This paper classifies and determines the length of the shortest filling pairs on a specific type of surface.
problem Classifying and determining the length of the shortest filling pairs on a specific type of surface.
method Classifying and determining the length of the shortest filling pairs on a specific type of surface.
result The paper classifies and determines the length of the shortest minimal filling pairs on a genus two surface.
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 Sg for g≥3. The study finds an upper limit for the number of minimal origami pairs on a surface.
problem Counting the minimal origami pairs on a surface of genus g.
method Algorithm to count minimal origami pairs and using Ménage Problem to establish an upper bound.
result Established a new upper bound for the count of minimal origami pairs.
Proves Miyaoka-Yau inequality for minimal pairs using Kähler-Einstein metrics.
problem Proving Miyaoka-Yau inequality for minimal pairs.
method Using Kähler-Einstein metrics with conical and cuspidal singularities.
result Proves Miyaoka-Yau inequality for all minimal pairs.
New method for decomposing surfaces with minimal intersecting filling pairs.
problem Decomposing surfaces with minimal intersecting filling pairs.
method Explicit algebraic means to determine homeomorphism class and decomposition criteria.
result Explicit means to determine homeomorphism class and decomposition criteria for surfaces with minimally intersecting filling pairs.
Let Sg denote the closed orientable surface of genus g. We construct exponentially many mapping class group orbits of pairs of simple closed curves which fill Sg and intersect minimally, by showing that such orbits are in correspondence with the solutions of a certain permutation equation in the symmetric g…
The paper proves conditions for the Abundance conjecture in minimal projective klt pairs.
problem Proving the Abundance conjecture for minimal klt pairs with non-zero canonical bundle.
method Analyzing asymptotic behavior of multiplier ideals and properties of supercanonical currents.
result Supercanonical currents are central to proving the Abundance conjecture.
Study fills a surface with odd, non-3 curves.
problem Determining filling pairs for surfaces with odd, non-3 punctures.
method Constructed minimally intersecting pairs of curves.
result Completed the classification of filling pairs for all surfaces.
The paper extends local calibration pairs to global ones and finds mass-minimizing submanifolds.
problem Extending local calibration pairs to global ones in various Riemannian manifolds.
method Analyzing mass-minimizing properties and using conformal classes.
result Homologically mass-minimizing submanifolds exist in some Riemannian manifolds that cannot be calibrated by smooth calibrations.
The paper provides Weierstrass representations for minimal space-like surfaces in Minkowski space-time.
problem Minimal space-like surfaces in Minkowski space-time.
method Obtained canonical Weierstrass representations via two holomorphic functions.
result Established geometric correspondence between minimal space-like surfaces and pairs of holomorphic functions.
Improves off-policy evaluation weights for balanced state-action pair distribution.
problem Imbalance in importance sampling weights for off-policy evaluation of contextual bandits.
method Balanced Off-Policy Evaluation (B-OPE) method that minimizes imbalance to desired counterfactual distribution of state-action pairs.
result Experimental evidence shows B-OPE improves offline policy evaluation in both discrete and continuous action spaces.
Researchers found multiple surfaces with same topological and symmetry properties.
problem Determining unique free boundary minimal surfaces from topology and symmetry.
method Provided pairs of non-isometric surfaces with same genus, boundary components, and symmetry group.
result Infinitely many pairs of surfaces with same topology and symmetry group exist.
We give an explicit construction of any simply-connected superconformal surface φ:M2→R4 in Euclidean space in terms of a pair of conjugate minimal surfaces g,h:M2→R4. That φ is superconformal means that its ellipse of curvature is a circle at any point. We characterize the pairs (g,h) of …
The face pairing graph of a 3-manifold triangulation is a 4-valent graph denoting which tetrahedron faces are identified with which others. We present a series of properties that must be satisfied by the face pairing graph of a closed minimal P^2-irreducible triangulation. In addition we present constraints upon the co…
Computes minimal dilatation for Thurston maps on surfaces.
problem Finding the minimal dilatation of Thurston maps on surfaces.
method Explicit computation using spectral radius in a congruence subgroup of PSL2(Z).
result Explicitly computes minimal dilatation for Thurston maps.
New origamis found for surfaces with minimal intersections.
problem Finding pairs of curves on surfaces with minimal intersections.
method Using new techniques, constructed exponentially-many to factorial-many pairs of curves.
result Pairs of curves naturally give rise to origamis with minimal intersections.
We show that φ-invariant submanifolds of metric contact pairs with orthogonal characteristic foliations make constant angles with the Reeb vector fields. Our main result is that for the normal case such submanifolds of dimension at least 2 are all minimal. We prove that an odd-dimensional φ-invariant submanifold …
Study h-cobordisms of complexity 2 in 5D, finding obstructions and examples.
problem Understanding h-cobordisms of complexity 2 in 5D. method Compute monopole Floer homology and action of twisting involution.
result Obtained obstructions and constructed examples of high complexity.
It is well-known that any pair of closed orientable 3-manifolds are related by a finite sequence of Dehn surgeries on knots. Furthermore Kawauchi showed that such knots can be taken to be hyperbolic. In this article, we consider the minimal length of such sequences connecting a pair of 3-manifolds, in particular, a pai…
PAIR optimizes machine learning models to generalize better to out-of-distribution data.
problem Optimization of machine learning models for out-of-distribution (OOD) generalization often leads to compromises that weaken robustness.
method Introduces a multi-objective optimization (MOO) perspective and a new optimization scheme called PAreto Invariant Risk Minimization (PAIR).
result PAIR improves robustness of OOD objectives by cooperatively optimizing with other objectives, yielding top OOD performances.
The paper explores linked cycles in graphs and their properties.
problem Understanding the structure of linked cycles in graphs.
method Analyzing the set of all pairs of disjoint cycles in graphs and showing conditions for minimally linked sets.
result A minimally linked set of cycles in a complete graph Kp+q has at most eighteen elements. Characterizes conjugacy classes of pairs in SU(3,1) using symmetry.
problem Classifying conjugacy classes of pairs of matrices in SU(3,1).
method Minimal global coordinate system on SL(4,C)-character variety, symmetry analysis.
result 22 coordinates subject to 5 relations determine conjugacy classes.
Paper connects surfaces in 4D and 3D spacetime.
problem Finding relations between Lorentz surfaces in different spacetime dimensions.
method Weierstrass-type representations for null curves and surfaces.
result Relation between minimal Lorentz surfaces in R24 and R13. Solves natural PDE system for minimal surfaces in 4D Euclidean space.
problem Determining minimal surfaces in 4D Euclidean space.
method Explicitly solves the system of natural PDE's using two holomorphic functions.
result Expresses any solution of the system of natural PDE's by two holomorphic functions in the Gauss plane.
New chiral minimal surfaces derived from quartz network.
problem Finding new triply-periodic minimal surfaces.
method Using dual graphs of quartz and its dual, generating area-minimizing meshes, and identifying flat point structures.
result Identified a new family of chiral triply-periodic minimal surfaces.
Optimizes trading pairs of stocks to reduce cross-impact costs.
problem Minimizing costs from trades of one stock affecting another.
method Develops a strategy to minimize cross-impacts by optimizing trading rates and periods.
result An optimal trading strategy for stock pairs is found.
Geometrically interprets and computes intersection pairings for higher laminations.
problem Understanding and computing intersection pairings for higher laminations.
method Realization of higher laminations as points in the affine building, geometric interpretation of pairings, use of combinatorial results.
result Intersection pairings can be computed as the length of minimal weighted networks in the building.
The paper constructs minimal realizations of signed Gauss paragraphs using graph theory.
problem Constructing minimal realizations of signed Gauss paragraphs on surfaces.
method Theory of embedded graphs on oriented and compact PL-surfaces, intersection pairing of immersed PL-normal curves.
result The genus of the ambient surface can be a function of the maximum number of Carter's circles.
FSBM improves matching efficiency with minimal supervision.
problem Scalability vs. minimal supervision in matching frameworks.
method FSBM uses a small portion of pre-aligned pairs as state feedback to guide non-coupled samples.
result FSBM accelerates training and enhances generalization.
A general study of minimal surfaces of the Riemannian product of two spheres S^2xS^2 is tackled. We stablish a local correspondence between (non-complex) minimal surfaces of S^2xS^2 and certain pair of minimal surfaces of the sphere S^3. This correspondence also allows us to link minimal surfaces in S^3 and in the Riem…
A new method for conditional sampling using paired Wasserstein Autoencoders.
problem Conditional sampling from complex data distributions.
method Derive a novel loss function for Wasserstein Autoencoders to enable sampling from OT-type couplings.
result Learned cost-optimal transport maps and conditional sampling from an OT-type coupling.
Minimal surfaces proof via Darboux transformations.
problem Minimal surface properties and transformations.
method Christoffel, Goursat, and Darboux transformations of isothermic surfaces.
result Simple proof of Darboux pairs relation.
We study a pair (\mathcal{S}_0,\mathcal{S}) of irreducible Hermitian Symmetric Spaces of compact type (cHSS) in this paper, with the first aim being classifying all the admissible pairs (\mathcal{S}_0,\mathcal{S})). This notion is a natural generalization of the pairs of sub-diagram type originated by Jaehyun Hong and …
In this paper we show that the convergence of complete Kahler-Einstein hypersurfaces in complex torus in the sense of Cheeger-Gromov will canonically degenerate the underlying manifolds into "pair of pants" decomposition. We also construct minimal Lagrangian tori that represent the vanishing cycles of the degeneration.
We prove that a connected properly immersed minimal surface in Euclidean 3-space with infinite symmetry group whose intersection with a ball of radius R is less than 2\piR^2 is a plane, a catenoid or a Scherk singly-periodic minimal surface. In particular, we prove that the only periodic minimal desingularization of a …
Minimal surfaces in 4D space characterized with specific parameters and Weierstrass formulas.
problem Characterizing minimal surfaces in Euclidean 4-space.
method Characterization with canonical parameters and derivation of Weierstrass representations.
result Minimal surfaces in 4D space correspond to pairs of minimal surfaces in 3D space.
We study invariant submanifolds of manifolds endowed with a normal or complex metric contact pair with decomposable endomorphism field φ. For the normal case, we prove that a φ-invariant submanifold tangent to a Reeb vector field and orthogonal to the other one is minimal. For a φ-invariant submanifold N everyw…
A geometric construction is provided that associates to a given flat front in H3 a pair of minimal surfaces in R3 which are related by a Ribaucour transformation. This construction is generalized associating to a given frontal in H3 , a pair of frontals in R3 that are env…
Paper solves NP-hard haplotyping problem using matrix completion.
problem Reconstructing inherited genetic variations from DNA sequencing data.
method Binary matrix factorization and alternating minimization.
result The proposed technique achieves lower haplotype reconstruction error.
Equivalence proven between algebraic stability and geometric stability.
problem Equivalence of algebraic and geometric stability criteria.
method Algebraic proof of equivalence, existence and uniqueness of minimal centers.
result Existence and uniqueness of minimal optimal destabilizing centers.
We consider the problem of distortion minimal morphing of n-dimensional compact connected oriented smooth manifolds without boundary embedded in Rn+1. Distortion involves bending and stretching. In this paper, minimal distortion (with respect to stretching) is defined as the infinitesimal relative change in vol…
A contact pair on a manifold always admits an associated metric for which the two characteristic contact foliations are orthogonal. We show that all these metrics have the same volume element. We also prove that the leaves of the characteristic foliations are minimal with respect to these metrics. We give an example wh…
Solves PDE system for minimal space-like surfaces in Minkowski space-time.
problem Solving the system of natural PDE's for minimal space-like surfaces.
method Using canonical Weierstrass representations, solves the system explicitly.
result Expresses solutions by means of two holomorphic functions.
Proves accuracy guarantees for self-supervised learning with correlated positive pairs.
problem Lack of theoretical guarantees for self-supervised learning with correlated positive pairs.
method Novel augmentation graph concept and spectral decomposition loss.
result Provably accurate features under linear probe evaluation.
Minimal cylinders in Heisenberg group characterized using loop group method.
problem Characterizing minimal cylinders in the Heisenberg group.
method Generalized Weierstrass type representation and loop group method.
result Characterization of all non-vertical minimal cylinders in terms of pairs of closed plane curves.
The paper characterizes a helicoid in a cylinder with minimal area and unique boundary conditions.
problem Characterize the helicoid in a cylinder with minimal area and specific boundary conditions.
method Characterizes the helicoid HC in a solid cylinder C from two perspectives: area minimality and boundary conditions. result The helicoid HC is the unique minimal surface with the specified boundary conditions. Study of surface singularities and their deformations.
problem Characterize and classify quotient surface singularities and their deformations.
method Computation of resolutions, dual graphs, dimensions, Milnor numbers, and Milnor fibers.
result 6 pairs of minimal symplectic fillings are shown to be diffeomorphic.
Using techniques of integrable systems, we study a Weierstrass representation formula for timelike surfaces with prescribed mean curvature in Minkowski 3-space. It is shown that timelike minimal surfaces are obtained by integrating a pair of Lorentz holomorphic and Lorentz antiholomorphic null curves in Minkowski 3-spa…