Negative / Null Result ReportOpen accessMathematics
Fintan Costello, Paul Watts · 2022 · arXiv
There is a well-known problem in Null Hypothesis Significance Testing: many statistically significant results fail to replicate in subsequent experiments. We show that this problem arises because standard `point-form null' significance tests consider only within-experiment but ignore between-experiment variation, and so systematically underestimate the degree of random variation in results. We give an extension to standard significance testing that addresses this problem by analysing both within- and between-experiment variation. This `distributional null' approach does not underestimate exper
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Justin Boutilier, Jonas Oddur Jonasson, Hannah Li et al. · 2024 · arXiv
We study RCTs that evaluate the impact of service interventions, for example, teachers or advisors conducting proactive outreach to at-risk students, medical providers giving medication adherence support by calling or texting, or social workers that conduct home visits. A defining feature of service interventions is that they are delivered by a capacity-constrained resource -- teachers, healthcare providers, or social workers -- whose limited availability creates causal inference complications. Because participants share a finite service capacity, adding more participants can reduce the timeli
View details →Negative / Null Result ReportOpen accessMathematics
Luca Chiantini, Łucja Farnik, Giuseppe Favacchio et al. · 2023 · arXiv
This article introduces a previously unrecognized combinatorial structure underlying configurations of skew lines in $\mathbb{P}^3$, and reveals its deep and surprising connection to the algebro-geometric concept of geproci sets. Given any field $\mathbb{K}$ and a finite set $\mathcal L$ of 3 or more skew lines in $\mathbb{P}^3_\mathbb{K}$, we associate to it a group $G_{\mathcal L}$ and a groupoid $C_{\mathcal L}$ whose action on the union $\cup_{L\in\mathcal L}L$ provides orbits which have a rich combinatorial structure. We characterize when $G_{\mathcal L}$ is abelian and give partial resul
View details →Negative / Null Result ReportOpen accessMathematics
Ilmari Kangasniemi · 2019 · arXiv
Suppose that $M$ is a closed, connected, and oriented Riemannian $n$-manifold, $f \colon \mathbb{R}^n \to M$ is a quasiregular map automorphic under a discrete group $Γ$ of Euclidean isometries, and $f$ has finite multiplicity in a fundamental cell of $Γ$. We show that if $Γ$ has a sufficiently large translation subgroup $Γ_T$, then $\dim Γ\in \{0, n-1, n\}$. If $f$ is strongly automorphic and induces a non-injective Lattès-type uniformly quasiregular map, then the same holds without the assumption on the size of $Γ_T$. Moreover, an even stronger restriction holds in the Lattès case if $M$ is
View details →Negative / Null Result ReportOpen accessMathematics
Utkarsh, Chris Elrod, Yingbo Ma et al. · 2022 · arXiv
Numerically solving ordinary differential equations (ODEs) is a naturally serial process and as a result the vast majority of ODE solver software are serial. In this manuscript we developed a set of parallelized ODE solvers using extrapolation methods which exploit "parallelism within the method" so that arbitrary user ODEs can be parallelized. We describe the specific choices made in the implementation of the explicit and implicit extrapolation methods which allow for generating low overhead static schedules to then exploit with optimized multi-threaded implementations. We demonstrate that wh
View details →Negative / Null Result ReportOpen accessMathematics
Nguyen Ngoc Hung · 2015 · arXiv
A classical theorem of John Thompson on character degrees asserts that if the degree of every ordinary irreducible character of a finite group $G$ is 1 or divisible by a prime $p$, then $G$ has a normal $p$-complement. We obtain a significant improvement of this result by considering the average of $p'$-degrees of irreducible characters. We also consider fields of character values and prove several improvements of earlier related results.
View details →Negative / Null Result ReportOpen accessMathematics
Kunyu Guo, Hansong Huang · 2013 · arXiv
In studying commutants of analytic Toeplitz operators, Thomson proved a remarkable theorem which states that under a mild condition, the commutant of an analytic Toeplitz operator is equal to that of Toeplitz operator defined by a finite Blaschke product. Cowen gave an significant improvement of Thosom's result. In this paper, we will present examples in Cowen's class which does not lie in Thomson's class.
View details →Replication FailureOpen accessMathematics
Georg Ostrovski · 2011 · arXiv
Let X and Y be compact, simply connected and locally connected subsets of R^2, and let f : X -> Y be a homeomorphism isotopic to the identity on X. Generalizing Brouwer's plane translation theorem for self-maps of the plane, we prove that f has no recurrent (in particular, no periodic) points if it has no fixed points.
View details →Negative / Null Result ReportOpen accessMathematics
Mark Rubin · 2024 · arXiv
One justification for preregistering research hypotheses, methods, and analyses is that it improves the transparent evaluation of the severity of hypothesis tests. In this article, I consider two cases in which preregistration does not improve this evaluation. First, I argue that, although preregistration may facilitate the transparent evaluation of severity in Mayo's error statistical philosophy of science, it does not facilitate this evaluation in Popper's theory-centric approach. To illustrate, I show that associated concerns about Type I error rate inflation are only relevant in the error
View details →Negative / Null Result ReportOpen accessMathematics
Andrea Schioppa · 2015 · arXiv
For each $β>1$ we construct a family $F_β$ of metric measure spaces which is closed under the operation of taking weak-tangents (i.e.~blow-ups), and such that each element of $F_β$ admits a $(1,P)$-Poincaré inequality if and only if $P>β$.
View details →Negative / Null Result ReportOpen accessMathematics
Mark Rubin · 2020 · arXiv
Preregistration entails researchers registering their planned research hypotheses, methods, and analyses in a time-stamped document before they undertake their data collection and analyses. This document is then made available with the published research report to allow readers to identify discrepancies between what the researchers originally planned to do and what they actually ended up doing. This historical transparency is supposed to facilitate judgments about the credibility of the research findings. The present article provides a critical review of 17 of the reasons behind this argument.
View details →Methods Dead-EndOpen accessMathematics
Hao Luo, Alexandre Bouchard-Côté, Gabriela Cohen Freue et al. · 2016 · arXiv
We extend the constrained maximum likelihood estimation theory for parameters of a completely identified model, proposed by Aitchison and Silvey (1958), to parameters arising from a partially identified model. With a partially identified model, some parameters of the model may only be identified through constraints imposed by additional assumptions. We show that, under certain conditions, the constrained maximum likelihood estimator exists and locally maximize the likelihood function subject to constraints. We then study the asymptotic distribution of the estimator and propose a numerical algo
View details →Negative / Null Result ReportOpen accessMathematics
Subha Maity, Debarghya Mukherjee, Mikhail Yurochkin et al. · 2020 · arXiv
Many instances of algorithmic bias are caused by subpopulation shifts. For example, ML models often perform worse on demographic groups that are underrepresented in the training data. In this paper, we study whether enforcing algorithmic fairness during training improves the performance of the trained model in the \emph{target domain}. On one hand, we conceive scenarios in which enforcing fairness does not improve performance in the target domain. In fact, it may even harm performance. On the other hand, we derive necessary and sufficient conditions under which enforcing algorithmic fairness l
View details →Negative / Null Result ReportOpen accessMathematics
Alexander Tolmachev · 2024 · arXiv
Determining the maximal density $m_1(\mathbb{R}^2)$ of planar sets without unit distances is a fundamental problem in combinatorial geometry. This paper investigates lower bounds for this quantity. We introduce a novel approach to estimating $m_1(\mathbb{R}^2)$ by reformulating the problem as a Maximal Independent Set (MIS) problem on graphs constructed from flat torus, focusing on periodic sets with respect to two non-collinear vectors. Our experimental results, supported by theoretical justifications of proposed method, demonstrate that for a sufficiently wide range of parameters this approa
View details →Negative / Null Result ReportOpen accessMathematics
Nicolas Burq, Nicolas Camps, Mickaël Latocca et al. · 2024 · arXiv
We consider the Wick ordered cubic Schrödinger equation (NLS) posed on the two-dimensional sphere, with initial data distributed according to a Gaussian measure. We show that the second Picard iteration does not improve the regularity of the initial data in the scale of the classical Sobolev spaces. This is in sharp contrast with the Wick ordered NLS on the two-dimensional tori, a model for which we know from the work of Bourgain that the second Picard iteration gains one half derivative. Our proof relies on identifying a singular part of the nonlinearity. We show that this singular part is re
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Gilles Chardon · 2014 · arXiv
The scattering of waves by obstacles in a 2D setting is considered, in particular the computation of the scattered field via the collocation or the least-squares methods. In the case of multiple scattering by smooth obstacles, we prove that the scattered field can be uniformly approximated by sums of multipoles. For a unique obstacle, the choice of the number of points and their positions for the estimation of the error on the border of the scatterer is studied, showing the benefit of using a non-uniform distribution of points dependent on the scatterer and the approximation scheme. In general
View details →Negative / Null Result ReportOpen accessMathematics
Nicolas Dupin · 2019 · arXiv
The discrete unit commitment problem with min-stop ramping constraints optimizes the daily production of thermal power plants (coal, gas, fuel units). For this problem, compact Integer Linear Programming (ILP) formulations have been designed to solve exactly small instances and heuristically real-size instances. This paper investigates whether Dantzig-Wolfe reformulation allows to improve the previous exact method and matheuristics. The extended ILP formulation is presented with the column generation algorithm to solve its linear relaxation. The experimental results show that the Dantzig-Wolfe
View details →Negative / Null Result ReportOpen accessMathematics
Martina Zizza · 2024 · arXiv
In this paper we examine the discrete Shnirelman's inequality [Shnirelman A., 1985], which relates the $L^2$-distance of two discrete configurations of a fluid to the $L^1_tL^2_x$-norm of the vector field connecting them. Our proof is inspired by [Shnirelman A., 1985], where it was obtained $α=\frac{1}{64}$ in dimension $ν=2$, while here we get $α\geq\frac{2}{7}$. Moreover we prove that $α\geq\frac{1}{ν+1}$ for any dimension $ν\geq 3$. We point out that, even if this does not improve the bound in the continuous version, where it was proved that $α\geq\frac{2}{4+ν}$, with $ν\geq 3$, our bound i
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Aihua Xia, Fuxi Zhang · 2011 · arXiv
Random events in space and time often exhibit a locally dependent structure. When the events are very rare and dependent structure is not too complicated, various studies in the literature have shown that Poisson and compound Poisson processes can provide adequate approximations. However, the accuracy of approximations does not improve or may even deteriorate when the mean number of events increases. In this paper, we investigate an alternative family of approximating point processes and establish Stein's method for their approximations. We prove two theorems to accommodate respectively the po
View details →Negative / Null Result ReportOpen accessMathematics
Peter Bürgisser · 2022 · arXiv
Consider a system $f_1(x)=0,\ldots,f_n(x)=0$ of $n$ random real polynomials in $n$ variables, where each $f_i$ has a prescribed set of exponent vectors described by a set $A_i \subseteq \mathbb{Z}^n$ of cardinality $t_i$, whose convex hull is denoted $P_i$. Assuming that the coefficients of the $f_i$ are independent standard Gaussian, we prove that the expected number of zeros of the random system in the positive orthant is at most $(2π)^{-\frac{n}{2}} V_0 (t_1-1)\ldots (t_n-1)$. Here $V_0$ denotes the number of vertices of the Minkowski sum $P_1+\ldots + P_n$. However, this bound does not imp
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Karunia Putra Wijaya, Dipo Aldila · 2017 · arXiv
Investigating the seasonality of disease incidences is very important in disease surveillance in regions with periodical climatic patterns. In lieu of the paradigm about disease incidences varying seasonally in line with meteorology, this work seeks to determine how well standard epidemic models can capture such seasonality for better forecasts and optimal futuristic interventions. Once incidence data are assimilated by a periodic model, asymptotic analysis in relation to the long-term behavior of the disease occurrences can be performed using the classical Floquet theory, which explains the s
View details →Failed Experiment ReportOpen accessMathematics
Anh-Huy Phan, Petr Tichavský, Andrzej Cichocki · 2017 · arXiv
In CANDECOMP/PARAFAC tensor decomposition, degeneracy often occurs in some difficult scenarios, e.g., when the rank exceeds the tensor dimension, or when the loading components are highly collinear in several or all modes, or when CPD does not have an optimal solution. In such the cases, norms of some rank-1 terms become significantly large and cancel each other. This makes algorithms getting stuck in local minima while running a huge number of iterations does not improve the decomposition. In this paper, we propose an error preservation correction method to deal with such problem. Our aim is
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Alessandro Arsie, Emilio Frazzoli · 2006 · arXiv
In this paper we consider a class of dynamic vehicle routing problems, in which a number of mobile agents in the plane must visit target points generated over time by a stochastic process. It is desired to design motion coordination strategies in order to minimize the expected time between the appearance of a target point and the time it is visited by one of the agents. We propose control strategies that, while making minimal or no assumptions on communications between agents, provide the same level of steady-state performance achieved by the best known decentralized strategies. In other words
View details →Negative / Null Result ReportOpen accessMathematics
Rujie Zhu, Xiaodong Xu, Stanisław Radziszowski · 2015 · arXiv
Let $Δ_s=R(K_3,K_s)-R(K_3,K_{s-1})$, where $R(G,H)$ is the Ramsey number of graphs $G$ and $H$ defined as the smallest $n$ such that any edge coloring of $K_n$ with two colors contains $G$ in the first color or $H$ in the second color. In 1980, Erdős and Sós posed some questions about the growth of $Δ_s$. The best known concrete bounds on $Δ_s$ are $3 \le Δ_s \le s$, and they have not improved since the stating of the problem. In this paper we present some constructions, which imply in particular that $R(K_3,K_s) \ge R(K_3,K_{s-1}-e) + 4$. This does not improve the lower bound of 3 on $Δ_s$, b
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Shibdas Roy, Ian R. Petersen, Elanor H. Huntington · 2015 · arXiv
We study a coherent-classical estimation scheme for a class of linear quantum systems, where the estimator is a mixed quantum-classical system that may or may not involve coherent feedback. We show that when the quantum plant or the quantum part of the estimator (coherent controller) is an annihilation operator only system, coherent-classical estimation without coherent feedback can provide no improvement over purely-classical estimation. Otherwise, coherent-classical estimation without feedback can be better than classical-only estimation for certain homodyne detector angles, although the for
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Courtney Paquette, Elliot Paquette · 2021 · arXiv
We analyze a class of stochastic gradient algorithms with momentum on a high-dimensional random least squares problem. Our framework, inspired by random matrix theory, provides an exact (deterministic) characterization for the sequence of loss values produced by these algorithms which is expressed only in terms of the eigenvalues of the Hessian. This leads to simple expressions for nearly-optimal hyperparameters, a description of the limiting neighborhood, and average-case complexity. As a consequence, we show that (small-batch) stochastic heavy-ball momentum with a fixed momentum parameter pr
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David Conlon, Lior Gishboliner, Yevgeny Levanzov et al. · 2019 · arXiv
Let $f(n,v,e)$ denote the maximum number of edges in a $3$-uniform hypergraph not containing $e$ edges spanned by at most $v$ vertices. One of the most influential open problems in extremal combinatorics then asks, for a given number of edges $e \geq 3$, what is the smallest integer $d=d(e)$ so that $f(n,e+d,e) = o(n^2)$? This question has its origins in work of Brown, Erdős and Sós from the early 70's and the standard conjecture is that $d(e)=3$ for every $e \geq 3$. The state of the art result regarding this problem was obtained in 2004 by Sárközy and Selkow, who showed that $f(n,e + 2 + \lf
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D. R. Heath-Brown · 2026 · arXiv
We show that there are $O(B^{3/5-3/1555+\ep})$ triples $(x,y,z)$ of square-full integesr up to $B$ satisfying the equation $x+y=z$ for any fixed $\ep>0$. This is the first improvement over the `easy' exponent $3/5$, given by Browning and Van Valckenborgh. One new tool is a strong uniform bound for the counting function for equations $aX^3+bY^3=cZ^3$.
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John Rozmarynowycz, Seungki Kim · 2023 · arXiv
We report the finding of the new upper bound on the lowest positive integer $x$ for which the Mertens conjecture \begin{equation*} \left| \sum_{1 \leq n \leq x} μ(n) \right| < \sqrt{x} \end{equation*} fails to hold: $x < \exp(1.017 \times 10^{29})$, an improvement over previously known $\exp(1.59 \times 10^{40})$ due to Kotnik and te Riele [7].
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Francesco Orabona, Ryan D'Orazio · 2025 · arXiv
The Polyak stepsize has been proven to be a fundamental stepsize in convex optimization, giving near optimal gradient descent rates across a wide range of assumptions. The universality of the Polyak stepsize has also inspired many stochastic variants, with theoretical guarantees and strong empirical performance. Despite the many theoretical results, our understanding of the convergence properties and shortcomings of the Polyak stepsize or its variants is both incomplete and fractured across different analyses. We propose a new, unified, and simple perspective for the Polyak stepsize and its va
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