arXiv research

Talked about the Veech group of a specific surface.

This paper reviews golden Riemannian manifolds over the past decade.

Study on CR-lightlike submanifolds in golden semi-Riemannian manifolds.

In this paper, we study slant submanifolds of Riemannian manifolds with Golden structure. A Riemannian manifold $(\tilde{M},\tilde{g},{\varphi})$ is called a Golden Riemannian manifold if the $(1,1)$ tensor field ${\varphi}$ on $\tilde{M}$ is a golden structure, that is ${\varphi}^{2}={\varphi}+I$ and the metric $\tild…

Mack's estimator improves chain ladder prediction for large exposure insurance models.

The Golden Ratio is fascinating topic that continually generated news ideas. A Riemannian manifold endowed with a Golden Structure will be called a Golden Riemannian manifold. The main purpose of the present paper is to study the geometry of radical transversal lightlike submanifolds and transversal lightlike submanifo…

The abstract introduces golden Finsler structures and explores their local and global properties.

Golden L surface has unbounded bunching of saddle connections

Characterizes quasiconformally homogeneous ladder surfaces.

In this work, almost product and almost golden structures are studied. Conditions for those structures being Integrable and parallel are investigated. Also harmonicity of a map between almost pruduct or almost golden manifolds with pure or hyperbolic metric is discussed under certain conditions.

A method for analysing the risk of taking a too low reserve level by use of Chain Ladder method is developed. We give an answer to the question of how much safety loading in terms of the Chain Ladder standard error has to be added to the Chain Ladder reserve in order to reach a specified security level in loss reservin…

We examine spaces of connected tri-/univalent graphs subject to local relations which are motivated by the theory of Vassiliev invariants. It is shown that the behaviour of ladder-like subgraphs is strongly related to the parity of the number of rungs: there are similar relations for ladders of even and odd lengths, re…

Study gluing of Lorentzian length spaces and their causal ladder properties.

The aim of our paper is to focus on some properties of hemi-slant submanifolds in metallic (and Golden) Riemannian manifolds. We give some characterizations for submanifolds to be hemi-slant submanifolds in metallic (or Golden) Riemannian manifolds and we obtain integrability conditions for the distributions involved. …

We used the Ladder Network [Rasmus et al. (2015)] to perform Hyperspectral Image Classification in a semi-supervised setting. The Ladder Network distinguishes itself from other semi-supervised methods by jointly optimizing a supervised and unsupervised cost. In many settings this has proven to be more successful than o…

On each nonorientable surface of odd genus $g \geq 5$, we give a mapping class whose dilatation on an invariant subsurface is the golden ratio.

We classify all groups which can occur as the orientation preserving topological symmetry group of some embedding of a Möbius ladder graph in $S^3$.

Parallel transport is an important step in many discrete algorithms for statistical computing on manifolds. Numerical methods based on Jacobi fields or geodesics parallelograms are currently used in geometric data processing. In this last class, pole ladder is a simplification of Schild's ladder for the parallel transp…

The aim of our paper is to focus on some properties of slant and semi-slant submanifolds of metallic Riemannian manifolds. We give some characterizations for submanifolds to be slant or semi-slant submanifolds in metallic or Golden Riemannian manifolds and we obtain integrability conditions for the distributions involv…

Semi-supervised learning (SSL) partially circumvents the high cost of labeling data by augmenting a small labeled dataset with a large and relatively cheap unlabeled dataset drawn from the same distribution. This paper offers a novel interpretation of two deep learning-based SSL approaches, ladder networks and virtual …

The main purpose of the present paper is to study the geometry of screen transversal lightlike submanifolds and radical screen transversal lightlike submanifolds and screen transversal anti-invariant lightlike submanifolds of Golden Semi-Riemannian manifolds. We investigate the geometry of distributions and obtain nece…

New ladder methods improve numerical accuracy in parallel transport on manifolds.

An almost Golden Riemannian structure $(\varphi ,g)$ on a manifold is given by a tensor field $\varphi$ of type (1,1) satisfying the Golden section relation $\varphi ^{2}=\varphi +1$, and a pure Riemannian metric $g$, i.e., a metric satisfying $g(\varphi X,Y)=g(X,\varphi Y)$. We study connections adapted to such a str…

The paper finds pseudo-Anosov-like maps on an infinite ladder surface.

We briefly review selected contributions to immersion-theoretic topology, from S. Smale's immersion theory for spheres to M. Gromov's convex integration theory, during the early "golden" period from about 1959-1973. Historical remarks are included and technical concepts are presented informally.

Golden age of mathematical finance in the late 20th century.

The paper proposes incentivizing human annotators with 'golden questions' to improve data quality.

In this paper, we study the existence of proper warped product submanifolds in metallic (or Golden) Riemannian manifolds and we discuss about semi-invariant, semi-slant and, respectively, hemi-slant warped product submanifolds in metallic and Golden Riemannian manifolds. Also, we provide some examples of warped product…

The full causal ladder of spacetimes is constructed, and their updated main properties are developed. Old concepts and alternative definitions of each level of the ladder are revisited, with emphasis in minimum hypotheses. The implications of the recently solved ``folk questions on smoothability'', and alternative prop…

We give an explicit formula for the limiting gap distribution of slopes of saddle connections on the golden L, or any translation surface in its SL(2, R)-orbit, in particular the double pentagon. This is the first explicit computation of the distribution of gaps for a flat surface that is not a torus cover.

Method solves Gaussian graphical models on ladder graphs efficiently.

We propose a recurrent extension of the Ladder networks whose structure is motivated by the inference required in hierarchical latent variable models. We demonstrate that the recurrent Ladder is able to handle a wide variety of complex learning tasks that benefit from iterative inference and temporal modeling. The arch…

This paper introduces a new market making approach using scaled beta distributions.

Improved variational inequality algorithms using adaptive step sizes.

New causal distances improve evaluation of causal discovery algorithms.

Variational Autoencoders are powerful models for unsupervised learning. However deep models with several layers of dependent stochastic variables are difficult to train which limits the improvements obtained using these highly expressive models. We propose a new inference model, the Ladder Variational Autoencoder, that…

Chain-ladder reserving is sensitive to outliers, leading to unreliable estimates.

Sum of Lagrange numbers equals a specific formula.

A novel SVR parameter optimization method using GSA outperforms other meta-heuristics in stock market forecasting.

We combine supervised learning with unsupervised learning in deep neural networks. The proposed model is trained to simultaneously minimize the sum of supervised and unsupervised cost functions by backpropagation, avoiding the need for layer-wise pre-training. Our work builds on the Ladder network proposed by Valpola (…

We prove that the HOMFLYPT polynomial of a link, colored by partitions with a fixed number of rows is a $q$-holonomic function. Specializing to the case of knots colored by a partition with a single row, it proves the existence of an $(a,q)$ super-polynomial of knots in 3-space, as was conjectured by string theorists. …

We show that all GL(2, R)-equivariant point markings over orbit closures of primitive genus two translation surfaces arise from marking pairs of points exchanged by the hyperelliptic involution, Weierstrass points, or the golden points in the golden eigenform locus. As corollaries, we classify the holomorphically varyi…

Over the past half-century, the empirical finance community has produced vast literature on the advantages of the equally weighted S\&P 500 portfolio as well as the often overlooked disadvantages of the market capitalization weighted Standard and Poor's (S\&P 500) portfolio (see \cite{Bloom}, \cite{Uppal}, \cite{Jacobs…

The leaderboard in machine learning competitions is a tool to show the performance of various participants and to compare them. However, the leaderboard quickly becomes no longer accurate, due to hack or overfitting. This article gives two pieces of advice to prevent easy hack or overfitting. By following these advice,…

The use of unsupervised data in addition to supervised data in training discriminative neural networks has improved the performance of this clas- sification scheme. However, the best results were achieved with a training process that is divided in two parts: first an unsupervised pre-training step is done for initializ…

The study of pseudo-Anosov maps with minimum expansion factor using train tracks.

New method simplifies individual claims reserving.

We establish a quadratic identity for the Yamada polynomial of ribbon cubic graphs in 3-space, extending the Tutte golden identity for planar cubic graphs. An application is given to the structure of the flow polynomial of cubic graphs at zero. The golden identity for the flow polynomial is conjectured to characterize …