Minimal surfaces found in finite volume manifolds.
problem Existence of minimal hypersurfaces in complete manifolds of finite volume.
method Independent result on volume sweeping by hypersurfaces; main tool is a volume constraint result.
result Proves existence of minimal hypersurfaces in complete non-compact manifolds of finite volume.
We establish a min-max estimate on the volume width of a closed Riemannian manifold with nonnegative Ricci curvature. More precisely, we show that every closed Riemannian manifold with nonnegative Ricci curvature admits a PL Morse function whose level set volume is bounded in terms of the volume of the manifold. As a c…
Our goal is to generalize the Choe-Hoppe helicoid and Clifford cones in Euclidean space. By sweeping out L indpendent Clifford cones in R2N+2 via the multi-screw motion, we construct minimal submanifolds in RL(2N+2)+1. Also, we sweep out the L-rays Clifford cone (introduced in Sectio…
3D spheres can't be swept by short curves, complicating geodesic length estimates.
problem Obstructing geodesic length estimates in 3D spheres.
method Constructing specific 3D spheres with controlled diameter and volume.
result Min-max methods for geodesic lengths fail for certain 3D spheres.
Continuous Sweep improves binary quantifier performance.
problem Estimating class prevalence in datasets.
method Parametric binary quantifier inspired by Median Sweep, using parametric class distributions and mean of Adjusted Count estimates.
result Continuous Sweep outperforms other quantifiers in simulations and empirical data analysis.
Two sweeps of the Brennan-Schwartz algorithm solve American options under negative rates.
problem Inability of the Brennan-Schwartz algorithm to solve American options under negative interest rates.
method Two sweeps of the Brennan-Schwartz algorithm in two directions.
result Recovery of the exact solution for American options under negative rates.
The study bounds Morse indices of Willmore spheres in relation to min-max sweep-outs.
problem Estimating Morse indices of Willmore spheres.
method Analyzing the sum of Morse indices of Willmore spheres in min-max sweep-outs.
result At most one Willmore sphere can have index 1 among those realising min-max sphere eversion.
We prove the absence of a universal diameter bound on lengths of curves in a sweep-out of a Riemannian 2-sphere. If such bound existed it would yield a simple proof of existence of short geodesic segments and closed geodesics on a sphere of small diameter.
A new method calculates the minimum volume swept by a sphere's homotopy in 3D space.
problem Finding the minimum volume swept by a sphere's homotopy in 3D space.
method Cable system approach to define and compute cable indices.
result A linear-time algorithm computes all cable indices and achieves the lower bound for the swept volume.
Paper estimates area covered by a line-sweep sensor in robotics.
problem Accurately estimating the area covered by a line-sweep sensor.
method Relies on coverage measure and topological degree in the plane.
result Guaranteed characterization of the explored area using interval analysis.
Trading floors need to be twice as deep as electronic markets to compete.
problem Informed traders prefer fast electronic markets over slow trading floors.
method Examined the performance of trading floors and electronic markets in a hybrid system.
result Trading floors need to be twice as deep as electronic markets to compete.
New 4-manifold invariants from Khovanov-Rozansky link homology.
problem Defining invariants for 4-manifolds.
method Using Khovanov-Rozansky gl(N) link homology, constructing skein modules from 4-categories with duals.
result Proof of the sweep-around property for well-defined link homologies in the 3-sphere.
New algorithm learns efficiently in multi-agent settings.
problem Efficient learning in multi-agent Markov decision processes.
method Cooperative Prioritized Sweeping: model-based reinforcement learning with sample efficiency.
result Outperforms state-of-the-art on SysAdmin and randomized environments.
The paper proves the existence of CMC surfaces with controlled topology in 3-manifolds.
problem Proving the existence of constant mean curvature surfaces with specific topological constraints.
method Min-max construction and convergence to a CMC-parametrized varifold.
result Existence of a non-trivial, branched immersion of a closed Riemann surface with constant mean curvature in a 3-manifold.
Develops an algorithm to find the best subset of points for maximizing the coefficient of determination.
problem Finding the optimal subset of points for maximizing the coefficient of determination in robust correlation analysis.
method The extit{quadratic sweep} method, which involves projecting points into \(\mathbb{R}^5\) and iterating over linearly separable \(k\)-subsets.
result The method optimally finds the best subset of points for maximizing the coefficient of determination without error over several million trials up to \(n=30\).
New example shows open subset of anti-self-dual metrics is not closed.
problem Understanding the structure of moduli spaces of anti-self-dual metrics.
method Link between harmonic functions on hyperbolic 3-manifolds and self-dual harmonic 2-forms.
result The subset of anti-self-dual metrics is not generally closed.
Paper tackles non-uniform coverage planning for robots.
problem Non-uniform coverage planning for robots that need to visit some points more frequently.
method Proposes a novel reinforcement learning approach in a Semi-Markov Decision Process.
result Significant improvement over existing greedy approach in simulations.
Study efficient power iteration for tensor models, proving convergence under specific conditions.
problem Simultaneous alternating power iteration for fixed-order asymmetric rank-one spiked tensor models.
method Finite-iteration local theory, geometrically decaying transient, fixed-order multilinear noise event, warm-start mechanism.
result Convergence to the unique informative local fixed point under specific conditions.
Continuous sweepouts cover manifolds with bounded curve lengths.
problem Covering closed Riemannian manifolds with bounded curve lengths.
method Continuous family of 1-cycles parametrized by a sphere, with length bounds in terms of volume and dimension.
result Polyhedral 1-waist equals filling radius up to a constant factor.
Accelerated Gibbs sampling for Gaussian graphical models using dual factor graphs.
problem Improving convergence rate of Gibbs sampling for Gaussian graphical models.
method Dual normal factor graph approach to accelerate convergence.
result Universal convergence rate improvement in dual domain for all homogeneous models.
SMC analysis reveals key transient effects in macroeconomic ABM.
problem Analysis of complex ABMs is challenging and often relies on ad hoc methods.
method Statistical model checking (SMC) implemented through MultiVeStA.
result Clear contrast across parameter families in macro-financial and structural sweeps.
Study on 3D surfaces and tangles formed by Poncelet triangles.
problem Geometric and topological properties of 3D surfaces and tangles.
method Exploration of Poncelet triangles and associated points.
result Properties of 3D surfaces and tangles formed by Poncelet triangles.
We give a stereological version of the Gauss-Bonnet formula in order to compute the Euler characteristic of a domain with boundary in a smooth orientable surface in R^3, by looking at contacts with a "sweeping" plane.
We observe that the maximal open set of constant curvature k in a Riemannian manifold with curvature bounded below or above by k has a convexity type property, which we call "two-convexity". This statement is used to prove a number of rigidity statements in comparison geometry.
We present a novel method in the family of particle MCMC methods that we refer to as particle Gibbs with ancestor sampling (PG-AS). Similarly to the existing PG with backward simulation (PG-BS) procedure, we use backward sampling to (considerably) improve the mixing of the PG kernel. Instead of using separate forward a…
TOG-Net optimizes grasping for tool manipulation in simulated self-supervised learning.
problem Optimizing grasping for tool manipulation in robots.
method Simulated self-supervised learning with Task-Oriented Grasping Network (TOG-Net).
result Achieved 71.1% task success rate for sweeping and 80.0% for hammering.
Proves local noncollapsing estimate for mean curvature flow.
problem Ensuring noncollapsing in mean curvature flow.
method Combining local estimate with earlier work on ancient solutions.
result Ancient convex solutions that sweep out entire space are noncollapsed.
Particle Markov chain Monte Carlo (PMCMC) is a systematic way of combining the two main tools used for Monte Carlo statistical inference: sequential Monte Carlo (SMC) and Markov chain Monte Carlo (MCMC). We present a novel PMCMC algorithm that we refer to as particle Gibbs with ancestor sampling (PGAS). PGAS provides t…
15 Einstein 4-manifolds with positive conformal curvature are classified.
problem Classifying compact Einstein 4-manifolds with positive conformal curvature.
method Classification based on previous results and new insights into Einstein moduli spaces.
result Exactly 15 manifolds carry such metrics, each with one connected component in the moduli space.
A new principle for optimizer selection improves training speed and performance.
problem Finding the best optimizer hyperparameters for faster training.
method Formulate optimizer selection as maximizing the expected drop rate in loss, treating gradients and updates as signals and an optimizer as a causal filter.
result Greedy optimizer selection yields stable and effective momentum rules.
We analyse all Mini Flash Crashes (or Flash Equity Failures) in the US equity markets in the four most volatile months during 2006-2011. In contrast to previous studies, we find that Mini Flash Crashes are the result of regulation framework and market fragmentation, in particular due to the aggressive use of Intermarke…
Ancient pancake solutions found for curvature flows.
problem Finding unique ancient solutions to curvature flows.
method Constructing and analyzing O(1)imesO(n)-invariant ancient solutions. result Unique O(n)-invariant ancient solutions found. Page's Einstein metric on CP_2 # (-CP_2) is conformally related to an extremal Kaehler metric. Here we construct a family of conformally Kähler solutions of the Einstein-Maxwell equations that deforms the Page metric, while sweeping out the entire Kaehler cone of CP_2 # (-CP_2).The same method also yields analogous sol…
A general theory of partial balayage on Riemannian manifolds is developed, with emphasis on compact manifolds. Partial balayage is an operation of sweeping measures, or charge distributions, to a prescribed density, and it is closely related to (construction of) quadrature domains for subharmonic functions, growth proc…
When a Dehn filled link manifold contains a geometrically incompressible one-sided surface, it is shown there is a unique boundary incompressible position that the surface can take in the link space. The proof uses a version of the sweep-out technique from two-sided Heegaard splitting theory. When applied to one-sided …
Paper analyzes human vocal sentiment using various techniques.
problem Improving accuracy in emotion-level classification of human vocal expressions.
method Conventional vocal feature extraction, deep-learning approaches, context-level analysis, hyperparameter sweeps, data augmentation.
result Improved performance in emotion-level classification.
Efficiently infers cluster assignments in probabilistic models.
problem Efficiently inferring cluster assignments in probabilistic models.
method Amortized approximate Bayesian inference mapping cluster representations into conditional probabilities.
result Parallelizable, yields iid samples with similar computational cost to Gibbs sampling.
New distances for comparing heterogeneous probability measures efficiently.
problem Comparing probability measures across different spaces.
method Introducing Anchor Energy (AE) and Anchor Wasserstein (AW) distances, and a sweep line algorithm for exact computation.
result Exact computation of AE and AW distances in log-quadratic time, significantly faster than GW.
Flip symmetry on knot diagrams affects Khovanov homology.
problem Understanding the flip map on Khovanov homology.
method Analyzing the behavior of the flip map on unlinks and using it to determine the involution.
result The flip map is the identity map over \(\mathbb{F}_2\), confirming a conjecture.
We prove that given a three manifold with an arbitrary metric (M3,g) of positive Ricci curvature, there exists a sweepout of M by surfaces of genus ≤3 and areas bounded by Cvol(M3,g)2/3. We use this result to construct a sweepout of M by 1-cycles of length at most Cvol(M3,g)1/3. The sweepo…
Unified framework for SGMoE resolves estimation and selection issues.
problem Non-identifiability, coupled differential relations, and tight coupling in softmax-Gated models.
method Unified statistical framework with Voronoi-type loss functions and dendrograms of mixing measures.
result Consistent selection of the number of experts without model sweeps, optimal parameter rates under overfitting.
The present paper attempts to show an alternative approach with regards to rational Pythagorean-hodograph (PH) curves and especially more natural approach for rational PH helices (i.e. rational helices). It exploits geometric features of rational helices to obtain a simpler construction of these curves and apply this t…
A new method for feature selection in high-dimensional data reduces search cost while maintaining performance.
problem Feature selection in very-high-dimensional datasets is computationally expensive and challenging.
method Stochastic Sequential Search (SSS) using temperature-controlled softmax sampling and dependency-aware statistics.
result The method significantly reduces search cost while maintaining or improving performance.
We propose a new approach to the problem of neural network expressivity, which seeks to characterize how structural properties of a neural network family affect the functions it is able to compute. Our approach is based on an interrelated set of measures of expressivity, unified by the novel notion of trajectory length…
This is a simple mathematical introduction into Feynman diagram technique, which is a standard physical tool to write perturbative expansions of path integrals near a critical point of the action. I start from a rigorous treatment of a finite dimensional case (which actually belongs more to multivariable calculus than …
Develops a method to construct entire minimal graphs of odd dimensions.
problem Constructing entire minimal graphs of odd dimensions and arbitrary codimensions.
method Evolving-plane ansatz reducing minimal surface system to geodesic equation on Grassmannian.
result Yields a rich family of explicit entire minimal graphs of odd dimension and arbitrary codimension.
Monge surfaces and planar geodesic foliations are studied, revealing unique global properties.
problem Characterizing and understanding Monge surfaces and their foliations.
method Analyzing the geometric properties of Monge surfaces and foliations of planar geodesics.
result The only compact orientable PGF surfaces are tori, which are globally Monge surfaces.
In this paper we study the classification of ancient convex solutions to the mean curvature flow in Rn+1. An open problem related to the classification of type II singularities is whether a convex translating solution is k-rotationally symmetric for some integer 2≤k≤n, namely whether its level set is a …