A new method for combining shapes in log-radius profiles.
problem Combining shape features accurately and intuitively.
method Log-radius profile representation and a new operation for curve combination.
result Accurately combines shape features in a visually intuitive manner.
We prove a comparison theorem for the isoperimetric profiles of simple closed curves evolving by the normalized curve shortening flow: If the isoperimetric profile of the region enclosed by the initial curve is greater than that of some `model' convex region with exactly four vertices and with reflection symmetry in bo…
It is known that for any non-zero Min(−1/4,infty), if we roll the conic {(x,y): 4 x^2-y^2/M}=1} on a line in a plane, and then we rotate about this line the trace of a focus, then we obtain a surface of revolution D(M) with mean curvature 1. If M<=0, D(M) is embedded and it is called unduloid, if M>0, D(M) is not e…
In a previous paper the author introduced the notion of TreadmillSled of a curve, which is an operator that takes regular curves in R^2 to curves in R^2. This operator turned out to be very useful to describe helicoidal surfaces, for example, it provides an interpretation for the profile curve of helicoidal surfaces wi…
Study of surfaces with zero mean curvature in a specific pseudo-Euclidean space.
problem Characterizing surfaces with zero mean curvature in a pseudo-Euclidean space.
method Solving differential equations to determine profile curves and explicit parametrizations.
result Explicit parametrizations of maximal and timelike surfaces with zero mean curvature.
We study the shape of inflated surfaces introduced in \cite{B1} and \cite{P1}. More precisely, we analyze profiles of surfaces obtained by inflating a convex polyhedron, or more generally an almost everywhere flat surface, with a symmetry plane. We show that such profiles are in a one-parameter family of curves which w…
Study on special surfaces in 4D pseudo-Euclidean space with specific Gauss maps.
problem Characterizing rotational surfaces with pointwise 1-type Gauss maps in E4-2.
method Analyzing surfaces with spacelike profile curves in E4-2.
result Characterizations for surfaces to have pointwise 1-type Gauss maps.
Predict player lifetime value based on engagement metrics.
problem User profiling in video games.
method Survival curves, deep learning, long short-term memory.
result Deep learning predicts player lifetime value.
New theorems on compactness and finiteness for specific types of self-shrinkers.
problem Characterizing rotationally symmetric self-shrinkers with constraints.
method Compactness and finiteness theorems for self-shrinkers with specific symmetries and constraints.
result Existence of entropy minimizing self-shrinkers diffeomorphic to S1imesSn−1 for each n≥2. Paper studies surface knotting and its fold curves.
problem Understanding the knotting of surfaces and their fold curves.
method Examines the relationship between surface knotting and fold curves, defines a new invariant.
result Every surface can be isotoped so that its fold curves form an unlink.
Study identifies subphenotypes of pediatric sepsis to improve ML predictive performance.
problem Enhance machine learning predictive performance in pediatric sepsis.
method Latent profile analysis of clinical data to identify subphenotypes, followed by ML experiments.
result Improved predictive performance of ML models targeting specific subphenotypes of pediatric sepsis.
The paper computes spectra of Laplacian and Jacobi operators on rotational cmc hypersurfaces of spheres.
problem Computing spectra of Laplacian and Jacobi operators on rotational cmc hypersurfaces of spheres.
method Analyzing eigenvalues of second order Hill's equations and proving inequalities for stability index and eigenvalues.
result Proves that the stability index of minimal rotational examples is greater than 3n+4 and there are at least 2 positive Laplacian eigenvalues smaller than n. Study of special solutions to surface diffusion flow of ribbons.
problem Investigating the dynamics of special solutions to the surface diffusion flow.
method Complete classification of stationary solutions, qualitative results on shrinkers, translators, and rotators, explicit parametrisation of a shrinking figure eight curve.
result Explicit parametrisation of a shrinking figure eight curve.
We prove a comparison theorem for the isoperimetric profiles of solutions of the normalized Ricci flow on the two-sphere: If the isoperimetric profile of the initial metric is greater than that of some positively curved axisymmetric metric, then the inequality remains true for the isoperimetric profiles of the evolved …
Study on curve shortening flow with boundary conditions, proving convergence or contraction.
problem Analyzing curve shortening flow with free boundaries.
method Introduced a reflected chord-arc profile and obtained chord-arc estimates.
result Proved that flows either converge to a critical chord or contract to a round half-point.
Develops a framework for modeling liquidity risk using convex risk measures.
problem Modeling liquidity risk using convex risk measures.
method Exploits concentration of measure techniques to bound liquidity risk profiles.
result Derives tractable necessary and sufficient conditions for concentration inequalities of liquidity risk profiles.
The study classifies totally umbilical surfaces in warped product manifolds.
problem Classifying totally umbilical surfaces in warped product manifolds.
method Analyzing surfaces in warped product M(κ)fimesI and finding first integrals. result Totally umbilical surfaces in M(κ)fimesI are invariant by isometries. We obtain isometric minimal helicoidal and rotational surfaces using generalized Bour's theorem in three dimensional Minkowski space. In addition, we show that the surfaces preserve minimality when their Gauss maps identically equal, choosing any diffentiable functions on the profile curve.
The study explores isometric deformations of surfaces of translation.
problem Determine the ways surfaces of translation bend isometrically.
method Analyzes existence conditions and provides closed-form expressions for infinitesimal and finite bendings of surfaces of translation.
result Surfaces of translation admit various infinitesimal and finite bendings, including purely torsional and torsion-free.
K-Models clusters functional data with ordinal constraints for better interpretability.
problem Challenges in extracting meaningful insights from functional data due to lack of interpretability.
method Integrates ordinal constraints into clustering to improve interpretability and structure identification.
result Enhances interpretability of clustering results while maintaining performance.
Study of fastest paths in anisotropic media via Finsler geometry.
problem Optimal paths in media with varying speeds and interfaces.
method Finsler geodesics refracted at interfaces, satisfying specific conditions.
result Establishes generalized Snell's and reflection laws.
The paper analyzes high-dimensional kernel regression, showing different risk curves based on data and regularization.
problem Characterizing generalization properties of high-dimensional kernel ridge regression.
method Bias-variance decomposition of the expected excess risk, considering different regularization schemes and data eigen-profiles.
result The risk curve of kernel regression can be double-descent-like, bell-shaped, or monotonic, depending on n, d, and regularization level.
Study finds non-CMC biconservative hypersurfaces in spheres, proving their existence but not embeddability.
problem Characterizing and proving the existence of non-CMC biconservative hypersurfaces in spheres.
method Analyzing p-elastic curves of profile curves of biconservative rotational hypersurfaces in space forms. result Existence of a discrete biparametric family of non-CMC closed biconservative hypersurfaces in Sn(ρ), none of which can be embedded. The paper classifies surfaces with constant skew curvature in 3-space forms.
problem Classifying surfaces with constant skew curvature in 3-space forms.
method Variational characterization and flow of binormal vector field.
result Classification of rotational surfaces with constant skew curvature.
Study nonnegatively curved Alexandrov spaces, proving isoperimetric conditions and structure at infinity.
problem Characterize Alexandrov spaces with nonnegative curvature and structure at infinity.
method Variational approach, focusing on volume growth, cylinder asymptotics, and isoperimetric sets.
result Equivalence of conditions on volume growth, cylinder asymptotics, and isoperimetric profile.
Gaussian DP improves reporting of ML algorithms' differential privacy guarantees.
problem Incomplete and misleading DP guarantees for ML algorithms.
method Using non-asymptotic Gaussian Differential Privacy (GDP) to provide accurate bounds on privacy profiles of ML algorithms.
result GDP captures the entire privacy profile of DP-SGD and related algorithms with virtually no error.
The paper studies how curves evolve under area constraints and converges to a critical point.
problem Evolution of plane curves with fixed area under elastic energy gradient.
method Local and global existence of the flow, simplicity assumption, Łojasiewicz--Simon inequality.
result The evolving curve's length remains bounded and converges to a critical point.
Variational approximations for curve flows on Riemannian manifolds.
problem Approximating solutions to curvature and elastic flow problems on Riemannian manifolds.
method Variational formulations, finite element approximations, piecewise linear elements, stability analysis.
result Derived schemes can compute rotationally symmetric self-shrinkers and geodesics.
Existence and uniqueness of spherical helicoidal surfaces in 3-sphere via spherical curves.
problem Existence and uniqueness of spherical helicoidal surfaces in 3-sphere.
method Continuous function of distance to axis, spherical angular momentum of spherical curves.
result Existence and uniqueness theorem for spherical helicoidal surfaces in 3-sphere.
Study helicoidal surfaces from frontals, revealing geometric rigidity and stability of singularities.
problem Investigate helicoidal surfaces of frontals in Euclidean space.
method Using Legendre curves and framed surfaces, derive curvature expressions and analyze deformations.
result Singularities of curves persist under deformations, revealing geometric rigidity and stability.
New ancient and eternal solutions found for mean curvature flow from minimal surfaces.
problem Finding new examples of mean curvature flow solutions.
method Constructing embedded ancient and eternal solutions related to unstable minimal hypersurfaces.
result Found nonconvex, non-soliton solutions to mean curvature flow.
New comparison theorems for rotationally symmetric self-shrinkers help in proving the uniqueness of the Angenent torus.
problem Uniqueness of the Angenent torus in rotationally symmetric self-shrinkers
method Analyzing profile curves and vertical points of rotationally symmetric self-shrinkers
result Proving the existence and monotonicity of horizontal-point trajectories
We investigate activities that have different periods of duration. We define the profit intensity as a measure of this economic category. The profit intensity in a repeated trading has a unique property of attaining its maximum at a fixed point regardless of the shape of demand curves for a wide class of probability di…
This note is the updated outline of the article "Interpolational properties of planar spiral curves", Fund. and Applied Math., 2001, Vol.7, N.2, 441-463, published in Russian. The main result establishes boundary regions for spiral and piecewise spiral splines, matching given data. The width of such region can serve as…
Minimal surfaces found in 4D space.
problem Minimal surfaces in 4D space.
method Reduced biharmonic equation to ODEs, excluded non-minimal solutions.
result Biharmonic rotational surfaces in 4D are minimal.
The paper improves stability estimates for soap bubble theorem in curved domains.
problem Stability estimates for the Soap Bubble Theorem in curved domains.
method Leveraging Gagliardo-Nirenberg-type interpolation inequalities.
result Optimal stability estimates for Lr deviations of mean curvature from being constant. Classifies Tinder dating profiles using facial embeddings.
problem Automatically review and classify online dating profiles.
method Uses FaceNet facial embeddings to extract features and train logistic regression models.
result Simple logistic regression on 20 profiles achieved 65% validation accuracy.
Discontinuous isoperimetric profile found for a Riemannian manifold.
problem Finding discontinuous isoperimetric profiles in Riemannian manifolds.
method First known example provided.
result Discontinuous isoperimetric profile exists for a Riemannian manifold.
Paper warns against assuming all unreported compound-target binding profiles are negative.
problem Assumption of all unreported compound-target binding profiles being negative is unreliable.
method Proposes a framework to jointly recover unreported profiles and learn predictive models.
result Explicit recovery of unreported profiles improves prediction performance.
ARBO-DART optimizes battery storage dispatch in day-ahead and real-time markets.
problem Optimizing battery storage dispatch in day-ahead and real-time markets.
method Adaptive Refinement Bayesian Optimization (ARBO) for Day-Ahead and Real-Time (ARBO-DART) markets.
result ARBO-DART optimizes battery storage dispatch without requiring analytic gradients or finite-scenario approximations.
The paper introduces Poincaré profiles for metric spaces and groups, linking them to conformal dimension.
problem Understanding the properties of metric measure spaces and groups with polynomial growth.
method Introducing and analyzing Poincaré profiles for groups and hyperbolic spaces.
result Connection between Poincaré profiles and conformal dimension, leading to non-existence of coarse embeddings.
In this work we investigate the following isoperimetric problem: to find the regions of prescribed volume with minimal boundary area between two parallel horospheres in hyperbolic 3-space (the area of the part of the boundary contained in the horospheres is not included). We reduce the problem to the study of rotationa…
Profile entropy measures learnability and compressibility of discrete distributions.
problem Understanding the learnability and compressibility of discrete distributions.
method Investigates profile entropy, showing its role in estimation, inference, and compression.
result Profile entropy is a fundamental measure unifying estimation, inference, and compression.
Modeling trading volume curves using hierarchical Poisson processes.
problem Predicting trading volume curves for financial instruments.
method Hierarchical Poisson process model based on hierarchical Dirichlet process with MCMC algorithm.
result Demonstrated scalability on NASDAQ stocks, including Apple.
A method to describe Riemann surfaces using graph profiles is proposed.
problem Describing Riemann surfaces in a graph-theoretic framework.
method Graph profiles to represent Riemann surfaces, establishing necessary and sufficient conditions for their existence.
result A criterion for the existence of Riemann surfaces with a given signature.
New closed non-CMC biconservative surfaces found in round 3-sphere.
problem Existence of closed biconservative surfaces in space forms.
method Characterization of profile curves and proof of existence using curvature energy.
result Existence of a discrete family of closed, non-CMC biconservative surfaces in S3(ρ). Method controls extrapolation in prediction profiles for statistical and machine learning models.
problem Avoiding invalid predictions due to extrapolation in prediction profiles.
method Genetic algorithm optimization over constrained factor regions.
result Optimal factor settings without constraint are often invalid and extrapolated.
XSP profiles ML models across hardware and software stacks.
problem Challenges in profiling ML model performance across different layers of the stack.
method XSP uses distributed tracing to aggregate data from various sources and introduces a leveled, iterative measurement approach.
result XSP provides insights into ML model execution not easily discernible otherwise.