arXiv research

Study finds a linear lower bound on conformal dimension for random hyperbolic groups.

Explains visual metrics on hyperbolic space boundaries.

Algorithm removes leaves to find root in uniform trees.

We present a parallel algorithm that computes the ask and bid prices of an American option when proportional transaction costs apply to the trading of the underlying asset. The algorithm computes the prices on recombining binomial trees, and is designed for modern multi-core processors. Although parallel option pricing…

Classifier evasion consists in finding for a given instance $x$ the nearest instance $x'$ such that the classifier predictions of $x$ and $x'$ are different. We present two novel algorithms for systematically computing evasions for tree ensembles such as boosted trees and random forests. Our first algorithm uses a Mixe…

Boosted decision trees enjoy popularity in a variety of applications; however, for large-scale datasets, the cost of training a decision tree in each round can be prohibitively expensive. Inspired by ideas from the multi-arm bandit literature, we develop a highly efficient algorithm for computing exact greedy-optimal d…

A new algorithm improves sample complexity for thresholding in Monte Carlo Tree Search.

We propose a simple yet powerful framework for modeling integer-valued data, such as counts, scores, and rounded data. The data-generating process is defined by Simultaneously Transforming and Rounding (STAR) a continuous-valued process, which produces a flexible family of integer-valued distributions capable of modeli…

In spectral clustering, one defines a similarity matrix for a collection of data points, transforms the matrix to get the Laplacian matrix, finds the eigenvectors of the Laplacian matrix, and obtains a partition of the data using the leading eigenvectors. The last step is sometimes referred to as rounding, where one ne…

Technical trading rules and linear regressive models are often used by practitioners to find trends in financial data. However, these models are unsuited to find non-linearly separable patterns. We propose a decision tree forecasting model that has the flexibility to capture arbitrary patterns. To illustrate, we constr…

Study on membranes under confinement, proving existence and regularity of minimizers.

Counterfactual regret minimization (CFR) is the most popular algorithm on solving two-player zero-sum extensive games with imperfect information and achieves state-of-the-art performance in practice. However, the performance of CFR is not fully understood, since empirical results on the regret are much better than the …

Novel unsupervised random forests improve density estimation and data synthesis.

The paper proves a new method to find the maximum Laplace eigenvalues on surfaces.

Machine learning classifiers often stumble over imbalanced datasets where classes are not equally represented. This inherent bias towards the majority class may result in low accuracy in labeling minority class. Imbalanced learning is prevalent in many real-world applications, such as medical research, network intrusio…

In this short paper we investigate whether meta-learning techniques can be used to more effectively tune the hyperparameters of machine learning models using successive halving (SH). We propose a novel variant of the SH algorithm (MeSH), that uses meta-regressors to determine which candidate configurations should be el…

Boosting for off-policy learning reduces empirical risk.

Reciprocating interactions represent a central feature of all human exchanges. They have been the target of various recent experiments, with healthy participants and psychiatric populations engaging as dyads in multi-round exchanges such as a repeated trust task. Behaviour in such exchanges involves complexities relate…

Gradient descent with biased rounding errors converges faster under certain conditions.

Round surgery diagrams represent 3-manifolds in $S^3$.

The Milnor fiber conjecture is proven for splice type singularities.

Contact round surgeries on $(\mathbb{S}^3,ξ_{st})$ help in constructing and understanding contact 3-manifolds.

In this article, we extend Huisken's theorem that convex surfaces flow to round points by mean curvature flow. We construct certain classes of mean convex and non-mean convex hypersurfaces that shrink to round points and use these constructions to create pathological examples of flows. We find a sequence of flows that …

Optimizes sample and round complexity in adaptive sampling from multiple distributions.

Consider an analytic map of a neighborhood of 0 in a vector space to a Euclidean space. Suppose that this map takes all germs of lines passing through 0 to germs of circles. Such a map is called rounding. We introduce a natural equivalence relation on roundings and prove that any rounding, whose differential at 0 has r…

New findings show infinitely many knots cannot be smoothly round handle slices.

We discuss the integrability of orthogonal almost complex structures on Riemannian products of even-dimensional round spheres and give a partial answer to the question raised by E. Calabi concerning the existence of complex structures on a product manifold of a round 2-sphere and a round 4-sphere.

This work investigates how multi-round reasoning improves LLM performance.

New findings on $κ$-solutions with round cylinder as asymptotic shrinker.

Round balls minimize liquid drop model volumes ≤ 1.

Gradient descent stagnates in low-precision, but unbiased rounding schemes improve convergence.

Round cylinders are rigid in Ricci shrinkers close to the standard product.

A half-geodesic is a closed geodesic realizing the distance between any pair of its points. All geodesics in a round sphere are half-geodesics. Conversely, this note establishes that Riemannian spheres with all geodesics closed and sufficiently many half-geodesics are round.

We show that if the entropy of any closed hypersurface is close to that of a round hyper-sphere, then it is close to a round sphere in Hausdorff distance. Generalizing the result of \cite{BW1} to higher dimensions.

In this paper, we study the limiting behavior of the Brown-York mass and Hawking mass along nearly round surfaces at infinity of an asymptotically flat manifold. Nearly round surfaces can be defined in an intrinsic way. Our results show that the ADM mass of an asymptotically flat 3-manifold can be approximated by some …

The study characterizes round spheres in Euclidean space based on r-mean curvature conditions.

Contact round surgery of contact 3-manifolds is introduced in this paper. By using this method, an alternative proof of the existence of a contact structure on any closed orientable 3-manifold is given. It is also proved that any contact structure on any closed orientable 3-manifold is constructed from the standard con…

In recent work, the notion of Double Convexity for a foliation of a conical null hypersurface was introduced to give a proof, if satisfied, of the Null Penrose Inequality. Double Convexity constrains the geometry of a Marginally Outer Trapped Surface (MOTS), called a quasi-round MOTS. In the first part of this paper, f…

Study cohomology rings of 3D manifolds with round fold maps into the plane.

Research explores real algebraic realization of round fold maps of codimension -1.

We classify the radially symmetric connections in vector bundles over round spheres by proving that they are all parallel.

New Einstein metrics found on a 10-dimensional sphere.

New compact mean convex hypersurfaces found for positive λ.

We prove that the well-rounded retract of SO_n\SL_n(R) is a minimal SL_n(Z)-invariant spine.

We present the Round Handle Problem, proposed by Freedman and Krushkal. It asks whether a collection of links, which contains the Generalised Borromean Rings, are slice in a 4-manifold R constructed from adding round handles to the four ball. A negative answer would contradict the union of the surgery conjecture and th…

High-frequency traders can act as either small informed traders or round-trippers, affecting price discovery and liquidity.

One-round FL method improves robustness and reduces communication rounds.

Eigenvalues on spheres are compared to the unit round sphere, proving a sharp bound and equality condition.