrovin's integrable hierarchies, defined using the Gromov-Witten theory of a closed symplectic manifold, generalizes to Hamiltonian Floer theory. In particular, we show how the required generalization of the PSS isomorphism, relating Gromov-Witten theory and Hamiltonian Floer theory, ca…