Study end sum for surfaces and prove uniqueness results.
problem Uniqueness of end sum for surfaces and related manifolds.
method Analyzing end sum and adding a 1-handle at infinity for surfaces.
result The end sum of two surfaces with compact boundary is uniquely determined by the chosen ends.
Researchers found multiple ways to end-sum 4-manifolds, contradicting a previous conjecture.
problem Nonuniqueness of end-sums in 4-manifolds.
method Explicit examples and detailed discussion of end-cohomology algebra.
result Uncountably many distinct proper homotopy types from end-sums.
The paper explores when end summing is unique for manifolds at infinity.
problem Nonuniqueness of end summing in manifolds with specific fundamental group behavior at infinity.
method Examines various categories (TOP, PL, DIFF) and types of 0- and 1-handles.
result Uniqueness is proved for Mittag-Leffler ends and generalized to handle slides and cancellations.
An end sum is a non-compact analogue of a connected sum. Suppose we are given two connected, oriented n-manifolds M1 and M2. Recall that to form their connected sum one chooses an n-ball in each Mi, removes its interior, and then glues together the two Sn−1 boundary components thus created by an orien…
Study of non-metrizable manifolds' ends, generalizing Nyikos's theorem.
problem Characterizing non-metrizable surfaces with ends.
method Introducing short and long ends, developing theory of spaces of ends.
result Characterization of surfaces as metrizable manifolds plus long pipes.
Classifies 4-manifolds up to connected sum with complex projective planes.
problem Classifying 4-manifolds up to connected sum with complex projective planes.
method Classification based on fundamental group, orientation character, and extension class involving second homotopy group.
result Closed, connected 4-manifolds up to connected sum with copies of the complex projective plane are classified in terms of fundamental group, orientation character, and an extension class involving the second homotopy group.
New algorithm improves performance in nontransitive games.
problem Nontransitive games lack a clear winner.
method Geometric framework for agent objectives, PSRO_rN algorithm.
result PSRO_rN consistently outperforms alternatives in nontransitive games.
Ends and cohomology theory for noncompact spaces.
problem Study of noncompact spaces and their invariants.
method Exposition of ends theory, introduction of reduced end cohomology, proof of theorems.
result Proof of a theorem on end cohomology of end sums of manifolds.
Sum of Lagrange numbers equals a specific formula.
problem Proving the Markov Uniqueness Conjecture (MUC).
method Combining McShane's identity and Schmutz's work.
result MUC is equivalent to the given sum formula.
For a complete minimal surface in the Euclidean 3-space, the so-called flux vector corresponds to each end. The flux vectors are balanced, i.e., the sum of those over all ends are zero. Consider the following inverse problem: For each balanced n vectors, find an n-end catenoid which attains given vectors as flux. Here,…
We construct the Seiberg-Witten theory on 3-manifolds with Euclidean ends (connected sums of R3 and a compact manifold) with perturbations which approximate ∗dx3 at infinity, and describe the structure of the moduli spaces. The setup is inspired by Taubes's program of relating the 4-dimensional Seiberg-Witten in…
Method constructs G2-instantons over twisted connected sums.
problem Constructing G2-instantons over complex manifolds.
method Gluing G2-instantons from holomorphic bundles over building blocks.
result Explicit examples from semi-Fano 3-folds.
The gluing technique is used to construct hypersurfaces in Euclidean space having approximately constant prescribed mean curvature. These surfaces are perturbations of unions of finitely many spheres of the same radius assembled end-to-end along a line segment. The condition on the existence of these hypersurfaces is t…
In this paper we announce a gluing theorem for conformal structures with anti-self-dual (ASD) Weyl tensor that applies in geometrical situations that are more general than those considered by previous authors. By adapting a method proposed by Floer, sufficient conditions are given for the existence of ASD conformal str…
For each end of complete minimal surface in the Euclidean 3-space, the flux vector is defined. It is well-known that the sum of the flux vector over all ends are zero. Consider the following inverse problem: For each balanced n-vectors, find an n-end catenoid which realizes these vectors as flux. Here, an n-end catenoi…
Proves non-existence of metrics with positive curvature for certain connected sums.
problem Non-existence of metrics with positive curvature for specific connected sums.
method Using μ-bubbles, proves non-existence for various dimensions and manifolds.
result Connected sums do not admit metrics of positive scalar or intermediate curvature.
A system for federated learning with private data, adding discrete Gaussian noise and secure aggregation.
problem Training models on private data distributed across devices while ensuring privacy.
method Discretizes data, adds discrete Gaussian noise, and uses secure aggregation to protect privacy.
result Matches the accuracy of central differential privacy with less than 16 bits of precision per value.
Let Gamma be a non-elementary Kleinian group acting on the closed n-dimensional unit ball and assume that its Poincare series converges at the exponent alpha. Let M_Gamma be the Gamma-quotient of the open unit ball. We consider certain families E = {E_1,...,E_p} of open subsets of M_Gamma such that M_Gamma minus the un…
In non-compact manifolds, geodesic flowers exist.
problem Existence of geodesic flowers in non-compact manifolds.
method Proving the existence of non-trivial geodesic flowers in complete non-compact manifolds with locally convex ends.
result Non-trivial geodesic flowers exist in every complete non-compact manifold with locally convex ends.
Mutation improves FTRL convergence in zero-sum games.
problem Lack of last-iterate convergence in FTRL variants.
method Introduced mutation to perturb action probabilities in FTRL.
result M-FTRL converges to Nash equilibria under full-information feedback.
Grimaldi-Pansu metrics are constructed for manifolds with multiple ends.
problem Volume growth on manifolds with more than one end.
method Constructing Riemannian metrics with bounded geometry and uniform bounds for volume growth.
result Uniform bounds for volume growth of Grimaldi-Pansu metrics in certain manifolds.
In this paper we produce families of complete non compact Riemannian metrics with positive constant σk-curvature by performing the connected sum of a finite number of given n-dimensional Delaunay type solutions, provided 2≤2k<n. The problem is equivalent to solve a second order fully nonlinear elliptic eq…
The paper proves Hölder continuity for solutions of degenerate parabolic equations in any dimension.
problem Proving Hölder continuity for solutions of degenerate parabolic equations in arbitrary dimensions.
method Establishing Alexandroff-Bakelman-Pucci estimate, Harnack inequality, Hölder regularity, and Schauder estimates for a class of degenerate parabolic equations.
result The paper proves Hölder continuity for solutions of degenerate parabolic equations in all dimensions.
Convex clustering recovers tree structures from point data.
problem Recovering tree structures from point data.
method Minimizes a convex clustering objective function to reconstruct tree structures.
result The convex clustering solution path reconstructs tree structures exactly when affinities reflect a tree structure.
Paper tackles learning unknown game parameters from observations.
problem Learning unknown game parameters in games where parameters are not known to all agents.
method Proposes a differentiable, end-to-end learning framework for normal and extensive form games.
result Demonstrates effective learning of game parameters in poker and security game tasks.
Policy optimization converges to Nash equilibria in zero-sum LQ games.
problem Finding Nash equilibria in zero-sum linear quadratic games.
method Developed three projected nested-gradient methods to converge to NE.
result Policy optimization methods converge to Nash equilibria in zero-sum LQ games.
This paper concerns the class of contractible open 3-manifolds which are ``locally finite strong end sums'' of eventually end-irreducible Whitehead manifolds. It is shown that whenever a 3-manifold in this class is a covering space of another 3-manifold the group of covering translations must be a free group. It follow…
The paper examines spaces with indecomposable Higson coronae and their properties.
problem Characterizing spaces with indecomposable Higson coronae.
method Analyzing properties of Higson coronae of non-compact metric spaces.
result Spaces with indecomposable Higson coronae are coarsely equivalent to the space of natural numbers.
We propose a method to construct G_2-instantons over a compact twisted connected sum G_2-manifold, applying a gluing result of Sá Earp and Walpuski to instantons over a pair of 7-manifolds with a tubular end (see arXiv:1310.7933). In our example, the moduli spaces of the ingredient instantons are non-trivial, and their…
We give a general procedure for gluing together possibly noncompact manifolds of constant scalar curvature which satisfy an extra nondegeneracy hypothesis. Our aim is to provide a simple paradigm for making `analytic' connected sums. In particular, we can easily construct complete metrics of constant positive scalar cu…
This paper proposes a new method to automatically learn optimal return functions in reinforcement learning.
problem Learning optimal policies in reinforcement learning can be slow and inefficient.
method The authors propose a general mathematical form for the return function and use meta-learning to automatically learn the optimal form.
result Their method significantly speeds up the learning of optimal policies in reinforcement learning.
Constructs exotic proper 2-knots from open 2-handles.
problem Proving topological equivalence of exotic proper knotted surfaces.
method Flexible construction of exotic open 2-handles, distinguishing through genus functions and end Floer homology.
result Constructs infinite families of irreducible exotic proper knotted surfaces.
A deep learning beamformer improves ultrasound imaging quality across varying conditions.
problem Poor image quality in ultrasound due to limited channel subsampling.
method A universal deep learning beamformer trained on data-driven methods.
result Significantly improved ultrasound images generated from sub-sampled data.
Let u be a positive solution of the ultraparabolic equation \begin{equation*} \partial_t u=\sum_{i=1}^n \partial_{x_i}^2 u+\sum_{i=1}^k x_i\partial_{x_{n+i}}u \hspace{8mm} \mbox{on} \hspace{4mm} \mathbb{R}^{n+k}\times (0,T), \end{equation*} where 1≤k≤n and 0<T≤+∞. Assume that u and its derivat…
We express any Courant algebroid bracket by means of a metric connection, and construct a Courant algebroid structure on any orthogonal Whitney sum E⊕C where E is a given Courant algebroid and C is a flat, pseudo- Euclidean vector bundle. Then, we establish the general expression of the bracket of a transitive …
A new method decomposes Bayesian uncertainty into per-class contributions for safer classification.
problem Bayesian uncertainty metrics fail to distinguish between safe and critical classes in safety-critical classification tasks.
method Decomposes mutual information into per-class contributions using a second-order Taylor expansion and a weighting correction.
result The per-class uncertainty vector Ck reduces selective risk and improves out-of-distribution detection compared to traditional metrics. Decomposes epistemic uncertainty into per-class contributions for safer classification.
problem Asymmetric costs in safety-critical classification.
method Decomposes mutual information into per-class vector Ck using second-order Taylor expansion. result Decomposition improves selective risk by 34.7% and 56.2% over existing metrics.
This note justifies approximations of arithmetic forwards using weighted averages of overnight forwards.
problem Theoretical justification for approximations of arithmetic forwards.
method Presentation of a central equation and computationally cheaper methods to approximate Fa. result Theoretical bounds and closed-form expressions for arithmetic factors in Gaussian HJM models.
The paper connects Nahm's equations to rational maps between projective spaces.
problem Solving Nahm's equations with specific boundary conditions.
method Identifying moduli spaces with spaces of rational maps and using symplectic geometry.
result Dimensions of rational maps correspond to holomorphic charge.
This paper improves 3D pose recovery from 2D images using non-convex regularization.
problem 3D object pose recovery from 2D images.
method Proposes non-convex regularization with leaky capped ℓ1-norm (LCNR) and multi-stage optimization.
result Theoretical analysis shows estimation error decreases with optimization stages.
We define a local Riemann-Roch number for an open symplectic manifold when a complete integrable system without Bohr-Sommerfeld fiber is provided on its end. In particular when a structure of a singular Lagrangian fibration is given on a closed symplectic manifold, its Riemann-Roch number is described as the sum of the…
We consider framed chord diagrams, i.e. chord diagrams with chords of two types. It is well known that chord diagrams modulo 4T-relations admit Hopf algebra structure, where the multiplication is given by any connected sum with respect to the orientation. But in the case of framed chord diagrams a natural way to define…
PSD models simplify probability density estimation.
problem Effective modeling of probability densities for inference.
method Positive semi-definite (PSD) models for non-negative functions.
result PSD models efficiently support product and sum rules.
We prove that mapping tori of 3-manifolds have zero simplicial volume.
problem The simplicial volume of mapping tori of 3-manifolds.
method Analysis of self-homeomorphisms of reducible 3-manifolds and introduction of a new technique for computing simplicial volume.
result We prove that any mapping torus of a closed 3-manifold has zero simplicial volume.
Combines neural networks and probabilistic graphical models for efficient higher-order inference.
problem Lack of efficient higher-order relational information in graph neural networks and probabilistic graphical models.
method Derives efficient approximate sum-product loopy belief propagation for higher-order PGMs, embeds into neural network, proposes methods for constructing higher-order factors.
result Substantially outperforms state-of-the-art k-order graph neural networks in molecular datasets.
Haken n-manifolds have been defined and studied by B. Foozwell and H. Rubinstein in analogy with the classical Haken manifolds of dimension 3, based upon the the theory of boundary patterns developed by K. Johannson. The Euler characteristic of a Haken manifold is analyzed and shown to be equal to the sum of the Charne…
A neural network method optimizes power control in multi-user channels.
problem Maximizing sum rate in multi-user interference channels.
method PCNet, a multi-layer neural network, directly maximizes sum rate; ePCNet is an ensemble of multiple PCNets.
result ePCNet outperforms existing power control methods by 1.2%-4.6%.
Paper analyzes robust strategies in a pension plan game with ambiguous financial markets.
problem Analyzing robust strategies in a defined benefit pension plan game with ambiguous financial markets.
method Formulated and solved two robust non-zero-sum games using stochastic dynamic programming.
result Explicit forms and optimality of the solutions are shown for the firm and union.