A math surface has varying perimeter rules.
problem Finding a surface with a non-continuous isoperimetric profile.
method Constructed a 2D Riemannian manifold.
result Discovered a surface with a discontinuous isoperimetric profile.
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48 results for “discontinuous profile”
The first known example of a complete Riemannian manifold whose isoperimetric profile is discontinuous is given.
We construct sequences of `expander manifolds' and we use them to show that there is a complete connected 2-dimensional Riemannian manifold with discontinuous isoperimetric profile, answering a question of Nardulli and Pansu. Using expander manifolds in dimension 3 we show that for any there is a Riemannian 3-…
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.
Machine learning predicts biologic therapy outcomes in psoriasis patients.
problem Predicting long-term biologic therapy outcomes in psoriasis patients.
method Machine learning algorithms were used to predict drug discontinuation and treatment duration.
result Machine learning models accurately predict outcomes with high diagnostic accuracy and low MAE.
New method resolves causal heterogeneity by defining a resolution profile.
problem Causal subgroup analyses often oversimplify heterogeneity into a small number of groups.
method Introduces a resolution profile as a functional of the causal feature law, using Bayesian-bootstrap inference.
result Shows that the resolution profile is a continuous path with discontinuities at knots, providing integer-valued subgroup numbers.
Proves nonemptyness of domains for specific group actions.
problem Nonemptyness of domains of proper discontinuity for Anosov groups of affine Lorentzian transformations.
method Proof of nonemptyness of domains of proper discontinuity.
result Proves nonemptyness of domains for Anosov groups of affine Lorentzian transformations.
We consider the deformation of a discontinuous group acting on the Euclidean space by affine transformations. A distinguished feature here is that even a `small' deformation of a discrete subgroup may destroy proper discontinuity of its action. In order to understand the local structure of the deformation space of disc…
Cut-DeepONet handles discontinuities and sharp transitions in neural operators.
problem Neural operators struggle with discontinuities and sharp transitions in PDEs.
method Two-stage training framework that explicitly models discontinuities via a lifting strategy and input-dependent discontinuity prediction.
result Cut-DeepONet outperforms state-of-the-art methods on benchmark PDEs with low-resolution datasets.
Study proves existence of equilibrium in incomplete economies with discontinuous volatility.
problem Existence of incomplete Radner equilibrium with nondegenerate endogenous volatility.
method Established existence of solution for Markovian quadratic BSDEs with discontinuous generators using unique continuation and backward uniqueness.
result Existence of incomplete Radner equilibrium with nondegenerate endogenous volatility.
New domains of discontinuity found for Anosov representations.
problem Understanding Anosov representations acting on homogeneous spaces.
method Constructing open domains of discontinuity for Anosov representations acting on specific homogeneous spaces.
result Describes the largest possible open domains of discontinuity for Zariski dense Anosov representations.
As early as 1972, Penrose - in a purely formal way - introduced a "discontinuous coordinate transformation", which relates a continuous representation of the metric of impulsive pp-waves to a discontinuous one. On the basis of the invertibility concept for generalized functions developed recently by the first author, w…
Quantifying discontinuitymath.MG
Study the discontinuity of functions not embeddable in Euclidean space.
problem Understanding discontinuity of non-embeddable functions.
method Define a modulus of discontinuity and establish lower bounds.
result Quantified nonembeddability results and topological Tverberg theorem.
Bayesian nonparametric discontinuity design improves causal inference without randomization.
problem Causal inference in non-randomized settings with additional assumptions.
method Bayesian model comparison and Gaussian process regression.
result BNDD can detect discontinuities of any order and spectral features.
Study new symmetries in non-symmetric spaces and discontinuous groups.
problem Analyze symmetries in non-symmetric homogeneous spaces and discontinuous groups.
method Investigate discrete series, discontinuous groups, and analysis on pseudo-Riemannian spaces.
result New insights into symmetries of non-symmetric homogeneous spaces and discontinuous groups.
Improved method for estimating derivatives of discontinuous functions using stochastic algorithmic differentiation and regression.
problem High Monte-Carlo error in finite difference approximation of discontinuous functions.
method Combining stochastic algorithmic differentiation and regression to estimate derivative of expectations of discontinuous functions.
result Reduction in Monte-Carlo error through decoupling integration of Dirac delta and conditional expectation.
Paper finds surface groups can deform in reductive symmetric spaces.
problem Finding deformations of discontinuous groups in reductive symmetric spaces.
method Analyzing Zariski dense surface subgroups and their deformations.
result Surface groups of high genus can deform in reductive symmetric spaces.
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.
Donors who defer their donations volunteer less in the future.
problem Volunteer labor can be less beneficial to charities than its costs.
method Regression discontinuity design with a procedure to handle manipulation.
result Donor manipulation invalidates standard regression discontinuity design, but a new method provides partial identification bounds.
Develops a framework for modeling interest rate markets with jumps.
problem Stochastic discontinuities in interest rate markets.
method Extended HJM framework with stochastic discontinuities, affine semimartingales.
result Fundamental theorem of asset pricing based on NAFLVR.
We construct finite time blow-up solutions to the 2-dimensional harmonic map flow into the sphere , \begin{align*} u_t & = Δu + |\nabla u|^2 u \quad \text{in } Ω\times(0,T) \\ u &= \varphi \quad \text{on } \partial Ω\times(0,T) \\ u(\cdot,0) &= u_0 \quad \text{in } Ω, \end{align*} where is a bounded, smooth do…
New method estimates active subspaces for jump-discontinuous functions.
problem Estimating active subspaces for discontinuous functions like ABMs.
method Extending active subspaces to discontinuous functions, using Gaussian process.
result Identifies important parameters in ABM simulations of refugee movement.
This article gives an up-to-date account of the theory of discrete group actions on non-Riemannian homogeneous spaces. As an introduction of the motifs of this article, we begin by reviewing the current knowledge of possible global forms of pseudo-Riemannian manifolds with constant curvatures, and discuss what kind of …
Paper analyzes error in stochastic approximation for discontinuous functions.
problem Estimating expected error in discontinuous stochastic approximation.
method Uses finite differences and error estimate for discontinuous functions.
result Achieves error estimate of for discontinuous stochastic representation.
Bayesian emulator tackles models with discontinuities efficiently.
problem Uncertainty quantification of models with multiple discontinuities.
method TENSE framework, designed correlation structures, single emulator object.
result Efficient emulation of complex models with multiple discontinuities.
New algorithms solve time-dependent navigation problems, including zig-zag paths.
problem Finding optimal paths in moving water with varying speed profiles.
method Lorentz-Finsler geometry, novel computational algorithms.
result Optimal paths may involve zig-zag trajectories due to tacking behavior.
We characterise completely when limit sets, as parametrised by Cannon-Thurston maps, move discontinuously for a sequence of algebraically convergent quasi-Fuchsian groups.
Study proves rigid spectral properties of planets with metric discontinuities.
problem Establishing spectral rigidity for spherically symmetric planets with discontinuities.
method Novel trace formula applied to two wave types in spherically symmetric manifolds with boundary and interior interfaces.
result Spectral rigidity of spherically symmetric planets with discontinuities is proven.
Properly Discontinuous Isometric Actions on the Unit Sphere of Infinite Dimensional Hilbert Spacesmath.DG
We study the properly discontinuous and isometric actions on the unit sphere of infinite dimensional Hilbert spaces and we get some new examples of Hilbert manifold with costant positive sectional curvature. We prove some necessary conditions for a group to act isometrically and properly discontinuously and in the case…
This work models overnight rates with jumps and discontinuities, extending classical short-rate models.
problem Capturing the jump behavior and discontinuities in overnight rates for accurate modeling.
method Developed a term structure modeling framework based on overnight rates, accommodating stochastic discontinuities.
result Simple specifications can capture the jump behavior of overnight rates, and explicit valuation formulas are provided.
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.
Zariski-dense deformations of standard discontinuous groups for pseudo-Riemannian homogeneous spacesmath.DG
The study explores deformations of discrete subgroups in non-compact homogeneous spaces.
problem Addressing the proper discontinuity of discrete subgroups in non-compact homogeneous spaces.
method Classification results for deformations of standard discontinuous groups in pseudo-Riemannian homogeneous spaces.
result Conditions for local rigidity and Zariski-dense deformations in standard quotients.
Paper analyzes SGHMC for non-convex optimization with discontinuous gradients.
problem Training neural networks with ReLU activation.
method Non-asymptotic convergence analysis of SGHMC with discontinuous gradients.
result Explicit upper bounds for expected excess risk in non-convex optimization.
This paper tackles discontinuous neural networks for better approximation of piecewise continuous functions.
problem Limitation of neural networks in approximating piecewise continuous functions due to discontinuities.
method Proposes a decoupled two-step procedure to train a discontinuous deep neural network model.
result Provides approximation guarantees for the proposed model in piecewise continuous function spaces.
In the present paper, we prove that no infinite group acts isometrically, effectively, and properly discontinuously on a certain class of Lorentzian manifolds that are not necessarily homogeneous.
Framework uses deep learning and statistical models to solve PDEs with discontinuous coefficients.
problem Solving PDEs with discontinuous coefficients.
method Two-stage physics-informed deep learning and statistical mixture models.
result Framework achieves adaptability and accurate parameter identification.
The paper extends HMC for inference in probabilistic programs with discontinuities.
problem Handling discontinuities in probabilistic programs using HMC.
method Designing a SPPL with language restrictions and a compilation scheme to preserve statistical and syntactic interpretation of if-else statements.
result Inference in probabilistic programs with discontinuities is possible using HMC extensions.
In this article we study properly discontinuous actions on Hilbert manifolds giving new examples of complete Hilbert manifolds with nonnegative, respectively nonpositive, sectional curvature with infinite fundamental group. We also get examples of complete infinite dimensional Kähler manifolds with positive holomorphic…
Estimates discontinuous optimal transport maps between a discrete and continuous distribution.
problem Estimating discontinuous optimal transport maps between a discrete and continuous distribution.
method Entropic optimal transport estimator, computationally efficient.
result The estimator converges at the minimax-optimal rate in the semi-discrete setting.
Let be a CAT(0) space, and a discrete cyclic group of isometries of . We investigate the domain of discontinuity for the action of on the boundary .
Anosov representations lead to compact domains in flag manifolds.
problem Constructing cocompact domains of discontinuity for Anosov representations.
method Systematic approach to domains of discontinuity using flag manifolds.
result Every cocompact domain of discontinuity arises from a construction, with exceptions in low rank.
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.
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.
We study the action of the group of polynomial automorphisms of C^n (n>2) which preserve the Markoff-Hurwitz polynomial H(x):= x_1^2 + x_2^2 + ... + x_n^2 - x_1 x_2 ... x_n. Our main results include the determination of the group, the description of a non-empty open subset of C^n on which the group acts properly discon…
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.
Proposes a new adaptive design strategy for discontinuous regression functions.
problem Designing input variables for discontinuous regression functions.
method Sequential adaptive design strategy using statistical properties.
result Effective design points selection for discontinuous regression functions.
In cheminformatics, compound-target binding profiles has been a main source of data for research. For data repositories that only provide positive profiles, a popular assumption is that unreported profiles are all negative. In this paper, we caution audience not to take this assumption for granted, and present empirica…
Study of domains of discontinuity in oriented flag manifolds for semi-simple Lie groups.
problem Identifying domains of discontinuity in oriented flag manifolds for semi-simple Lie groups.
method Combinatorial description of proper discontinuity and cocompactness of domains identified by removing a set obtained from the limit set of Γ.
result First examples of cocompact domains of discontinuity in oriented Grassmannians for Hitchin representations.