Examines medial axis in pseudo-Euclidean spaces.
problem No specific problem stated; focuses on new context.
method Follows Birbrair and Denkowski's approach.
result Feasibility of medial axis in pseudo-Euclidean spaces checked.
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48 results for “AXI”
An axis of a link projection is a closed curve which lies symmetrically on each region of the link projection. In this paper we define axis systems of link projections and characterize axis systems of the standard projections of twist knots.
Axis bundles in free-by-cyclic groups have non-generic monodromies.
problem Characterizing monodromies in free-by-cyclic groups.
method Analyzing monodromy actions on outer space and using properties of axis bundles.
result Monodromies having a 'lone axis' are non-generic and projectively discrete.
A Case for AXIq-fin.RM
AXI assesses bank funding costs transparently, improving loan pricing and reducing financial risk.
problem Lack of credit-sensitive funding benchmarks after LIBOR transition.
method AXI aggregates unsecured funding transactions across maturities, producing a daily credit spread.
result AXI correlates with financial conditions and market stress, reducing funding risk and offering spread discounts.
The Blum medial axis rigidity is studied in terms of cross ratios and differential geometry.
problem Examining rigidity properties of the Blum medial axis under diffeomorphisms.
method Using cross ratios from projective geometry and differential geometry.
result Cross ratios and differential geometry uniquely determine the angles between smooth sheets.
Proposes a diagnostic method to evaluate factor models using cap-axis integrals.
problem Improving factor model evaluation in low-dimensional spaces.
method Lifts pricing errors into a bridge-alpha curve along the market-capitalization rank axis.
result The cap-axis norm is distinct from Sharpe gain and size exposure.
Proposes a diagnostic method to evaluate factor models using cap-axis integrals.
problem Improving factor model evaluation for low-dimensional models.
method Lifts pricing errors into a bridge-alpha curve along the market-capitalization rank axis.
result The cap-axis norm is distinct from Sharpe gain and size exposure.
Study rectifying submanifolds with anti-torqued axis in Riemannian manifolds.
problem Characterize submanifolds with anti-torqued axis in Riemannian manifolds.
method Determine necessary and sufficient conditions for anti-torqued vector fields, characterize submanifolds, and derive rectifying submanifolds as warped products.
result Rectifying submanifolds with anti-torqued axis are warped products with specific warping functions.
Decomposes axis bundles into cubist structures for fully irreducible outer automorphisms.
problem Understanding the geometry and structure of axis bundles for fully irreducible outer automorphisms.
method Develops a 'cubist' decomposition into branched cubes with special combinatorics.
result Locates a canonical finite collection of periodic fold lines in each axis bundle.
Isophote curve consists of a locus of surface points whose normal vectors make a constant angle with a fixed vector (the axis). In this paper, we define an isophote curve on a spacelike surface in Lorentz-Minkowski space and then find its axis as timelike and spacelike vectors via the Darboux frame. Besides, we give so…
Two-dimensional embeddings remain the dominant approach to visualize high dimensional data. The choice of embeddings ranges from highly non-linear ones, which can capture complex relationships but are difficult to interpret quantitatively, to axis-aligned projections, which are easy to interpret but are limited to biva…
A new method for unsupervised disentanglement using axis-aligned cliffs.
problem Unsupervised disentanglement of latent factors under nonlinear maps.
method Encouraging axis-aligned discontinuities (cliffs) in the estimated density of factors.
result Cliff method outperforms baselines on disentanglement benchmarks.
Subspace Determination through Local Intrinsic Dimensional Decomposition: Theory and Experimentationcs.LG
Axis-aligned subspace clustering generally entails searching through enormous numbers of subspaces (feature combinations) and evaluation of cluster quality within each subspace. In this paper, we tackle the problem of identifying subsets of features with the most significant contribution to the formation of the local n…
This paper establishes that sutured annular Khovanov homology is not invariant for braid closures under axis-preserving mutations. This follows from an explicit relationship between sutured annular Khovanov homology and the classical Burau representation for braid closures.
GmGM models multi-axis data for faster analysis.
problem Efficiently modeling multi-axis data across multiple tensors.
method Generalizes Gaussian Graphical Model to learn sparse graph representations across shared axes.
result Achieves significant speedup (order of magnitude) for large multi-modal datasets.
This paper diagnoses factor-model pricing errors using a new method.
problem Measuring pricing errors in factor models with general characteristic axes.
method Developed a method to measure factor-model pricing errors as bridge-alpha curves, using a predetermined characteristic order and prefix portfolios.
result Adding a counterpart factor flips the curve's sign on every axis, but only HML and CMA overcorrect enough to be rejected.
We let be an ageometric fully irreducible outer automorphism so that its Handel-Mosher axis bundle consists of a single unique axis. We show that the centralizer of the cyclic subgroup generated by equals the stabilizer of the attracting lamina…
Volume-preserving mean curvature flow of revolution hypersurfaces in a Rotationally Symmetric Spacemath.DG
In an ambient space with rotational symmetry around an axis (which include the Hyperbolic and Euclidean spaces), we study the evolution under the volume-preserving mean curvature flow of a revolution hypersurface M generated by a graph over the axis of revolution and with boundary in two totally geodesic hypersurfaces …
Random Tessellation Forestsstat.ML
Space partitioning methods such as random forests and the Mondrian process are powerful machine learning methods for multi-dimensional and relational data, and are based on recursively cutting a domain. The flexibility of these methods is often limited by the requirement that the cuts be axis aligned. The Ostomachion p…
Leveraging Axis-Aligned Subspaces for High-Dimensional Bayesian Optimization with Group Testingcs.LG
GTBO uses group testing to optimize high-dimensional functions efficiently.
problem Optimizing expensive, high-dimensional functions with limited data.
method Group testing to identify active dimensions, then guide optimization.
result GTBO outperforms state-of-the-art methods on high-dimensional benchmarks.
Isophote comprises a locus of the surface points whose normal vectors make a constant angle with a fixed vector. Main objective of this paper is to find the axis of an isophote curve via its Darboux frame and afterwards to give some characterizations about isophote and its axis. Particularly, for isophotes lying on a c…
Solves curvature prescription on rotational surfaces.
problem Prescribing different types of curvatures on rotational surfaces.
method Using arbitrary continuous functions of distance from axis of revolution.
result Complete classification of surfaces with specific curvature relationships.
See http://youtu.be/Mf4IE8gWcJs for a YouTube video showing part of the results in this paper. We consider helicoidal immersions in the Euclidean space whose axis of symmetry is the z-axis that are solutions of the equation 2 H=Λ_0-a 1/2 R^2 where H is the mean curvature of the surface, R is the distance form the point…
Distributional Reinforcement Learning (RL) differs from traditional RL in that, rather than the expectation of total returns, it estimates distributions and has achieved state-of-the-art performance on Atari Games. The key challenge in practical distributional RL algorithms lies in how to parameterize estimated distrib…
We study the Lipschitz metric on Outer Space and prove that fully irreducible elements of Out(F_n) act by hyperbolic isometries with axes which are strongly contracting. As a corollary, we prove that the axes of fully irreducible automorphisms in the Cayley graph of Out(F_n) are stable, meaning that a quasi-geodesic wi…
New method learns complex cell networks from millions of cells.
problem Existing methods fail to scale to large datasets.
method Multi-axis Gaussian graphical models.
result Method scales to millions of cells in minutes.
We prove by variational means the existence of a complete, properly embedded, genus-one minimal surface in R^3 that is asymptotic to a helicoid at infinity. We also prove existence of surfaces that are asymptotic to a helicoid away from the helicoid's axis, but that have infinitely many handles arranged periodically al…
The paper diagnoses factor models using characteristic axes and zero-curve restrictions.
problem Tackles systematic sign reversals and overcorrections in factor model pricing errors.
method Extends cap-axis integral diagnostic to general characteristic axes, measuring pricing errors as bridge-alpha curves.
result Axis-level pricing errors are nearly orthogonal to maximum-Sharpe gains, showing systematic sign reversals and overcorrections.
Decision forests, including Random Forests and Gradient Boosting Trees, have recently demonstrated state-of-the-art performance in a variety of machine learning settings. Decision forests are typically ensembles of axis-aligned decision trees; that is, trees that split only along feature dimensions. In contrast, many r…
The paper diagnoses factor-model pricing errors using characteristic axes and bridge-alpha curves.
problem Tackles systematic sign reversals and overcorrections in factor-model pricing errors.
method Extends cap-axis integral diagnostic to characteristic axes, measures pricing errors as bridge-alpha curves, and uses a predetermined characteristic order to generate zero-curve restrictions.
result Axis-level pricing errors are nearly orthogonal to maximum-Sharpe gains, showing significant sign reversals and overcorrections.
Oblique BART improves tree-based predictions.
problem Axis-aligned decision rules in BART can be suboptimal.
method Developed an oblique version of BART using data-adaptive hyperplane partitions.
result Oblique BART outperformed axis-aligned BART and other tree methods on benchmarks.
In this work, we give a survey on non characteristic domains of Heisenberg groups. We prove that bounded domains which are diffeomorphic to the solid torus having the center of the group as rotation axis, are non characteristic. Then, we state the following conjecture : The bounded non characteristic domains of the Hei…
The Complex Axis theorem states that any endomorphism of a finite-dimensional complex vector space affords an eigen-vector (or "invariant axis"). A geometric proof of this geometric result was given by A. de Medeiros, transforming the endomorphism into a topological self-map with Lefschetz number not equal to zero. We …
New kernel interprets 3D anisotropic data with rotations and improved predictions.
problem Capturing rotated anisotropy in 3D spatial fields.
method Introduces a Lie-algebraic kernel with three principal length-scales and an explicit rotation.
result Posterior recovers rotated anisotropy and improves prediction over axis-aligned kernels.
The paper counts conjugacy classes of pseudo-Anosov homeomorphisms in Teichmüller space.
problem Counting conjugacy classes of pseudo-Anosov homeomorphisms in Teichmüller space.
method Analyzes the asymptotic behavior of conjugacy classes as the radius of a ball in Teichmüller space increases.
result Asymptotics for the number of pseudo-Anosov homeomorphisms conjugate to a given homeomorphism within a ball of radius R centered at X.
Reconstruct trapezoidal surfaces from point clouds.
problem Reconstructing trapezoidal surfaces from point clouds.
method Kinematic approach: find axis direction, polygonal path, and reconstruct surface.
result Reconstructs trapezoidal surfaces from point clouds.
Helicoidal surfaces in Minkowski space with constant mean curvature and constant Gauss curvaturemath.DG
In this work we find all helicoidal surfaces in Minkowski space with constant mean curvature whose generating curve is a the graph of a polynomial or a Lorentzian circle. In the first case, we prove that the degree of the polynomial is or and that the surface is ruled. If the generating curve is a Lorentzian ci…
Bending the Helicoidmath.DG
We construct Colding-Minicozzi limit minimal laminations in open domains in $\rth$ with the singular set of -convergence being any properly embedded -curve. By Meeks' -regularity theorem, the singular set of convergence of a Colding-Minicozzi limit minimal lamination is a locally finit…
BO method identifies sparse subspaces for efficient high-dimensional optimization.
problem Efficient optimization of high-dimensional black-box functions.
method Sparse Gaussian process surrogate models on axis-aligned subspaces with Hamiltonian Monte Carlo inference.
result SAASBO achieves excellent performance on synthetic and real-world problems.
The paper broadens the helix concept in 3D space.
problem Defining helices in three-dimensional space.
method Introducing a new vector field and angle condition.
result Natural equations and geometric integrations of helices.
Research shows curves in Walker 3-manifolds can lie in flat cylinders.
problem Understanding curves in Walker 3-manifolds.
method Showed curves lie in flat cylinders, constructed an example.
result Curves in Walker 3-manifolds can be contained in flat cylinders.
Study inverse curve shortening flow on hyperbolic plane, classifying solitons.
problem Understanding the behavior of curves in hyperbolic geometry under a specific flow.
method Classifying solitons with respect to vector fields and studying their properties.
result Parabolic solitons are graphs on the y-axis, conformal solitons on the x-axis.
Chirality for crooked curvescond-mat.soft
Tensor measures chirality for curves, even those with rough edges.
problem Quantifying chirality for complex, possibly irregular curves.
method Developed a tensorial chirality measure for rigid filaments and curves.
result A curve's chirality can be determined by its twist about perpendicular axes.
We provide an example in each rank of an ageometric fully irreducible outer automorphism whose ideal Whitehead graph has a cut vertex. Consequently, we show that there exist examples in each rank of Handel-Mosher axis bundles that are not just a single axis, as well as of "nongeneric" behavior in the sense of the "trai…
We construct a sequence of compact embedded minimal disks in a ball in Euclidean 3-space, whose boundaries lie in the boundary of the ball, such that the curvature blows up only at a prescribed discrete (and hence, finite) set of points on the x_3-axis. This extends a result of Colding and Minicozzi, who constructed a …
The paper examines deformations of simple dotted graphs made of circles.
problem Investigating reducibility of admissible dotted graphs.
method Analyzes deformations of admissible dotted graphs consisting of standard circles.
result Identifies specific conditions under which certain dotted graphs can be reduced.
New symplectic annular Khovanov homology connects knot theory to Floer homology.
problem Understanding the relationship between knot theory and Floer homology.
method Introducing a new version of symplectic annular Khovanov homology and establishing spectral sequences.
result Established spectral sequences linking different knot homologies.
Paper defines new topological invariants for DP tangles.
problem Classifying and understanding doubly periodic tangles.
method Organized components into interlinked compounds; introduced axis-motif.
result Directional type is an invariant of DP tangles.