arXiv research

A note on extending Chernoff bound for unit interval random variables.

By the Thurston stability theorem, a group of C^1 orientation-preserving diffeomorphisms of the closed unit interval is locally indicable. We show that the local order structure of orbits gives a stronger criterion for nonsmoothability that can be used to produce new examples of locally indicable groups of homeomorphis…

It is proved that for every fractal continuous mapping F: I\to I^2 of the unit interval onto the unit square there is a pair of points x,y\in I, such that |F(x)-F(y)|^2\ge 5|x-y|.

Proposes a non-crossing deep neural network quantile regression method.

The paper addresses selection bias in conformal prediction for focal units.

We investigate the classification of topological quandles on some simple manifolds. Precisely we classify all Alexander quandle structures, up to isomorphism, on the real line and the unit circle. For the closed unit interval $[0, 1]$, we conjecture that there exists only one topological quandle structure on it, i.e. t…

New method refines prediction intervals for individual treatment effects using cross-world correlation.

We show that there are infinitely many nonisomorphic quandle structures on any topogical space $X$ of positive dimension. In particular, we disprove the conjecture, asserting that there are no nontrivial quandle structures on the closed unit interval $[0,1]$.

Paper proves almost all stabilizer subgroups of Thompson's group satisfy Alexander's theorem.

Paper improves confidence intervals and variance estimation for deep learning models.

Introduces mobility algebra for modeling geodesics on n-spheres.

CRUs model irregular time series with continuous hidden states.

In [SWW], S. Seto, L. Wang and G. Wei proved that the gap between the first two Dirichlet eigenvalues of a convex domain in the unit sphere is at least as large as that for an associated operator on an interval with the same diameter, provided that the domain has the diameter at most $π/2$. In this paper, we extend Set…

A divide is a relative generic immersion of a finite union of copies of the unit interval in the unit disk. A divide defines a classical link in the 3- sphere, which is a fibered link if the image of the immersion is connected. We prove in this paper, that the Lefschetz number of the monodromy is 0. This result was kno…

Several complex tasks that arise in organizations can be simplified by mapping them into a matrix completion problem. In this paper, we address a key challenge faced by our company: predicting the efficiency of artists in rendering visual effects (VFX) in film shots. We tackle this challenge by using a two-fold approac…

Let $I \subseteq \R$ be an open interval, $f : I \to \R$ a strictly positive function and denote by $\E^2$ the Euclidean plane. We classify all surfaces in the warped product manifold $I \times_f \E^2$ for which the unit normal makes a constant angle with the direction tangent to $I$.

We consider families of Dirac operators on the unit interval which depend on parameters via boundary conditions. We study the associated eta forms and Maslov cocyles. With this simple example we show how previous results of Lesch/Woiciechowski and the first author on the eta invariant of cylinders generalize to the fam…

We study and classify topologically invariant $σ$-ideals with a Borel base on the Hilbert cube and evaluate their cardinal characteristics. One of the results of this paper solves (positively) a known problem whether the minimal cardinalities of the families of Cantor sets covering the unit interval and the Hilbert cub…

It was proved by H. Whitney in 1933 that a Serre fibration of compact metric spaces admits a global section provided every fiber is homeomorphic to the unit interval [0,1]. Results of this paper extend Whitney theorem to the case when all fibers are homeomorphic to a given compact two-dimensional manifold.

Let $\F$ be a compact surface and let $I$ be the unit interval. This paper gives a standard form for all 2-sided incompressible surfaces in the 3-manifold $\F \times I$. Since $\F \times I$ is a handlebody when $\F$ has boundary, this standard form applies to incompressible surfaces in a handlebody.

Improved statistical inference for expensive data using machine learning predictions.

We develop a novel method for counterfactual analysis based on observational data using prediction intervals for units under different exposures. Unlike methods that target heterogeneous or conditional average treatment effects of an exposure, the proposed approach aims to take into account the irreducible dispersions …

The family of Wilder continua in cubes of dimension > 2 and its two subfamilies-of continuum-wise Wilder continua and of hereditarily arcwise connected continua-are recognized as coanalytic absorbers in the hyperspace of subcontinua of the cubes. In particular, each of them is homeomorphic to the set of all nonempty co…

Study collapsing geometry of hyperkähler 4-manifolds and prove conjectures.

In this paper, we consider the problem of predicting demographics of geographic units given geotagged Tweets that are composed within these units. Traditional survey methods that offer demographics estimates are usually limited in terms of geographic resolution, geographic boundaries, and time intervals. Thus, it would…

We prove a computable version of de Finetti's theorem on exchangeable sequences of real random variables. As a consequence, exchangeable stochastic processes expressed in probabilistic functional programming languages can be automatically rewritten as procedures that do not modify non-local state. Along the way, we pro…

A new method for online prediction uncertainty quantification in non-exchangeable panel data.

Improved online algorithm for convex losses with near-optimal swap regret.

We investigate the probability distribution of the volatility return intervals $τ$ for the Chinese stock market. We rescale both the probability distribution $P_{q}(τ)$ and the volatility return intervals $τ$ as $P_{q}(τ)=1/\barτ f(τ/\barτ)$ to obtain a uniform scaling curve for different threshold value $q$. The scali…

Let $M$ be a quasi-Fuchsian three-manifold that contains a closed incompressible surface with principal curvatures within the range of the unit interval, for a prescribed function $H$ (with mild conditions) on $M$, we construct a closed incompressible surface with mean curvature $H$ . A direct application is the existe…

Study uses exchangeable GPs for staggered-adoption policy evaluation in panel data.

We provide a new angle and obtain new results on a class of metrics on length-normalized curves in $d$ dimensions, represented by their unit tangents expressed as a function of arc-length, which are functions from the unit interval to the $(d-1)$-dimensional unit sphere. These metrics are derived from the combined acti…

For neural networks (NNs) with rectified linear unit (ReLU) or binary activation functions, we show that their training can be accomplished in a reduced parameter space. Specifically, the weights in each neuron can be trained on the unit sphere, as opposed to the entire space, and the threshold can be trained in a boun…

We show that a group of diffeomorphisms $\D$ on the open unit interval $I,$ equipped with the topology of uniform convergence on any compact set of the derivatives at any order, is non regular: the exponential map is not defined for some path of the Lie algebra. this result extends to the group of diffeomorphisms of fi…

Simple method for estimating missing panel data entries with confidence intervals.

Paper proves Simon's third gap conjecture for minimal surfaces in spheres.

Proves Riemannian starshape of capacitary potential levels.

For a ribbon graph $G$ we consider an alternating link $L_G$ in the 3-manifold $G\times I$ represented as the product of the oriented surface $G$ and the unit interval $I$. We show that the Kauffman bracket $[L_G]$ is an evaluation of the recently introduced Bollobas-Riordan polynomial $R_G$. This results generalizes t…

PyDTS analyzes survival data with discrete intervals and competing risks.

We introduce the notion of strip complex. A strip complex is a special type of complex obtained by gluing "strips" along their natural boundaries according to a given graph structure. The most familiar example is the one dimensional complex classically associated with a graph, in which case the strips are simply copies…

CAP algorithm controls FCR in online selective prediction.

We establish basic geometric and topological properties of Thurston's Master Teapot and the Thurston set for superattracting unimodal self-maps of intervals. In particular, the Master Teapot is connected, contains the unit cylinder, and its intersection with a set $\mathbb{D} \times \{c\}$ grows monotonically with $c$.…

It was proved by H. Whitney in 1933 that a Serre fibration of compact metric spaces admits a global section provided every fiber is homeomorphic to the unit interval [0,1]. An extension of the Whitney's theorem to the case when all fibers are homeomorphic to some fixed compact two-dimensional manifold was proved by the…

Improved nearest neighbors for missing data in latent factor models.

Enhanced TSFMs improve time series forecasting accuracy and reliability.

New method for estimating counterfactual means in adaptive experiments.

We study how to efficiently estimate average treatment effects (ATEs) using adaptive experiments. In adaptive experiments, experimenters sequentially assign treatments to experimental units while updating treatment assignment probabilities based on past data. We start by defining the efficient treatment-assignment prob…

Paper proposes a new method to improve BART model predictions outside training data range.