arXiv research

EMG analysis quantifies bipedal standing quality in SCI patients.

FORK improves model-free reinforcement learning performance.

Method learns to map dynamics of different systems.

Progressive reinforcement learning combines expert policies for multi-skilled motion control.

Investigates conditions for Poincaré map existence and uniqueness in systems with impulse effects.

SMiRL learns to minimize surprise in unstable environments, improving agent performance.

The purpose of this article is twofold. First, we motivate the need for a new type of stand-alone retirement income insurance product that would help individuals protect against personal longevity risk and possible "retirement ruin" in an economically efficient manner. We label this product a ruin-contingent life annui…

STAND-DA improves AD in DA target domains with limited data.

Researchers predict butt rot volume using harvester data and remote sensing.

CP-DRL improves curriculum reinforcement learning by leveraging causal relationships.

SWD approximates GP for faster regression.

Study shows not all ML models are uniquely identifiable from data.

Paper tackles skill transfer in RL for morphologically different agents.

SFC aims to protect the Amazon with a digital currency and smart contracts.

New open books solve a long-standing surface mapping class group question.

Paper solves long-standing problem of infinite ideal polyhedra in hyperbolic space.

We show that on simple surfaces the geodesic ray transform acting on solenoidal symmetric tensor fields of arbitrary order is injective. This solves a long standing inverse problem in the two-dimensional case.

A new index measures how many changes are needed to turn virtual links into simple ones.

In this paper, we study Zermelo navigation on Riemannian manifolds and use that to solve a long standing problem in Finsler geometry. Namely, the complete classification of strongly convex Randers metrics of constant flag curvature.

Symbolic regression constructs simple equations for complex systems.

We prove a long-standing conjecture about complex reflection arrangements.

Novel duality theory for operator Frobenius algebras solves long-standing hydrodynamic integrable systems problem.

Paper solves a long-standing problem with curvature estimates.

LemonadeBench evaluates LLMs' economic intuition through a simulated lemonade stand.

We address a long-standing and long-investigated problem in combinatorial topology, and break the exponential barrier for triangulations of real projective space, constructing a trianglation of $\mathbb{RP}^n$ of size $e^{(\frac{1}{2}+o(1))\sqrt{n}{\log n}}$.

The long standing classification problem in the theory of Heegaard splittings of 3-manifolds is to exhibit for each closed 3-manifold a complete list, without duplication, of all its irreducible Heegaard surfaces, up to isotopy. We solve this problem for non Haken hyperbolic 3-manifolds.

EvaSylv software evaluates forest management with natural risk considerations.

This article is based on the methods developed in [AGG]. We construct a complex hyperbolic structure on a trivial disc bundle over a closed orientable surface $Σ$ (of genus 2) thus solving a long standing problem in complex hyperbolic geometry (see [Gol1, p. 583] and [Sch, p. 14]). This example answers also [Eli, Open …

Proves almost flat spin^c manifolds bound compact manifolds.

New unknots with geometric constraints exist, proving a long-standing conjecture.

Two machine learning models detect anomalies in ER claims, saving up to 40% in improper payments.

The aim of this paper is to present a complete description of all rotational linear Weingarten surface into the Euclidean sphere S3. These surfaces are characterized by a linear relation aH+bK=c, where H and K stand for their mean and Gaussian curvatures, respectively, whereas a; b and c are real constants.

In this note the long standing problem of the definition of a Poisson bracket in the framework of a multisymplectic formulation of classical field theory is solved. The new bracket operation can be applied to forms of arbitary degree. Relevant examples are discussed and important properties are stated with proofs sketc…

New mappings solve long-standing problems in 3-space.

Explains isometric immersions and their applications.

This work establishes a new upper bound on the number of samples sufficient for PAC learning in the realizable case. The bound matches known lower bounds up to numerical constant factors. This solves a long-standing open problem on the sample complexity of PAC learning. The technique and analysis build on a recent brea…

These lecture notes are a friendly introduction to monopole Floer homology. We discuss the relevant differential geometry and Morse theory involved in the definition. After developing the relation with the four-dimensional theory, our attention shifts to gradings and correction terms. Finally, we sketch the analogue in…

This tutorial introduces the CMA Evolution Strategy (ES), where CMA stands for Covariance Matrix Adaptation. The CMA-ES is a stochastic, or randomized, method for real-parameter (continuous domain) optimization of non-linear, non-convex functions. We try to motivate and derive the algorithm from intuitive concepts and …

In this paper, we prove there exist at least four geometrically distinct closed characteristics on every compact convex hypersurface $\Sg$ in $\R^8$. This gives a confirmed answer in the case $n=4$ to a long standing conjecture in Hamiltonian analysis since the time of A. M. Liapounov in 1892 (cf. P. 235 of \cite{Eke3}…

The long-standing problem of the perfectness of the compactly supported equivariant homeomorphism group on a $G$-manifold (with one orbit type) is solved in the affirmative. The proof is based on an argument different than that for the case of diffeomorphisms. The theorem is a starting point for computing $H_1(\mathcal…

New findings on knot operations challenge a long-standing conjecture.

A long-standing conjecture of Farrell and Zdravkovska and independently S.~T.~Yau states that every almost flat manifold is the boundary of a compact manifold. This paper gives a simple proof of this conjecture when the holonomy group is cyclic or quaternionic. The proof is based on the interaction between flat bundles…

First example of a 5D manifold with K-contact but no Sasakian structure.

We prove a differential Harnack inequality for the solution of the parabolic Allen-Cahn equation $\frac{\partial f}{\partial t}=\triangle f-(f^3-f)$ on a closed n-dimensional manifold. As a corollary we find a classical Harnack inequality. We also formally compare the standing wave solution to a gradient estimate of M…

A previous paper of the authors' contained an error in the proof of a key claim, that Rasmussen's knot-invariant s(K) is equal to its gauge-theory counterpart. The original paper is included here together with a corrigendum, indicating which parts still stand and which do not. In particular, the gauge-theory counterpar…

New theorem for 4D links simplifies characterisation problem.

We show that Jacobi's bound for the order of a system of ordinary differential equations stands in the case of a diffiety defined by a quasi-regular system. We extend the result when there are less equations than variables and characterize the case when the bound is reached.

Solving a long-standing open question in convex geometry, we will show that typical convex surfaces contain points of infinite curvature in all tangent directions. To prove this, we use an easy curvature definition imitating the idea of Alexandrov spaces of bounded curvature, and show continuity properties for this not…