Develops Lie-theoretic perspective on Hitchin's equations for cyclic G-Higgs bundles.
problem Analytic and geometric properties of harmonic maps.
method Lie-theoretic perspective on Hitchin's equations for cyclic G-Higgs bundles.
result Proves Dai-Li's conjecture on the monotonicity of the energy density and negative curvature conjecture for Coxeter cyclic G-Higgs bundles.
Brenier isotonic regression extends multi-output isotonic regression using optimal transport.
problem Enforcing cyclic monotonicity in multi-output regression.
method Leverage Kantorovich's optimal transport to find cyclically monotone couplings.
result Brenier isotonic regression outperforms baselines in probability calibration.
A new learning rule consistently reduces error over data samples.
problem Finding a learning rule that consistently reduces error over all data distributions.
method A deterministic, data-dependent partitioning rule that only partitions cyclic intervals with sufficient empirical diversity of labels.
result The expected error is monotone non-increasing with the sample size under every data distribution.
The paper examines properties of GW optimal transport plans, showing they can be sparse and permutation-supported.
problem Properties of Gromov-Wasserstein optimal transport plans.
method Exploration of sparsity, permutation support, and cyclical monotonicity properties.
result GW optimal plans can be sparse and permutation-supported under certain conditions.
This work clarifies different transport map constructions and their causal interpretations.
problem Identifying distinct transport map constructions and their equivalence.
method Comparative analysis of three transport map constructions: cyclically monotone, quantile-preserving, and triangular monotone.
result Conditions for equivalence of different transport map constructions.
Develops a method to efficiently compute Wasserstein barycenters with variational distributions.
problem High computational burden in computing Wasserstein barycenters for high-dimensional and continuous settings.
method Introduces a variational distribution to approximate the continuous Wasserstein barycenter, reformulating the problem as an optimization with c-cyclical monotonicity.
result The method provides a tractable dual formulation for efficient computation of Wasserstein barycenters, demonstrated on real applications.
A hyperbolic polygon is defined to be cyclic, horocyclic, or equidistant if its vertices lie on a metric circle, horocycle, or a component of the equidistant locus to a hyperbolic geodesic, respectively. Convex such n-gons are parametrized by the subspaces of (0,∞)n that contain their side length collections,…
The paper establishes general results in Lorentzian optimal transport theory.
problem Establishing strong duality and optimality conditions in Lorentzian optimal transport.
method Providing non-trivial assumptions on measures, characterizing optimality, and proving regularity results.
result Regularity results for c-convex functions and (weak) Kantorovich potentials do not extend to the Lorentzian setting, but under suitable assumptions, they are locally semconvex. A new copula model for multi-attribute data using optimal transport.
problem Relaxing the Gaussian assumption for multi-attribute graphical models.
method Introducing a new copula (Cyclically Monotone Copula) and using optimal transport theory.
result The model allows arbitrary continuous distributions and is more flexible than classical methods.
Study shows universal circles for taut foliations in 3-manifolds.
problem Understanding foliations in 3-manifolds.
method Analyzes pseudo-Anosov flows and taut foliations, defines universal circles.
result Action of pi_1(M) on flow space defines universal circles for taut foliations.
New method for regression in high-dimensional space using mixture modeling and optimal transport.
problem Regression in high-dimensional space with unordered data.
method Mixture modeling and optimal transport for permutation recovery and denoising.
result Explicit upper bounds on mean squared denoising error for Gaussian noise.
By investigating model-independent bounds for exotic options in financial mathematics, a martingale version of the Monge-Kantorovich mass transport problem was introduced in \cite{BeiglbockHenry LaborderePenkner,GalichonHenry-LabordereTouzi}. In this paper, we extend the one-dimensional Brenier's theorem to the present…
We study the optimal transport between two probability measures on the real line, where the transport plans are laws of one-step martingales. A quasi-sure formulation of the dual problem is introduced and shown to yield a complete duality theory for general marginals and measurable reward (cost) functions: absence of a…
We introduce sparse random projection, an important dimension-reduction tool from machine learning, for the estimation of discrete-choice models with high-dimensional choice sets. Initially, high-dimensional data are compressed into a lower-dimensional Euclidean space using random projections. Subsequently, estimation …
Develops a first-order interior-point method for solving constrained variational inequalities.
problem Solving constrained variational inequalities with nontrivial constraints.
method ADMM-based interior-point method for constrained VIs (ACVI).
result First-order interior-point method with global convergence guarantees for general cVI problems.
In this paper, we introduce the Lp geominimal surface area for all −n=p<1, which extends the classical geominimal surface area (p=1) by Petty and the Lp geominimal surface area by Lutwak (p>1). Our extension of the Lp geominimal surface area is motivated by recent work on the extension of the Lp a…
This paper introduces 'General Cyclical Training' for neural networks.
problem Improving training efficiency and performance of neural networks.
method Cyclical training phases with varying hyperparameters, batch sizes, loss functions, and data augmentation.
result Cyclical weight decay, softmax temperature, and gradient clipping enhance model accuracy.
The paper generalizes cyclic metrics in homogeneous Finsler geometry.
problem Understanding cyclic metrics in homogeneous Finsler spaces.
method Generalization of cyclic metrics, proving conditions for symmetry, and constructing cyclic metrics.
result A Finsler cyclic Lie group with an Abelian Lie algebra.
In this paper we study the connections between cyclic presentations of groups and branched cyclic coverings of (1,1)-knots. In particular, we prove that every n-fold strongly-cyclic branched covering of a (1,1)-knot admits a cyclic presentation for the fundamental group encoded by a Heegaard diagram of genus n.
Characterizes non-degenerate cyclic metric Lie algebras.
problem Understanding the structure of non-solvable cyclic metric Lie algebras.
method Using sufficient conditions, cyclic quadruples, and double extension method.
result Complete characterization of non-degenerate cyclic metric Lie algebras.
The study classifies and explores SU(2)-cyclic and SU(2)-abelian 3-manifolds.
problem Classifying SU(2)-cyclic and SU(2)-abelian 3-manifolds. method Analysis of geometric 3-manifolds and representation theory of fundamental groups.
result Examples of hyperbolic 3-manifolds with specific properties.
Proves almost profinite rigidity for certain free-by-cyclic groups.
problem Profinite rigidity of free-by-cyclic groups.
method Analyzes ranks of fibres, characteristic polynomials, and stretch factors of monodromies.
result Generic free-by-cyclic groups are almost profinitely rigid.
We study the connections among the mapping class group of the twice punctured torus, the cyclic branched coverings of (1,1)-knots and the cyclic presentations of groups. We give the necessary and sufficient conditions for the existence and uniqueness of the n-fold strongly-cyclic branched coverings of (1,1)-knots, thro…
New cyclicity measures defined in weighted Besov spaces, with stability and geometric analysis.
problem Characterizing cyclicity in weighted Besov spaces.
method Defining cyclicity indices based on potential theory and capacity, studying stability under perturbations, and linking zero set structure to cyclicity.
result Novel invariants and conditions for cyclicity in various function spaces.
We refine the cyclic cohomological apparatus for computing the Hopf cyclic cohomology of the Hopf algebras associated to infinite primitive Cartan-Lie pseudogroups, and for the transfer of their characteristic classes to foliations. The main novel feature is the precise identification as a Hopf cyclic complex of the im…
In this paper, we study quandles of cyclic type, which form a particular subclass of finite quandles. The main result of this paper describes the set of isomorphism classes of quandles of cyclic type in terms of certain cyclic permutations. By using our description, we give a direct classification of quandles of cyclic…
Cyclical learning rates improve DRL performance without manual tuning.
problem Manual hyperparameter tuning in DRL is time-consuming and error-prone.
method Proposes cyclical learning rates for DRL problems.
result Cyclical learning achieves similar or better results than fixed learning rates.
The paper investigates cyclic arbitrage opportunities in decentralized exchanges.
problem Price discrepancies in decentralized exchanges lead to arbitrage opportunities.
method Theoretical framework and analysis of transaction-level data.
result Traders have executed over 292,606 cyclic arbitrages over eleven months, exploiting more than 138 million USD in revenue.
Unified rigidity theorem for cyclic and alternating surfaces.
problem Infinitesimal rigidity of equivariant minimal maps.
method Unified Lie-theoretic framework connecting cyclic surfaces and cyclic harmonic bundles.
result Infinitesimal rigidity for irreducible cyclic surfaces under various variations.
In spin geometry, traceless cyclic homogeneous Riemannian manifolds equipped with a homogeneous spin structure can be viewed as the simplest manifolds after Riemannian symmetric spin spaces. In this paper, we give some characterizations and properties of cyclic and traceless cyclic homogeneous Riemannian manifolds and …
The abstract introduces a new cyclic structure for surfaces.
problem Defining a cyclic structure for surfaces.
method Endowing surfaces with a structure of a (co)cyclic object in 3D cobordisms.
result 3D TQFTs induce (co)cyclic modules, which are computed algebraically.
Study integrable discretizations of cyclic systems with circular coordinate lines.
problem Integrable discretizations of 3D cyclic systems with circular coordinate lines.
method Investigate circle congruences and flat connections in the context of discrete cyclic systems.
result Characterization of circle congruences and existence of certain flat connections.
We give a construction of cyclic cocycles representing the equivariant characteristic classes of equivariant bundles. Our formulas generalize Connes' Godbillon-Vey cyclic cocycle. An essential tool of our construction is Connes-Moscovici's theory of cyclic cohomology of Hopf algebras.
A surgery on a knot in 3-sphere is called SU(2)-cyclic if it gives a manifold whose fundamental group has no non-cyclic SU(2) representations. Using holonomy perturbations on the Chern-Simons functional, we prove that the distance of two SU(2)-cyclic surgery coefficients is bounded by the sum of the absolute values of …
New definite 4-manifolds found with non-cyclic groups.
problem Finding exotic smooth structures on 4-manifolds with specific fundamental groups.
method Constructing infinitely many non-diffeomorphic structures.
result Infinitely many pairwise non-diffeomorphic definite 4-manifolds with Z/2imesZ/2 fundamental group. Cyclic projections in Hadamard spaces can be irregular, unlike in Hilbert spaces.
problem Understanding the behavior of cyclic projections in Hadamard spaces compared to Hilbert spaces.
method Constructing an example of convex subsets in a Hadamard space.
result Cyclic product of projections is not asymptotically regular in Hadamard spaces.
Cyclic covers of knots uniquely determine the original knot.
problem Determining knots from their branched covers.
method Examining n-fold cyclic branched covers of alternating prime knots.
result The n-fold cyclic cover of an alternating prime knot uniquely determines the original knot.
New framework for cyclic quantum causal models with graph separation property.
problem Understanding causal relationships in feedback processes and exotic scenarios.
method Introducing a robust probability rule and a novel graph-separation property, p-separation.
result Established graph-separation properties for all consistent cyclic causal models.
New Heegaard Floer homology for orbifolds with cyclic singularities.
problem Defining Heegaard Floer homology for orbifolds with arbitrary cyclic singularities.
method Generalizing recent work by defining Heegaard Floer homology for orbifolds with arbitrary cyclic singularities.
result Defined a new Heegaard Floer homology for orbifolds with arbitrary cyclic singularities.
A central result here is the computation of the entire cyclic homology of canonical smooth subalgebras of stable continuous trace C*-algebras having smooth manifolds M as their spectrum. More precisely, the entire cyclic homology is shown to be canonically isomorphic to the continuous periodic cyclic homology for these…
The paper extends the uniqueness of complete harmonic metrics to subharmonic weights and proves their existence on the unit disc.
problem Finding complete harmonic metrics on Riemann surfaces for subharmonic weights.
method Extending Li-Mochizuki's theorem to subharmonic weights and proving existence on the unit disc.
result Complete harmonic metrics exist on the unit disc for subharmonic weights.
Let M be an irreducible, compact, connected, orientable 3-manifold whose boundary is a torus. We show that if M is hyperbolic, then it admits at most six finite/cyclic fillings of maximal distance 5. Further, the distance of a finite/cyclic filling to a cyclic filling is at most 2. If M has a non-boundary-paralle…
Consider an equity market with n stocks. The vector of proportions of the total market capitalizations that belong to each stock is called the market weight. The market weight defines the market portfolio which is a buy-and-hold portfolio representing the performance of the entire stock market. Consider a function th…
The image of the Gauss map of any oriented isoparametric hypersurface of the unit standard sphere Sn+1(1) is a minimal Lagrangian submanifold in the complex hyperquadric Qn(C). In this paper we show that the Gauss image of a compact oriented isoparametric hypersurface with g distinct constant princi…
We discuss 3-manifolds which are cyclic coverings of the 3-sphere, branched over 2-bridge knots and links. Different descriptions of these manifolds are presented: polyhedral, Heegaard diagram, Dehn surgery and coloured graph constructions. Using these descriptions, we give presentations for their fundamental groups, w…
Study counterfactuals in cyclic systems with shifts and scales.
problem Counterfactual inference in cyclic systems with shifts and scales.
method Shift-scale interventions in cyclic SCMs.
result Valid inference in cyclic systems with shifts and scales.
The paper defines cyclic sets from ribbon string links and connects them to quantum invariants.
problem Defining and relating cyclic sets from ribbon string links.
method Endowing ribbon string links with cyclic and cocyclic structures, relating to coend of a ribbon category via quantum invariants.
result Established a relationship between ribbon string links and quantum invariants.
Cyclical MCMC tackles high-dimensional multimodal distributions, showing convergence under certain conditions.
problem High-dimensional multimodal posterior distributions in deep learning.
method Cyclical MCMC framework that tracks tempered versions of the target distribution over time.
result Cyclical MCMC converges to the target distribution under fast mixing kernels but fails in slow mixing cases.