arXiv research

This paper reviews golden Riemannian manifolds over the past decade.

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

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…

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

The study proves unique harmonic functions and combinatorial properties of vertex-transitive graphs.

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.

Talked about the Veech group of a specific surface.

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. …

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.

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…

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…

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…

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.

The study improves bounds on pseudo-Anosov maps and certifies minimum and accumulation points of normalized dilatations.

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…

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.

Improved variational inequality algorithms using adaptive step sizes.

Sum of Lagrange numbers equals a specific formula.

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…

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

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 …

We establish a relation between the trace evaluation in SO(3) topological quantum field theory and evaluations of a topological Tutte polynomial. As an application, a generalization of the Tutte golden identity is proved for graphs on the torus.

Generative network integrates into ROM for PDEs, matching measurements and estimating uncertainties.

In this paper, we study metallic structures, i.e. polynomial structures with the structure polynomial $Q\left( J\right) =J^{2}-aJ-bI$ on manifolds using the metallic ratio, which is a generalization of the Golden proportion. We investigate for integrability and parallelism conditions of metallic structures. Also, we gi…

Distribution grids are currently challenged by frequent voltage excursions induced by intermittent solar generation. Smart inverters have been advocated as a fast-responding means to regulate voltage and minimize ohmic losses. Since optimal inverter coordination may be computationally challenging and preset local contr…

In this paper, we find all constant slope surfaces in the Euclidean 3-space, namely those surfaces for which the position vector of a point of the surface makes constant angle with the normal at the surface in that point. These surfaces could be thought as the bi-dimensional analogue of the generalized helices. Some pi…

This work introduces significativity indices for agreement values between classifiers.

The aim of our paper is to focus on some properties of submanifolds in Riemannian manifolds endowed with endomorphisms that generalize the Golden Riemannian structure, named metallic Riemannian structures. We focus on the properties of the structure induced on submanifolds, named by us $Σ$-metallic Riemannian structure…

New geometric structures derived from Hessian metrics and tensors.

This paper gives mathematical models for flat knotted ribbons, and makes specific conjectures for the least length of ribbon (for a given width) needed to tie the trefoil knot and the figure eight knot. The first conjecture states that (for width one) the least length of ribbon needed to tie an open-ended trefoil knot …

This paper introduces a conceptual framework, in the context of quantum topology and the algebras underlying it, for analyzing relations obeyed by the chromatic polynomial χ(Q) of planar graphs. Using it we give new proofs and substantially extend a number of classical results concerning the combinatorics of the chroma…

In this paper, the second in a series of eight we continue our development of the basic tools of the multivector and extensor calculus which are used in our formulation of the differential geometry of smooth manifolds of arbitrary topology . We introduce metric and gauge extensors, pseudo-orthogonal metric extensors, g…

The paper analyzes the reward improvement of aligned policies in large language models.

Limiting the model size of a kernel support vector machine to a pre-defined budget is a well-established technique that allows to scale SVM learning and prediction to large-scale data. Its core addition to simple stochastic gradient training is budget maintenance through merging of support vectors. This requires solvin…

New formulas for knot polynomial evaluations from covering spaces.

We present a modification of the so-called Parrondo's paradox where one is allowed to choose in each turn the game that a large number of individuals play. It turns out that, by choosing the game which gives the highest average earnings at each step, one ends up with systematic loses, whereas a periodic or random seque…

This paper studies the empirical tracking performance of leveraged ETFs on gold, and their price relationships with gold spot and futures. For tracking the gold spot, we find that our optimized portfolios with short-term gold futures are highly effective in replicating prices. The market-traded gold ETF (GLD) also exhi…

New loss function connects learning rate and momentum.

Using the mechanics of creep in material sciences as a metaphor, we present a general framework to understand the evolution of financial, economic and social systems and to construct scenarios for the future. In a nutshell, highly non-linear out-of-equilibrium systems subjected to exogenous perturbations tend to exhibi…

The paper calculates gap distributions for translation surfaces, focusing on the double heptagon.

This is the first paper in a series (of four) designed to show how to use geometric algebras of multivectors and extensors to a novel presentation of some topics of differential geometry which are important for a deeper understanding of geometrical theories of the gravitational field. In this first paper we introduce t…

As the decade turns, we reflect on nearly thirty years of successful manipulation of the world's public equity markets. This reflection highlights a few of the key enabling ingredients and lessons learned along the way. A quantitative understanding of market impact and its decay, which we cover briefly, lets you move l…

In this paper, we develop a new accelerated stochastic gradient method for efficiently solving the convex regularized empirical risk minimization problem in mini-batch settings. The use of mini-batches is becoming a golden standard in the machine learning community, because mini-batch settings stabilize the gradient es…