The paper classifies hypersurfaces in Riemannian manifolds with constant inner product and torse-forming axes.
problem Understanding hypersurfaces in Riemannian manifolds with specific geometric properties.
method Analyzing hypersurfaces with constant inner product and torse-forming axes.
result Classification of hypersurfaces with torse-forming axes.
Paper transforms torse-forming vector fields into simpler forms.
problem Generalizing vector fields and their transformations.
method Present techniques to transform torse-forming vector fields into simpler cases.
result Concrete examples of transformations are provided.
The study examines properties of biharmonic hypersurfaces with torse-forming vector fields.
problem Properties of biharmonic hypersurfaces in Riemannian manifolds.
method Investigates biharmonic hypersurfaces with torse-forming vector fields.
result Provides properties of biharmonic hypersurfaces with torse-forming vector fields.
The paper studies special solitons on Riemannian manifolds with specific vector fields.
problem Characterizing conformal and ∗-Yamabe solitons with torse forming potential vector fields. method Analyzing solitons under different connections (Riemannian, semi-symmetric, projective semi-symmetric) and developing examples.
result Characterizations and properties of conformal and ∗-Yamabe solitons with torse forming vector fields. In this paper geometrical aspects of perfect fluid spacetime with torse-forming vector field ξare discribed and Ricci soliton in perfect fluid spacetime with torse-forming vector field ξare determined. Conditions for the Ricci soliton to be expanding, steady or shrinking are also given.
Study on almost Riemann solitons with gradient or torse-forming vector fields.
problem Characterizing almost Riemann solitons with specific vector fields.
method Using Bochner formula and properties of gradient and torse-forming vector fields.
result Explicit expressions for the soliton function λ under gradient and torse-forming conditions. The paper studies prescribed angle surfaces in Riemannian manifolds with torse-forming vector fields.
problem Characterizing surfaces with prescribed angles in Riemannian geometry.
method Introducing and analyzing prescribed angle hypersurfaces associated with torse-forming vector fields.
result Classification of prescribed angle surfaces in 3D Riemannian manifolds.
The paper defines and proves the existence of curves in Riemannian manifolds with prescribed angles to torse-forming vector fields.
problem Existence of curves with prescribed angles to torse-forming vector fields in Riemannian manifolds.
method Introducing the notion of a prescribed angle curve and proving its existence for torse-forming vector fields.
result Existence of prescribed angle curves in Riemannian manifolds associated with torse-forming vector fields.
Study on Yamabe solitons on specific complex manifolds, focusing on torse-forming vector fields.
problem Exploring Yamabe solitons on a specific class of complex manifolds.
method Analyzing Yamabe solitons on almost contact complex Riemannian manifolds with a vertical torse-forming vector field.
result Explicit examples of 5-dimensional Lie groups characterized by the study.
Study on Schouten solitons on Kenmotsu manifolds, focusing on torse-forming vector fields.
problem Characterizing ∗-η-Schouten solitons on Kenmotsu manifolds. method Investigation of ∗-η-Schouten solitons on Kenmotsu manifolds with torse-forming potential vector fields. result Characterization of the soliton and derivation of scalar curvature for Kenmotsu manifolds.
Study on a new type of solitons on specific geometric manifolds.
problem Characterizing new types of solitons in geometric structures.
method Generalization of Ricci-like solitons with specific properties and conditions.
result Conditions for these solitons to be equivalent to almost Einstein-like metrics.
Study on Ricci-like solitons on specific geometric manifolds.
problem Characterizing Ricci-like solitons on almost contact B-metric manifolds.
method Introduced and analyzed Ricci-like solitons with Reeb vector fields on these manifolds, considering special cases and providing examples.
result Ricci-like solitons on these manifolds coincide with Einstein-like structures.
The paper characterizes ∗-Ricci-Bourguignon solitons on Kenmotsu manifolds.
problem Characterizing ∗-Ricci-Bourguignon solitons on Kenmotsu manifolds. method Analyzing conditions for compressing, balancing, or enlarging ∗-Ricci-Bourguignon on Kenmotsu manifolds; estimating curvature properties; featuring with torse-forming vector fields; providing an example. result Found conditions and curvature properties for ∗-Ricci-Bourguignon solitons on Kenmotsu manifolds. Study properties of specific solitons on submanifolds with special vector fields.
problem Characterize almost η-Ricci and Yamabe solitons on submanifolds. method Analyze submanifolds isometrically immersed into Riemannian manifolds with specific potential vector fields.
result Necessary and sufficient conditions for hypersurfaces in the unit sphere to be solitons.
The paper studies geometric structures in perfect fluid spacetimes with specific metrics.
problem Analyzing the geometric properties of perfect fluid spacetimes with specific metrics.
method Investigates conditions for conformal Ricci-Yamabe soliton and derives Laplace equations.
result Conditions for expanding, steady, or shrinking conformal Ricci-Yamabe solitons are identified.
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.
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.
Characterizes ∗-k-Ricci-Yamabe solitons on Kenmotsu manifolds.
problem Understanding ∗-k-Ricci-Yamabe solitons on Kenmotsu manifolds. method Analyzes the geometry of ∗-k-Ricci-Yamabe solitons and gradient solitons on Kenmotsu manifolds. result Characterizes the nature of ∗-k-Ricci-Yamabe solitons and gradient solitons. The study characterizes mixed super quasi-Einstein manifolds with Ricci-Bourguignon solitons.
problem Characterizing mixed super quasi-Einstein manifolds with Ricci-Bourguignon solitons.
method Exploring properties of mixed super quasi-Einstein manifolds, including conformal Ricci pseudosymmetry and Einstein's field equation. Characterizing manifolds that admit Ricci-Bourguignon solitons and providing a detailed eigenvalue problem characterization.
result Characterization of mixed super quasi-Einstein manifolds with Ricci-Bourguignon solitons, including a detailed eigenvalue problem and an example construction.
Study of Yamabe solitons on specific geometric manifolds.
problem Characterizing Yamabe solitons on almost contact complex Riemannian manifolds.
method Investigation of two cases: Sasaki-like and torse-forming potentials.
result Explicit examples and theoretical properties confirmed in 3D.
Bayesian optimization finds best hyperparameters for deep learning models.
problem Finding optimal hyperparameters in high-dimensional space.
method Bayesian optimization, Gaussian processes, and adaptive experimentation.
result Ax, BoTorch, and GPyTorch provide a powerful and simple framework for hyperparameter optimization.
Method evaluates disentanglement in DLVMs, including those not aligned with latent axes.
problem Evaluate disentanglement in DLVMs, especially those not aligned with latent axes.
method Proposes a statistical method to discover generative factors of a dataset.
result Empirically demonstrates the advantage of the method on two 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.
Paper proposes AXE loss for non-autoregressive machine translation, improving performance.
problem Challenges in training non-autoregressive models due to lack of autoregressive factors and cross entropy loss penalties.
method Proposes aligned cross entropy (AXE) loss function using a differentiable dynamic program for better word order alignment.
result AXE-based training improves performance on major WMT benchmarks and sets a new state of the art for non-autoregressive models.
New method flattens decision boundary by targeting shortcut-aligned axes in disentangled latent space.
problem Shortcut learning in neural networks, leading to poor out-of-distribution generalization.
method Injects targeted anisotropic noise to regularize classifier sensitivity along shortcut-aligned axes.
result Achieves state-of-the-art OOD performance without shortcut labels or conflicting samples.
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…
Self-focal points on ellipsoids of dimension 3 or higher are rare.
problem Existence of self-focal points on Riemannian manifolds of dimension 3 or higher.
method Analyzing geodesics and umbilic points on ellipsoids of various dimensions.
result Ellipsoids of dimension 3 or higher with at least 4 distinct axes have no self-focal points.
The object of this paper is to study η-Ricci solitons on (ε)-almost paracontact metric manifolds. We investigate η-Ricci solitons in the case when its potential vector field is exactly the characteristic vector field ξ of the (ε)-almost paracontact metric manifold and when the potential ve…
AXE evaluates explanations to avoid misleading Rashomon set model selection.
problem Evaluating explanations for Rashomon set models to avoid false selection.
method Proposed AXE method to evaluate explanation quality.
result AXE detects adversarial fairwashing with 100% success rate.
The class of the two-axes pseudo-Finslerian metrics which is specified by the condition of the angle-separation in the involved characteristic functions is proposed and studied. The complete Total Set of algebraic and differential equations is derived in all rigor which are necessary and sufficient in order that a pseu…
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.
The Conclusive Theorem has been established to determine the dependence of the three-axes positive-definite Finsleroid metric functions F on the Finsleroid azimuthal angle θ in the three-dimensional case N=3, provided that the condition of the angle-separation in the involved characteristic functions is implied. …
Proposes σ-PCA to learn identifiable linear transformations without whitening.
problem Cannot identify axes with equal variances in PCA.
method Unified model for linear and nonlinear PCA, introducing a missing piece to eliminate rotational indeterminacy.
result Eliminates subspace rotational indeterminacy in PCA.
Study on 3D trans-Sasakian manifolds with η-Einstein solitons.
problem Characterizing 3D trans-Sasakian manifolds with η-Einstein solitons.
method Analyzing properties of Codazzi type and cyclic parallel Ricci tensors on 3D trans-Sasakian manifolds.
result Examples and properties of 3D trans-Sasakian manifolds with η-Einstein solitons.
In Garside groups, axes of Morse elements are strongly contracting.
problem Understanding the dynamics of Morse elements in Garside groups.
method Analyzing the Cayley graph of Garside groups modulo their center, using Garside generators.
result Morse elements act loxodromically on the additional length graph of Garside groups.
Recent results using inverse scattering techniques interpret every solution φ(x,y) of the sine-Gordon equation as a non-linear superposition of solutions along the axes x=0 and y=0. Here we provide a geometric method of integration, as well as a geometric interpretation. Specifically, every weakly regular surface…
This paper consists of two parts. In the first one we study the behaviour of medial axes (skeletons) of closed sets in a connected complete Riemannian manifold M under deformations. The second one is devoted to a similar study of conflict sets. We apply a new approach to the deformation process. Instead of …
Simpler proof for non-basic sets in 2D.
problem Proving non-basic sets in 2D.
method Defining Sternfeld arrays and proving non-basic sets.
result Simpler proof of non-basic sets in 2D.
On a Riemannian 2-torus (T2,g) we study the geodesic flow in the case of low complexity described by zero topological entropy. We show that this assumption implies a nearly integrable behavior. In our previous paper \cite{GK} we already obtained that the asymptotic direction and therefore also the rotation number ex…
We consider the problem of estimating an unknown signal x0 from noisy linear observations y=Ax0+z∈Rm. In many practical instances, x0 has a certain structure that can be captured by a structure inducing convex function f(⋅). For example, ℓ1 norm can be used to encourage a sparse solution. T…
We construct helicoid-like embedded minimal disks with axes along self-similar curves modeled on logarithmic spirals. The surfaces have a self-similarity inherited from the curves and the nature of the construction. Moreover, inside of a "logarithmic cone", the surfaces are embedded.
We show that some riemannian manifolds diffeomorphic to the sphere have the property that the cut loci of general points are smoothly embedded closed disks of codimension one. Ellipsoids with distinct axes are typical examples of such manifolds.
The position vector field x is the most elementary and natural geometric object on a Euclidean submanifold M. The position vector field plays very important roles in mathematics as well as in physics. Similarly, the tangential component x^T of the position vector field is the most natural vector field tangent to the …
We consider non-elementary Kleinian groups Γ, without invariant plane, generated by an elliptic and a hyperbolic element with their axes lying in one plane. We find presentations and a complete list of orbifolds uniformized by such Γ.
New approach classifies rotational Weingarten surfaces in Lorentz-Minkowski space.
problem Classifying rotational Weingarten surfaces in Lorentz-Minkowski space.
method Using geometric linear momentum of generatrix curves with respect to axes of revolution.
result Unified framework for three causal types of rotation axes.
The paper classifies geometric structures of δ-almost Yamabe solitons on paracontact metric manifolds.
problem Characterizing δ-almost Yamabe solitons on paracontact metric manifolds.
method Investigation of geometric structures under specific assumptions, including quarter-symmetric non-metric connections.
result Conditions for δ-almost Yamabe solitons to be expanding, steady, or shrinking.
Unified scheme combining softmax and ResNet for deep learning.
problem Combining softmax and ResNet for deep learning.
method Theoretical analysis of a unified scheme combining softmax regression and ResNet.
result Unified scheme connects previously unrelated fields and provides insights into loss landscape and optimization.
PRUDEX-Compass evaluates FinRL methods on 6 axes for financial market investments.
problem Insufficient evaluation of FinRL methods in financial markets.
method Introduces PRUDEX-Compass with 6 axes and 17 measures for evaluation.
result Demonstrates the effectiveness of PRUDEX-Compass on 4 real-world datasets.