We derive simple explicit formulas for the character of a cycle in the Connes' (b,B)-bicomplex of cyclic cohomology and give applications to the Fredholm modules and equivariant characteristic classes.
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48 results for “characteristic cycles”
This paper studies business cycle patterns in UK sectoral output. It analyzes the distinction between white noise processes and their non-white noise counterparts in the frequency domain and further examines the associated features and patterns for the process where white noise conditions are violated. The characterist…
We find that factors explaining bank loan recovery rates vary depending on the state of the economic cycle. Our modeling approach incorporates a two-state Markov switching mechanism as a proxy for the latent credit cycle, helping to explain differences in observed recovery rates over time. We are able to demonstrate ho…
Study characteristic classes of a specific type of determinantal varieties.
problem Understanding the geometric properties of a special class of determinantal varieties.
method Used Schubert calculus to derive explicit formulas for Chern-Schwartz-MacPherson and Chern-Mather classes.
result Explicit formulas for sectional Euler characteristics, characteristic cycles, and polar classes were obtained.
We propose two new approaches to the Tannakian Galois groups of holonomic D-modules on abelian varieties. The first is an interpretation in terms of principal bundles given by the Fourier-Mukai transform, which shows that they are almost connected. The second constructs a microlocalization functor relating characterist…
Proves a conjecture about graph complexes without specific cycle lengths.
problem Graph complexes without specific cycle lengths.
method Proves stronger statements about independence complexes being contractible or homotopy equivalent to spheres.
result Independence complexes are either contractible or homotopy equivalent to spheres.
New proof confirms operations on constructible functions match theory.
problem Matching operations on constructible functions with generalized valuations theory.
method Comparison with characteristic cycles approach.
result Operations on constructible functions match generalized valuations theory under mild assumptions.
Real Milnor fibres become contractible after attaching handles, matching classical results.
problem Topology of real isolated hypersurface singularities.
method Proving real Milnor fibres contractible after attaching handles, defining real vanishing cycles.
result Integer homology groups of real Milnor fibres are isomorphic to those of a bouquet of spheres under certain conditions.
Study on flat connections with controlled irregularity.
problem Boundedness of algebraic flat connections with limited irregularity.
method Analysis of families of algebraic flat connections and holonomic D-modules.
result Established boundedness of families of algebraic flat connections with controlled irregularity.
We study the asymptotic properties of the conormal cycle of nodal sets associated to a random superposition of eigenfunctions of the Laplacian on a smooth compact Riemannian manifold without boundary. In the case where the dimension is odd, we show that the expectation of the corresponding current of integration equidi…
CDLF predicts product life-cycles in cold-start phases with high accuracy.
problem Forecasting new products in early phases when data is scarce.
method Conditional Diffusion Life-cycle Forecaster (CDLF) combining static descriptors, reference trajectories, and new observations.
result CDLF outperforms classical models in accuracy and probabilistic forecasting.
The paper extends a conjecture about Euler characteristics of perverse sheaves on certain Kähler manifolds.
problem The conjecture about Euler characteristics of perverse sheaves on compact aspherical Kähler manifolds.
method The method involves expressing the Euler characteristic as an intersection number involving the characteristic cycle, and using curvature conditions to deduce non-negativity. For the second result, the local system is shown to underlie a complex variation of Hodge structures, leading to the desired inequality from curvature properties of the period map.
result The conjecture holds for compact aspherical Kähler manifolds with non-positive holomorphic bisectional curvature and for projective manifolds with a faithful semi-simple rigid local system.
The paper proves a conjecture about the positivity of the Euler characteristic for complex projective manifolds.
problem Proving the positivity of the Euler characteristic for complex projective manifolds with large fundamental groups.
method Introducing a vanishing cycle functor of multivalued one-forms and applying non-abelian Hodge theory techniques.
result The paper proves a stronger statement about the positivity of the Euler characteristic for complex projective manifolds with large fundamental groups and almost faithful linear representations.
We produce new cohomology for non-uniform arithmetic lattices using a technique of Millson--Raghunathan. From this, we obtain new characteristic classes of manifold bundles with fiber a closed -dimensional manifold with indefinite intersection form of signature . These classes are defined on …
PerCDL learns personalized dictionaries for physiological signals combining global and local structures.
problem Representing datasets with both global and local structures in human physiological signals.
method Personalized Convolutional Dictionary Learning (PerCDL) that combines a global and personalized local dictionary.
result PerCDL effectively learns interpretable representations for human locomotion data.
We consider convex SGD updates with a block-cyclic structure, i.e. where each cycle consists of a small number of blocks, each with many samples from a possibly different, block-specific, distribution. This situation arises, e.g., in Federated Learning where the mobile devices available for updates at different times d…
Observation of the workings of productive organizations shows that the characteristics of a trade, backed by nature given to a technological environment, determine the productive combination implemented by the decision maker, and the structure of the operating cycle which is related. The choice of the production functi…
I construct the real counterparts (which I call Borel-Bott classes) of the R/Z classes constructed in "Characteristic classes in symplectic topology", to appear, in the cohomology of volume-preserving and symplectomorhisms of a compact (symplectic) manifold.I show that, for the symplectic action of the mapping class gr…
We give a construction of the Floer homology of the pair of {\it non-compact} Lagrangian submanifolds, which satisfies natural continuity property under the Hamiltonian isotopy which moves the infinity but leaves the intersection set of the pair compact. This construction uses the concept of Lagrangian cobordism and ce…
Odd crossing numbers and even rotation numbers for cycles in plane immersions.
problem Analyzing crossing and rotation numbers of cycles in plane immersions of graphs.
method Generic immersions and Legendrian embeddings of graphs, focusing on cycles of specific lengths.
result Sum of rotation numbers of all 5-cycles is even, and sum of crossing numbers is odd.
We present a feature engineering pipeline for the construction of musical signal characteristics, to be used for the design of a supervised model for musical genre identification. The key idea is to extend the traditional two-step process of extraction and classification with additive stand-alone phases which are no lo…
New link topology connects permutation discrepancies to Diaconis-Graham inequalities.
problem Characterize permutations for which Diaconis-Graham inequalities hold with equality.
method Relate permutation discrepancies to the Euler characteristic of their associated links.
result Permutation discrepancies are directly related to the Euler characteristic of their associated links.
Proves inequality for 1-dimensional cycles.
problem Proving the Parametric Coarea Inequality for 1-cycles.
method Analytical proof based on conjecture by Guth and Liokumovich.
result Proved the Parametric Coarea Inequality for 1-cycles.
This work introduces novel methods to identify and compare cycles across topological objects.
problem Identifying and comparing topological features, particularly cycles, across different topological objects.
method Two complementary approaches: dendrogram-based merge-tree algorithms and Stratified Gradient Sampling.
result Transformed cycle matching into hierarchical clustering and topological optimization framework.
This article introduces proximal planar vortex 1-cycles, resembling the structure of vortex atoms introduced by William Thomson (Lord Kelvin) in 1867 and recent work on the proximity of sets that overlap either spatially or descriptively. Vortex cycles resemble Thomson's model of a vortex atom, inspired by P.G. Tait's …
This paper identifies the unique efficient cycle for most hyperbolic manifolds but not for the figure-8 knot complement.
problem Identifying the unique efficient cycle for hyperbolic manifolds.
method Analyzing the limit of fundamental cycles and their -norm convergence.
result The uniqueness of the efficient cycle is proven for most hyperbolic manifolds but not for the figure-8 knot complement.
Study Agol cycles for pseudo-Anosov 3-braids.
problem Conditions for equivalent Agol cycles of pseudo-Anosov 3-braids.
method Investigate necessary and sufficient conditions.
result Necessary and sufficient conditions for equivalent Agol cycles of pseudo-Anosov 3-braids.
Study shows credit expansion in mortgage markets influenced U.S. business cycle.
problem Lack of causal evidence in cross-country business cycle studies.
method Unique research design combining cross-metropolitan U.S. data.
result Credit expansion caused stronger booms and busts in house-related industries.
Researchers compute Connes-Chamseddine cycle on 6D manifolds using noncommutative integral.
problem Computing the Connes-Chamseddine cycle for 6D manifolds.
method Using noncommutative integral on 6D manifolds, they compute the cycle.
result The Connes-Chamseddine cycle on 6D manifolds is computed.
Gauss diagrams' properties can change with Hamiltonian cycle choice.
problem The impact of Hamiltonian cycle choice on Gauss diagrams.
method Examined realizable and unrealizable Gauss diagrams, and proved preservation of realizability under certain Hamiltonian cycle changes.
result Properties of Gauss diagrams can vary with Hamiltonian cycle choice.
Proximal algorithms applied to current deformation into cycles.
problem Deformation of de Rham currents into cycles.
method Proximal algorithms, total variation denoising for differential forms.
result Calibrated cycles constructed in calibrated manifolds.
New algorithm for learning causal structures with disjoint cycles in linear non-Gaussian models.
problem Learning causal structures with cycles in linear non-Gaussian models.
method Characterizing when graphs determine the same model, using quadratic and cubic polynomial relations, and a strategy of decorrelating cycles and multivariate regression.
result Consistent and computationally efficient algorithm for learning causal structures with disjoint cycles.
In Vitro Fertilization (IVF) Cumulative Pregnancy Rate Prediction from Basic Patient Characteristicsq-bio.QM
Tens of millions of women suffer from infertility worldwide each year. In vitro fertilization (IVF) is the best choice for many such patients. However, IVF is expensive, time-consuming, and both physically and emotionally demanding. The first question that a patient usually asks before the IVF is how likely she will co…
Credit expansion led to stronger household leverage cycles during the U.S. business cycle.
problem Understanding the role of credit supply in the U.S. business cycle.
method Causal evidence from 1999-2010 U.S. business cycle data.
result Credit expansion, particularly in private-label mortgages, caused stronger household leverage cycles.
In the current article we study complex cycles of higher multiplicity in a specific polynomial family of holomorphic foliations in the complex plane. The family in question is a perturbation of an exact polynomial one-form giving rise to a foliation by Riemann surfaces. In this setting, a complex cycle is defined as a …
In this paper, we introduce a novel task for machine learning in healthcare, namely personalized modeling of the female hormonal cycle. The motivation for this work is to model the hormonal cycle and predict its phases in time, both for healthy individuals and for those with disorders of the reproductive system. Becaus…
AdaBoost cycles in probability simplex dynamics.
problem Understanding cycling behavior in AdaBoost.
method Computational methods and dynamical systems analysis.
result Correspondence between AdaBoost cycling and continued fractions dynamics.
Smooth approximation of integral cycles mod 2 in Riemannian manifolds.
problem Approximating mod 2 integral cycles by smooth submanifolds.
method Approximation of mod 2 integral cycles by smooth submanifolds with controlled singularities.
result Every mod 2 integral cycle can be approximated by a smooth submanifold with a controlled singular set.
Constructs an explicit cycle in arithmetic group cohomology.
problem Cohomology of SL at virtual cohomological dimension.
method Geometric rigidity of Voronoi tessellations and abstract framework for polyhedral tessellations.
result Explicit canonical cycle in top-dimensional homology of Voronoi complex.
Using Kontsevich's identification of the homology of the Lie algebra l_infty with the cohomology of Out(F_r), Morita defined a sequence of 4k-dimensional classes mu_k in the unstable rational homology of Out(F_{2k+2}). He showed by a computer calculation that the first of these is non-trivial, so coincides with the uni…
We introduce a notion of vanishing Maslov index for lagrangian varifolds and lagrangian integral cycles in a Calabi-Yau manifold. We construct mass-decreasing flows of lagrangian varifolds and lagrangian cycles which satisfy this condition. The flow of cycles converges, at infinite time, to a sum of special lagrangian …
We give an algorithm to compute the integer cohomology groups of any real partial flag manifold, by computing the incidence coefficients of the Schubert cells. For even flag manifolds we determine the integer cohomology groups, by proving that any torsion class has order 2 (generalizing a result of Ehresmann). We conje…
Approximates cycles in planar and bounded-genus graphs.
problem Finding many disjoint cycles in planar and bounded-genus graphs.
method Constant-factor approximation algorithms for vertex-disjoint and edge-disjoint cycles.
result First algorithms for vertex-disjoint paths in fully planar and bounded-genus instances.
Study examines cash conversion cycle in manufacturing firms, finding negative relationships with profitability and size.
problem Understanding cash conversion cycle in manufacturing firms and its impact on profitability and size.
method Empirical study of 30 manufacturing firms in Dhaka Stock Exchanges, categorizing them into six industries, analyzing industry averages and relationships with size and profitability.
result Negative relationship between cash conversion cycle and profitability, especially ROE; negative relationship with firm size in terms of net sales.
By generalizing the measurements on the game experiments of mixed strategy Nash equilibrium, we study the dynamical pattern in a representative dynamic stochastic general equilibrium (DSGE). The DSGE model describes the entanglements of the three variables (output gap [], inflation [] and nominal interest rate [$…
We present a necessary and sufficient condition for existence of a contractible, non-separating and noncontractible separating Hamiltonian cycle in the edge graph of polyhedral maps on surfaces. In particular, we show the existence of contractible Hamiltonian cycle in equivelar triangulated maps. We also present an alg…
Endogenous business cycles explain higher comovement across countries.
problem Standard models struggle to explain high comovement in business cycles across countries.
method Developed a demand-driven reduced-form model with strategic complementarities and international trade linkages.
result Combining endogenous business cycles with exogenous shocks matches empirical comovement levels.
Study Agol cycles in pseudo-Anosov 3-braids.
problem Understanding conjugacy invariants of pseudo-Anosov maps.
method Investigate train tracks associated with Farey intervals and describe Agol cycles.
result Complete description of Agol cycles in pseudo-Anosov 3-braids.