Paper improves zero-shot protein stability prediction by clarifying free-energy foundations.
problem Improving zero-shot protein stability prediction using inverse folding models.
method Clarifying the free-energy foundations of inverse folding models and proposing better estimates of relative stability.
result Significant gains in zero-shot performance can be achieved with simple methods.
Paper proves zero stability for one-row colored sl₃-Jones polynomials.
problem Stability of coefficients in colored Jones polynomials.
method Linear skein theory based on Kuperberg's sl₃-webs.
result Zero stability for B-adequate links with anti-parallel twist regions.
Schoen-Yau's zero mass theorem stability remains an open question.
problem Geometric stability of Schoen-Yau's zero mass theorem.
method Review of geometric stability, examples, and convergence notions.
result Open question on geometric stability of Schoen-Yau's zero mass theorem.
Study on ρ-Einstein solitons with zero scalar curvature, proving stability and flatness.
problem Characterizing ρ-Einstein solitons with specific curvature properties. method Analyzing ρ-Einstein solitons conformal to pseudo-Euclidean spaces with invariant pseudo-orthogonal group. result Stability and flatness of ρ-Einstein solitons with zero scalar curvature. Study uses VIX for zero-coupon Treasury rates, proving long-term stability and returns.
problem Modeling zero-coupon Treasury rates with VIX for volatility.
method Multivariate autoregressive stochastic volatility model, proving stability and Law of Large Numbers.
result VIX accurately models zero-coupon Treasury rates and returns.
The paper proves a stability conjecture for manifolds with zero Euler characteristic.
problem Stability of manifolds with zero Euler characteristic under certain curvature conditions.
method Analyzes manifolds with dimensions 5 or more, proving stability under specific curvature and completeness conditions.
result 2006 Rosenberg's S1-stability holds for manifolds with zero Euler characteristic. Non-asphericity of strata of genus-one differentials
problem Strata of genus-one differentials
method Non-asphericity
result Infinitely many counterexamples to conjectures
Stabilizes complex systems using diffusion models trained on Lyapunov functions.
problem Generating stabilizing controllers for complex dynamical systems.
method Trains a diffusion model on pairs of asymptotically stable vector fields and their Lyapunov functions to identify the closest stable field and adjust control functions.
result Efficient and rapid stabilization of unseen systems, showcasing generalizability.
The paper studies tautological rings of strata of differentials, proving cohomological stability and no relations in specific degrees.
problem Understanding the structure of tautological rings of strata of differentials.
method Analyzing degrees of relations and cohomological stability for strata with different numbers of simple zeros.
result For strata with more than 4g/3 simple zeros, there are no relations in degrees less than ⌊g/3floor+1. We show that the existence of a Fredholm element of the zero calculus of pseudodifferential operators on a compact manifold with boundary with a given elliptic symbol is determined, up to stability, by the vanishing of the Atiyah-Bott obstruction. It follows that, up to small deformations and stability, the same symbol…
Stability of positive mass theorem for hyperbolic manifolds studied.
problem Stability of the positive mass theorem for asymptotically hyperbolic manifolds.
method Adapted intrinsic flat distance approach to show stability for a class of manifolds.
result Stability of the positive mass theorem for a class of asymptotically hyperbolic graphical manifolds.
New cyclicity measures defined in weighted Besov spaces, with stability and geometric analysis.
problem Characterizing cyclicity in weighted Besov spaces.
method Defining cyclicity indices based on potential theory and capacity, studying stability under perturbations, and linking zero set structure to cyclicity.
result Novel invariants and conditions for cyclicity in various function spaces.
Study on entropy stability in product spaces of negatively curved symmetric spaces.
problem Stability of minimal entropy rigidity in product spaces of negatively curved symmetric spaces.
method Analysis of minimal entropy sequences and proof of intrinsic uniqueness of spherical Plateau solutions.
result Entropy-minimizing sequences converge to the model space after removing subsets whose n-volume converges to zero.
Homology of abelian differentials stabilizes with more zeros.
problem Understanding the homology of abelian differentials with many simple zeros.
method Developed an h-principle for these strata, valid in a range of homological degrees.
result Homology stabilizes in a range where the number of simple zeros is large.
We introduce a norm on the space of test configurations, which we call the minimum norm. We conjecture that uniform K-stability with respect to this norm is equivalent to the existence of a constant scalar curvature Kähler metric. This notion of uniform K-stability is analogous to coercivity of the Mabuchi functional. …
The paper studies Yamabe metrics and stability in Riemannian manifolds.
problem Existence of complete Yamabe metrics with zero scalar curvature.
method Yamabe flow and local L1-stability analysis. result Local L1-stability of the Yamabe flow on manifolds with non-negative Ricci curvature. This paper proposes a new approach to describe the stability of linear time-invariant systems via the torsion τ(t) of the state trajectory. For a system r˙(t)=Ar(t) where A is invertible, we show that (1) if there exists a measurable set E1 with positive Lebesgue measure, such that r(0)∈E1 implies t…
Paper studies competitive networks where teams aim to minimize their own objectives, adapting to each other's strategies.
problem Competitive networks where teams have conflicting objectives.
method Proposes diffusion learning algorithms for two classes of network games: zero-sum and non-zero-sum.
result Stability performance of proposed algorithms analyzed and demonstrated through experiments.
This paper focuses on using the first curvature κ(t) of trajectory to describe the stability of linear time-invariant system. We extend the results for two and three-dimensional systems [Y. Wang, H. Sun, Y. Song et al., arXiv:1808.00290] to n-dimensional systems. We prove that for a system r˙(t)=Ar(t), (i) i…
The paper establishes a correspondence between Higgs torsors and connections on curves.
problem Establishing a correspondence between Higgs torsors and connections on curves.
method Introduced a stability condition on filtered Stokes local systems and used it to prove a one-to-one correspondence.
result One-to-one correspondence between stable meromorphic parahoric Higgs torsors and stable meromorphic parahoric connections.
In this paper we prove some results concerning stability of hypersurfaces in the four dimensional Euclidean space with zero scalar curvature. First we prove there is no complete stable hypersurface with zero scalar curvature, polynomial growth of integral of the mean curvature, and with the Gauss-Kronecker curvature bo…
The rigidity of the Positive Mass Theorem states that the only complete asymptotically flat manifold of nonnegative scalar curvature and zero mass is Euclidean space. We study the stability of this statement for spaces that can be realized as graphical hypersurfaces in Euclidean space. We prove (under certain technical…
In this paper, we study distribution of the zeros of the Alexander polynomials of knots and links in S^3. We call a knot or link "real stable" (resp. "circular stable") if all the zeros of its Alexander polynomial are real (resp. unit complex). We give a general construction of real stable and circular stable knots and…
The problem of resource allocation of nonlinear networked control systems is investigated, where, unlike the well discussed case of triggering for stability, the objective is optimal triggering. An approximate dynamic programming approach is developed for solving problems with fixed final times initially and then it is…
Study on stability of quaternion-Kähler manifolds using eigenvalue estimates.
problem Stability problem for positive quaternion-Kähler manifolds.
method Description of infinitesimal Einstein deformations and destabilising directions in terms of Laplace eigenfunctions and symmetric 2-tensors. Improved eigenvalue estimates for the Hodge-Laplacian on 2-forms.
result Sharp lower bound for the first non-zero eigenvalue on the parallel subbundle Sym^2 E of the 2-form bundle.
New stability conditions identified from quadratic differentials on surfaces.
problem Identifying stability conditions from quadratic differentials.
method Comparison of exchange graphs from tilting hearts and flipping mixed angulations.
result Spaces of stability conditions identified with moduli spaces of quadratic differentials.
We prove that a pair (X, D) with X Fano and D a smooth anti-canonical divisor is K-unstable for negative angles, and K-semistable for zero angle.
New method stabilizes deep neural networks by setting Lyapunov exponent to zero.
problem Stability issues in deep neural networks with low width.
method Lyapunov initialization method to set Lyapunov exponent to zero.
result Lyapunov exponent governs stability of deep networks; standard methods fail for low width.
Paper studies constrained control games with a novel approximation method.
problem Games with constrained control directions.
method Approximation procedure based on L1-stability estimates and almost sure convergence. result Existence of game's value and optimal strategy for the stopper.
Paper proves stability and Dirichlet problem for translating hypersurfaces.
problem Stability and Dirichlet problem for translating hypersurfaces.
method Analyzes translating solitons in en+k, proves stability conditions, and studies Dirichlet problem. result Proves the infimum of mean curvature is zero for translating solitons and conditions for stability.
The paper explores identifiability and stability in drifting fields using companion-elliptic kernels.
problem Identifying and stabilizing drifting fields in generative modeling.
method Introduces companion-elliptic kernel families and analyzes their properties to address identifiability and stability issues.
result Established field identifiability for arbitrary Borel probability measures and demonstrated that field convergence alone does not guarantee weak convergence.
We study a tower of normal coverings over a compact Kähler manifold with holomorphic line bundles. When the line bundle is sufficiently positive, we obtain an effective estimate, which implies the Bergman stability. As a consequence, we deduce the equidistribution for zero currents of random holomorphic sections. Furth…
Study shows boundedness of klt singularities in 3D or with bounded Kollár components.
problem Boundedness of klt singularities in algebraic geometry.
method Analysis of Kollár components and local volumes.
result Minimal log discrepancies of Kollár components are bounded in dimension 3.
On a 4-dimensional compact symplectic manifold, we consider a smooth family of compatible almost-complex structures such that at time zero the induced metric is Hermite-Einstein almost-Kähler metric with zero or negative Hermitian scalar curvature. We prove, under certain hypothesis, the existence of a smooth family of…
The paper connects moment maps to the stability of holomorphic fibrations.
problem Stability of holomorphic fibrations.
method Use of moment maps and K-stability criteria.
result Existence of optimal symplectic connections implies stability of fibrations.
We prove stability of solutions of the complex Monge-Ampère equation on compact Hermitian manifolds, when the right hand side varies in a bounded set in Lp,p>1 and it is bounded away from zero. Such solutions are shown to be Hölder continuous. As an application we extend a recent result of Székelyhidi and Tosatti o…
Define the 1-handle stabilization distance between two surfaces properly embedded in a fixed 4-dimensional manifold to be the minimal number of 1-handle stabilizations necessary for the surfaces to become ambiently isotopic. For every nonnegative integer m we find a pair of 2-knots in the 4-sphere whose stabilization…
The paper calculates asymptotic Betti numbers and homology multiplicities for graph configuration spaces.
problem Understanding the homology of ordered configuration spaces of graphs.
method Explicit formulas for asymptotic Betti numbers and homology multiplicities in characteristic zero.
result Explicit formulas for asymptotic multiplicities in homology of irreducible representations of the symmetric group.
Strong stability of ergodic iterations proven without ergodic driving sequence.
problem Ensuring strong stability of ergodic iterations under non-ergodic driving sequences.
method Revisiting processes driven by stationary ergodic sequences, proving strong stability under mild conditions on recursive maps.
result Strong stability of iterations proven without ergodic driving sequence.
Unified approach to stability conditions on surfaces with quadratic differentials.
problem Identifying spaces of stability conditions on triangulated categories.
method Perverse schober and their global sections, mixed-angulations, flips, finite-length hearts, tilts.
result Identification of moduli spaces of quadratic differentials with arbitrary singularity types.
Adapts Stein's method for geometric inequalities, addressing boundary terms.
problem Geometric inequalities and their stability under constraints.
method Uses elliptic PDE with oblique boundary condition to handle boundary terms.
result Stability results for various geometric inequalities with respect to a new distance.
We introduce a technique for proving quantitative representation stability theorems for sequences of representations of certain finite linear groups over a field of characteristic zero. In particular, we prove a vanishing result for higher syzygies of VIC- and SI-modules, which can be thought of as a weaker version of …
This work analyzes the stability of graph filters under large perturbations.
problem Stability of graph filters under large edge rewires.
method Proves a bound on stability using frequency response and community structure.
result Graph filter stability depends on perturbation to community structure.
We prove the linear stability of Schwarzschild-Tangherlini spacetimes and their Anti-de Sitter counterparts under Ricci flow for a special class of perturbations. This is useful in the choice of suitable initial conditions in numerical Ricci-flow-based algorithms for obtaining new solutions to the Einstein equation whe…
We consider the geometric inverse problem of determining a closed Riemannian manifold from measurements of the heat kernel in an open subset of the manifold. In this paper we analyze the stability of this problem in the class of n-dimensional Riemannian manifolds with bounded diameter and sectional curvature. It is w…
The paper proves quaternion projective space is unstable.
problem Stability of quaternion projective space.
method Analyzing index of identity map on quaternion space forms.
result Quaternion projective space is unstable.
The paper constructs solutions to the Allen-Cahn equation using special minimal hypersurfaces.
problem Constructing solutions to the Allen-Cahn equation with specific properties.
method Using special minimal hypersurfaces asymptotic to a Lawson cone.
result Constructs solutions to the Allen-Cahn equation with infinite Morse index.
Study finite group actions on manifolds with non-zero degree maps to nilmanifolds.
problem Understanding finite group actions on manifolds with specific properties.
method Analyzes effective actions, bounds discrete degrees, studies toral rank conjecture, and introduces iterated actions.
result Proves Homeo(M) is Jordan and bounds the discrete degree of symmetry.