arXiv research

Positive representations on surfaces have positive cross-ratios and satisfy a collar lemma.

Let S be a closed orientable surface of genus at least 2 and let G be a semisimple real algebraic group of non-compact type. We consider a class of representations from the fundamental group of S to G called positively ratioed representations. These are Anosov representations with the additional condition that certain …

Study k-positive surface group representations and their degenerations.

Collar lemma proven for certain surface group representations.

Positive representations of surface groups in PO(p,q) form connected components of character varieties.

Paper extends ranking metrics theory for financial positions.

Paper extends ranking metrics theory for financial positions.

We derive generalizations of McShane's identity for higher ranked surface group representations by studying a family of mapping class group invariant functions introduced by Goncharov and Shen which generalize the notion of horocycle lengths. In particular, we obtain McShane-type identities for finite-area cusped conve…

A novel method for learning DAGs from positive-valued data.

Sharp volume growth ratio for 3D manifolds with positive scalar curvature.

The paper tests if optimal hedge ratios for Bitcoin are position-dependent.

TRE improves density-ratio estimation for highly dissimilar densities.

New ANN method for imputing rounded zeros in compositional data.

We define a family of four-point invariants for Shilov boundaries of bounded symmetric domains of tube type, which generalizes the classical four-point cross ratio on the unit circle. This generalization, which is based on a similar construction of Clerc and Ørsted, is functorial and well-behaved under products; these …

Benchmarking deep learning models for financial time series, focusing on risk-adjusted performance.

In this paper, we mainly study the mean curvature flow in Kähler surfaces with positive holomorphic sectional curvatures. We prove that if the ratio of the maximum and the minimum of the holomorphic sectional curvatures is less than 2, then there exists a positive constant $δ$ depending on the ratio such that $\cosα\ge…

Optimizes hedge ratio for delta-neutral liquidity positions in AMMs.

We study Hitchin representations and maximal symplectic representations of surface groups, which can be both thought of as generalisations of Fuchsian representations. We show that the corresponding energy functionals are proper on Teichmuller space. We also prove that the mapping class group acts properly on the corre…

Study analyzes factors affecting capital adequacy in Bangladesh's banks.

The main result of this paper is: Given any constant C, there is $(ε,k,L)$ such that if a complete, orientable, noncompact odd-dimensional manifold with bounded positive sectional curvature contains a $(ε,k,L)$-neck, then the asymptotic scalar curvature ratio is bigger or equal to C. As a application we proved that the…

The paper studies curves of constant-ratio in pseudo-Galilean space.

Riesz regression connects to density ratio estimation for causal inference.

Study maximal representations of surface groups via pleated surfaces in pseudo-Riemannian space.

Researchers calculate the volume of Seifert representations for graph manifolds and their covers.

The paper generalizes deformation results for Fuchsian representations and shows proper affine actions.

The authors give a short survey of previous results on $δ$-homogeneous Riemannian manifolds, forming a new proper subclass of geodesic orbit spaces with non-negative sectional curvature, which properly includes the class of all normal homogeneous Riemannian manifolds. As a continuation and an application of these resul…

Paper connects contrastive learning to MI maximization and establishes robust methods for nonlinear ICA and subspace estimation.

In this paper, we reformulate the forest representation learning approach as an additive model which boosts the augmented feature instead of the prediction. We substantially improve the upper bound of generalization gap from $\mathcal{O}(\sqrt\frac{\ln m}{m})$ to $\mathcal{O}(\frac{\ln m}{m})$, while $λ$ - the margin r…

We present GradientDICE for estimating the density ratio between the state distribution of the target policy and the sampling distribution in off-policy reinforcement learning. GradientDICE fixes several problems of GenDICE (Zhang et al., 2020), the state-of-the-art for estimating such density ratios. Namely, the optim…

Derives formula for skew stickiness ratio in asset price and volatility dynamics.

We introduce a new measure of performance of investment strategies, the monotone Sharpe ratio. We study its properties, establish a connection with coherent risk measures, and obtain an efficient representation for using in applications.

We discuss - in what is intended to be a pedagogical fashion - a criterion, which is a lower bound on a certain ratio, for when a stock (or a similar instrument) is not a good investment in the long term, which can happen even if the expected return is positive. The root cause is that prices are positive and have skewe…

Paper improves VaR risk allocation by avoiding zero probability events.

Study on signatures of positive braids with bounds derived.

New $Θ$-positive representations of surface groups discovered.

The paper connects mass, harmonic functions, and capacity in asymptotically flat 3-manifolds.

Tests factor models by decomposing market into body and tail legs, revealing inconsistent results.

We generalise in this article the Mc Shane-Mirzakhani identities in hyperbolic geometry to arbitrary cross ratios. We give an expression of them in the case of Hitchin representations of surface groups in PSL(n, R) in a suitable choice of Fock-Goncharov coordinates.

Study shows death ratio of COVID-19 deaths increases financial volatility.

The position of the EWS (economy-wide substitution)-ratio vector determines the Rybczynski sign pattern, which expresses the factor endowment--commodity output relationships, and the Stolper-Samuelson sign pattern, which expresses the commodity price--factor price relationships in a three-factor two-good general equili…

In supervised machine learning for author name disambiguation, negative training data are often dominantly larger than positive training data. This paper examines how the ratios of negative to positive training data can affect the performance of machine learning algorithms to disambiguate author names in bibliographic …

Study finds no consistent return predictability using payout ratios across 16 countries.

Gradient descent converges linearly in finite-width networks with positive NTK and compatible conditions.

A twisted curve in Euclidean 3-space E^3 can be considered as a curve whose position vector can be written as linear combination of its Frenet vectors. In the present study we study the twisted curves of constant ratio in E^3 and characterize such curves in terms of their curvature functions. Further, we obtain some re…

New theorem shows curvature concentration depends linearly on volume ratio.

Researchers parametrize spaces of positive representations for Lie groups.

Unified framework for estimating density ratios in causal inference.

Theory of Θ-positive representations for real closed fields.