Order positions are key variables in algorithmic trading. This paper studies the limiting behavior of order positions and related queues in a limit order book. In addition to the fluid and diffusion limits for the processes, fluctuations of order positions and related queues around their fluid limits are analyzed. As a…
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48 results for “Position limits”
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.
Study shows limits of metrics with positive scalar curvature on spheres.
problem Non-negativity of scalar curvature is not preserved under certain limits.
method Examined metrics conformal to the round metric on for .
result Any conformal metric to the round metric on for can be a limit of metrics with positive scalar curvature.
Study on positive scalar curvature and its impact on Ricci limit spaces.
problem The influence of uniformly positive scalar curvature on Ricci limit spaces.
method Investigates uniformly positive scalar curvature on non-collapsed Ricci limit spaces.
result Proves a limit space splits at most n-2 lines or R-factors.
Describes geometry of positive configurations in limiting buildings.
problem Understanding positive representations and their limits in buildings.
method Uses positivity properties of Hitchin representations and Parreau's compactification.
result Explicitly describes the geometry of preferred apartments in limiting buildings.
Study of conformal limits for special opers in Lie groups.
problem Analyzing conformal limits in specific Lie groups.
method Investigates Gaiotto's conformal limit for -Hitchin equations.
result Identifies -positive opers as a new class of solutions.
Trading strategies are limited by position limits, leading to a finite number of unique strategies.
problem Limiting the number of long and short positions in trading strategies.
method Formulas and distributions derived for the number of unique trading strategies, transactions, and do-nothing actions.
result A discrete distribution of actions and their properties are presented.
We prove a central limit theorem for the components of the largest eigenvectors of the adjacency matrix of a finite-dimensional random dot product graph whose true latent positions are unknown. In particular, we follow the methodology outlined in \citet{sussman2012universally} to construct consistent estimates for the …
Solves asset allocation for investors with utility functions and limits.
problem Investor risk and utility with position limits.
method Analytical solution for piecewise-linear utility function with position limits.
result Simple functional form representing risk cost.
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…
Classifies Zariski closures of positive representations in Lie groups.
problem Classifying Zariski closures of positive representations in Lie groups.
method Classifies the Lie algebra of the Zariski closure of a discrete subgroup with specific properties.
result Obtains a new proof of Guichard's classification of Zariski closures of Hitchin representations.
New examples of manifolds with positive scalar curvature and infinitely many poles.
problem Constructing manifolds with positive scalar curvature and understanding their limits.
method Extending previous examples to create new sequences of manifolds.
result Found new examples of manifolds with infinitely many poles and positive scalar curvature.
Optimal diameter estimates for 3D spaces with non-negative Ricci curvature.
problem Estimating the diameter of 3D spaces with non-negative Ricci curvature.
method Proving positive scalar curvature passes to Ricci limit spaces of non-negative curvature.
result Optimal Bonnet-Myers upper bound for 3D spaces.
Develops methods to create manifolds with positive scalar curvature.
problem Creating sequences of manifolds with positive scalar curvature.
method Two new methods of constructing sequences of manifolds with positive scalar curvature.
result Examples of sequences of manifolds with positive scalar curvature converge to limit spaces with pulled regions.
Improved solver maintains positivity and accuracy across all time steps.
problem Linear second-order schemes for Fokker-Planck equation cannot preserve positivity.
method Flux-Corrected Diagonal Frog (FCDF) framework using nonlinear extension and iterative limiter.
result FCDF schemes are unconditionally positive across all time steps and maintain second-order accuracy.
In [5] Herzlich proved a new positive mass theorem for Riemannian 3-manifolds whose mean curvature of the boundary allows some positivity. In this paper we study what happens to the limit case of the theorem when, at a point of the boundary, the smallest positive eigenvalue of the Dirac operator of the boundar…
Study shows mass distribution of random holomorphic sections follows a central limit theorem.
problem Understanding mass distribution of random holomorphic sections.
method Proved a central limit theorem for mass distribution of random holomorphic sections associated with positive line bundles.
result Almost every sequence of random holomorphic sections exhibits quantum ergodicity.
The study sets limits on scalar curvature in positive curvature manifolds.
problem Bounding scalar curvature in positive curvature manifolds.
method Establishing inequalities for manifolds with positive scalar curvature and scalar curvature bounded from below.
result Established inequalities for manifolds with positive scalar curvature.
The paper proves that Kähler manifolds with positive holomorphic sectional curvature have a limited diameter.
problem Diameter rigidity of Kähler manifolds with positive holomorphic sectional curvature.
method Establishing diameter rigidity for Kähler manifolds with positive holomorphic sectional curvature.
result Kähler manifolds with positive holomorphic sectional curvature have a limited diameter.
We confirm a conjecture of Hamilton: On compact manifolds the normalized Ricci flow evolves metrics with positive curvature operators to limit metrics with constant curvature.
The paper shows how to create manifolds with no geodesics converging to a sphere.
problem Creating manifolds with specific geometric properties.
method Constructing a sequence of Riemannian manifolds converging to a unit sphere in intrinsic flat sense.
result The resulting limit space has no geodesics achieving distances between points.
The study examines exceptional sets for radial limits of superharmonic functions on curved manifolds.
problem Understanding exceptional sets for radial limits of superharmonic functions on curved manifolds.
method Analysis of radial geodesic rays, Poisson integrals, Green potentials, and Riesz decomposition.
result Sharp bounds on Hausdorff dimensions of exceptional sets for superharmonic functions.
Proves CM line bundle positivity for K-stable klt Fano varieties.
problem Proving ampleness of the CM line bundle for K-stable klt Fano varieties.
method Algebraic approach, including probability theory for limit computations.
result Proves semi-positivity and positivity statements for K-semi-stable and uniform K-stable cases.
The study of random positive 3-strand braids reveals patterns in the roots of their Alexander polynomials.
problem Investigating the roots of Alexander polynomials of random positive 3-strand braids.
method Experimental data analysis, conjectures refinement, and proof of results using tools like the signature function of links and Lyapunov exponent of the Burau representation.
result Generically, at least 69% of the roots of Alexander polynomials are on the unit circle, with a large root-free region near the origin.
New method combines DPW and Opening Nodes for positive curvature surfaces.
problem Constructing surfaces of positive constant mean curvature.
method Combining DPW method and Opening Nodes.
result Embedded surfaces with Delaunay ends constructed in Euclidean space.
Optimal volume limit found for Kähler manifolds with positive Ricci curvature.
problem Bounding the volume of Kähler manifolds with positive Ricci curvature.
method Using δ-invariants and Newton--Okounkov bodies.
result Derive the optimal volume upper bound and new characterization of the complex projective space.
Application of Machine Learning and Convex Limiting to Subgrid Flux Modeling in the Shallow-Water Equationsphysics.comp-ph
Combines machine learning and convex limiting for accurate subgrid flux modeling in shallow-water equations.
problem Accurate subgrid flux modeling in shallow-water equations.
method Machine learning and flux limiting for property-preserving subgrid scale modeling.
result The proposed method produces meaningful closures even in untrained scenarios.
We analyze the limit of the p-form Laplacian under a collapse, with bounded sectional curvature and bounded diameter, to a smooth limit space. As an application, we characterize when the p-form Laplacian has small positive eigenvalues in a collapsing sequence.
Paper studies Hausdorff dimension of limit sets for Kleinian groups.
problem Understanding Hausdorff dimension of limit sets for Kleinian groups.
method Constructs geometrically infinite Fuchsian groups and proves properties for finitely generated groups.
result Hausdorff dimension of nonconical limit set equals zero for some groups.
Two types of nonidentifiability in latent position graphs identified and characterized.
problem Identifying and characterizing nonidentifiability in latent position random graph models.
method Defined and examined subspace nonidentifiability and model-based nonidentifiability, providing examples and characterizing limits.
result Characterized the limits of model-based nonidentifiability and obtained additional limiting results for specific graph models.
Solves Lempert's question on Nakano semi-positivity preservation.
problem Preserving Nakano semi-positivity under limits of metrics.
method Establishes extension theorem and uses multiplier submodule sheaves.
result Affirmative solution to Lempert's question on Nakano semi-positivity.
A Compactness Theorem for Rotationally Symmetric Riemannian Manifolds with Positive Scalar Curvaturemath.DG
Proves conjecture for symmetric manifolds with positive scalar curvature.
problem Compactness theorem for symmetric Riemannian manifolds with positive scalar curvature.
method Proves conjecture for sequences of rotationally symmetric warped product manifolds.
result Limit spaces have nonnegative scalar curvature and Euclidean tangent cones almost everywhere.
Survey of nonnegative scalar curvature sequences and their limits.
problem Understanding sequences of manifolds with nonnegative scalar curvature.
method Analyzing sequences of manifolds with nonnegative scalar curvature and proving convergence.
result Proved the GH and SWIF convergence of an extreme example.
New method learns from either positive or negative feedback alone.
problem Limited applicability of existing preference optimization methods in scenarios with only unpaired feedback.
method Decouples learning from positive and negative feedback, using expectation-maximization (EM) to optimize probability of positive outcomes and explicitly incorporate negative examples.
result Stable learning from negative feedback alone demonstrated.
New examples of manifolds in tangent cones of non-collapsed Ricci limit spaces.
problem Uncertainty in homeomorphism types of tangent cones of non-collapsed Ricci limit spaces.
method Construction of limit spaces in all dimensions at least 5.
result Any finite collection of manifolds can appear as cross sections of tangent cones of the same point.
Generative Adversarial Positive-Unlabeled Learning tackles binary PU data classification.
problem Overfitting in conventional PU models with limited positive data.
method Innovative generative adversarial framework with multiple discriminators and generators.
result GenPU framework can recover both positive and negative data distributions at equilibrium.
We use the notion of intrinsic flat distance to address the almost rigidity of the positive mass theorem for asymptotically hyperbolic manifolds. In particular, we prove that a sequence of spherically symmetric asymptotically hyperbolic manifolds satisfying the conditions of the positive mass theorem converges to hyper…
The paper examines compactness of scalar curvature sequences on conformal manifolds.
problem Compactness of sequences of Riemannian manifolds with positive scalar curvature.
method Analyzes the conformal case of Riemannian manifolds, focusing on compactness and convergence properties.
result Compactness of conformal factors and convergence away from a singular set.
In the bordered Floer theory, gluing thickened torus of positive meridional Dehn twist to the boundary of a knot complement result in the knot complement of increased framing. For a fixed knot K, we construct a direct system of positively framed knot complements and study the direct limit. We also study the morphism sp…
New method for Transformer models to encode position information without sequential bias.
problem Lack of flexible and learnable position encoding for Transformer models.
method Continuous dynamical model to learn position encoding.
result Consistent improvements over baselines in various NLP tasks.
Ancient Ricci flows with bounded girth found in 3D and higher.
problem Finding ancient Ricci flows with bounded girth in dimensions 3 and higher.
method Invariant conditions on curvature and its derivatives under symmetry, proving Ricci flow invariance.
result Construction of new ancient Ricci flows with positive curvature operator and bounded girth.
New flow expands hypersurfaces in hyperbolic space, showing round limiting shape for certain powers.
problem Understanding the limiting shape of hypersurfaces expanding in hyperbolic space.
method Introduced shifted inverse curvature flow with positive power for a smooth curvature function.
result For , limiting shape is always round as maximal existence time is approached.
Modified Perceptron handles strategic agents with limited position changes.
problem Learning linear classifiers in the presence of strategic agents that can manipulate their positions.
method Developed a modified Perceptron algorithm with bounded mistakes under various manipulation costs.
result The modified Perceptron achieves bounded mistakes even when manipulation costs are unknown.
New manifolds with negative curvature limit to one with negative curvature.
problem Preserving nonnegative scalar curvature under intrinsic flat convergence.
method Constructing sequences of manifolds with positive scalar curvature.
result Intrinsic flat limit of manifolds with negative scalar curvature.
We show that the limiting Khovanov chain complex of any infinite positive braid categorifies the Jones-Wenzl projector. This result extends Lev Rozansky's categorification of the Jones-Wenzl projectors using the limiting complex of infinite torus braids. We also show a similar result for the limiting Lipshitz-Sarkar-Kh…
Two approaches extend graph embedding to unseen vertices.
problem Extending graph embedding to new data points.
method Least-squares and maximum-likelihood formulations.
result Both methods estimate latent positions with the same error rate under latent position models.
Reduced computational complexity for indoor positioning.
problem Efficiently positioning users in large areas with limited data.
method Segmentation, Jaccard index, LASSO feature selection, Bayesian MAP estimation.
result Positioning accuracy with a subset of features and sub-regions is equivalent to full data, but computation time is reduced.
In this paper we consider Riemannian manifolds of dimension , with semi-positive -curvature and non-negative scalar curvature. Under these assumptions we prove the Paneitz operator satisfies a strong maximum principle; the Paneitz operator is a positive operator; and its Gree…