arXiv research

Finite distortion maps cannot have compact branch sets under growth conditions.

The paper calculates subgroup distortions in 3-manifold groups.

The study shows exponential distortion in virtually special groups containing free subgroups.

Predictive rate-distortion analysis suffers from the curse of dimensionality: clustering arbitrarily long pasts to retain information about arbitrarily long futures requires resources that typically grow exponentially with length. The challenge is compounded for infinite-order Markov processes, since conditioning on fi…

Study the tradeoff between signal distortion and human perception over finite channels.

We consider the group of smooth diffeomorphisms of the circle. We show that any recurrent $f$ (in the sense that $\{f^n\}_{n \in Z}$ is not discrete) is in fact a distortion element (in the sense that its iterates can be written as short compositions involving finitely many smooth diffeomorphisms). Thus rotations are d…

Sharp bounds for distortion risk metrics under uncertain distributions.

Study bounds on curvature for special Finsler metrics.

Given a finite metric CW complex $X$ and an element $α\in π_n(X)$, what are the properties of a geometrically optimal representative of $α$? We study the optimal volume of $kα$ as a function of $k$. Asymptotically, this function, whose inverse, for reasons of tradition, we call the volume distortion, turns out to be an…

This study analyzes communication constraints in MoE architectures using information theory.

Framework uses IRL and RL to elicit and optimize risk preferences robustly to noise.

We solve the vector embedding problem by minimizing total distortion under constraints.

We study the problem asking if one can embed manifolds into finite dimensional Euclidean spaces by taking finite number of eigenvector fields of the connection Laplacian. This problem is essential for the dimension reduction problem in massive data analysis. Singer-Wu proposed the vector diffusion map which embeds mani…

Study shows pooling scores for conformal prediction distorts group coverage.

Vertex distortion detects if a knot is unknot.

Establishes a link between risk measures and uniform integrability in finance.

Distorted surfaces in graph manifolds have specific distortion properties.

Let $1 \rightarrow H \rightarrow G \rightarrow \mathbb{Z} \rightarrow 1$ be an exact sequence of hyperbolic groups induced by a fully irreducible automorphism $φ$ of the free group $H$. Let $H_1 (\subset H)$ be a finitely generated distorted subgroup of $G$. Then $H_1$ is of finite index in $H$. This is an analog of a …

Finding surface mappings with least distortion arises from many applications in various fields. Extremal Teichmüller maps are surface mappings with least conformality distortion. The existence and uniqueness of the extremal Teichmüller map between Riemann surfaces of finite type are theoretically guaranteed [1]. Rece…

We demonstrate the existence of spherically-symmetric truly naked black holes (TNBH) for which the Kretschmann scalar is finite on the horizon but some curvature components including those responsible for tidal forces as well as the energy density $\barρ$ measured by a free-falling observer are infinite. We choose a ra…

New method corrects complex distortions in single view images.

Algorithm finds optimal affine transformation to minimize overall distortion.

Study homeomorphism groups of ordinals, proving strong distortion and normal generators.

We analyze the obstruction to metrics of positive scalar curvature within a given bounded distortion class of metrics. This obstruction lives in a non-Hausdorff cohomology group Poincare dual to the uniformly finite homology studied by Block and Weinberger. One of the applications is a converse to their theorem on infi…

Vertex distortion measures how far lattice knots deviate from straight lines.

We consider the problem of distortion minimal morphing of $n$-dimensional compact connected oriented smooth manifolds without boundary embedded in $\R^{n+1}$. Distortion involves bending and stretching. In this paper, minimal distortion (with respect to stretching) is defined as the infinitesimal relative change in vol…

This paper shows how to calculate risk measures for sums of two counter-monotonic risks.

A new family of stochastic dominance orders based on distortion functions.

Study distortion risk measures for step-weighted distributions.

The distortion of a curve measures the maximum arc/chord length ratio. Gromov showed any closed curve has distortion at least pi/2 and asked about the distortion of knots. Here, we prove that any nontrivial tame knot has distortion at least 5pi/3; examples show that distortion under 7.16 suffices to build a trefoil kno…

Bayesian investor learns unknown asset drift, trades mean-variance optimal portfolio, but policy is robust to observation model distortion.

Computed distortion coefficients for the α-Grushin plane.

Study on risk measures using distorted Choquet integrals with random distortions.

Sharp bounds on distortion of surfaces in 3D space.

New study shows tradeoffs between compression quality, distortion, and perception.

The distortion of a curve is the supremum, taken over distinct pairs of points of the curve, of the ratio of arclength to spatial distance between the points. Gromov asked in 1981 whether a curve in every knot type can be constructed with distortion less than a universal constant C. Answering Gromov's question seems to…

This paper examines an optimal investment problem in a continuous-time (essentially) complete financial market with a finite horizon. We deal with an investor who behaves consistently with principles of Cumulative Prospect Theory, and whose utility function on gains is bounded above. The well-posedness of the optimisat…

Estimates rate-distortion function for large datasets using neural networks.

Introduces new performance criteria for investment under distorted probabilities.

Improved defense against data poisoning attacks by aggregating smaller subsets.

Computes distortion of surfaces in non-geometric 3-manifolds.

Introduces a new conditional expectation under distorted probabilities, addressing time-inconsistency.

Study stabilizers in handlebody group; meridians are undistorted, others are exponentially distorted.

New coding theorem shows achievable rate matches theoretical limit.

Paper proposes a new black-box attack approach to minimize visual distortion.

We construct 2-dimensional CAT(-1) groups which contain free subgroups with arbitrary iterated exponential distortion, and with distortion higher than any iterated exponential.

Study dynamic risk measures and performance indices using distortion functions.

New bounds on knot distortion and Seifert surface properties.