The paper studies volumes of direct images for high tensor powers of ample bundles.
problem Understanding asymptotics of Monge-Ampère volumes for high tensor powers of ample line bundles.
method Analyzes the leading term of asymptotics and classifies bundles saturating a topological bound.
result Provides a characterization of bundles admitting projectively flat Hermitian structures in the case of high symmetric powers of ample vector bundles.
A simpler edge-based discretization method without dual volumes.
problem Efficiently computing edge-based discretization vectors without forming dual volumes.
method Directly compute edge-midpoint vectors and reduce dual volume formation.
result Significant reduction in computing time for tetrahedral grids.
In this paper, we show that the derivative of the genus-1 Virasoro conjecture for Gromov-Witten invariants along the direction of quantum volume element holds for all smooth projective varieties. This result provides new evidence for the Virasoro conjecture.
Paper studies metric ribbon graphs and provides a recursion for their volumes.
problem Calculating volumes of combinatorial moduli spaces of directed metric ribbon graphs.
method Decomposes directed ribbon graphs into simpler graphs with one vertex, proving a canonical recursion scheme for volumes.
result Explicit recursion for volumes of four-valent metric ribbon graphs provided.
Study uses deep learning to predict asset prices, finds complex target processes lead to meaningless predictions.
problem Complexity of successful price prediction models hinders understanding.
method Deep learning models for high-frequency price prediction, focusing on volatility and directional prediction.
result Inadequately defined target price process renders predictions meaningless.
DVAO predicts volumetric ambient occlusion for real-time volume rendering.
problem Predicting per-voxel ambient occlusion in volumetric data sets.
method Deep learning neural network that considers global information through transfer function.
result DVAO supports real-time volume interaction and generalizes to various modalities.
We study the Lipschitz simplicial volume, which is a metric version of the simplicial volume. We introduce the piecewise straightening procedure for singular chains, which allows us to generalize the proportionality principle and the product inequality to the case of complete Riemannian manifolds of finite volume with …
Constructs ε-splitting maps for geodesic balls with non-negative Ricci curvature.
problem Constructing ε-splitting maps for geodesic balls with non-negative Ricci curvature.
method Induction and stratified almost Gou-Gu Theorem for finding directional points; error estimates for projections.
result Constructs ε-splitting maps on concentric geodesic balls with uniformly small radius. We establish the proportionality principle between the Riemannian volume and locally finite simplicial volume for Q-rank 1 locally symmetric spaces covered by products of hyperbolic spaces, giving the first examples for manifolds whose cusp groups are not necessarily amenable. Also, we give a simple direct proof of the…
SLS optimizes minimum-volume regions for conditional quantiles, bypassing density estimation.
problem Constructing minimum-volume prediction regions that satisfy conditional coverage.
method Super-level-set regression (SLS) directly optimizes geometric boundaries of conditional level sets.
result SLS optimizes regions directly, capturing complex conditional structures end-to-end.
The paper proves a fibration theorem for collapsing sequences of Alexandrov spaces.
problem Understanding the structure of collapsing sequences of Alexandrov spaces.
method Constructing almost Lipschitz submersions and proving locally trivial fibrations.
result A locally trivial fibration is established under certain conditions on volumes and singularity weakness.
Weyl's intrinsic volumes converge to the Euler characteristic of the base manifold under certain metrics.
problem Convergence of intrinsic volumes on Riemannian manifolds.
method Defined a new metric and used it to study the convergence of intrinsic volumes.
result Intrinsic volumes converge to the Euler characteristic of the base manifold.
New compactification of Teichmüller space via renormalized volume.
problem Compactify Teichmüller space with new distance.
method Horocompactification with renormalized volume.
result Translation length of pseudo-Anosov mapping classes equals hyperbolic volume of mapping tori.
Study finds option volume imbalance predicts equity market returns.
problem Predicting equity market returns using option volume imbalance.
method Nonlinear analysis of option volumes decomposed into five market participant classes.
result Strong signals of predictability of excess market returns from Market-Maker volumes.
Positive simplicial volume found for certain non-positively curved manifolds with specific submanifolds.
problem Determining conditions for positive simplicial volume in non-positively curved manifolds.
method Analyzing isolated, closed totally geodesic submanifolds of codimension one and their impact on simplicial volume.
result Positive simplicial volume for certain non-positively curved manifolds with specific submanifolds.
Negative curvature manifolds have vanishing bounded volume class if and only if Cheeger constant is positive.
problem Negative curvature manifolds and their volume classes.
method Integration of volume forms and isoperimetric constants.
result Vanishing of bounded volume class implies positivity of Cheeger constant and vice versa.
Researchers create non-homogeneous finite-volume ends on quaternionic Kähler manifolds.
problem Constructing non-homogeneous quaternionic Kähler manifolds with finite volume ends.
method Using cohomogeneity one deformation of symmetric spaces, the researchers constructed manifolds with specific fundamental groups.
result The constructed manifolds are aspherical and have finite volume ends, not locally homogeneous.
Deep neural network predicts knot volume from Jones polynomial.
problem Recovering hyperbolic volume of a knot directly from the Jones polynomial.
method Used a deep neural network to approximate the hyperbolic volume of a knot.
result Achieved 97.6% accuracy in predicting knot volume from Jones polynomial.
The paper validates a classifier for identifying intraday regime shifts in MNQ futures.
problem Developing reliable trading signals from intraday regime shifts in MNQ futures.
method Constructed a composite day-classification system using three observable conditions.
result Classifier-positive days exhibit distinct intraday behavior but fail to generate profitable trading signals.
We are generalizing to higher dimensions the Bavard-Ghys construction of the hyperbolic metric on the space of polygons with fixed directions of edges. The space of convex d-dimensional polyhedra with fixed directions of facet normals has a decomposition into type cones that correspond to different combinatorial types …
Survey on 4-manifolds with specific curvature properties.
problem Understanding the structure of 4-manifolds with nonnegative Ricci curvature and Euclidean volume growth.
method Analysis of blow-downs and cone-like structures at infinity.
result Manifolds look like cones over spherical space forms at infinity.
Let M be a smooth compact connected oriented manifold of dimension at least two endowed with a volume form. Assuming certain conditions on the fundamental group π1(M) we construct quasi-isometric embeddings of either free Abelian or direct products of non-Abelian free groups into the group of volume preserving diffe…
Study proposes deep learning for VWAP execution in crypto markets, outperforming traditional methods.
problem Challenges in achieving VWAP due to dynamic volume and price factors.
method Direct optimization of VWAP execution using deep learning, bypassing volume curve prediction.
result Deep learning approach consistently achieves lower VWAP slippage in volatile markets.
A new topic modeling method that minimizes topic simplex volume.
problem Topic modeling efficiency and accuracy.
method Reformulates LDA as minimizing topic simplex volume, uses convex relaxation and ADMM.
result Relaxed problem has same global minimum as original under assumptions.
New framework uses trading volume instead of volatility for stock pricing.
problem Improving stock price dynamics understanding and market data gap.
method Proposes a new stock pricing model using trading volume instead of volatility, based on two hypotheses.
result The new framework can be applied to option pricing and points to a new direction in finance.
We prove the following entropy-rigidity result in finite volume: if X is a negatively curved manifold with curvature −b2≤KX≤−1, then Enttop(X)=n−1 if and only if X is hyperbolic. In particular, if X has the same length spectrum of a hyperbolic manifold X0, the it is isometric to X0 (we a…
Volume gaps for minimal submanifolds in spheres are proven.
problem Volume gaps for minimal submanifolds in spheres.
method Analyzing height functions and multiplicity in direction p.
result Volume inequalities for minimal submanifolds in spheres.
The study proves properties of intersections of horospheres in harmonic spaces.
problem Properties of intersections of horospheres in harmonic spaces.
method Constructing volume preserving mappings using Busemann functions.
result Upper bound of the volume of intersection of horospheres is independent of Busemann function differences.
The paper examines how market trade values and volumes affect price autocorrelation.
problem Understanding the impact of market trade values and volumes on price autocorrelation.
method Derives the dependence of price statistical moments and volatility on trade values and volumes, and assesses statistical moments and correlations by conventional frequency-based probabilities.
result Highlights the impact of market trade randomness on price statistical moments and autocorrelation.
Proposes a new model for traffic flow on directed graphs.
problem Modeling advection on directed graphs for traffic flow.
method Reformulates graph advection operator as finite difference scheme; proposes DGAMGP model.
result Effective modeling of traffic flow and uncertainty as an advective process.
New proof shows affine manifolds with parallel volume are Riemannian-flat.
problem Characterize compact affine manifolds with parallel volume.
method Construct a representative metric with Levi-Civita connection, using Hessian of volume-normalized distance functions.
result Affine manifolds with parallel volume are Riemannian-flat.
Quantum approach to volume computation from colored Jones polynomials.
problem Computing volumes of hyperbolic 3-manifolds from knot polynomials.
method Categorification of Jones polynomials and asymptotic analysis of skein elements.
result Asymptotic growth rate of Kauffman bracket relates to volumes of ideal octahedra.
It is classically known that closed geodesics on a compact Riemann surface with a metric of negative curvature strictly minimize length in their free homotopy class. We'd like to generalize this to Lagrangian submanifolds in Kähler manifolds of negative Ricci curvature. The only known result in this direction is a theo…
Study volume conjecture for links with multiple hyperbolic pieces.
problem Volume conjecture for links with more than one hyperbolic piece.
method Constructing infinite families of prime links, analyzing their complements, and using colored Jones polynomials and simplicial volume.
result Exponential growth rates of colored Jones polynomials capture the simplicial volume of link complements.
Dead-Direction Signatures (DDS) provide a cheap, closed-form spectral reading of a network's singular complexity.
problem Estimating the complexity of deep networks through their loss singularities.
method DDS replaces the SGLD posterior chain with spectral linear algebra.
result DDS observables rank-track the network's singular complexity at the framework-predicted sign.
Experts assess fairness in machine learning, identifying promising research directions.
problem Understanding and ensuring fairness in machine learning algorithms.
method Convened a workshop of experts to assess the state of fairness research.
result Identified promising research directions in fairness in machine learning.
The SIP's accuracy is questioned, leading to skewed returns for high-volume stocks.
problem Inaccuracy of the SIP in reporting trades and quotes.
method Analysis of Trade and Quote data, use of first differences to highlight latency and inaccuracy.
result Up to 60% of trades are reported out of sequence, skewing returns.
Sharp isoperimetric inequalities for the sine transform of even isotropic measures are established. The corresponding reverse inequalities are obtained in an asymptotically optimal form. These new inequalities have direct applications to strong volume estimates for convex bodies from data about their sections or projec…
We study the localization of sets with constant nonlocal mean curvature and prescribed small volume in a bounded open set with smooth boundary, proving that they are {\em sufficiently close} to critical points of a suitable non-local potential. We then consider the fractional perimeter in half-spaces. We prove the exis…
Novel weak solutions for volume-preserving mean curvature flow established.
problem Existence and uniqueness of solutions to volume-preserving mean curvature flow.
method Introducing varifold solutions coupled with phase volumes and new calibrations.
result Uniqueness of classical solutions among varifold solutions.
Study σ2-curvature and volume of compact manifolds, proving conditions for Einstein metrics and geodesic balls.
problem Understanding σ2-curvature and volume in compact manifolds. method Critical point analysis, volume comparison, variational properties, geodesic balls.
result Sufficient and necessary condition for a critical metric to be Einstein, volume comparison results.
Introduces Alexandrov spaces with curvature below, covering various theorems.
problem Understanding spaces with curvature constraints.
method Explains comparison conditions, globalization, tangent spaces, etc.
result Globalization theorem and other theorems established for Alexandrov spaces.
Given a warped product space R×fN with logarithmically convex warping function f, we prove a relative isoperimetric inequality for regions bounded between a subset of a vertical fiber and its image under an almost everywhere differentiable mapping in the horizontal direction. In particular, given…
We present some new Stokes' type theorems on complete non-compact manifolds that extend, in different directions, previous work by Gaffney and Karp and also the so called Kelvin-Nevanlinna-Royden criterion for (p-)parabolicity. Applications to comparison and uniqueness results involving the p-Laplacian are deduced.
Given a pair of integers m and n such that 1 < m < n, we show that every n-dimensional manifold admits metrics of arbitrarily small total volume, and possessing the following property: every m-dimensional submanifold of less than unit m-volume is necessarily torsion in homology. This result is different from the case o…
In this note, we obtain a sharp volume estimate for complete gradient Ricci solitons with scalar curvature bounded below by a positive constant. Using Chen-Yokota's argument we obtain a local lower bound estimate of the scalar curvature for the Ricci flow on complete manifolds. Consequently, one has a sharp estimate of…
Study geodesics in 3-torus, determining complements' topology.
problem Understanding the topology of geodesic complements in 3-torus.
method Analyzes the orbit of direction vectors under PSL3(Z) action and uses Farey graph distances. result Determines homeomorphism type of geodesic complements in 3-torus.
Machine learning models predict EUR/USD currency direction with 58.52% accuracy.
problem Predicting the directional movement of EUR/USD in the Foreign Exchange market.
method Comparative analysis of machine learning models, including decorrelated and non-decorrelated feature sets, and meta-estimators.
result 58.52% accuracy for one-day ahead forecasts.