The paper classifies pretzel links with 2 components and gives conditions for those with 3 or more.
problem Classifying pretzel links based on their self delta-equivalence.
method Using Conway polynomials to determine self delta-equivalence for links with 2 or more components.
result Necessary and sufficient conditions for self delta-equivalence of pretzel links with 3 or more components.
Link-homotopy and self Delta-equivalence are equivalence relations on links. It was shown by J. Milnor (resp. the last author) that Milnor invariants determine whether or not a link is link-homotopic (resp. self Delta-equivalent) to a trivial link. We study link-homotopy and self Delta-equivalence on a certain componen…
We consider the operation of Whitehead double on a component of a link and study the behavior of Milnor invariants under this operation. We show that this operation turns a link whose Milnor invariants of length < k are all zero into a link with vanishing Milnor invariants of length < 2k, and we provide formulas for th…
New methods for delta-moves on algebraically split links identified.
problem Understanding delta-moves on algebraically split links.
method Introducing self and mixed delta-moves, proving equivalence, and calculating delta-splitting numbers.
result Two links are mixed delta-equivalent if they have the same pairwise linking number and components.
For an n-component link L, the Milnor's isotopy invariant is defined for each multi-index $I=i_1i_2...i_m (i_j\in\n)$. Here m is called the length. Let r(I) denote the maximam number of times that any index appears. It is known that Milnor invariants with r=1 are link-homotopy invariant. N. Habegger and X. S.…
The paper analyzes how to combine self-protection and self-insurance for risk reduction.
problem Combining self-protection and self-insurance for risk reduction when market insurance is absent.
method The approach uses Value-at-Risk and Tail Value-at-Risk to evaluate residual risk and solves the problem using isoquant geometry based on marginal-balance curves.
result The analysis identifies the conditions under which self-protection and self-insurance behave as substitutes or complements.
Self-PU combines self-training with PU learning for improved binary classification.
problem Binary classification from unlabeled data and few labeled positives.
method Integrates self-paced training, self-calibrated loss, and self-distillation.
result Significantly improved performance on Alzheimer's Disease classification.
S4 learns new self-supervision automatically, improving accuracy with less human effort.
problem Lack of direct supervision in machine learning.
method Combines deep learning and probabilistic logic to automatically generate and verify new self-supervision.
result S4 can automatically propose accurate self-supervision, matching supervised methods with less human effort.
The paper extends rigidity results for λ-self-expanders to hyperplanes, spheres, and cylinders.
problem Characterizing λ-self-expanders as hyperplanes, spheres, and cylinders. method Extending results on self-expanders to λ-self-expanders, proving rigidity results. result Characterizes hyperplanes, spheres, and cylinders as λ-self-expanders. We investigate Mean Curvature Flow self-shrinking hypersurfaces with polynomial growth. It is known that such self shrinkers are unstable. We focus mostly on self-shrinkers of the form Sk×Rn−k⊂Rn+1. We use a connection between the stability operator and the quantum harmonic oscillator Ham…
Self-crossing geodesics on convex surfaces are studied.
problem Understanding patterns of geodesics crossing themselves.
method Analyzing closed geodesics on convex surfaces.
result Self-crossing geodesics exist on convex surfaces.
Researchers set entropy limits for specific types of self-shrinkers.
problem Understanding entropy limits for self-shrinkers with symmetries.
method Derived explicit entropy bounds for two specific classes of self-shrinkers using isoparametric foliations and symmetry analysis.
result Entropy bounds generalized to new classes of self-shrinkers, extending previous findings.
Study bounds on self-shrinkers with bounded HA for applications.
problem Understanding bounds on self-shrinkers with bounded HA.
method Integral and pointwise bounds on the second fundamental form of self-shrinkers.
result Gap and compactness results for self-shrinkers.
Using a maximum principle for self-shrinkers of the mean curvature flow, we give new proofs of a rigidity theorem for rotationally symmetric compact self-shrinkers and a result about the asymptotic behavior of self-shrinkers. This comparison argument also implies a linear bound for the second fundamental form of self-s…
Surveying methods to create spaces with non-trivial self covers.
problem Creating spaces with non-trivial self covers.
method Surveying techniques for constructing spaces, including low and high dimension continua.
result Discussion of open problems related to self covering phenomena.
New self-expander found between two given asymptotic ones.
problem Finding new self-expanders between given asymptotic ones.
method Developed a min-max theory for asymptotically conical self-expanders of mean curvature flow.
result Existence of a new asymptotically conical self-expander trapped between two given ones.
New construction of self-dual black holes using quadrics.
problem Hidden features of self-dual black holes obscured by twistor theory.
method Holomorphic quadrics in dual twistor space.
result Directly encoded geometry of self-dual black holes in quadrics.
We prove that the only self-similar surfaces of Euclidean 3-space which are foliated by circles are the self-similar surfaces of revolution discovered by S. Angenent and that the only ruled, self-similar surfaces are the cylinders over planar self-similar curves.
Notions of self-dual and anti self-dual almost quaternionic structures are introduced. The complete classification of self-dual and anti self-dual generalized Kaehler manifolds is obtained.
Study pinches Weyl curvature on 4-manifolds, proving anti-self-duality.
problem Understanding Weyl curvature pinching on 4-manifolds.
method Analyzing harmonic and pinched self-dual Weyl curvature, proving anti-self-duality.
result Proves anti-self-duality for compact 4-manifolds with pinched self-dual Weyl curvature.
Study finds unique self-expanders for mean curvature flow.
problem Finding solutions to mean curvature flow.
method Derived equation based on generalized Lawson-Osserman cone and modified equilibria theory.
result Existence and uniqueness of self-expanders proved.
Self-supervision improves GCNs' generalizability and robustness.
problem Improving graph convolutional networks' performance.
method Three mechanisms of self-supervision, multi-task learning, and graph adversarial training.
result Self-supervision enhances GCNs' robustness and generalizability.
A rigidity theorem for smooth Legendrian self-shrinkers is proven.
problem Understanding the structure of Legendrian self-shrinkers.
method Estimating weighted volume to prove optimal volume growth.
result Rigidity theorem for entire smooth Legendrian self-shrinkers.
The paper proves uniqueness and convergence of asymptotically conical self-shrinkers and self-expanders.
problem Proving uniqueness and convergence of asymptotically conical self-shrinkers and self-expanders.
method Analyzing properly immersed mean curvature flow self-shrinkers and self-expanders asymptotic to cones.
result Proves uniqueness and convergence of asymptotically conical self-shrinkers and self-expanders.
Study self-intersections of arcs on a pair of pants, proving natural number spectrum.
problem Understanding self-intersections of arcs on a pair of pants.
method Algorithm to compute self-intersection number, bounds established in terms of word length.
result Spectrum of self-intersection numbers covers all natural numbers.
Self-play is an unsupervised training procedure which enables the reinforcement learning agents to explore the environment without requiring any external rewards. We augment the self-play setting by providing an external memory where the agent can store experience from the previous tasks. This enables the agent to come…
Self-focal points on ellipsoids of dimension 3 or higher are rare.
problem Existence of self-focal points on Riemannian manifolds of dimension 3 or higher.
method Analyzing geodesics and umbilic points on ellipsoids of various dimensions.
result Ellipsoids of dimension 3 or higher with at least 4 distinct axes have no self-focal points.
The paper studies scalar curvature of self-shrinkers and proves curvature bounds.
problem Proving curvature bounds for self-shrinkers.
method Analyzing scalar curvature of self-shrinkers in Euclidean space.
result Proves that the scalar curvature R of self-shrinkers is bounded by n−1. Self-training improves model accuracy by refining pseudo-labels.
problem Improving semi-supervised learning with self-training.
method Theoretical insights into self-training algorithm with a focus on linear classifiers.
result Self-training iterations can improve model accuracy even if stuck in sub-optimal fixed points.
Generalizes halfspace theorems to higher dimensions for self-shrinkers.
problem Limitations of halfspace theorems in higher dimensions for self-shrinkers.
method Extends codimension 1 results to arbitrary codimension.
result Establishes new halfspace theorems for self-shrinkers in arbitrary codimension.
GSA-Nets apply group equivariance to self-attention for vision tasks.
problem Improving self-attention networks for vision tasks.
method Define group-equivariant positional encodings.
result GSA-Nets outperform non-equivariant self-attention networks on vision benchmarks.
GRAC improves reinforcement learning by self-guiding and self-regularizing.
problem Learning divergence and slow updates in reinforcement learning algorithms.
method Self-regularized TD-learning and self-guided policy improvement.
result Achieved or outperformed state-of-the-art results on OpenAI gym tasks.
New self-exciting random evolutions (SEREs) for modeling traffic and transport processes.
problem Modeling self-exciting and clustering effects in traffic and transport processes.
method Introducing a new process based on a superposition of a Markov chain and a Hawkes process, and constructing self-exciting random evolutions (SEREs).
result Developed new models and limit theorems for SEREs, including averaging and diffusion approximation.
The paper calculates self-intersections on a pair of pants using Bowen and Series' coding.
problem Computing the number of self-intersections of closed geodesics on a pair of pants.
method Used Bowen and Series' coding to compute self-intersections.
result Proved a conjecture and provided bounds for self-intersection numbers.
Unified description of aesthetic curves through self-affinities.
problem Characterizing log-aesthetic curves and their properties.
method Reformulating and proving self-affinities of planar curves, integrating equiaffine geometry.
result Unified characterization of constant curvature curves in similarity and equiaffine geometries.
Theoretical analysis shows LLMs can self-correct responses through in-context learning.
problem Understanding how large language models improve through self-correction.
method Theoretical analysis based on simplified alignment task, focusing on softmax attention, multi-head attention, and MLP blocks.
result LLMs can refine responses in an in-context way when given accurate self-examinations as rewards.
The paper classifies self-replicating 3D shapes using algebraic models.
problem Understanding self-replicating 3D shapes.
method Using idempotents in the (2+1)-cobordism category to classify 3-manifolds.
result A classification theorem for self-replicating 3-manifolds.
New theorem shows noncompact self shrinkers are unknotted.
problem Understanding the structure of noncompact self shrinkers.
method Used mean curvature flow to extend theorem to noncompact cases.
result Noncompact self shrinkers without knotted components.
Classifies self-dual almost-Kähler 4-manifolds, proving uniqueness up to rescaling.
problem Classifying self-dual almost-Kähler four-manifolds.
method Using LeBrun's result and properties of Ricci tensor, the authors classify manifolds of different types.
result Any self-dual almost-Kähler metric on CP2 is the Fubini-Study metric up to rescaling. Study self shrinkers with medium entropy in 4D space.
problem Analyzing self shrinkers with entropy bounds.
method Smooth asymptotically conical self shrinkers in R^4.
result Entropy bounded above by Λ_1.
Existence proof of noncompact self-shrinkers with arbitrary genus.
problem Existence of noncompact self-shrinkers with arbitrary genus.
method Employing min-max techniques to rigorously prove existence.
result Confirmation of one asymptotically conical end for large genus self-shrinkers.
Lipschitz equivalence of self-similar sets is an important area in the study of fractal geometry. It is known that two dust-like self-similar sets with the same contraction ratios are always Lipschitz equivalent. However, when self-similar sets have touching structures the problem of Lipschitz equivalence becomes much …
This article gives an alternative approach to the self-shrinking and self-expanding solutions of the curve shortening flow, which are related to singularity formation of the mean curvature flow. The motivation for the self-similar solutions arises from natural area preserving rescaling. Further we describe the self-sim…
Constructs self-expanders of positive genus for cones in R^3.
problem Creating self-expanders of positive genus for cones in R^3.
method Constructs self-expanders asymptotic to cones, uses mean curvature flow.
result Constructs self-expanders with unbounded genus asymptotic to a rotationally symmetric cone.
Paper proves finite Morse index for certain self-shrinkers.
problem Finite Morse index of self-shrinkers.
method Sufficient condition for finite Morse index of complete properly self-shrinkers.
result Proves finite Morse index for self-shrinkers with finite asymptotically conical or cylindrical ends.
Paper stabilizes generative model training with synthetic data.
problem Self-consuming loops in generative model training.
method Introducing an idealized correction function and self-correction functions.
result Self-consuming loops can be exponentially more stable with the right correction.
Characterizes sequences from two-component link diagrams.
problem Understanding information from non-self crossing sequences of link diagrams.
method Investigated and characterized pairs of non-self OU sequences of two-component link diagrams.
result Completely characterized pairs of non-self OU sequences of diagrams of two-component links.
Study of complete space-like self-expanders in Minkovski space.
problem Characterize complete space-like self-expanders in Minkovski space.
method Use of maximum principle of Omori-Yau type to prove rigidity theorems.
result Classification of 2-dimensional complete space-like self-expanders with constant squared norm of the second fundamental form.