Paper proves unique energy-minimizing curves in constrained spaces.
problem Uniqueness of energy-minimizing curves in constrained spaces.
method Investigated energy-minimizing curves with fixed endpoints in a constrained space.
result Proved that the set of points for which the energy-minimizing curve is not unique has no interior points.
The paper classifies a special family of knots in lens spaces using knot Floer homology.
problem Classifying constrained knots in lens spaces.
method Parameterization by five integers, characterization via spinc structures, and knot Floer homology calculations. result Complete classification of constrained knots based on knot Floer homology.
We show that the homogeneous and the 2-lobe Delaunay tori in the 3-sphere provide the only isothermic constrained Willmore tori in 3-space with Willmore energy below 8π. In particular, every constrained Willmore torus with Willmore energy below 8π and non-rectangular conformal class is non-degenerated.
Develops G-MLKM for better data-target association in constrained spaces.
problem Data-target association problem in constrained spaces with limited sensor information.
method Graph-based multi-layer k-means++ (G-MLKM) method, including MLKM for local space and G-MLKM for general constrained space.
result Improves data-target association accuracy through error correction mechanisms.
Study geodesics in constrained curve spaces, including elastic curves and concentric circles.
problem Geodesics in constrained curve spaces with Sobolev metrics.
method Intrinsic and constructive approaches.
result Construct geodesics in elastic curve and concentric circle spaces.
Constrained Willmore surfaces are conformal immersions of Riemann surfaces that are critical points of the Willmore energy W=∫H2 under compactly supported infinitesimal conformal variations. Examples include all constant mean curvature surfaces in space forms. In this paper we investigate more generally the crit…
Algorithm optimizes constrained reinforcement learning with dual variables.
problem Minimizing convex functional subject to convex constraint in large state spaces.
method VPDPO algorithm using Lagrangian and Fenchel duality.
result Achieves sublinear regret and constraint violation, globally optimal policy.
Constrained Willmore surfaces are critical points of the Willmore functional under conformal variations. As shown in [5] one can associate to any conformally immersed constrained Willmore torus f a compact Riemann surface Σ, such that f can be reconstructed in terms of algebraic data on Σ. Particularly interesting exam…
FOCOPS optimizes agent's behavior while adhering to constraints.
problem Optimizing agent's behavior while respecting safety constraints.
method FOCOPS solves a constrained optimization problem in policy space, then projects the solution back into the parametric space.
result FOCOPS achieves better performance on constrained robotics tasks.
Study minimizers of quasi-perimeters in RCD spaces with volume constraints.
problem Regularity and topological properties of volume constrained minimizers in RCD spaces.
method New Deformation Lemma and study of interior and exterior points.
result Volume constrained minimizers are open bounded sets with Ahlfors regular boundary.
New algorithms for sampling in constrained domains without learning rates.
problem Sampling in constrained domains with fairness constraints and post-selection inference.
method Coin betting ideas from convex optimisation and a unifying framework for constrained sampling.
result Our algorithms achieve competitive performance without hyperparameter tuning.
New model generates data on constrained sets without losing tractability.
problem Generating data on constrained sets without losing tractability.
method Mirror Diffusion Models (MDM) learn diffusion processes in a dual space constructed from a mirror map.
result MDM generates data on convex constrained sets without losing tractability.
Study compares constrained and decoupled moduli spaces of manifolds with particles and discs.
problem Comparing constrained and decoupled moduli spaces of manifolds with embedded particles and discs.
method Generalized Bödigheimer--Tillmann's work to higher dimensions and different tangential structures.
result New results for surfaces with different tangential structures and higher dimensional manifolds.
This work is dedicated to the study of the Moebius invariant class of constrained Willmore surfaces and its symmetries. We define a spectral deformation by the action of a loop of flat metric connections; Baecklund transformations, by applying a dressing action; and, in 4-space, Darboux transformations, based on the so…
Paper revisits DP-SCO in Euclidean and ℓpd spaces, focusing on constrained and bounded sets.
problem Differentially private stochastic convex optimization in constrained and bounded sets in Euclidean and ℓpd spaces. method Proposes methods achieving excess population risks dependent on Gaussian width of the constraint set, and novel algorithms for unconstrained and heavy-tailed data.
result Theoretical results for DP-SCO in ℓpd spaces, including optimal bounds for strongly convex functions. This article reviews and explains HMC-based methods for sampling constrained continuous distributions.
problem Sampling from continuous distributions with constraints.
method HMC and related methods for constrained sampling.
result HMC and related methods are more efficient for constrained sampling.
New discrete curves defined in space forms with geometric properties.
problem Defining discrete elastic and constrained elastic curves in space forms.
method Extending discrete Euclidean curvature to space forms and using Bäcklund transformations.
result Discrete elastic and constrained elastic curves are elements of a curve hierarchy.
New method for constrained sampling using gradient flows.
problem Sampling from constrained domains.
method Introducing a boundary condition for gradient flow to confine particles within the domain.
result Provable continuous-time convergence in total variation for constrained sampling.
Study of star-shaped hypersurfaces with capillary boundary using constrained mean curvature flow.
problem Understanding the evolution of hypersurfaces with capillary boundaries.
method Locally constrained mean curvature flow for star-shaped hypersurfaces in the half-space.
result Established new Alexandrov-Fenchel inequalities for convex hypersurfaces with capillary boundary.
New algorithm improves sampling from constrained spaces.
problem Sampling from constrained spaces efficiently.
method Metropolis-adjusted Mirror Langevin algorithm.
result Unbiased sampling with improved mixing time.
The paper proves geometric inequalities for pinched convex hypersurfaces in de Sitter space.
problem Geometric inequalities for convex hypersurfaces in de Sitter space.
method Locally constrained flows with initial compact spacelike hypersurfaces pinched in de Sitter space.
result Established geometric inequalities related to quermassintegrals and weighted curvature integrals.
Study flow on de Sitter space for convex hypersurfaces.
problem Behavior of locally constrained inverse curvature flow in de Sitter space.
method Analyze flow on de Sitter space with specific initial conditions and inequalities.
result Derive Alexandrov-Fenchel type inequalities.
Statistical models with constrained probability distributions are abundant in machine learning. Some examples include regression models with norm constraints (e.g., Lasso), probit, many copula models, and latent Dirichlet allocation (LDA). Bayesian inference involving probability distributions confined to constrained d…
Proposes a constrained labeling method for weakly supervised learning.
problem Combining weak supervision signals while navigating misleading correlations.
method Randomized constrained labeling within a defined space.
result Randomized constrained labeling converges after few iterations and outperforms other methods.
The paper proves geometric inequalities in sphere using locally constrained flows.
problem Deriving geometric inequalities in sphere.
method Established the longtime existence and convergence of a locally constrained flow.
result Proved new families of three-term geometric inequalities in sphere.
In-BO optimizes complex constrained domains using SIn-GP surrogate models.
problem Optimizing in complex constrained domains with irregular shapes.
method Sparse Intrinsic Gaussian Processes (SIn-GP) on manifolds with heat kernel estimation.
result In-BO outperforms traditional BO in complex constrained domains.
Method reformulates constrained optimization as latent space inference.
problem Optimizing black-box functions with hard constraints.
method Posterior inference in latent space using flow-based models and diffusion models.
result Method achieves superior performance across various tasks.
Let S be a complete flat surface, such as the Euclidean plane. We obtain direct characterizations of the connected components of the space of all curves on S which start and end at given points in given directions, and whose curvatures are constrained to lie in a given interval, in terms of all parameters involved.…
New algorithm samples constrained distributions efficiently.
problem Sampling from distributions with statistical constraints.
method Primal-dual Langevin Monte Carlo (PD-LMC) using gradient descent-ascent dynamics.
result PD-LMC algorithm successfully samples constrained distributions.
Using results on the topology of moduli space of polygons [Jaggi, 92; Kapovich and Millson, 94], it can be shown that for a planar robot arm with n segments there are some values of the base-length, z, at which the configuration space of the constrained arm (arm with its end effector fixed) has two disconnected com…
In this paper we consider two special classes of constrained Willmore tori in the 3-sphere. The first class is given by the rotation of closed elastic curves in the upper half plane - viewed as the hyperbolic plane - around the x-axis. The second is given as the preimage of closed constrained elastic curves, i.e., elas…
The class of non-rigid registration methods proposed in the framework of PDE-constrained Large Deformation Diffeomorphic Metric Mapping is a particularly interesting family of physically meaningful diffeomorphic registration methods. PDE-constrained LDDMM methods are formulated as constrained variational problems, wher…
We study configuration spaces of linkages whose underlying graph are polygons with diagonal constrains, or more general, partial two-trees. We show that (with an appropriate definition) the oriented area is a Bott-Morse function on the configuration space. Its critical points are described and Bott-Morse indices are co…
The paper solves a conjecture about spacelike hypersurfaces in de Sitter space.
problem Proving an Alexandrov-Fenchel inequality for closed 2-convex spacelike hypersurfaces in de Sitter space.
method Investigating the locally constrained inverse curvature flow to establish the inequality.
result Established an Alexandrov-Fenchel inequality for closed 2-convex spacelike hypersurfaces in de Sitter space.
A new framework uses an Incremental Transformer to design geopolymer mixtures efficiently.
problem Designing geopolymer mixtures with limited data and physical constraints.
method Topology-aware surrogate framework guided by Incremental Transformer.
result The design space is redundant, with fewer effective mixture regimes.
We prove that the critical points of various energies such as the area, the Willmore energy, the frame energy for tori...etc among possibly branched immersions constrained to evolve within a smooth sub-manifold of the Teichmüller space satisfy the corresponding constrained Euler Lagrange equation. We deduce that critic…
CEI achieves convergence rates for constrained Bayesian optimization.
problem Constrained Bayesian optimization with theoretical convergence rates.
method Analyzing simple regret upper bound for CEI in RKHS and Gaussian process settings.
result CEI achieves convergence rates of t−21log2d+1(t) and t2ν+d−νlog2ν+dν(t) for squared exponential and Matérn kernels, respectively. New flow for capillary surfaces converges to spherical caps.
problem Optimizing capillary surfaces in space forms.
method Constrained mean curvature flow.
result Flow converges to spherical caps globally.
Bayesian neural network (BNN) priors are defined in parameter space, making it hard to encode prior knowledge expressed in function space. We formulate a prior that incorporates functional constraints about what the output can or cannot be in regions of the input space. Output-Constrained BNNs (OC-BNN) represent an int…
Diffeologies unify infinite-dimensional geometry and PDEs, enhancing classical function spaces.
problem Combining infinite-dimensional geometry and PDEs for optimization problems.
method Review and extension of classical function spaces and mapping spaces.
result Diffeologies provide a unified framework for evolution equations and optimization problems.
Shielded LMC samples from non-convex spaces with repulsive drift.
problem Sampling from non-convex spaces with convex holes.
method Combining adaptive temperature and repulsive drift.
result Advantages over unconstrained sampling in constrained spaces.
We propose a class of intrinsic Gaussian processes (in-GPs) for interpolation, regression and classification on manifolds with a primary focus on complex constrained domains or irregular shaped spaces arising as subsets or submanifolds of R, R2, R3 and beyond. For example, in-GPs can accommodate spatial domains arising…
Let S be a complete flat surface, such as the Euclidean plane. We determine the homeomorphism class of the space of all curves on S which start and end at given points in given directions and whose curvatures are constrained to lie in a given open interval, in terms of all parameters involved. Any connected compone…
PAC-MOO optimizes constrained multi-objective problems with preferences.
problem Optimizing with constraints and practitioner preferences over objectives.
method Preference-aware constrained multi-objective Bayesian optimization.
result Efficacy demonstrated on real-world analog circuit design problems.
We improve Riemannian metrics for constrained systems control.
problem Controlling mechanical systems with configuration constraints.
method Constructing complete Riemannian metrics by modifying incomplete ones.
result A controller can be found to satisfy a design criterion.
Proposes Constrained Q-learning for reinforcement learning with constraints.
problem Optimizing multiple objectives while adhering to constraints in reinforcement learning.
method Directly restricts the action space in Q-update to learn optimal Q-function for constrained MDP.
result Improves safety and optimality in high-level decision making for autonomous driving.
Let (M,g) be a 3-dimensional Riemannian manifold. The goal of the paper it to show that if P0∈M is a non-degenerate critical point of the scalar curvature, then a neighborhood of P0 is foliated by area-constrained Willmore spheres. Such a foliation is unique among foliations by area-constrained Willmore …
Automatic Chemical Design is a framework for generating novel molecules with optimized properties. The original scheme, featuring Bayesian optimization over the latent space of a variational autoencoder, suffers from the pathology that it tends to produce invalid molecular structures. First, we demonstrate empirically …