Study systole of large genus minimal surfaces in positive Ricci curvature.
problem Understanding the systole of minimal surfaces in manifolds with positive Ricci curvature.
method Colding--Minicozzi lamination theory.
result Results on the systole of large genus minimal surfaces.
Constructs infinitely many examples of large manifolds with circle bundles of positive scalar curvature.
problem Existence of circle bundles over large manifolds with positive scalar curvature metrics.
method Symplectic geometry techniques.
result Infinitely many examples of macroscopically large manifolds with circle bundles of positive scalar curvature.
Shows large unknotting number for simple knots.
problem Finding minimum crossing changes for unknotting.
method Positive-to-negative crossing changes without increasing genus.
result Genus non-increasing totally positive unknotting number can be large.
Approximations to utility indifference prices are provided for a contingent claim in the large position size limit. Results are valid for general utility functions on the real line and semi-martingale models. It is shown that as the position size approaches infinity, the utility function's decay rate for large negative…
Study examines trading strategies against a disorderly liquidation of a large position.
problem Trading against a hedge fund's disorderly liquidation of a risky asset.
method Classified market participants into three types: fully informed, partially informed, and uninformed. Analyzed their optimal trading and wealth processes.
result Different types of investors have distinct optimal trading strategies and wealth processes.
We prove an obstruction at the level of rational cohomology in small degrees to the existence of positively curved metrics with large symmetry rank. The symmetry rank bound is logarithmic in the dimension of the manifold. As an application, we provide evidence for a generalized conjecture of Hopf that says that no symm…
The study finds constraints on scalar curvature using maps and potential theory.
problem Largeness constraints in scalar curvature geometry.
method Basic splitting results and potential theory on singular area minimizing hypersurfaces.
result Non-existence of positive scalar curvature metrics on enlargeable manifolds.
We give the first examples of rationally inessential but macroscopically large manifolds. Our manifolds are counterexamples to the Dranishnikov rationality conjecture. For some of them we prove that they do not admit a metric of positive scalar curvature, thus satisfy the Gromov positive scalar curvature conjecture. Fu…
The study finds large Betti numbers in minimal hypersurfaces with positive Ricci curvature.
problem Minimal hypersurfaces with large Betti numbers in manifolds with positive Ricci curvature.
method Constructing sequences of manifolds with embedded minimal hypersurfaces.
result Minimal hypersurfaces have unbounded first Betti numbers.
We study the spectrum of complete noncompact manifolds with bounded curvature and positive injectivity radius. We give general conditions which imply that their essential spectrum has an arbitrarily large finite number of gaps. In particular, for any noncompact covering of a compact manifold, there is a metric on the b…
Study manifolds with positive intermediate Ricci curvature and large symmetry rank.
problem Closed, simply connected manifolds with positive 2nd-intermediate Ricci curvature and large symmetry rank.
method New tools for studying isometric actions on closed manifolds with positive kth-intermediate Ricci curvature, including isotropy rank lemma, symmetry rank bound, and connectedness principle.
result Even dimensional manifolds with large symmetry rank must have trivial odd degree integral cohomology and are either spheres or complex projective spaces.
A large class of positive finite presentations of the braid groups is found and studied. It is shown that no presentations but known exceptions in this class have the property that equivalent braid words are also equivalent under positive relations.
Study k-positive surface group representations and their degenerations.
problem Understanding the behavior of surface group representations under degenerations.
method Introduced k-positive representations and studied their degenerations using a limit theorem for positively ratioed representations.
result Degenerations of k-positive representations can lead to limits that are at least (k-3)-positive and irreducible limits are (k-1)-positive.
The study finds infinitely many different geometries for odd-dimensional manifolds with positive Ricci curvature.
problem Finding different geometries for odd-dimensional manifolds with positive Ricci curvature.
method Examining closed manifolds in odd dimensions n≥5. result Large classes of manifolds admit infinitely many different geometries of positive Ricci curvature.
Manifolds admitting positive sectional curvature are conjectured to have rigid homotopical structure and, in particular, comparatively small Euler charateristics. In this article, we obtain upper bounds for the Euler characteristic of a positively curved Riemannian manifold that admits a large isometric torus action. W…
Paper proves MS convergence for radially symmetric kernels with large bandwidths.
problem Proving convergence of mean shift algorithm with radially symmetric kernels.
method Analyzes convergence of mean shift algorithm with radially symmetric, positive definite kernels.
result Guaranteed convergence for sufficiently large bandwidth in any dimension.
The paper defines and computes a knot complement invariant for simple links.
problem Defining and computing a knot complement invariant for simple links.
method Using the large color R-matrix to study the Gukov-Manolescu series.
result Presentation of strange identities for positive braid knots.
We examine homogeneous metrics on spheres and determine which ones have positive sectional curvature. The answer is subtle and surprisingly difficult to prove. In some cases we also determine their pinching constants. This completes the classification of all homogeneous metrics with positive curvature (apart from one s…
5 minimal tori found in 3-spheres with positive Ricci curvature.
problem Existence of at least 5 embedded minimal tori in 3-spheres with positive Ricci curvature.
method Combination of min-max theory and mean curvature flow heuristics.
result Confirms B. White's conjecture for positive Ricci curvature.
Let (M,g) be a complete 3-dimensional asymptotically flat manifold with everywhere positive scalar curvature. We prove that, given a compact subset K of M, all volume preserving stable constant mean curvature surfaces of sufficiently large area will avoid K. This complements the work of G. Huisken and S.-T. Yau and J. …
We study a functional on the boundary of a compact Riemannian 3-manifold of nonnegative scalar curvature. The functional arises as the second variation of the Wang-Yau quasi-local energy in general relativity. We prove that the functional is positive definite on large coordinate spheres, and more general on nearly roun…
Crowdsourced algorithms identify fake news on Twitter.
problem Identifying fake news on social media platforms.
method Evaluation of reputation algorithms on a large dataset of Twitter news.
result Simple crowdsourcing-based algorithms can identify a significant portion of fake news with low false positive rates.
New method to decompose 4-manifolds with positive scalar curvature.
problem Understanding and decomposing 4-manifolds with positive scalar curvature.
method 0 and 1-surgeries on topologically PSC 4-orbifolds.
result Every closed, oriented, topologically PSC 4-manifold can be obtained from a specific type of 4-orbifold.
Study shows how 3+1D cosmologies can evolve to de Sitter space under certain conditions.
problem Understanding the evolution of 3+1D cosmologies with specific symmetry constraints.
method Mean Curvature Flow methods applied to cosmologies with positive cosmological constant and specific symmetry groups.
result Asymptotically, 3+1D cosmologies evolve to de Sitter space under certain conditions.
We construct new examples of manifolds of positive Ricci curvature which, topologically, are vector bundles over compact manifolds of almost nonnegative Ricci curvature. In particular, we prove that if E is the total space of a vector bundle over a compact manifold of nonnegative Ricci curvature, then the product of E …
Study detects and explains positional bias in financial LLMs.
problem Positional bias in financial decision-making using LLMs.
method Unified framework and benchmark for detecting and quantifying bias in Qwen2.5 models.
result Positional bias is pervasive, scale-sensitive, and resurfaces under nuanced prompt designs.
Nonnegative Matrix Factorization (NMF) is a widely used technique in many applications such as face recognition, motion segmentation, etc. It approximates the nonnegative data in an original high dimensional space with a linear representation in a low dimensional space by using the product of two nonnegative matrices. …
Uniform RC-positivity results for direct image bundles.
problem Understanding the relation between rational connectedness and RC-positivity.
method Analyzing vector bundles and their direct images, using weak RC-positivity as a starting point.
result Uniform RC-positivity of direct image bundles under weak RC-positivity conditions.
Study shows foreign institutional investment increases liquidity commonality in large Australian stocks.
problem Impact of foreign institutional investment on liquidity commonality in Australian stocks.
method Cross-sectional and time-series analysis of Australian equity market data.
result Foreign institutional investment contributes to increased exposure of large stocks to unexpected liquidity events.
Minimal surfaces with negative curvature found in large spheres.
problem Existence of minimal surfaces with negative curvature in large dimensional spheres.
method Applied Song's strategy to closed Riemann surfaces with large automorphism groups, resulting in almost hyperbolic minimal surfaces.
result Existence of closed minimal surfaces with negative induced curvature in any sphere of large dimension.
Proves mass theorem for manifolds with arbitrary ends.
problem Proving the positive mass theorem for manifolds with various ends.
method Quantitative analysis of scalar curvature on manifolds with arbitrary ends.
result Proves the positive mass theorem for a wide class of manifolds.
This paper explores GNN functions on random graphs, highlighting the importance of node Positional Encodings.
problem Understanding the expressive power of GNNs on large random graphs.
method General convergence notions, input node features, and Positional Encodings (PEs).
result GNNs can converge to certain functions on large random graphs, emphasizing the role of PEs.
We extend Witten's spinor proof of the positive mass theorem to large classes of complete asymptotically flat non-spin manifolds, including all manifolds of dimension less than or equal to 11 and all manifolds of dimension less than 26 which admit a codimension 3 immersion in Euclidean space.
The paper proves conditions for vector bundles to be Kobayashi and Griffiths positive.
problem Conditions for vector bundles to be Kobayashi and Griffiths positive.
method Comparing the curvature of (detE∗)k and SkE for large k and using duality of convex Finsler metrics. result Conditions for vector bundles to be Kobayashi and Griffiths positive.
Copulas reveal strong positive dependencies in stock demand fluctuations due to volume imbalances.
problem Analyzing dependencies of stock demands using local volume fluctuations.
method Copula analysis of empirical data to model dependence structures.
result Large local fluctuations of signed traded volumes increase positive dependencies in demand but slightly lower negative ones.
We study utility indifference prices and optimal purchasing quantities for a contingent claim, in an incomplete semi-martingale market, in the presence of vanishing hedging errors and/or risk aversion. Assuming that the average indifference price converges to a well defined limit, we prove that optimally taken position…
Researchers found unique large stable spheres in specific 3D space.
problem Characterizing large stable spheres in specific types of 3D space.
method Unconditional characterization of spheres using Riemannian geometry.
result Global uniqueness of large stable spheres in asymptotically flat Riemannian three-manifolds.
In this paper, we develop a general study of contributions at infinity of Bochner-Weitzenböck-type formulas on asymptotically flat manifolds, inspired by Witten's proof of the positive mass theorem. As an application, we show that similar proofs can be obtained in a much more general setting as any choice of an irreduc…
STRING improves 2D and 3D position encodings for better performance.
problem Efficient and accurate position encoding for 2D and 3D applications.
method STRING extends Rotary Position Encodings with a unifying theoretical framework, maintaining translation invariance and low computational cost.
result STRING shows substantial gains in open-vocabulary object detection and robotics.
Leon Green obtained remarkable rigidity results for manifolds of positive scalar curvature with large conjugate radius and/or injectivity radius. Using Ck,α convergence techniques, we prove several differentiable stability and sphere theorem versions of these results and apply those also to the study of Einstein m…
Bayesian deep learning improves deep learning's capabilities across diverse settings.
problem Overlooked metrics, tasks, and data types in deep learning.
method Revisits strengths of Bayesian deep learning and addresses challenges.
result Bayesian deep learning can elevate deep learning's capabilities across diverse settings.
Study identifies prime strongly positive amphicheiral knots with double symmetry.
problem Characterizing prime strongly positive amphicheiral knots with specific symmetries.
method Examined knots up to 16 crossings, identified prime knots with double symmetry, and presented almost doubly symmetric diagrams.
result Found the first prime strongly positive amphicheiral knot not slice.
New links show arbitrarily large torsion in Khovanov cohomology.
problem Understanding large torsion in Khovanov cohomology.
method Constructing specific links with desired torsion.
result Found direct summands of arbitrarily large torsion in Khovanov cohomology.
Positive knots are minimal in a specific knot ordering.
problem Understanding the minimal structure of positive knots in a specific knot ordering.
method Analyzing ribbon concordance and using properties of rational Alexander modules.
result Positive knots are minimal in the ribbon concordance ordering.
The paper argues for prioritizing identifying structure over complex models for scientific discovery.
problem Underdetermination of mechanisms in high-dimensional data, leading to unreliable explanations.
method Proposes concrete standards for 'mechanistic ML' to avoid collapsing explanations.
result Large language models (LLMs) can collapse large equivalence classes of explanations, making it hard to distinguish between mechanisms.
New MCMC methods improve efficiency for large network inference.
problem Efficiency of Metropolis within Gibbs for large networks.
method Combination of split Hamiltonian Monte Carlo and Firefly Monte Carlo.
result New methods outperform Metropolis within Gibbs on synthetic and real networks.
The paper proves conditions for the existence of small Urysohn width hypersurfaces in manifolds with positive scalar curvature.
problem Conditions for the existence of small Urysohn width hypersurfaces in manifolds with positive scalar curvature.
method Adaptation of Guth's macroscopic version of the Schoen-Yau descent argument.
result A complete Riemannian manifold with positive macroscopic scalar curvature contains a non-nullhomologous hypersurface of small Urysohn width.
Positive paths connect diffeomorphisms on contact manifolds.
problem Defining and analyzing positivity in diffeomorphism groups of manifolds with contact structures.
method By examining paths of diffeomorphisms that are positively transverse to the contact distribution, showing flexibility and connecting diffeomorphisms.
result Any two diffeomorphisms on standard contact structure of R^(2n+1) can be connected by a positive path.