We find a splitting in a special cohomology theory for complex manifolds.
problem Finding a splitting in a specific cohomology theory.
method Construct Hodge filtered function spaces and show they satisfy an unstable splitting.
result Obtain an analog of Quillen's theorem for Hodge filtered Brown-Peterson cohomology.
The paper determines modular cohomotopy groups up to extensions using classical and unstable homotopy methods.
problem Determining modular cohomotopy groups up to extensions.
method Classical methods of primary cohomology operations and unstable homotopy theory of Moore spaces.
result Determines modular cohomotopy groups up to extensions and specific groups like π3(X;Z(2)). Study crystallographic groups for positive scalar curvature conditions.
problem Examining positive and negative results for Gromov-Lawson-Rosenberg Conjecture.
method Analyzing split extensions of free abelian by cyclic groups.
result Produce infinite counterexamples for the Gromov-Lawson-Rosenberg Conjecture.
Let f be the gluing map of a Heegaard splitting of a 3-manifold W. The goal of this paper is to determine the information about W contained in the image of f under the symplectic representation of the mapping class group. We prove three main results. First, we show that the first homology group of the three man…
Survival trees exhibit end-cut preference, leading to biased splits.
problem End-cut preference in survival trees causes biased splits and poor interpretability.
method Proposed a smooth sigmoid surrogate (SSS) approach to replace hard-threshold indicator function.
result Smooth sigmoid surrogate (SSS) effectively mitigates end-cut preference in survival trees.
New minimal surface theory disproves a conjecture in symmetric spaces.
problem Proving the existence of unstable minimal maps in symmetric spaces.
method Using Hitchin representations and equivariant maps, with a new index bound.
result Disproves the Labourie conjecture for PSL(n,R) with n≥4. J Hempel [Topology, 2001] showed that the set of distances of the Heegaard splittings (S,V, h^n(V)) is unbounded, as long as the stable and unstable laminations of h avoid the closure of V in PML(S). Here h is a pseudo-Anosov homeomorphism of a surface S while V is the set of isotopy classes of simple closed curves in …
Anosov diffeomorphisms with integrable subbundles have coherent dynamics and spectral rigidity.
problem Characterizing Anosov diffeomorphisms with integrable subbundles.
method Joint integrability of strong stable and unstable subbundles leads to coherent dynamics and spectral rigidity.
result Anosov diffeomorphisms with integrable subbundles are dynamically coherent and have spectral rigidity.
Minimal Heegaard surfaces are shown to have index 1 for generic metrics.
problem Existence and properties of minimal Heegaard surfaces in 3-manifolds.
method Generic metrics and min-max procedure for 3-spheres, strongly irreducible Heegaard sweepouts for 3-manifolds.
result Strongly irreducible Heegaard splittings can be isotoped to minimal surfaces of index at most 1 or one-sided minimal Heegaard surfaces.
The paper is devoted to finding conditions to the existence of a self-indexing energy function for Morse-Smale diffeomorphisms on a 3-manifold. These conditions involve how the stable and unstable manifolds of saddle points are embedded in the ambient manifold. We also show that the existence of a self-indexing energy …
We prove the existence of extremal, non-csc, Kähler metrics on certain unstable projectivised vector bundles ¶(E)→M over a cscK-manifold M with discrete holomorphic automorphism group, in certain adiabatic Kähler classes. In particular, the vector bundles E→M under consideration are assumed to split as a …
We investigate certain natural connections between subriemannian geometry and hyperbolic dynamical systems. In particular, we study dynamically defined horizontal distributions which split into two integrable ones and ask: how is the energy of a subriemannian geodesic shared between its projections onto the integrable …
Unstable minimal surfaces are the unstable stationary points of the Dirichlet-Integral. In order to obtain unstable solutions, the method of the gradient flow together with the minimax-principle is generally used. The application of this method for minimal surfaces in the Euclidean spacce was presented in \cite{s3}. We…
Ricci flow simulations show unstable Fubini-Study metrics develop singularities.
problem Understanding the behavior of unstable perturbations in Ricci flow.
method Numerical simulations of Ricci flow starting from unstable Fubini-Study metrics.
result Ricci flow solutions from unstable Fubini-Study metrics develop local singularities.
Study finds limits for conical Kähler-Einstein metrics on unstable surfaces.
problem Optimal upper bounds for conical Kähler-Einstein metrics on K-unstable del Pezzo surfaces.
method Established optimal upper bounds for cone angles of Kähler-Einstein metrics with conical singularities.
result Optimal upper bounds for conical Kähler-Einstein metrics on K-unstable del Pezzo surfaces.
Noncompact Ricci-flat solutions have infinite unstable dimensions.
problem Understanding unstable dimensions of noncompact Ricci-flat solutions.
method Derived sufficient conditions for infinite-dimensional unstable manifolds.
result Noncompact Ricci-flat solutions have uncountably many unstable perturbations.
Bi-invariant Einstein metric on G2 unstable under Ricci flow.
problem Stability of bi-invariant Einstein metrics on Lie groups under Ricci flow.
method Analysis of the bi-invariant Einstein metric on G2 using Ricci flow. result The bi-invariant Einstein metric on G2 is dynamically unstable. A class of groups is investigated, each of which has a fairly simple presentation . For example the group R=(a,b,c,d∣a3=b3=c3=d3=1,ba−1=dc−1,ca−1=db−1) is in the class. Such a group does not have as a homomorphic image any group which is a 2-orbifold group or which is a group of i…
Argentum is a crypto coin for saving and investment in unstable countries.
problem Stable purchasing power for savings in unstable economies.
method Designing a crypto coin backed by investment instruments.
result Provides a stabilization instrument for savings in unstable economies.
New loss function helps learn unstable dynamical systems.
problem Gradient descent fails to learn unstable dynamical systems.
method Introduced a time-weighted logarithmic loss function.
result Time-weighted loss function effectively learns unstable systems.
Unstable minimal surfaces in n-space link to hyperbolic products.
problem Characterizing unstable minimal surfaces in Rn and their product counterparts. method Lifting to R-trees, deforming to hyperbolic products, and proving instability equivalence. result Unstable minimal surfaces in Rn imply unstable surfaces in product hyperbolic spaces. Segre varieties' hyperplane sections are unstable under certain conditions.
problem Stability of hyperplane sections of Segre varieties under different conditions.
method Proving instability with respect to any polarization for non-smooth or meqn cases. result Normal hyperplane sections of Segre varieties are K-unstable under specified conditions.
A faster method for estimating effects in large data using fixed-point trees.
problem Estimating heterogeneous effects in large dimensions with computational efficiency.
method Fixed-point approximation to eliminate Jacobian estimation and speed up GRFs.
result Significant computational efficiency improvement without sacrificing statistical accuracy.
Nearly Kähler 6-manifolds are unstable under Ricci flow.
problem Stability of nearly Kähler 6-manifolds under Ricci flow.
method Analysis of Betti numbers and entropy of Perelman.
result Strict nearly Kähler 6-manifolds are dynamically unstable.
Existence of unstable shrinking solutions in fractional mean curvature flow.
problem Existence and stability of self-shrinkers in fractional mean curvature flow.
method Existence proof of homothetically shrinking solutions with prescribed boundary conditions.
result Unstable shrinking solutions, except the ball, for fractional mean curvature flow.
Proves transitivity of real Anosov diffeomorphisms with specific properties.
problem Transitivity of real Anosov diffeomorphisms with specific properties.
method Proves transitivity using specific properties of real Anosov diffeomorphisms.
result Proves transitivity of real Anosov diffeomorphisms.
Study shows instability of specific cone solutions in high-dimensional spaces.
problem Unstable solutions of minimal graphs in high codimension.
method Min-max technique applied to Euclidean spaces.
result First examples of non-smooth unstable minimal graphs.
Algorithm identifies and transfers unstable features to create robust classifiers.
problem Developing unbiased classifiers from input-label pairs alone.
method Contrast different data environments in source tasks to encode unstable features, then cluster target task data and minimize worst-case risk.
result Our method maintains robustness across synthetic and real-world environments.
New algorithm learns unstable, partially observable systems.
problem Learning in unstable and partially observable Gaussian Process State-Space Models.
method Structured variational inference with efficient forward-backward pass and modified conditioning step.
result Good test performance in stable and unstable real systems with hidden states.
Survey of computations for Riemann surface moduli spaces, focusing on unstable homology.
problem Computing unstable homology of moduli spaces of Riemann surfaces.
method Integral, mod-2, and rational coefficient computations; use of homology operations.
result Explicit generators of unstable homology for most cases determined.
SFB uses stable features to adapt unstable ones for better performance.
problem Improving classifier performance on out-of-distribution data by leveraging stable features.
method SFB learns a predictor that separates stable and unstable features, then adapts unstable predictions using stable predictions.
result SFB can learn an asymptotically-optimal predictor without test-domain labels.
Constructs a family to handle unstable fibers on complex surfaces.
problem Handling unstable fibers on complex surfaces.
method Uses Teichmüller theory to construct a degenerating family over the moduli space.
result Any fibered complex surface with unstable fibers can be pulled back from the constructed family.
A stable approach to eigendecomposition for deep learning networks.
problem Numerical instability in backpropagation of eigendecomposition results.
method A numerically stable and differentiable approach to eigendecomposition.
result Better robustness of the new approach over standard methods for ZCA whitening and PCA denoising.
For a symmetric Hamiltonian system, lower bounds for the number of relative equilibria surrounding stable and formally unstable relative equilibria on nearby energy levels are given.
We study the structure of the smooth manifold which is defined as the intersection of a stable manifold and an unstable manifold for an invariant Morse-Smale function.
In this paper, we introduce a non linear ODE method to construct CMC surfaces in Riemannian manifolds with symmetry. As an application we construct unstable CMC spheres and outlying CMC spheres in asymptotically Schwarzschild manifolds with metrics like gij=(1+l1)2δij+O(l−2). The existence of uns…
Decoding, ie prediction from brain images or signals, calls for empirical evaluation of its predictive power. Such evaluation is achieved via cross-validation, a method also used to tune decoders' hyper-parameters. This paper is a review on cross-validation procedures for decoding in neuroimaging. It includes a didacti…
New proof associates partitions to isotopic pseudo-Anosov homeomorphisms.
problem Stable and unstable foliations for pseudo-Anosov homeomorphisms.
method Geometric realization of Fathi's result for isotopic homeomorphisms.
result Associated stable and unstable partitions for isotopic pseudo-Anosov homeomorphisms.
We show that the pair (X,−KX) is K-unstable for a del Pezzo manifold X of degree five with dimension four or five. This disprove a conjecture of Odaka and Okada.
In this paper we conjecture the stability and vanishing of a large piece of the unstable rational cohomology of SL_n Z, of mapping class groups, and of Aut(F_n).
The paper proves regularity of states on manifolds with unstable dynamics.
problem Propagation of regularity in dynamical systems with unstable manifolds.
method Leafwise semiclassical pseudodifferential calculus adapted to foliated spaces.
result Pollicott-Ruelle resonant states are smooth over entire manifolds if smooth on unstable leaves.
We give examples of smooth surfaces with negative first Chern class which are slope unstable with respect to certain polarisations, and so have Kahler classes that do not admit any constant scalar curvature Kahler metrics. We also compare this to the work of Song-Weinkove on the J-flow.
Node2vec embeddings are unstable and unstable with parameter choices.
problem Stability and robustness of node2vec embeddings for graph classification.
method Analysis of node2vec embeddings from multiple perspectives.
result Node2vec embeddings are unstable with respect to parameter choices.
DAGgr aggregates multiple DAGs to stabilize causal structure learning.
problem Stability in learning causal structure from data.
method Model averaging of candidate DAGs weighted by predictive likelihood, with acyclicity enforced.
result DAGgr consistently outperforms individual DAGs and bootstrap-aggregation baselines.
The paper shows measures equidistribute on affine submanifolds with a rate.
problem Understanding equidistribution of measures on affine invariant submanifolds.
method Analyzing unstable foliations and using results from homogeneous dynamics.
result Measures of large dimension equidistribute on affine invariant submanifolds with an effective rate.
The paper explores maximal destabilizers for both K-stability and Chow-stability in unstable situations.
problem Exploring maximal destabilizers for K-stability and Chow-stability in unstable situations.
method Using non-Archimedean pluripotential theory and idealistic assumptions, the paper provides a route to show that maximal K-destabilizers are quantized by maximal Chow-destabilizers.
result Maximal K-destabilizers are quantized by maximal Chow-destabilizers.
Study finds Kähler-Einstein metrics on two Pasquier varieties.
problem Existence of Kähler-Einstein metrics on specific varieties.
method Analyzes Pasquier's two-orbits varieties to find metrics.
result New example of K-unstable Fano manifold with Picard number one.
Article examines stability of geodesic X-ray transforms and artifacts.
problem Stability of geodesic X-ray transforms and artifacts.
method Analyzes the impact of weight and geometry on stability, and examines artifacts in unstable cases.
result Landweber algorithm cannot provide accurate reconstruction in unstable cases.