arXiv research

Introduces new weighted floating functions and affine surface areas.

Proves existence of weighted-cscK metrics on Kähler manifolds.

Study concavity of solutions to elliptic equations under conformal deformations.

Let $Ω$ be an open half-space or slab in $\mathbb{R}^{n+1}$ endowed with a perturbation of the Gaussian measure of the form $f(p):=\exp(ω(p)-c|p|^2)$, where $c>0$ and $ω$ is a smooth concave function depending only on the signed distance from the linear hyperplane parallel to $\partialΩ$. In this work we follow a varia…

New weighted surface area measures for convex bodies with applications.

New algorithm samples neural network posteriors efficiently.

Study on a metric space derived from Kähler manifolds.

The market impact (MI) of Volume Weighted Average Price (VWAP) orders is a convex function of a trading rate, but most empirical estimates of transaction cost are concave functions. How is this possible? We show that isochronic (constant trading time) MI is slightly convex, and isochoric (constant trading volume) MI is…

The goal of online prediction with expert advice is to find a decision strategy which will perform almost as well as the best expert in a given pool of experts, on any sequence of outcomes. This problem has been widely studied and $O(\sqrt{T})$ and $O(\log{T})$ regret bounds can be achieved for convex losses (\cite{zin…

It is well known that Expected Shortfall (also called Average Value-at-Risk) is a convex risk measure, i. e. Expected Shortfall of a convex linear combination of arbitrary risk positions is not greater than a convex linear combination with the same weights of Expected Shortfalls of the same risk positions. In this shor…

We analyze a reweighted version of the Kikuchi approximation for estimating the log partition function of a product distribution defined over a region graph. We establish sufficient conditions for the concavity of our reweighted objective function in terms of weight assignments in the Kikuchi expansion, and show that a…

A new model predicts price concavity and reversion after metaorder execution.

New algorithm for optimizing statistical utilities in bandits.

A new method lifts training of input-convex neural networks to avoid dead weights and plateaued loss.

We show that some specific market risk measures implied by current international capital regulation (the Basel Accords and the Capital Adequacy Directive of the European Union) violate the obvious requirement of convexity in some regions in the space of portfolio weights.

In a recent series of papers it has been established that variants of Gradient Descent/Ascent and Mirror Descent exhibit last iterate convergence in convex-concave zero-sum games. Specifically, \cite{DISZ17, LiangS18} show last iterate convergence of the so called "Optimistic Gradient Descent/Ascent" for the case of \t…

Optimizes portfolios using CPT utility via convex optimization.

The paper generalizes K-stability results to singular and weighted settings.

The paper extends localisation technique to multiple constraints in Euclidean spaces.

New method uses weighted SDEs to improve sampling from complex distributions.

Proves invariance of weighted extremal Kähler metrics under smooth blowups.

Study optimal portfolio choice with risk control for log-returns.

Investigates how rebalancing frequency and transaction costs affect log-optimal portfolios.

We prove some old and new isoperimetric inequalities with the best constant using the ABP method applied to an appropriate linear Neumann problem. More precisely, we obtain a new family of sharp isoperimetric inequalities with weights (also called densities) in open convex cones of $\mathbb{R}^n$. Our result applies to…

As surrogate functions of $L_0$-norm, many nonconvex penalty functions have been proposed to enhance the sparse vector recovery. It is easy to extend these nonconvex penalty functions on singular values of a matrix to enhance low-rank matrix recovery. However, different from convex optimization, solving the nonconvex l…

The paper establishes conditions for strict power concavity in convolutions.

Near-logarithmic regret per switch achieved for mixable/exp-concave losses.

Minimal graph level sets are concave if boundary is concave.

Proposes a neural network framework for feature selection in high-dimensional settings.

Proves log-concavity of cluster algebra coefficients for type $A_n$.

Study improves sampling from non-log-concave distributions using Fisher information.

Paper analyzes adversarial dynamics in neural networks.

Improved regret bounds for adversarial linear contextual bandits.

Established concavity principle for curved spaces.

Establishes log-concavity estimates for convex domains' first Dirichlet eigenfunctions.

This paper connects soliton-type metrics with weighted CSCK metrics on Fano manifolds.

New saddle network architectures preserve convex-concave geometry in optimization problems.

Heat flow fails to preserve concavity in curved spaces.

We present a simple connection between differential Harnack inequalities for hypersurface flows and natural concavity properties of their time-of-arrival functions. We prove these concavity properties directly for a large class of flows by applying a concavity maximum principle argument to the corresponding level set f…

Investigates concavity of spacetimes, showing conditions for local concavity.

The paper solves an insurance problem using mean-variance and rank-dependent utility theory.

We define a class of L-convex-concave subsets of $\Bbb{R}P^n$, where L is a projective subspace of dimension l in $\Bbb{R}P^n$. These are sets whose sections by any (l+1)-dimensional space L' containing L are convex and concavely depend on L'. We introduce an L-duality for these sets, and prove that the L-dual to an L-…

Geodesic concavity and hypersymplectic structures in $G2$-structures space.

Gradient methods converge exponentially in concave network games.

This study examines how earnings announcements affect option volatility and pricing.

Log-concavity of eigenfunctions on curved surfaces is proven, leading to fundamental gap estimates.

Improved sampling guarantees for weakly log-concave distributions.

We explain a general construction through which concave elliptic operators on complex manifolds give rise to concave functions on cohomology. In particular, this leads to generalized versions of the Khovanskii-Teissier inequalities.