By use of a natural extension map and a power series method, we obtain a local stability theorem for p-Kähler structures with the -th mild -lemma under small differentiable deformations.
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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…
Special Hermitian metricsmath.DG
Study on special Hermitian metrics and their stability.
problem Existence and stability of Hermitian metrics with specific properties.
method Analysis of Hermitian metrics with $∂ar{∂}ω^k=0$ for to .
result Stability of metrics at blow-up and deformations.
Proposes neural delay differential equations for stable system identification with partially observed states.
problem Learning stable models for systems with partial or delayed observations.
method Augments states with history, uses neural delay differential equations, and ensures stability through time delay analysis.
result The approach ensures stability of learned models for partially observed systems.
Study on scalar curvature deformations in pseudohermitian manifolds.
problem Deformation of scalar curvature in pseudohermitian manifolds.
method Analogy with Riemannian manifolds, introduction of -singular spaces, stability conditions, partial infinitesimal rigidity.
result Partial infinitesimal rigidity result for scalar curvature of compact pseudohermitian manifolds.
Study cohomologies of complex manifolds with symplectic forms and their stability.
problem Analyzing cohomologies of complex manifolds with symplectic forms.
method Investigate the Hard Lefschetz Condition on Dolbeault cohomology groups using a double complex.
result Stability of the -Lemma under small deformations of but not under complex structure.
In this note we define the stabilizer group of any adjoint-invariant -form on a complex simple Lie algebra. This result partially extend a previous result by Kable.
This paper advances sample-efficient learning for partially observable RL by introducing B-stability and new algorithms.
problem Hard sample complexity for learning near-optimal policies in partially observable RL.
method Proposes B-stability as a unified structural condition and develops new algorithms for sample-efficient learning.
result Any B-stable PSR can be learned with polynomial samples, improving over current best complexities.
New method stabilizes quantum ergodicity for mixed quantization and partial hyperbolicity.
problem Stabilizing quantum ergodicity for complex systems.
method Combines mixed quantization techniques with stable ergodicity results for partially hyperbolic systems.
result Establishes stable quantum ergodicity for spin Hamiltonians.
The paper examines the structure and stability of boundaries in noncollapsed RCD spaces.
problem Structuring and stability of boundaries in noncollapsed RCD spaces.
method Effective measure bounds and ε-regularity theorem.
result The boundary is homeomorphic to a manifold away from a set of codimension 2 and is rectifiable.
In this paper, we study compact convex Lefschetz fibrations on compact convex symplectic manifolds (i.e., Liouville domains) of dimension which are introduced by Seidel and later also studied by McLean. By a result of Akbulut-Arikan, the open book on , which we call \emph{convex open book}, induced b…
The paper computes torsion invariants for groups acting on complexes.
problem Computing torsion invariants for groups acting on complexes.
method Analyzes residually finite groups acting cocompactly on contractible complexes with specific stabilizers.
result Torsion limits to the torsion of the boundary subcomplex, independent of the chain of subgroups.
We describe partial semi-simplicial resolutions of moduli spaces of surfaces with tangential structure. This allows us to prove a homological stability theorem for these moduli spaces, which often improves the known stability ranges and give explicit stability ranges in many new cases. In each of these cases the stable…
In this paper, we shall prove that any Heegaard splitting of a -reducible 3-manifold , say , can be obtained by doing connected sums, boundary connected sums and self-boundary connected sums from Heegaard splittings of manifolds where is either a solid torus or a $…
The paper studies stability of discretized Anosov flows.
problem Global stability of discretized Anosov flows.
method Defined and proved equivalence with previous definitions, showed properties through openness and closedness, and established integrability and uniqueness of invariant foliations.
result Discretized Anosov flows are globally stable.
This paper deals with stability in the numerical solution of the prominent Heston partial differential equation from mathematical finance. We study the well-known central second-order finite difference discretization, which leads to large semi-discrete systems with non-normal matrices A. By employing the logarithmic sp…
Sharp stability of Alexandrov's theorem for domains in the small-excess regime
problem Stability of Alexandrov's theorem for domains in the small-excess regime
method Combines a version of Fuglede's spectral-gap argument, a star-shaped rearrangement for sets of finite perimeter, quantitative estimates for the part of the boundary contained in the tentacles, and a polyhedral approximation argument for the non-graphical region
result Sharp stability estimate in a genuinely non-parametric regime
New theorems on Hodge numbers and Kähler structures derived from complex differential forms.
problem Deformation invariance and local stability of Hodge numbers and Kähler structures.
method Using the exponential operator and power series method, the approach focuses on -closed extensions and foliated cases.
result Local stabilities of transversely -Kähler structures and new theorems on Hodge numbers.
Generalised Hermite-Einstein Fibre Metrics and Slope Stability for Holomorphic Vector Bundlesmath.AG
Extends classical stability results to new geometric settings.
problem Stability of holomorphic vector bundles on complex manifolds.
method Introduces -Hermite-Einstein and -stable conditions.
result Generalised Hermite-Einstein condition implies -semi-stability.
New method trains GFlowNets from partial episodes to improve convergence and stability.
problem Improving convergence and stability of GFlowNets training.
method Introducing SubTB() for GFlowNet training from partial action subsequences.
result SubTB() accelerates GFlowNet convergence and enables training in longer action sequences.
This review of the book "The Challenge of Financial Stability: A New Model and its Applications" by Goodhart C.A.E. and Tsomocos D.P. highlights the potential of the framework of strategic partial default of banks with credit chain on the interbank market for further theoretical and applied research on financial stabil…
Stability results for geometric equations in warped product spaces.
problem Geometric partial differential equations in warped product spaces.
method Stability theorem development for level sets of functions.
result Quantitative stability theorems for Serrin's problem and Alexandroff's theorem.
Stable solution found for manifold topology from boundary data.
problem Determining manifold properties from boundary data and eigenvalues.
method Quantitative stability estimates and unique continuation for the wave operator.
result Eigenvalues and boundary values determine a metric space close to the manifold.
Let denote a polarized toric Kähler manifold. Fix a toric submanifold and denote by the partial density function corresponding to the partial Bergman kernel projecting smooth sections of onto holomorphic sections of that vanish to order at least along…
Smooth actions on manifolds can be globally defined under certain conditions.
problem Globalizing partial smooth actions of Lie groupoids on smooth manifolds.
method Providing necessary and sufficient conditions for globalizability and analyzing orbit and stabilizer spaces.
result There exists a unique differentiable structure on the quotient space for free and proper actions.
The article recovers tensor fields from partial data using weighted divergent ray transforms.
problem Recovering tensor fields from partial data.
method Weighted divergent ray transforms, unique continuation property of fractional Laplacian, explicit reconstruction formulas.
result Recovery of symmetric -tensor fields and unique continuation for vector fields and symmetric 2-tensor fields.
Stability of non-abelian X-ray transform proven in higher dimensions.
problem Recovering matrix potentials from scattering data in higher dimensions.
method Injectivity proof using a novel method by Uhlmann-Vasy, with quantitative improvements.
result Hölder-type stability estimate established for non-abelian X-ray transform.
Algorithm identifies bilinear dynamical systems from noisy data.
problem Learning a realization of a partially observed bilinear dynamical system.
method Regression of outputs to highly correlated covariates for Markov-like parameters.
result High probability error bounds on identification algorithm under uniform stability assumption.
In this follow up work to [45, 33, 32, 46] we introduce and study a notion of geodesic stability restricted to rays with prescribed singularity types. A number of notions of interest fit into this framework, in particular algebraic- and transcendental K-polystability, equivariant K-polystability, and the geodesic K-pol…
We make a systematic study of the Hilbert-Mumford criterion for different notions of stability for polarised algebraic varieties ; in particular for K- and Chow stability. For each type of stability this leads to a concept of slope for varieties and their subschemes; if is semistable then $μ(Z)\leμ(X…
The outcome of a functional genomics pipeline is usually a partial list of genomic features, ranked by their relevance in modelling biological phenotype in terms of a classification or regression model. Due to resampling protocols or just within a meta-analysis comparison, instead of one list it is often the case that …
Central stability for the homology of congruence subgroups and the second homology of Torelli groupsmath.AT
We prove a representation stability result for the second homology groups of Torelli subgroups of mapping class groups and automorphism groups of free groups. This strengthens the results of Boldsen-Hauge Dollerup and Day-Putman. We also prove a new representation stability result for the homology of certain congruence…
Partially performative prediction studies how predictive models influence future data.
problem Distribution shift in predictive models due to endogenous and exogenous factors.
method Generalizing performative prediction to capture both endogenous and exogenous sources of distribution shift.
result Developed online analogues of performative stability and optimality for partially performative environments.
New method controls linear systems with partial info and disturbances.
problem Controlling linear dynamical systems under partial observation and adversarial disturbances.
method Double Spectral Control (DSC) using two-level spectral approximation strategy.
result Matches best known regret guarantees with exponential runtime improvement.
Proves stability of Minkowski space-time in Einstein-Yang-Mills system.
problem Stability of Minkowski space-time governed by Einstein-Yang-Mills system.
method Null frame decomposition, well-posedness of Cauchy development, convergence to Minkowski space-time.
result Exterior stability of Minkowski space-time in Lorenz gauge without spherical symmetry.
G. Tian and S.K. Donaldson formulated a conjecture relating GIT stability of a polarized algebraic variety to the existence of a Kahler metric of constant scalar curvature. In [Don02] Donaldson partially confirmed it in the case of projective toric varieties. In this paper we extend Donaldson's results and computations…
For a convex domain bounded by the hypersurface in a space of constant curvature we give sharp bounds on the width of a spherical shell with radii and that can enclose , provided that normal curvatures of are pinched by two positive constants. Furthermore, in the …
Constructs a moduli space for PDEs, linking stability to geometric metrics.
problem Moduli space construction for involutive ideal sheaves from PDEs.
method Introduces -Hilbert and -Quot functors, defines Spencer stability.
result Spencer poly-stability of PDE ideal implies Hermitian-Yang-Mills metric existence.
Neural DEs improve single image super-resolution.
problem Challenging tasks in image super-resolution.
method Applied Neural Differential Equations to image super-resolution, using variational methods and backpropagation.
result Differential models match state-of-the-art performance.
A lightweight framework improves convergence and stability of PINNs for complex PDEs.
problem Training instability and reduced accuracy in PINNs for complex PDEs.
method Adaptive curvature correction using secant information to optimize first-order optimizers.
result Consistent improvements in convergence speed, stability, and accuracy over standard optimizers.
We construct a simply-connected compact complex non-Kähler manifold satisfying the -Lemma, and endowed with a balanced metric. To this aim, we were initially aimed at investigating the stability of the property of satisfying the -Lemma under modifications of compact complex m…
Recently, Honda, Kazez and Matic described an adapted partial open book of a compact contact 3-manifold with convex boundary by generalizing the work of Giroux in the closed case. They also implicitly established a one-to-one correspondence between isomorphism classes of partial open book decompositions modulo positive…
It is well known that a countable group admits a left-invariant total order if and only if it acts faithfully on R by orientation preserving homeomorphisms. Such group actions are special cases of group actions on simply connected 1-manifolds, or equivalently, actions on oriented order trees. We characterize a class of…
Many conservative partial differential equations correspond to geodesic equations on groups of diffeomorphisms. Stability of their solutions can be studied by examining sectional curvature of these groups: negative curvature in all sections implies exponential growth of perturbations and hence suggests instability, whi…
Extends fractional uncertainty principles with extremizers and stability results.
problem Investigating uncertainty principles in fractional settings.
method Analyzing the fractional Schrödinger equation to find extremal functions and sharp constants.
result Proves stability of extremizers for fractional uncertainty inequalities.
We introduce -critical connections for holomorphic vector bundles and prove their existence under stability conditions.
problem Existence of -critical connections for holomorphic vector bundles.
method Associated geometric PDEs to Bridgeland stability conditions and used infinite dimensional moment maps.
result In the large volume limit, a sufficiently smooth holomorphic vector bundle admits a -critical connection if and only if it is asymptotically -stable.
In this paper, we introduce the notions of -Hermitian-symplectic and -pluriclosed compact complex manifolds as generalisations for an arbitrary positive integer not exceeding the complex dimension of the manifold of the standard notions of Hermitian-symplectic and SKT manifolds that correspond to the case $p=…
The limiting behavior of the normalized Kähler-Ricci flow for manifolds with positive first Chern class is examined under certain stability conditions. First, it is shown that if the Mabuchi K-energy is bounded from below, then the scalar curvature converges uniformly to a constant. Second, it is shown that if the Mabu…