New interpretation reconciles country and product complexity.
problem Difficulty in interpreting Economic and Product Complexity Indices.
method Spectral clustering algorithm to separately group similar countries and products.
result Indices identify two co-clusters of similar countries and products.
Study bigraded formality and Aeppli-Bott-Chern-Massey products on complex manifolds.
problem Formality and higher Aeppli-Bott-Chern-Massey products on complex manifolds.
method Introduce and study bigraded formality and Aeppli-Bott-Chern-Massey products, showing non-trivial pullbacks on blow-ups.
result Aeppli-Bott-Chern-Massey products on complex manifolds pull back non-trivially to blow-ups under certain conditions.
Formula for topological complexity of group free products derived.
problem Calculating the topological complexity of free product groups.
method Proved a formula using group cohomology.
result Formula for topological complexity of free products of groups.
Complex products trade through fewer countries, making them more fragile.
problem Fragility in the global economy due to centralized trade networks for complex products.
method Used network science and product complexity theory indicators to analyze trade networks.
result Products with higher complexity trade through fewer countries, making them more fragile.
Study cup products on CAT(0) cube complexes, proving quasimorphisms' vanishing results.
problem Understanding cup products in higher bounded cohomology groups.
method Extending vanishing results from Brooks quasimorphisms to median quasimorphisms on CAT(0) cube complexes.
result Vanishing results for cup products of median quasimorphisms on CAT(0) cube complexes.
Study on real hypersurfaces in products of complex space forms, proving rigidity and nonexistence results.
problem Existence and properties of totally umbilical real hypersurfaces in complex space forms.
method Analyzing shape operators and local product structures in products of complex space forms.
result Nonexistence and rigidity results for totally umbilical real hypersurfaces in products of complex space forms.
Study on harmonicity of complex structure on product of trans-Sasakian manifolds.
problem Investigating harmonicity of complex structure on product of trans-Sasakian manifolds.
method Analysis of Levi-Civita connection and conditions for harmonicity on product manifold.
result Conditions for harmonicity of complex structure on product manifold of trans-Sasakian manifolds.
The paper proves an equality involving torsion, volume, and a product for hyperbolic 3-manifolds.
problem Understanding the geometry and topology of hyperbolic 3-manifolds with cusps.
method Using Reidemeister torsion, complex volume, and Zograf's infinite product.
result Proves an equality linking these mathematical concepts.
Uniform criterion for vanishing products in bounded cohomology.
problem Vanishing of cup products and Massey products in bounded cohomology.
method Uniform vanishing criterion for products in bounded cohomology.
result Reproved and extended previous vanishing results.
New complexity notion connects finite decomposition and asymptotic property C.
problem Understanding and connecting different properties in metric spaces.
method Introducing finite APC-decomposition complexity and proving its implications.
result Finite APC-decomposition complexity implies property A for metric spaces.
The paper classifies product minimal Lagrangian submanifolds in complex space forms.
problem Understanding minimal Lagrangian submanifolds in complex space forms.
method Examining submanifolds as Riemannian products with constant sectional curvature.
result Complete classification of product minimal Lagrangian submanifolds.
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…
New results show how complex representations are needed to realize taut sutured handlebodies as homology products.
problem Understanding the complexity of representations needed for taut sutured handlebodies as homology products.
method Illustrates the relationship between taut sutured handlebody topology and the complexity of realizing them as homology products.
result Illustrates the complexity of representations needed for taut sutured handlebodies as homology products.
The study classifies stable submanifolds in product spaces of projective spaces.
problem Classifying stable submanifolds in product spaces of projective spaces.
method Provided a classification theorem for compact stable minimal immersions in product spaces of projective spaces.
result Characterized complex minimal immersions in the product of two complex projective spaces.
New private identity testers for high-dimensional distributions with improved sample complexity.
problem Testing goodness-of-fit for high-dimensional product distributions under differential privacy.
method Developed novel differentially private testers for multivariate product distributions, including Gaussians and binary product distributions.
result Achieved sample complexity matching the minimax sample complexity of O(d1/2/α2) in many parameter regimes. We construct homology theories with coefficients in L-spectra on the category of ball complexes and we define products in this setting. We also obtain signatures of geometric situations in these homology groups and prove product formulae which we hope will clarify products used in the theory of the total surgery obstru…
We study complex product structures on nilpotent Lie algebras, establishing some of their main properties, and then we restrict ourselves to 6 dimensions, obtaining the classification of 6-dimensional nilpotent Lie algebras admitting such structures. We prove that any complex structure which forms part of a complex pro…
Research preserves coarse property C and related dimensions through direct products.
problem Preserving properties in coarse geometry through direct products.
method Demonstrates preservation of coarse property C and related dimensions through finite coarse direct products.
result Coarse property C and related dimensions are preserved by direct products.
Complex structures found on product of Sasakian manifolds.
problem Exploring complex structures on the product of two Sasakian manifolds.
method Examined a family of complex structures on the product of two compact Sasakian manifolds, computed Dolbeault cohomology groups.
result None of the complex structures in the family admit compatible locally conformally Kähler metrics if both Sasakian manifolds are of dimension greater than 1.
We discuss the integrability of orthogonal almost complex structures on Riemannian products of even-dimensional round spheres and give a partial answer to the question raised by E. Calabi concerning the existence of complex structures on a product manifold of a round 2-sphere and a round 4-sphere.
Classifies complex structures on 6D Lie algebras as products.
problem Identifying all complex structures on 6D Lie algebras.
method Examined 6D Lie algebras of the form gimesg for integrable complex structures. result Listed all integrable complex structures on these Lie algebras.
Study of complex structures on product twistor spaces for 4D manifolds.
problem Understanding complex structures on product twistor spaces.
method Analyzing the product bundle of twistor spaces with Riemannian metrics and almost complex structures.
result Determined Gray-Hervella classes for 4D manifolds.
Products of LCK manifolds do not admit LCK structures.
problem Whether products of compact complex manifolds admit LCK metrics.
method Classifying known LCK manifolds and proving non-existence of LCK structures in product cases.
result Products of LCK manifolds do not admit LCK structures.
Modeling how network connectivity affects economic collapse and robustness.
problem Impact of network topology on systemic risk and collapse of complex economic systems.
method Proposed a model to study the effects of network structure on economic systems by varying connectivity.
result Emergent systemic risks arise with increased interconnections, leading to phase transitions and tipping points.
In this paper, we prove an equality which involves Reidemeister torsion, complex volume, and Zograf infinite product for closed hyperbolic 3-manifolds.
The paper explores structures on 3-Lie algebras, including product, complex, and symplectic.
problem Exploring structures on 3-Lie algebras.
method Introducing phase spaces, product structures, complex structures, and compatibility conditions.
result Four types of special integrability conditions for product, complex, and symplectic structures on 3-Lie algebras.
In this article, we give a geometric proof of the classification of complex vector cross product due to Lee-Leung.
Product of shellable complexes yields shellable triangulations under tameness conditions.
problem Understanding shellability in products of simplicial complexes.
method Definition and proof of shellability properties for products of complexes under tameness conditions.
result Product of shellable complexes yields shellable triangulations under certain conditions.
We provide an upper bound on the topological complexity of twisted products. We use it to give an estimate TC(X)≤TC(π1(X))+dimX of the topological complexity of a space in terms of its dimension and the complexity of its fundamental group.
We show that essential punctured spheres in the complement of links with distance three bridge spheres have bounded complexity. We define the operation of tangle product, a generalization of both connected sum and Conway product. Finally, we use the bounded complexity of essential punctured spheres to show that the bri…
New linking numbers link complex cycles to Calabi-Yau 3-folds.
problem Understanding complex analytic cycles and their Massey products.
method Relating ABC Massey products to holomorphic linking numbers.
result Constructed a family of Calabi-Yau 3-folds with non-vanishing Massey products.
Study warped product metrics on hyperbolic and complex hyperbolic manifolds.
problem Understanding curvature of warped product metrics.
method Prove curvature formulas for warped product metrics on hyperbolic and complex hyperbolic manifolds.
result Curvature formulas expressed in spherical coordinates about totally geodesic submanifolds.
Study reveals vanishing Massey products on compact complex surfaces, impacting their fundamental group structure.
problem Understanding the real homotopy type of compact complex surfaces.
method Analyzes Massey products and fundamental group presentations, providing explicit presentations in non-Kähler cases.
result Explicit presentations of fundamental groups based on first Betti numbers, vanishing Massey products beyond certain lengths.
Proves small cancellation free products have geometric actions on CAT(0) cube complexes.
problem Proving small cancellation free products have geometric actions on CAT(0) cube complexes.
method Using a blown-up complex of groups and a boundary separation criterion, proving wall stabilizers form a rich family of subgroups.
result Proves $C'( rac16)$--small cancellation free products of residually finite groups are residually finite.
We give several equivalent characterizations of orthogonal subbundles of the generalized tangent bundle defined, up to B-field transform, by almost product and local product structures. We also introduce a pure spinor formalism for generalized CRF-structure and investigate the resulting decomposition of the de Rham ope…
We show that every graph product of finitely generated abelian groups acts properly and cocompactly on a CAT(0) cubical complex. The complex generalizes (up to subdivision) the Salvetti complex of a right-angled Artin group and the Coxeter complex of a right-angled Coxeter group. In the right-angled Artin group case it…
The paper computes non-trivial triple Massey products on specific non-Kähler solvmanifolds.
problem Computing non-trivial triple Massey products on non-Kähler solvmanifolds.
method Explicit computations on specific non-Kähler solvmanifolds.
result Non-Kähler solvmanifolds have non-vanishing triple ABC-Massey products. A new method reduces the complexity of tensor products from cubic to quadratic, improving both speed and accuracy.
problem Efficiently computing high-dimensional tensor products for polynomial kernels.
method Complex-to-Real (CtR) modification of sketches using complex random projections.
result Achieves state-of-the-art performance in accuracy and speed.
The paper studies Blaschke products, proving uniformization and non-degeneracy of pressure metrics.
problem Analytic aspects of Blaschke products and their moduli space.
method Definition of complex structure and proof of uniformization theorem.
result Pressure semi-norms are non-degenerate outside the super-attracting locus.
The Cartesian subgroup in graph products of groups is studied with bounds and algorithms.
problem Understanding the structure of Cartesian subgroups in graph products of groups.
method Theory of polyhedral products, lower and upper bounds, algorithm for small presentations.
result Bounds on the number of relations and deficiency in presentations of Cartesian groups.
We abstract Morimoto's construction of complex structures on product manifolds to pairs of certain generalized F-structures on manifolds that are not necessarily global products. As applications we characterize invariant generalized complex structures on product manifolds in which one factor is a Lie group and we gen…
Predicting the future evolution of complex systems is one of the main challenges in complexity science. Based on a current snapshot of a network, link prediction algorithms aim to predict its future evolution. We apply here link prediction algorithms to data on the international trade between countries. This data can b…
Painlevé analysis identifies integrable cases of Ricci solitons over specific warped products and line bundles.
problem Finding integrable cases of Ricci solitons over warped products and line bundles.
method Painlevé analysis applied to cohomogeneity one steady Ricci soliton equations for two classes of solitons: warped products and complex line bundles over a Fano Kähler Einstein base.
result Integrable cases identified for specific dimensions and configurations of Ricci solitons.
With globalization, countries are more connected than before by trading flows, which currently amount to at least 36 trillion dollars. Interestingly, approximately 30-60 percent of global exports consist of intermediate products. Therefore, the trade flow network of a particular product with high added values can be re…
Study smooth hypersurfaces in product Riemann surfaces, classifying them.
problem Classify smooth hypersurfaces in direct products of closed hyperbolic Riemann surfaces.
method Classify hypersurfaces in terms of their fundamental groups, answering Delzant and Gromov's questions.
result Provide constraints on Kähler groups.
Study entanglement in complex manifold sections.
problem Entanglement properties of complex manifold sections.
method Kähler quantization for ample line bundles.
result Characterized entanglement in tensor products of sections.
Defines tensor products for A-infinity structures using diagonals.
problem No specific problem stated; focuses on new definitions.
method Uses diagonals of associahedra and multiplihedra to define tensor products.
result Defines tensor products for various A-infinity structures.
Defines a new free product for coarse spaces.
problem No specific problem stated; focuses on a new mathematical concept.
method Defines and analyzes free products for coarse spaces.
result Free products preserve coarse properties and have a dimension bound.