We study the intrinsic geometrical structure of hypersurfaces in 6-manifolds carrying a balanced Hermitian SU(3)-structure, which we call {\em balanced} SU(2)-{\em structures}. We provide conditions which imply that such a 5-manifold can be isometrically embedded as a hypersurface in a manifold with a balanced SU(3)-st…
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Study on balanced Hermitian structures on Lie algebras twisted by representations.
problem Conditions for balanced and locally conformally balanced Hermitian structures on Lie algebras.
method Analysis of Hermitian structures on twisted cartesian products of Lie algebras.
result Classification of six-dimensional balanced Hermitian twisted cartesian products Lie algebras.
Study balanced Hermitian structures on almost abelian Lie algebras, classifying six-dimensional cases.
problem Classify balanced Hermitian structures on almost abelian Lie algebras.
method Classify six-dimensional almost abelian Lie algebras with balanced structures, investigate flow of balanced metrics and anomaly flow.
result Prove conjecture for compact almost abelian solvmanifolds with left-invariant complex structures.
Paper proves non-existence of certain balanced metrics on six-manifolds.
problem Existence of balanced metrics on six-manifolds with specific properties.
method Analysis of cohomogeneity one actions and properties of balanced structures.
result Non-existence of balanced non-Kähler SU(3)-structures on six-manifolds.
Study on existence of -Kähler structures on nilmanifolds with nilpotent complex structures.
problem Existence of -Kähler structures on nilmanifolds with nilpotent complex structures.
method Determine optimal for existence of -Kähler structures and analyze the relationship between balanced metrics and degeneracy steps of the Frölicher spectral sequence.
result No -Kähler structures exist for an optimal on nilmanifolds with nilpotent complex structures.
Characterizes metrics on Lie groups, proving non-simultaneous existence of balanced and pluriclosed metrics.
problem Existence of balanced and pluriclosed metrics on real semisimple Lie groups.
method Characterization using Vogan diagrams and revisiting complex structure classification.
result Complex manifolds cannot simultaneously admit balanced and pluriclosed metrics.
Study non-Kähler metrics on complex nilmanifolds, proving torus structure under certain conditions.
problem Understanding special non-Kähler metrics on complex nilmanifolds.
method Analyzing locally conformally Kähler, -Gauduchon, balanced, and locally conformally balanced metrics on compact complex manifolds.
result Compact complex nilmanifolds with balanced or -Gauduchon metrics are tori, extending previous results.
On balanced HKT manifoldsmath.DG
Proves openness of balanced HKT cone and studies hyperholomorphic vector fields.
problem Understanding balanced HKT structures on compact hypercomplex manifolds.
method Analyzes Lie algebra of hyperholomorphic vector fields and proves harmonicity properties.
result Proves openness of balanced HKT cone and non-existence of certain fields.
Balanced metrics found on Lie groups and their quotients.
problem Existence of balanced metrics on Lie groups and quotients.
method Proved existence of invariant complex structures and Hermitian balanced metrics on Lie groups and quotients.
result Existence of balanced metrics on Lie groups and quotients, and no pluriclosed metrics.
Study on existence of balanced metrics on non-Kähler manifolds.
problem Existence of balanced metrics on non-Kähler complex manifolds.
method Analyzes obstructions and constructs examples, focusing on compact quotients of Lie groups.
result Proves non-existence on certain non-Kähler complex parallelizable manifolds and solvmanifolds.
Study on -Kähler structures on fibrations and Lie groups.
problem Existence of -Kähler structures on complex manifolds.
method Investigation of quasi-regular fibrations and reductive Lie groups with invariant complex structures.
result Construction of non-regular complex structures on Lie algebras for .
The invariant balanced Hermitian geometry of nilmanifolds of dimension 6 is described. We prove that the holonomy group of the associated Bismut connection reduces to a proper subgroup of SU(3) if and only if the complex structure is abelian. As an application we show that if J is abelian then any invariant balanced J-…
Proves conjecture about compatible SKT and balanced metrics on compact solvmanifolds.
problem Compact complex manifolds with both SKT and balanced metrics.
method Shear construction and classification of two-step solvable Lie algebras.
result Proves conjecture for compact two-step solvmanifolds with invariant complex structures.
The paper explores SKT, balanced, and generalized Kähler structures on specific Lie groups.
problem Investigating invariant SKT, balanced, and generalized Kähler structures on compact quotients of almost nilpotent Lie groups.
method Characterization and classification of Hermitian almost nilpotent Lie algebras, study of structures under flows, and non-existence results.
result Construction of new compact SKT manifolds and examples of non-split generalized Kähler structures.
The paper finds conditions for smooth curves of balanced metrics in Hermitian non-Kähler settings.
problem Balanced metrics under deformations of complex structures.
method Necessary conditions for smooth curves of balanced metrics.
result Existence of smooth curves of balanced metrics starting from a fixed balanced metric.
Study constructs balanced datasets for seismic failure prediction.
problem Imbalanced datasets limit machine learning performance in seismic failure prediction.
method Framework with three steps: GMF identification, probability density estimation, and sample transformation.
result Framework improves machine learning performance in seismic failure mode prediction.
We introduce spin-harmonic structures, a class of geometric structures on Riemannian manifolds of low dimension which are defined by a harmonic unitary spinor. Such structures are related to SU(2) (dim=4,5), SU(3) (dim=6) and G_2 (dim=7) structures; in dimension 8, a spin-harmonic structure is equivalent to a balanced …
Study of Hermitian structures on toric suspensions of balanced manifolds.
problem Exploring Hermitian structures on specific types of manifolds.
method Analysis of toric suspensions of Calabi-Yau and hyperkähler manifolds under holomorphic automorphisms.
result Suspensions of hyperkähler manifolds do not admit certain Hermitian metrics.
This work improves structured prediction by learning the balance between signal and random noise.
problem Structured prediction with random perturbations.
method Learning the variance of randomized structured predictors to balance signal and noise.
result Learning the balance improves structured prediction effectiveness.
By use of a natural map introduced recently by the first and third authors from the space of pure-type complex differential forms on a complex manifold to the corresponding one on the small differentiable deformation of this manifold, we will give a power series proof for Kodaira-Spencer's local stability theorem of Kä…
Study of complex structures on specific solvmanifolds, proving existence and non-existence results.
problem Classification and properties of complex structures on six-dimensional solvmanifolds.
method Classification of Lie algebras, analysis of complex structures, study of Hermitian metrics.
result Determination of new balanced solvmanifolds and confirmation of conjectures.
Study locally conformally balanced metrics on specific Lie algebras.
problem Characterize and classify locally conformally balanced metrics on almost abelian Lie algebras.
method Characterizations and classifications based on specific properties of Lie algebras.
result Classification of six-dimensional almost abelian Lie algebras with locally conformally balanced metrics.
Study on special metrics on complex nilmanifolds, proving existence and properties.
problem Existence and properties of special metrics on complex nilmanifolds.
method Analysis of astheno-Kähler, strongly Gauduchon, and balanced metrics.
result Existence of astheno-Kähler metrics implies specific properties of nilmanifolds.
We determine the 6-dimensional solvmanifolds admitting an invariant complex structure with holomorphically trivial canonical bundle. Such complex structures are classified up to isomorphism, and the existence of strong Kähler with torsion (SKT), generalized Gauduchon, balanced and strongly Gauduchon metrics is studied.…
Classifies complex structures on SL(2,C), finding new non-regular ones.
problem Classifying complex structures on SL(2,C) up to automorphisms.
method Classification via Lie group automorphisms and topological analysis.
result Found one new, non-regular complex structure.
Characterizes almost abelian Lie algebras with integrable complex structure
problem Classifying almost abelian Lie algebras
method Using presentations consisting of a real number, an element in a vector space, and an endomorphism
result Classifies -Kähler, -pluriclosed, Kähler, balanced, pluriclosed, and Gauduchon metrics
Signed Network Embedding with Application to Simultaneous Detection of Communities and Anomaliescs.SI
Unified model for signed networks separates balance and anomaly effects.
problem Ignoring sign information in signed networks leads to inaccurate analysis.
method Low rank plus sparse matrix decomposition with regularized formulation.
result The model accurately detects communities and anomalies in signed networks.
A hypercomplex structure on a differentiable manifold consists of three integrable almost complex structures that satisfy quaternionic relations. If, in addition, there exists a metric on the manifold which is Hermitian with respect to the three structures, and such that the corresponding Hermitian forms are closed, th…
Study shows compact Vaisman manifolds cannot have certain special Hermitian metrics.
problem Compact Vaisman manifolds and their compatibility with special Hermitian structures.
method Proof of non-existence of specific Hermitian metrics on compact Vaisman manifolds.
result Compact Vaisman manifolds cannot admit special Hermitian metrics like special -Gauduchon metrics or pluriclosed metrics.
In this work we apply the Poincare-Cartan formalism of the Classical Field Theory to study the systems of balance equations (balance systems). We introduce the partial k-jet bundles of the configurational bundle and study their basic properties: partial Cartan structure, prolongation of vector fields, etc. A constituti…
We study the existence of three classes of Hermitian metrics on certain types of compact complex manifolds. More precisely, we consider balanced, SKT and astheno-Kähler metrics. We prove that the twistor spaces of compact hyperkähler and negative quaternionic-Kähler manifolds do not admit astheno-Kähler metrics. Then w…
Kronheimer and Mrowka defined invariants of balanced sutured manifolds using monopole and instanton Floer homology. Their invariants assign isomorphism classes of modules to balanced sutured manifolds. In this paper, we introduce refinements of these invariants which assign much richer algebraic objects called projecti…
Proposes a balanced multi-component and multi-layer neural network for efficient function approximation.
problem Accurately and efficiently approximating complex functions with high degrees of freedom and computational cost.
method Inspired by a multi-component approach, MMNN combines single-layer networks with a multi-layer decomposition strategy.
result Significant reduction in training parameters, more efficient training process, and improved accuracy compared to FCNNs or MLPs.
New Ricci flow method for directed graphs with balancing factor.
problem Analyzing asymmetry in directed networks.
method Rigorous formulation of Ricci flow on directed weighted graphs with balancing factor.
result Existence and uniqueness of discrete Ricci flow solutions.
We prove a general criterion to establish existence and uniqueness of a short-time solution to an evolution equation involving "closed" sections of a vector bundle, generalizing a method used recently by Bryant and Xu for studying the Laplacian flow in G_2-geometry. We apply this theorem in balanced geometry introducin…
Global balance index measures systemic risk in financial networks.
problem Measuring systemic risk in financial networks.
method Defined global balance index based on a diffusive process and linear system.
result Global balance index correlates with systemic risk measures.
Study reveals structural differences in financial networks near and far from crises using balance theory.
problem Understanding the complex behavior of stocks and their collective behavior in financial crises.
method Investigates financial networks by triplet interaction in the framework of balance theory, focusing on higher-order interactions.
result Formation of an ordered structure in crisis networks makes them resistant to disorder, with a critical temperature measuring crisis strength.
Let be a -dimensional unimodular Lie algebra equipped with a Hermitian structure such that the complex structure is abelian and the fundamental form is balanced. We prove that the holonomy group of the associated Bismut connection reduces to a subgroup of , being the dim…
CUBE explains models by balanced experiments and contrasts.
problem Post-hoc explanation of trained predictive models.
method Design-based framework using balanced low-high probes.
result Reveals dominant learned effect structure and clarifies query efficiency.
New complex non-Kähler manifolds with specific properties are constructed.
problem Constructing complex non-Kähler manifolds with special properties.
method Using families of compact solvmanifolds and properties of the -Lemma.
result Provided families of compact -dimensional complex non-Kähler manifolds with specific properties.
Study geodesic equation on mixed-volume forms on balanced manifolds, proving existence of solutions.
problem Existence of solutions to the Calabi-Yau equation for balanced metrics.
method Introduced a metric space of mixed-volume forms and derived a geodesic equation.
result Existence of solutions to the Calabi-Yau equation on all balanced manifolds.
New method predicts graph structure changes over time.
problem Existing graph prediction methods assume static vertices, limiting their applicability.
method Combines time series prediction with adapted FBA for growing graphs.
result Efficacy demonstrated on synthetic and real datasets.
Symmetric Positive Definite (SPD) matrices have been used in many fields of medical data analysis. Many Riemannian metrics have been defined on this manifold but the choice of the Riemannian structure lacks a set of principles that could lead one to choose properly the metric. This drives us to introduce the principle …
This paper shows how we can build a model for transactions when goods are given away in the expectation of a later settlement. In settings where people keep track of their social accounts we are able to redefine concepts like account balance, yield curve and the law of diminishing returns. The model provides us with a …
We construct quantum invariants of balanced sutured 3-manifolds with a structure out of an involutive (possibly non-unimodular) Hopf superalgebra . If is the Borel subalgebra of , we show that our invariant is computed via Fox calculus and it is a normalization of Reidemeist…
New minimal surfaces derived from helicoids.
problem Existence of minimal surfaces with specific symmetries.
method Balance equations and nodal limit analysis.
result Existence of new screw motion invariant minimal surfaces.
Paper proposes a new model to prevent tariff wars by balancing trade balances.
problem Inequality in trade relations and tariff wars.
method Developed an algorithm to achieve zero trade balance for each country.
result Achieving zero trade balance prevents tariff wars and recession.
This review analyzes deep learning methods for electricity price forecasting across different markets.
problem Insufficient analysis of deep learning methods in electricity price forecasting.
method Unified taxonomy of deep learning components, analysis of trends across markets.
result Shift toward probabilistic, microstructure-centric, and market-aware designs.