arXiv research

Minimal surfaces and average area ratio found to be maximized by hyperbolic metrics.

The study finds the minimum average area ratio on hyperbolic manifolds and its relation to scalar curvature.

In 3-d the average projected area of a convex solid is 1/4 the surface area, as Cauchy showed in the 19th century. In general, the ratio in n dimensions may be obtained from Cauchy's surface area formula, which is in turn a special case of Kubota's theorem. However, while these latter results are well-known to those wo…

Study on ratio of intrinsic to extrinsic metrics and its relation to surface area.

Noise increases the Rashomon ratio, leading simpler models to perform similarly to complex ones.

Proves upper bound on systolic ratio for circle fillings.

This work proposes a model averaging method for SVM that avoids redundant covariates and achieves asymptotic optimality.

Average Oracle outperforms DCC+NLS in portfolio optimization.

Bayesian model averaging under predictor redundancy

Dynamic trading strategies, in the spirit of trend-following or mean-reversion, represent an only partly understood but lucrative and pervasive area of modern finance. Assuming Gaussian returns and Gaussian dynamic weights or signals, (e.g., linear filters of past returns, such as simple moving averages, exponential we…

We study the curve diffusion flow for closed curves immersed in the Minkowski plane $\mathcal{M}$, which is equivalent to the Euclidean plane endowed with a closed, symmetric, convex curve called an indicatrix that scales the length of a vector in $\mathcal{M}$ depending on its length. The indiactrix $\partial\mathcal{…

The complex, time-dependent statistical structures observed in the Dow Jones Industrial Average on a typical trading day are modeled with Lorentzian functions. The resonant-like structures are characterized by the values of the basic ratio: the average lifetime of the individual states associated with a given structura…

We analyze a gradient flow of closed planar curves minimizing the anisoperimetric ratio. For such a flow the normal velocity is a function of the anisotropic curvature and it also depends on the total interfacial energy and enclosed area of the curve. In contrast to the gradient flow for the isoperimetric ratio, we sho…

Riesz regression connects to density ratio estimation for causal inference.

Proposes AAA for efficient association estimation with confounders.

The study evaluates forecast risk-adjusted performance using various metrics.

New method uses geometric mean to avoid non-collapsibility in case-control studies.

Machine learning predicts mask mandates reduce COVID-19 deaths.

We give a short and simple proof of Cauchy's surface area formula, which states that the average area of a projection of a convex body is equal to its surface area up to a multiplicative constant in the dimension.

Study compares quantum and classical ML in crypto trading, finding hybrid models outperform.

An ODE variational calculation shows that an image principle curvature ratio factor can raise the lower bound, 2(Image Area), on energy of a harmonic map of a surface into Rn. In certain situations, including all radially symmetry harmonic maps, equality is achieved.

In this note, we study the relationship between the variational gap and the variance of the (log) likelihood ratio. We show that the gap can be upper bounded by some form of dispersion measure of the likelihood ratio, which suggests the bias of variational inference can be reduced by making the distribution of the like…

The isoperimetric ratio of an embedded surface in $R^3$ is defined as the ratio of the area of the surface to power three to the squared enclosed volume. The aim of the present work is to study the minimization of the Willmore energy under fixed isoperimetric ratio when the underlying abstract surface has fixed genus $…

In this article we show that for every finite area hyperbolic surface $X$ of type $(g,n)$ and any harmonic Beltrami differential $μ$ on $X$, then the magnitude of $μ$ at any point of small injectivity radius is uniform bounded from above by the ratio of the Weil-Petersson norm of $μ$ over the square root of the systole…

The study proves surfaces with high genus have a specific inequality.

Adapts Altman's model to compositional data for bankruptcy prediction.

The study connects polygon areas and projective structures in 3D space.

We give upper and lower bounds for the ratio of the volume of metric ball to the area of the metric sphere in Finsler-Hadamard manifolds with pinched S-curvature. We apply these estimates to find the limit at the infinity for this ratio. Derived estimates are the generalization of the well-known result in Riemannian ge…

We are interested in the maximum value achieved by the systole function over all complete finite area hyperbolic surfaces of a given signature $(g,n)$. This maximum is shown to be strictly increasing in terms of the number of cusps for small values of $n$. We also show that this function is greater than a function that…

Sequential hypothesis testing is a desirable decision making strategy in any time sensitive scenario. Compared with fixed sample-size testing, sequential testing is capable of achieving identical probability of error requirements using less samples in average. For a binary detection problem, it is well known that for k…

Faster algorithm for generalized mean densest subgraph problem.

An area-preserving diffeomorphism of an annulus has an "action function" which measures how the diffeomorphism distorts curves. The average value of the action function over the annulus is known as the Calabi invariant of the diffeomorphism, while the average value of the action function over a periodic orbit of the di…

We prove two weighted geometric inequalities that hold for strictly mean convex and star-shaped hypersurfaces in Euclidean space. The first one involves the weighted area and the area of the hypersurface and also the volume of the region enclosed by the hypersurface. The second one involves the total weighted mean curv…

Consider a random smooth Gaussian field $G(x):F\to\mathbb{R}$, where $F$ is a compact in $\mathbb{R}^d$. We derive a formula for average area of a surface generated by the equation $G(x)=0$ and give some applications. As an auxiliary result we obtain an integral expression for area of a surface induced by zeros of a \e…

The paper examines the unexpected losses and risk ratios for co-monotonic alternatives in large portfolios.

This paper addresses privacy concerns in ratio statistics using differential privacy.

We prove that the expected value of the ratio between the smooth four-genus and the Seifert genus of two-bridge knots tends to zero as the crossing number tends to infinity.

Computes constants for cyclic covers of translation surfaces.

While sample sizes in randomized clinical trials are large enough to estimate the average treatment effect well, they are often insufficient for estimation of treatment-covariate interactions critical to studying data-driven precision medicine. Observational data from real world practice may play an important role in a…

Study on tilings of the plane with two types of tiles of varying areas.

We study the systolic area (defined as the ratio of the area over the square of the systole) of the 2-sphere endowed with a smooth riemannian metric as a function of this metric. This function, bounded from below by a positive constant over the space of metrics, have the standard metric $g\_0$ for critic point, althoug…

We prove a sharp estimate on the expected value of the integral of the index of a simple random walk on the square or triangular lattice. This gives new lower bounds on the averaged Dehn function, which measures the expected area needed to fill a random curve with a disc.

Using a ramified cover of the two-sphere by the torus, we prove a local optimal inequality between the diastole and the area on the two-sphere near a singular metric. This singular metric, made of two equilateral triangles glued along their boundary, has been conjectured by E. Calabi to achieve the best ratio area over…

Deep RL optimizes dynamic portfolio weights in China's stock market.

In the first part of the paper we survey some nonlocal flows of convex plane curves ever studied so far and discuss properties of the flows related to enclosed area and length, especially the isoperimetric ratio and the isoperimetric difference. We also study a new nonlocal flow of convex plane curves and discuss its e…

When trading incurs proportional costs, leverage can scale an asset's return only up to a maximum multiple, which is sensitive to its volatility and liquidity. In a model with one safe and one risky asset, with constant investment opportunities and proportional costs, we find strategies that maximize long term returns …

This paper studies deep learning methodologies for portfolio optimization in the US equities market. We present a novel residual switching network that can automatically sense changes in market regimes and switch between momentum and reversal predictors accordingly. The residual switching network architecture combines …

Enhances UPSA to reduce noise in financial data.