A filling curve on a based surface determines a pseudo-Anosov homeomorphism of via the process of "point-pushing along ." We consider the relationship between the self-intersection number of and the dilatation of ; our main result is that the dilatation is bounded between $(i(γ)+1…
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This paper explores the nonconvexity of push-forward constraints in machine learning.
problem The nonconvexity of push-forward constraints in machine learning.
method The paper provides sufficient and necessary conditions for the (non)convexity of push-forward functions and maps.
result Push-forward constraints are generally nonconvex, which limits the design of convex optimization problems in machine learning.
Researchers find a way to bound the complexity of certain subgroup geometric invariants.
problem Understanding the geometric invariants of subgroups of direct products of free groups.
method Generalizing techniques for 'pushing fillings' into normal subgroups.
result Finitely presented subgroups of direct products of three free groups and subgroups of finiteness type in a direct product of free groups have Dehn functions bounded above by .
Top-N recommender systems have been investigated widely both in industry and academia. However, the recommendation quality is far from satisfactory. In this paper, we propose a simple yet promising algorithm. We fill the user-item matrix based on a low-rank assumption and simultaneously keep the original information. T…
Push-SAGA is a decentralized algorithm for directed graphs that converges linearly.
problem Finite-sum minimization over directed graphs with stochastic gradients.
method Combines variance reduction, gradient tracking, and consensus algorithms.
result Achieves linear convergence for smooth and strongly convex problems.
Deep Neural Networksstat.ML
Deep Neural Networks (DNNs) are universal function approximators providing state-of- the-art solutions on wide range of applications. Common perceptual tasks such as speech recognition, image classification, and object tracking are now commonly tackled via DNNs. Some fundamental problems remain: (1) the lack of a mathe…
The fast demographic growth, together with the concentration of the population in cities and the increasing amount of daily waste, are factors that push to the limit the ability of waste assimilation by Nature. Therefore, we need technological means to make an optimal management of the waste collection process, which r…
Smoothly isotopic 3-discs in 4-sphere become identical after 5-dimensional push.
problem Smooth isotopy of 3-discs in 4-sphere.
method Pushing 3-discs into 5-dimensional space.
result Isotopic 3-discs in 4-sphere become identical after 5-dimensional push.
Study finds anomalies in high-frequency S&P 500 price changes.
problem Anomalies in high-frequency S&P 500 price changes.
method Using NBBO event-time data, the study forms pairs of backward and forward price increments, standardizes them, and estimates expected responses on a fine grid of push magnitudes.
result Persistent structural shift in expected responses: near zero for short lags, pronounced tails for long lags, indicating correlation between larger historical pushes and nonzero responses.
We establish the Thom isomorphism in twisted K-theory for any real vector bundle and develop the push-forward map in twisted K-theory for any differentiable proper map (not necessarily K-oriented). The push-forward map generalizes the push-forward map in ordinary K-theory for any -oriented differentiable…
Learning Synergies between Pushing and Grasping with Self-supervised Deep Reinforcement Learningcs.RO
Skilled robotic manipulation benefits from complex synergies between non-prehensile (e.g. pushing) and prehensile (e.g. grasping) actions: pushing can help rearrange cluttered objects to make space for arms and fingers; likewise, grasping can help displace objects to make pushing movements more precise and collision-fr…
We study the maximal entropy per unit generator of push-point mapping classes on the punctured disk. Our work is motivated by fluid mixing by rods in a planar domain. If a single rod moves among N-fixed obstacles, the resulting fluid diffeomorphism is in the push-point mapping class associated with the loop in π_1(D^2 …
This paper presents a data-driven approach to model planar pushing interaction to predict both the most likely outcome of a push and its expected variability. The learned models rely on a variation of Gaussian processes with input-dependent noise called Variational Heteroscedastic Gaussian processes (VHGP) that capture…
On the push-out spacemath.DG
Let be an immersion where is a smooth connected -dimensional manifold without boundary. Then we construct a subspace of , namely push-out space. which corresponds to a set of embedded manifolds which are either parallel to , tubes around or, in…
Deep RL trains a robust humanoid push-recovery policy.
problem Training robust humanoid push-recovery policies.
method Model-free Deep Reinforcement Learning.
result Policy learns robust behaviors across the entire body.
We show that the minimum of asymptotic translation lengths of all point-pushing pseudo-Anosov maps on any one punctured Riemann surface is one.
Unified framework for stability and generalization of Push-Sum in decentralized learning over directed graphs.
problem Understanding stability and generalization of Push-Sum in decentralized learning over directed networks.
method Developed a unified uniform-stability framework for SGP algorithm, incorporating imbalance-aware consistency bounds.
result Established finite-iteration stability and optimization guarantees for convex and non-convex objectives.
Study of point-pushing actions on manifolds with boundary.
problem Analyzing point-pushing actions on manifolds with boundary.
method Examining the homomorphism from braid groups to homotopy classes of homotopy equivalences.
result Injectivity of the map from the k-th braid group to homotopy classes of homotopy equivalences.
Push-forward models struggle to fit multimodal distributions due to high Lipschitz constants.
problem Expressivity of push-forward generative models in fitting multimodal distributions.
method Analyzing the Lipschitz constant and its relation to the total variation distance and Kullback-Leibler divergence.
result Push-forward models require high Lipschitz constants to approximate multimodal distributions, leading to a trade-off between expressivity and stability.
In this note, we reconcile two approaches that have been used to construct stringy multiplications. The pushing forward after pulling back that has been used to give a global stringy extension of the functors K_0,K^{top},A^*,H^* [CR, FG, AGV, JKK2], and the pulling back after having pushed forward, which we have previo…
Let be a closed Riemann surface of genus with one point removed. In this paper, we identify those point-pushing pseudo-Anosov maps on that preserve at least one bi-infinite geodesic in the curve complex.
Market Mill Dependence Pattern in the Stock Market: Distribution Geometry, Moments and Gaussizationphysics.soc-ph
This paper continues a series of studies devoted to analysis of the bivariate probability distribution P(x,y) of two consecutive price increments x (push) and y (response) at intraday timescales for a group of stocks. Besides the asymmetry properties of P(x,y) such as Market Mill dependence patterns described in preced…
The Cannon-Thurston map's pushed measures on the circle are singular with respect to sphere measures.
problem Understanding the behavior of geodesics and measures on fibered hyperbolic 3-manifolds.
method Properties of geodesics and measures on the circle and sphere are analyzed to prove singularity.
result Natural measures on the circle become singular with respect to measures on the sphere.
Researchers examine various causal structures for spacetimes with continuous metrics.
problem Comparing causal structures for spacetimes with continuous but not necessarily smooth metrics.
method Examined three key properties: push-up lemma, openness of chronological futures, and existence of limit causal curves.
result Spacetimes with continuous metrics do not always satisfy all three key properties.
The Singular Asymptotics Lemma by Brüning and Seeley and the Push-Forward Theorem by Melrose lie at the very heart of their respective approaches to singular analysis. We review both and show that they deal with the same basic problem, giving solutions that emphasize different aspects of it. This also points to a possi…
KINet learns object interactions without supervision for robotic pushing.
problem Lack of supervised data for object-centric forward prediction.
method End-to-end unsupervised framework using keypoint representation and contrastive estimation.
result Automatically generalizes to unseen scenarios and accurately predicts future states.
In this paper, we address the problem of embedded feature selection for ranking on top of the list problems. We pose this problem as a regularized empirical risk minimization with -norm push loss function () and sparsity inducing regularizers. We leverage the issues related to this challenging optimization…
This research examines the geometry of latent spaces in push-forward generative models.
problem Tendency of deep generative models to output samples outside target distribution support.
method Geometric measure theory and truncation method to enforce simplicial cluster structure.
result Proves sufficient condition for optimality in latent space geometry.
Study Stein and Milnor fillings of links from surface singularities.
problem Comparing Stein and Milnor fillings of links from surface singularities.
method Analyzing the topology and obstructions of Stein fillings and Milnor fillings.
result Milnor fillings have bounded topology, while Stein fillings can be more varied.
Proves upper bound on systolic ratio for circle fillings.
problem Bounding systolic ratio for circle fillings.
method Proved upper bound on systolic ratio depending on genus.
result Filling Area Conjecture holds for large genus.
The paper constructs minimal coherent filling pairs on surfaces.
problem Finding minimal intersecting coherent filling pairs on surfaces.
method Geometric procedure starting from a torus filling pair.
result Construction of minimal intersecting coherent filling pairs on for .
Study of codimension-1 embeddings in 3-manifolds using twist maps and push maps.
problem Embedding 3-manifolds in specific topological spaces.
method Sphere twist maps and push maps to construct codimension-1 spun embeddings.
result Every closed orientable 3-manifold admits a codimension-1 spun embedding in specific spaces.
The study constructs a Lorentzian length space and explores its properties and relationships with metric and causal geometry.
problem Understanding the relationship between metric and causal geometry in Lorentzian spaces.
method Constructing a Lorentzian length space with an orthogonal splitting on a product of an interval and a metric space, and using synthetic time-like Ricci curvature bounds.
result Established sufficient conditions for global hyperbolicity and formulated time-like Ricci curvature bounds without push-up and regularity assumptions.
Point-pushing in 3-manifoldsmath.GT
We study the Birman exact sequence for compact 3-manifolds.
The paper classifies symplectic fillings of lens spaces and constructs cobordisms.
problem Classifying symplectic fillings of lens spaces and constructing cobordisms.
method Analyzing tight and universally tight contact structures, using plumbing of disk bundles, and constructing cobordisms.
result Maximal second homology Stein fillings of lens spaces are given by specific plumbing.
Computes A-polynomials of knots from Whitehead sister link fillings.
problem Computing A-polynomials for knots from Whitehead sister link fillings.
method Using results on A-polynomials of Dehn fillings, formulas are derived for the A-polynomials of knots.
result Formulas to compute A-polynomials for knots from Whitehead sister link fillings.
If a simple 3-manifold M admits a reducible and a toroidal Dehn filling, the distance between the filling slopes is known to be bounded by three. In this paper, we classify all manifolds which admit a reducible Dehn filling and a toroidal Dehn filling with distance 3.
We give three infinite families of examples of nonhyperbolic Dehn fillings on hyperbolic manifolds. A manifold in the first family admits two Dehn fillings of distance two apart, one of which is toroidal and annular, and the other is reducible and -reducible. A manifold in the second family has boundary consi…
Study negative definite spin fillings of knot covers.
problem Existence of negative definite spin fillings in branched double covers.
method Derive obstructions and characterize special knots.
result Characterization of special alternating knots.
The paper proves finiteness of cosmetic fillings on a specific type of 3-manifold.
problem Cosmetic fillings on specific 3-manifolds.
method Analysis of Dehn fillings on compact, orientable 3-manifolds with incompressible torus boundaries.
result There are only finitely many pairs of purely cosmetic fillings.
Study generalizes Lebesgue curves to new space-filling and fractal sets.
problem Generating space-filling curves from planar substitutions.
method Generalized Lebesgue's construction to new curves and fractal sets.
result Some substitutions create relatively dense fractal-like sets.
We use Menke's JSJ-type decomposition theorem for symplectic fillings to reduce the classification of strong and exact symplectic fillings of virtually overtwisted torus bundles to the same problem for tight lens spaces. For virtually overtwisted structures on elliptic or parabolic torus bundles, this gives a complete …
Let M be a simple 3-manifold with a toral boundary component partial_0 M. If Dehn filling M along partial_0 M one way produces a toroidal manifold and Dehn filling M along partial_0 M another way produces a boundary-reducible manifold, then we show that the absolute value of the intersection number on partial_0 M of th…
If a hyperbolic 3-manifold M admits a reducible and a finite Dehn filling, the distance between the filling slopes is known to be 1. This has been proved recently by Boyer, Gordon and Zhang. The first example of a manifold with two such fillings was given by Boyer and Zhang. In this paper, we give examples of hyperboli…
Affirmative proof that rank 3 3-manifolds have filling links.
problem Existence of filling links in rank 3 3-manifolds.
method Introduced and used the concept of filling links, proved for rank 3 manifolds.
result Every rank 3 closed orientable 3-manifold contains a filling link.
Study filling links in 3-manifolds to understand their topological properties.
problem Understanding the topological properties of 3-manifolds through filling links.
method Introduce and study filling links, prove their existence and injectivity properties.
result Existence of k-filling links in the 3-torus for each k>1.
New method fills cluster seeds with exact Lagrangian structures.
problem Surjectivity of map from Lagrangian fillings to cluster seeds.
method Construction of quiver with potential and Lagrangian disk surgeries.
result Trivial deformation space of quiver allows manipulation of fillings.
Study shows connectedness of Bowditch boundary persists in long Dehn fillings.
problem Persistence of Bowditch boundary connectedness in Dehn fillings.
method Analysis of relatively hyperbolic group pairs and peripheral subgroups.
result Connectedness of Bowditch boundary persists in sufficiently long Dehn fillings without needing restrictions.