Paper finds only one unique regular shrinker with 2 closed regions.
problem Characterizing blow-up limits of planar curve networks.
method Analysis of Huisken's monotonicity formula.
result There is only one regular shrinker with 2 closed regions.
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48 results for “closed regions”
We introduce a local move on a link diagram named a region freeze crossing change which is close to a region crossing change, but not the same. We study similarity and difference between region crossing change and region freeze crossing change.
No closed timelike geodesics in Kerr spacetimes, proving absence of closed causal geodesics.
problem Proving the nonexistence of closed timelike geodesics in Kerr spacetimes.
method Analyzing the Kerr-star spacetime, excluding closed null geodesics and proving the nonexistence of closed timelike geodesics.
result No closed timelike geodesics in Kerr spacetimes.
Generic smooth boundaries for isoperimetric regions in 8D manifolds.
problem Understanding boundaries of isoperimetric regions in high-dimensional spaces.
method Generic regularity results for isoperimetric regions in closed Riemannian manifolds of dimension eight.
result Smooth nondegenerate boundaries for isoperimetric regions for generic metrics and volumes.
In a compact orbifold, for small prescribed volume, an isoperimetric region is close to a small metric ball; in a Euclidean orbifold, it is a small metric ball.
Isoperimetry by stretchingmath.DG
Constructs isoperimetric regions from separating hypersurfaces.
problem Finding isoperimetric regions in closed manifolds.
method Constructs isoperimetric regions from separating hypersurfaces.
result Yields isoperimetric boundaries with diverse topological types and singular sets.
Study on bounds of knot untangling for specific types of knots.
problem Determining upper limits for knot untangling.
method Defined warping degree, examined diagrams combinatorially.
result Upper bounds for unknotting and region unknotting numbers.
Paper shows regions close to negatively curved metrics are minimal fillings and rigid.
problem Boundary rigidity and minimality of metrics near negatively curved ones.
method Generalizes previous work on filling volume minimality and boundary rigidity for almost hyperbolic metrics.
result Regions with metrics close to a negatively curved symmetric metric are strict minimal fillings and boundary rigid.
The paper finds singular isoperimetric regions in high-dimensional spaces.
problem Existence of singular isoperimetric regions in high-dimensional manifolds.
method Construction of specific manifolds with singular isoperimetric regions.
result Construction of manifolds with singular isoperimetric regions.
Conformal Prediction Regions match Imprecise Highest Density Regions under consonance.
problem Matching conformal prediction regions with highest density regions.
method Using consonance and the Imprecise Probability theory of clouds.
result Imprecise Highest Density Regions are equivalent to Conformal Prediction Regions under consonance.
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…
A Scale-Critical Trapped Surface Formation Criterion: A New Proof via Signature for Decay Ratesmath.AP
New proof of trapped surface formation using signature for decay rates.
problem Trapped surface formation in gravitational collapse.
method Systematic approach with signature for decay rates, rescaling argument.
result Reproof and extension of a scale-critical theorem.
New formulas for geodesics on Stiefel and flag manifolds using trust-region method.
problem Computing geodesics and logarithms on Stiefel and flag manifolds.
method Closed-form geodesic formulas, trust-region solver, Fréchet derivatives.
result Efficient computation of geodesic distance and logarithm map.
RYU framework constructs safe regions for optimization problems.
problem Optimization problems with specific component functions.
method RYU framework for constructing safe regions.
result RYU framework improves upon state-of-the-art methods.
Adam optimizer fails to stay close to optimal point under certain conditions.
problem Adam optimizer's tendency to deviate from the optimal point in training neural networks.
method Analyzed Adam's behavior in convex regions and proposed a new algorithm to correct this.
result Adam optimizer cannot stay close to the optimal point when effective learning rate exceeds a certain bound.
Study shows no closed trapped submanifolds can be tangent to certain spacelike hypersurfaces.
problem Existence of closed trapped submanifolds in spacetime regions foliated by specific hypersurfaces.
method Introduced future convex spacelike/null hypersurfaces and proved no dimensional closed trapped submanifolds can be tangent to these hypersurfaces from their future side.
result Closed trapped submanifolds cannot be found in open spacetime regions foliated by future convex hypersurfaces.
Soap bubbles and isoperimetric regions in the product of a closed manifold with Euclidean spacemath.DG
For any closed Riemannian manifold we prove that large isoperimetric regions in are of the form (Euclidean ball). We prove that if has non-negative Ricci curvature then the only soap bubbles enclosing a large volume are the products (Euclidean sphere). We give an example…
We consider a generic configuration of regions, consisting of a collection of distinct compact regions in which may be either smooth regions disjoint from the others or regions which meet on their piecewise smooth boundaries in a generic way. We introduce a skeletal linking …
We find a resonance free region polynomially close to the critical line on Conformally compact manifolds with polyhomogeneous metric.
New method uses conformalization to create classification regions from ambiguous labels.
problem Creating provable guarantees in classification with uncertain labels.
method Conformal methods applied to credal regions for classification problems.
result New method provides smaller and more disentangled prediction sets.
Enhances DES by removing noise and defining regions more accurately.
problem Incompetent classifier selection in noisy regions and true indecision regions.
method FIRE-DES++ uses equal number of samples from each class and removes noise to define regions more accurately.
result FIRE-DES++ outperforms FIRE-DES and state-of-the-art DES frameworks.
The closed string field theory minimal-area problem asks for the conformal metric of least area on a Riemann surface with the condition that all non-contractible closed curves have length at least 2π. Through every point in such a metric there is a geodesic that saturates the length condition, and saturating geodesics …
Modeling wormhole creation without singularities in relativity.
problem Creating wormholes without singularities in classical relativity.
method Topological surgery and Morse theory to construct a nonsingular wormhole.
result Wormholes can be created nonsingularly in classical relativity.
Many iterative procedures in stochastic optimization exhibit a transient phase followed by a stationary phase. During the transient phase the procedure converges towards a region of interest, and during the stationary phase the procedure oscillates in that region, commonly around a single point. In this paper, we devel…
Given closed Riemannian manifold of positive Ricci curvature we study isoperimetric regions on the spherical cone over . When is Einstein we use this to compute the Yamabe constant of and so to obtain lower bounds for the Yamabe invariant of $M\tim…
Tightening Fractional Covering Upper Bounds on the Partition Function for High-Order Region Graphscs.LG
In this paper we present a new approach for tightening upper bounds on the partition function. Our upper bounds are based on fractional covering bounds on the entropy function, and result in a concave program to compute these bounds and a convex program to tighten them. To solve these programs effectively for general r…
The paper divides minimal hypersurfaces in a ball into two parts.
problem Dividing minimal hypersurfaces in a ball into two parts.
method Analyzing hyperplanes and mean convex regions.
result Every hyperplane divides minimal hypersurfaces into two parts.
Stable capillary surfaces in weighted balls are disks.
problem Finding the shape of isoperimetric regions in weighted balls.
method Stability analysis and Hsiang symmetrization.
result Interior boundaries of isoperimetric regions in weighted balls are disks.
Null geodesics in Kerr spacetimes cannot be closed or bounded.
problem Existence of closed null geodesics in Kerr spacetimes.
method Analytical proof of non-existence of closed null geodesics in Kerr spacetimes.
result Null geodesics in Kerr spacetimes cannot be closed or contained in a compact subset.
The SPS method constructs confidence regions for true parameters with optimal sample complexity.
problem Constructing exact, non-asymptotic confidence regions for true system parameters.
method Sign-Perturbed Sums (SPS) method, generalized to various types of problems.
result High probability upper bounds for SPS confidence regions show optimal shrinkage rate.
Core groupsmath.GT
Core groups are link invariants defined by arc or region presentations.
problem Defining link invariants using different presentations of arcs and regions.
method Introducing core groups as link invariants defined by presentations involving arcs or regions, and extending these to virtual link diagrams.
result Properties of core groups and their extensions to virtual link diagrams are discussed.
This paper is a continuation of our paper about boundary rigidity and filling minimality of metrics close to flat ones. We show that compact regions close to a hyperbolic one are boundary distance rigid and strict minimal fillings. We also provide a more invariant view on the approach used in the above mentioned paper.
Proposes a recursive MPC scheme with probabilistic safety guarantees for uncertain dynamic systems.
problem Probabilistic safety guarantees for MPC in dynamic environments with unknown stochastic agents.
method Uses conformal prediction to derive high-confidence prediction regions and gradually relax safety constraints online.
result Ensures recursive feasibility of MPC schemes by relaxing safety constraints over time.
It has been shown in \cite{DPSU} that, under some additional assumptions, two simple domains with the same scattering data are equivalent. We show that the simplicity of a region can be read from the metric in the boundary and the scattering data. This lets us extend the results in \cite{DPSU} to regions with the same …
Convex hypersurfaces in curved spaces bound convex regions.
problem Characterizing convex hypersurfaces in curved spaces.
method Gauss-Codazzi equations, Schur comparison theorem, Alexandrov geometry.
result Closed convex hypersurfaces bound convex regions in curved spaces.
Every knot has a plat projection, obtained by closing up a braid with bridges. The plat projection is determined by the number of strands and the number of rows of twist regions in the braid, and an integer number of crossings in each twist region. In recent work, we showed that under certain restrictions, including th…
Adaptive Trust Region Policy Optimization: Global Convergence and Faster Rates for Regularized MDPscs.LG
TRPO adapts trust region methods for faster RL convergence.
problem Improving RL convergence rates in regularized MDPs.
method Adaptive scaling in TRPO for faster convergence rates.
result First RL result showing faster rates with regularization.
We show linear XOR classification is possible and propose equality separation for anomaly detection.
problem Linearly separating XOR data.
method Equality separation, adapting SVM objective for data within/outside margin.
result Equality separation can detect both seen and unseen anomalies.
Closed and broken electromagnetic orbits in Kerr-Newman spacetime
problem Constructing closed and broken electromagnetic orbits in the Kerr-Newman spacetime
method Constructing smooth closed electromagnetic orbits tangent to the axial Killing field and proving the existence of spherical electromagnetic orbits
result Proving the existence of spherical electromagnetic orbits and constructing closed broken electromagnetic orbits
New curvature condition helps organize high-curvature regions in geometric flows.
problem Organizing high-curvature regions in geometric flows.
method Introducing quasi-parallel mean curvature (QPMC) and proving canonical foliation.
result Bubblesheets can be placed in a suitable normal form.
Normal forms for strong magnetic systems on surfaces: Trapping regions and rigidity of Zoll systemsmath.DS
Normal forms prove dynamical results for magnetic fields on surfaces.
problem Existence and rigidity of Zoll flows on surfaces.
method Proved normal forms for strong magnetic fields and used them to derive dynamical results.
result Flow cannot be Zoll unless specific conditions hold.
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.
We provide an efficient algorithm to compute the minimum area of a homotopy between two closed plane curves, given that they divide the plane into finite number of regions. For any positive real number , we construct a closed plane curve such that the minimum area of a null homotopy of is l…
New insights into pseudo-Anosov flows with special periodic orbits.
problem Understanding pseudo-Anosov flows with periodic orbits in 3-manifolds.
method Analyzing the topological features corresponding to trees of scalloped regions and classifying flows with the same free homotopy data.
result Explicit examples of flows with the same free homotopy data but not orbit equivalent.
Proposes a new algorithm for solving optimization problems with stochastic objectives and equality constraints.
problem Optimization problems with stochastic objectives and deterministic equality constraints.
method Trust-region stochastic sequential quadratic programming (TR-StoSQP) with adaptive relaxation techniques.
result Established a global almost sure convergence guarantee for TR-StoSQP.
New bounds for Neyman-Pearson region using -divergences.
problem Bounding the Neyman-Pearson region for hypothesis testing.
method Establishing novel lower and upper bounds using -divergences.
result Best possible lower bound for the Neyman-Pearson boundary using hockey-stick -divergences.
Analyzes how learning algorithms affect and are affected by data manipulation.
problem Characterizing the closed-loop behavior of learning algorithms in the presence of decision-dependent data.
method Analyzes repeated risk minimization as perturbed gradient flows of performative risk minimization, considering multiple local minimizers.
result Characterizes the region of attraction for various equilibria and introduces performative alignment.
The use of EEG biometrics, for the purpose of automatic people recognition, has received increasing attention in the recent years. Most of current analysis rely on the extraction of features characterizing the activity of single brain regions, like power-spectrum estimates, thus neglecting possible temporal dependencie…