Tootfinder

This https://arxiv.org/abs/2312.10290 has been replaced.
link: https://scholar.google.com/scholar?q=a

Runtime Analysis of the SMS-EMOA for Many-Objective Optimization
This paper conducts the first rigorous runtime analysis of the SMS-EMOA for many-objective optimization. To this aim, we first propose a many-objective counterpart of the bi-objective OJZJ benchmark. We prove that SMS-EMOA computes the full Pareto front of this benchmark in an expected number of $O(μM n^k)$ iterations, where $n$ denotes the problem size (length of the bit-string representation), $k$ the gap size (a difficulty parameter of the problem), $M=(2n/m-2k+3)^{m/2}$ the size of the Par…

This https://arxiv.org/abs/2212.00636 has been replaced.
link: https://scholar.google.com/scholar?q=a

Newman's conjecture for the partition function modulo integers with at least two distinct prime divisors
Let $M$ be a positive integer and $p(n)$ be the number of partitions of a positive integer $n$. Newman's Conjecture asserts that for each integer $r$, there are infinitely many positive integers $n$ such that \[ p(n)\equiv r \pmod{M}. \] For a positive integer $d$, let $B_{d}$ be the set of positive integers $M$ such that the number of prime divisors of $M$ is $d$. In this paper, we prove that for each positive integer $d$, the density of the set of positive integers $M$ for which Newman's Conj…

This https://arxiv.org/abs/2203.15681 has been replaced.
link: https://scholar.google.com/scholar?q=a

Arbitrarily small spectral gaps for random hyperbolic surfaces with many cusps
Let $\mathcal{M}_{g,n(g)}$ be the moduli space of hyperbolic surfaces of genus $g$ with $n(g)$ punctures endowed with the Weil-Petersson metric. In this paper we study the asymptotic behavior of the Cheeger constants and spectral gaps of random hyperbolic surfaces in $\mathcal{M}_{g,n(g)}$, when $n(g)$ grows slower than $g$ as $g\to \infty$.

This https://arxiv.org/abs/2404.15996 has been replaced.
link: https://scholar.google.com/scholar?q=a

Asymptotically Fair and Truthful Allocation of Public Goods
We study the fair and truthful allocation of m divisible public items among n agents, each with distinct preferences for the items. To aggregate agents' preferences fairly, we focus on finding a core solution. For divisible items, a core solution always exists and can be calculated by maximizing the Nash welfare objective. However, such a solution is easily manipulated; agents might have incentives to misreport their preferences. To mitigate this, the current state-of-the-art finds an approxima…

This https://arxiv.org/abs/2210.03905 has been replaced.
link: https://scholar.google.com/scholar?q=a

Empirical Bayes Selection for Value Maximization
We study the problem of selecting the best $m$ units from a set of $n$ as $m / n \to α\in (0, 1)$, where noisy, heteroskedastic measurements of the units' true values are available and the decision-maker wishes to maximize the aggregate true value of the units selected. Given a parametric prior distribution, the empirical Bayes decision rule incurs $O_p(n^{-1})$ regret relative to the Bayesian oracle that knows the true prior. More generally, if the error in the estimated prior is of order $O_…

This https://arxiv.org/abs/2109.06078 has been replaced.
link: https://scholar.google.com/scholar?q=a

BV Functions and Sets of Finite Perimeter on Configuration Spaces
This paper contributes to foundations of the geometric measure theory in the infinite dimensional setting of the configuration space over the Euclidean space $\mathbb R^n$ equipped with the Poisson measure $π$. We first provide a rigorous meaning and construction of the $m$-codimensional Poisson measure -- formally written as "$(\infty-m)$-dimensional Poisson measure" -- on the configuration space. We then show that our construction is consistent with potential analysis by establishing the abs…

This https://arxiv.org/abs/2209.05806 has been replaced.
link: https://scholar.google.com/scholar?q=a

The Weyl tube theorem for Kähler manifolds
As sharpened in terms of Alesker's theory of valuations on manifolds, a classic theorem of Weyl asserts that the coefficients of the tube polynomial of an isometrically embedded riemannian manifold $M \hookrightarrow \mathbb R^n$ constitute a canonical finite dimensional subalgebra $\mathcal {L K}(M)$ of the algebra $\mathcal{V} (M)$ of all smooth valuations on $M$, isomorphic to the algebra of valuations on Euclidean space that are invariant under rigid motions. We construct an analogous, larg…

This https://arxiv.org/abs/2205.14296 has been replaced.
link: https://scholar.google.com/scholar?q=a

Approximability Landscape of Welfare Maximization within Fair Allocations
Fair allocation of indivisible goods studies allocating $m$ goods among $n$ agents in a fair manner. While fairness is a fundamental requirement in many real-world applications, it often conflicts with (economic) efficiency. This raises a natural and important question: How can we identify the most welfare-efficient allocation among all fair allocations? This paper answers from the perspective of computational complexity. Specifically, we study the problem of maximizing utilitarian social welfa…