arXiv research

Distance, normals, and double normals for real plane curves with singularities

The study of quotient structures in multi-graded bundles, including double vector bundles.

Study normal operators of double fibration transforms with conjugate points.

Paper introduces new estimator for continuous treatment effects.

A 1-bridge torus knot in a 3-manifold of genus $\le 1$ is a knot drawn on a Heegaard torus with one bridge. We give two types of normal forms to parameterize the family of 1-bridge torus knots that are similar to the Schubert's normal form and the Conway's normal form for 2-bridge knots. For a given Schubert's normal f…

Many key algorithms in 3-manifold topology involve the enumeration of normal surfaces, which is based upon the double description method for finding the vertices of a convex polytope. Typically we are only interested in a small subset of these vertices, thus opening the way for substantial optimization. Here we give an…

In low-dimensional topology, many important decision algorithms are based on normal surface enumeration, which is a form of vertex enumeration over a high-dimensional and highly degenerate polytope. Because this enumeration is subject to extra combinatorial constraints, the only practical algorithms to date have been v…

Let $M$ be a Riemannian manifold and ${\mathcal P}M$ be the space of all smooth paths on $M$. We describe geodesics on path space ${\mathcal P}M$. Normal neighbourhood structure on ${\mathcal P}M$ has been discussed. We identify paths on $M$ under "back-track" equivalence. Under this identification we show that if $M$ …

Constructs finite element spaces for $(p,q)$-forms, excluding one subspace.

A virtual link diagram is called normal if the associated abstract link diagram is checkerboard colorable, and a virtual link is normal if it has a normal diagram as a representative.In this paper, we introduce a method of converting a virtual link diagram to a normal virtual link diagram by use of the double covering …

Paper characterizes DLN distribution, its properties, and estimation methods.

New method for estimating parameters in inverse problems using double robustness.

Enhances Hamiltonian systems stability through generalized double bracket vector fields.

On a Poisson manifold endowed with a Riemannian metric we will construct a vector field that generalizes the double bracket vector field defined on semi-simple Lie algebras. On a regular symplectic leaf we will construct a generalization of the normal metric such that the above vector field restricted to the symplectic…

A virtual link diagram is called normal if the associated abstract link diagram is checkerboard colorable, and a virtual link is normal if it has a normal diagram as a representative. Normal virtual links have some properties similar to classical links.In this paper, we introduce a method of converting a virtual link d…

The paper uses double machine learning to estimate dynamic treatment effects robustly.

We introduce the concept of a standard form for two embedded maximal sphere systems in the doubled handlebody, and we prove an existence and uniqueness result. In particular, we show that pairs of maximal sphere systems in the doubled handlebody (up to homeomorphism) bijectively correspond to square complexes satisfyin…

We propose a generalized double Pareto prior for Bayesian shrinkage estimation and inferences in linear models. The prior can be obtained via a scale mixture of Laplace or normal distributions, forming a bridge between the Laplace and Normal-Jeffreys' priors. While it has a spike at zero like the Laplace density, it al…

Study Neumann problem for special Lagrangian type equations.

The group of bordism classes of unoriented surfaces in 4-space is determined. The bordism classes are characterized by normal Euler numbers,double linking numbers, and triple linking numbers.

Paper analyzes double twist knots using adjoint hyperbolic torsion polynomial.

We introduce a stochastic model to explain a double power-law distribution which exhibits two different Paretian behaviors in the upper and the lower tail and widely exists in social and economic systems. The model incorporates fitness consideration and noise fluctuation. We find that if the number of variables (e.g. t…

This paper explains why double descent sometimes occurs weakly or not at all from an optimization perspective.

Article studies symmetry in smooth vector bundles using advanced operations.

Invariant of 3-manifolds using Hopf algebra elements.

Paper proposes FPG algorithm for unbiased off-policy PG estimation.

A new DML method for continuous treatments uncovers causal mediation effects.

We show that the topological classification and the smooth classification are generically the same for certain families of plane curves in a semi-local case(the double local case). Especially we give the normal form of transversely jointed two families of plane curves with second order contact at the envelope.

R package xtdml uses DML for panel data models with fixed effects.

Two new rational formulae for normal implied volatility are presented.

Proposes HDBEN for heteroscedastic regression with improved sparsity and variance modeling.

The paper develops a new theory of double Johnson filtrations for mapping class groups.

Batch normalization (batch norm) is often used in an attempt to stabilize and accelerate training in deep neural networks. In many cases it indeed decreases the number of parameter updates required to achieve low training error. However, it also reduces robustness to small adversarial input perturbations and noise by d…

A mathematical analysis of the distribution of voting power in the Council of the European Union operating according to the Treaty of Lisbon is presented. We study the effects of Brexit on the voting power of the remaining members, measured by the Penrose--Banzhaf Index. We note that the effects in question are non-mon…

New method extracts joint and individual signals from multi-view data.

Proposes nAIPW for robust ATE estimation using neural networks.

New method improves robustness of double robust estimators under complete misspecification.

Let $ν$ be either the Ozsváth-Szabó $τ$-invariant or the Rasmussen $s$-invariant, suitably normalized. For a knot $K$, Livingston and Naik defined the invariant $t_ν(K)$ to be the minimum of $k$ for which $ν$ of the $k$-twisted positive Whitehead double of $K$ vanishes. They proved that $t_ν(K)$ is bounded above by $-T…

We study real lines on certain Moishezon threefolds which are potentially twistor spaces of 3CP^2. Here, line means a smooth rational curve whose normal bundle is O(1)^2 and the reality implies the invariance under an anti-holomorphic involution on the threefolds. Our threefolds are birational to double coverings of CP…

Improved estimators for causal inference using cross-fitting and undersmoothing.

This is the first of two companion papers in which a thorough study of the normal form and the first integrability conditions arising from {\em bi-conformal vector fields} is presented. These new symmetry transformations were introduced in {\em Class. Quantum Grav.} \textbf{21}, 2153-2177 and some of their basic proper…

New method bypasses global fit for LISA's Galactic binaries, extracting population parameters directly.

We introduce canonical coordinates on minimal time-like surfaces in the n-dimensional Minkowski space and prove the existence and the uniqueness of these parameters. With respect to these coordinates the coefficients of the first fundamental form are expressed by the invariants of the surface. On any time-like surface …

In recent years, a rich variety of shrinkage priors have been proposed that have great promise in addressing massive regression problems. In general, these new priors can be expressed as scale mixtures of normals, but have more complex forms and better properties than traditional Cauchy and double exponential priors. W…

Estimates long-term effects of new treatments using historical and short-term data.

Estimates impulse response functions using machine learning in time series data.

Annealing Double-Head calibrates deep neural networks during training.

Paper introduces GDR-learners for estimating potential outcomes from observational data.