Negative / Null Result ReportOpen accessMathematics
Paweł Pasteczka · 2013 · arXiv
In the present paper we are going to prove some necessary condition for a mean to be Hardy. This condition is then applied to completely characterize the Hardy property among the Gini means.
Negative / Null Result ReportOpen accessMathematics
Grigor Sargsyan · 2021 · arXiv
We show that in extender models there are no generic embeddings with critical point $ω_1$ that resemble the stationary tower at the second Woodin cardinal.
Negative / Null Result ReportOpen accessMathematics
Paweł Pasteczka · 2021 · arXiv
We establish the test which allows to show that a mean does not admit a weak-Hardy property. As a result we prove that Hardy and weak-Hardy properties are equivalent in the class of homogeneous, symmetric, repetition invariant, and Jensen concave mean on $\mathbb{R}_+$. More precisely, for every mean $\mathscr{M} \colon \bigcup_{n=1}^\infty \mathbb{R}_+^n \to \mathbb{R}$ as above, the inequality $$\mathscr{M}(a_1)+\mathscr{M}(a_1,a_2)+\dots<\infty$$ holds for all $a \in \ell^1(\mathbb{R}_+)$ if and only if there exists a positive, real constant $C$ (depending only on $\mathscr{M}$) such that $
Negative / Null Result ReportOpen accessComputer Science
Yishay Mansour, Richard Nock, Robert C. Williamson · 2022 · arXiv
A landmark negative result of Long and Servedio established a worst-case spectacular failure of a supervised learning trio (loss, algorithm, model) otherwise praised for its high precision machinery. Hundreds of papers followed up on the two suspected culprits: the loss (for being convex) and/or the algorithm (for fitting a classical boosting blueprint). Here, we call to the half-century+ founding theory of losses for class probability estimation (properness), an extension of Long and Servedio's results and a new general boosting algorithm to demonstrate that the real culprit in their specific
Negative / Null Result ReportOpen accessComputer Science
Simon Kuang, Yuezhu Xu, S. Sivaranjani et al. · 2026 · arXiv
The global Lipschitz constant of a neural network is related to robustness and generalization, yet unlike in many classical models, it is not plainly legible from the parameters. This has motivated sophisticated verification algorithms, especially semidefinite programming (SDP) based on incremental quadratic constraints on the activation functions, to improve on the fast but often loose product of layerwise Lipschitz constants (the trivial bound). We ask why Lipschitz verification is a problem in the first place. Our answer is that the difficulty is structural: estimating a network's Lipschitz
Negative / Null Result ReportOpen accessComputer Science
Kamyar Azizzadenesheli, Brandon Yang, Weitang Liu et al. · 2018 · arXiv
While many recent advances in deep reinforcement learning (RL) rely on model-free methods, model-based approaches remain an alluring prospect for their potential to exploit unsupervised data to learn environment model. In this work, we provide an extensive study on the design of deep generative models for RL environments and propose a sample efficient and robust method to learn the model of Atari environments. We deploy this model and propose generative adversarial tree search (GATS) a deep RL algorithm that learns the environment model and implements Monte Carlo tree search (MCTS) on the lear
Negative / Null Result ReportOpen accessMathematics
Christoph Schultheiss, Peter Bühlmann · 2022 · arXiv
We consider likelihood score-based methods for causal discovery in structural causal models. In particular, we focus on Gaussian scoring and analyze the effect of model misspecification in terms of non-Gaussian error distribution. We present a surprising negative result for Gaussian likelihood scoring in combination with nonparametric regression methods.
Failed Experiment ReportOpen accessComputer Science
Antoine Suarez · 2014 · arXiv
A Michelson-Morley-type experiment is described, which exploits two-photon interference between entangled photons instead of classical light interference. In this experimental context, the negative result (no shift in the detection rates) rules out David Bohm's postulate of an infinite-speed time-ordered "quantum potential", and thereby upholds the timeless standard quantum collapse.
Failed Experiment ReportOpen accessMathematics
Saharon Shelah · 2001 · arXiv
David Aspero asks on the possibility of having Forcing axiom FA_{aleph_2}(K), where K is the class of forcing notions preserving stationarity of subsets of aleph_1 and of aleph_2. We answer negatively, in fact we show the negative result for any regular lambda>aleph_1 even demanding adding no new sequence of ordinals of length<lambda.
Negative / Null Result ReportOpen accessPhysics
Valentin Voroshilov · 2014 · arXiv
A novel canonical transformation is offered as the mean for studying properties of a system of strongly correlated electrons. As an example of the utility of the transformation, it is used to demonstrate the existence of a quantum phase transition in a Hubbard model on a square lattice. An Appendix presents two cases with a negative result.
Negative / Null Result ReportOpen accessMathematics
Takahiro Hasebe · 2013 · arXiv
We prove that many of beta, beta prime, gamma, inverse gamma, Student t- and ultraspherical distributions are freely infinitely divisible, but some of them are not. The latter negative result follows from a local property of probability density functions. Moreover, we show that the Gaussian, ultraspherical and many of Student t-distributions have free divisibility indicator 1.
Negative / Null Result ReportOpen accessComputer Science
Samuel R. Bowman, Jennimaria Palomaki, Livio Baldini Soares et al. · 2020 · arXiv
Natural language inference (NLI) data has proven useful in benchmarking and, especially, as pretraining data for tasks requiring language understanding. However, the crowdsourcing protocol that was used to collect this data has known issues and was not explicitly optimized for either of these purposes, so it is likely far from ideal. We propose four alternative protocols, each aimed at improving either the ease with which annotators can produce sound training examples or the quality and diversity of those examples. Using these alternatives and a fifth baseline protocol, we collect and compare
Failed Experiment ReportOpen accessMathematics
Michael Joachim, Thomas Schick · 1999 · arXiv
The Gromov-Lawson-Rosenberg-conjecture for a group G states that a closed spin manifold M^n (n>4) with fundamental group G admits a metric with positive scalar curvature if and only if its C^*-index A(M) in KO_n(C^*_r(G)) vanishes. We prove this for groups G with low-dimensional classifying space, provided the assembly map for G is injective. On the other hand, we construct a spin manifold with no metric with scal>0 but so that already its KO-orientation in KO_*(B pi_1(M)) vanishes. Therefore a corresponding weakened version or the GLR-conjecture is wrong. Last we address non-orientable manifo
Negative / Null Result ReportOpen accessComputer Science
Robert Helling · 2000 · arXiv
We study the problem of more general kinematics for the finite N M(atrix)-Model than the simple straight line motion that has been used before. This is supposed to be related to momentum transferring processes in the dual super-gravity description. We find a negative result for classical, perturbative processes and discuss briefly the possibility of instianton like quantum mechanical tunneling processes.
Negative / Null Result ReportOpen accessComputer Science
Amin Karbasi, Kasper Green Larsen · 2023 · arXiv
The aim of boosting is to convert a sequence of weak learners into a strong learner. At their heart, these methods are fully sequential. In this paper, we investigate the possibility of parallelizing boosting. Our main contribution is a strong negative result, implying that significant parallelization of boosting requires an exponential blow-up in the total computing resources needed for training.
Failed Experiment ReportOpen accessComputer Science
David Berenstein · 2006 · arXiv
This paper studies the compatibility of having a grand unification scheme for particle physics, while at the same time having a perturbative string theory description of such a scheme on a D-brane. This is studied in a model independent approach and finds a negative result. Some additional observations related to model building on branes are made.
Negative / Null Result ReportOpen accessComputer Science
Marcelo Arenas, Pablo Barceló, Leopoldo Bertossi et al. · 2021 · arXiv
In Machine Learning, the $\mathsf{SHAP}$-score is a version of the Shapley value that is used to explain the result of a learned model on a specific entity by assigning a score to every feature. While in general computing Shapley values is an intractable problem, we prove a strong positive result stating that the $\mathsf{SHAP}$-score can be computed in polynomial time over deterministic and decomposable Boolean circuits. Such circuits are studied in the field of Knowledge Compilation and generalize a wide range of Boolean circuits and binary decision diagrams classes, including binary decisio
Negative / Null Result ReportOpen accessMathematics
Chenmin Sun, Ivonne Rivas · 2017 · arXiv
The internal control problem for the Kadomstev-Petviashvili II equation, known as KP-II, is the object of study in this paper. The controllability in $L^2(T)$ from vertical strip is proved using the Hilbert Unique Method through the techniques of semiclassical and microlocal analysis. Additionally, a negative result for the controllability in $L^2(T)$ from horizontal strip is also showed.
Negative / Null Result ReportOpen accessMathematics
Gerhard Larcher, Wolfgang Stockinger · 2018 · arXiv
We say that a sequence $(x_n)_{n \in \mathbb{N}}$ in $[0,1)$ has Poissonian pair correlations if \begin{equation*} \lim_{N \to \infty} \frac{1}{N} \# \left \lbrace 1 \leq l \neq m \leq N: \| x_l - x_m \| \leq \frac{s}{N} \right \rbrace = 2s \end{equation*} for every $s \geq 0$. The aim of this article is twofold. First, we will establish a gap theorem which allows to deduce that a sequence $(x_n)_{n \in \mathbb{N}}$ of real numbers in $[0,1)$ having a certain weak gap structure, cannot have Poissonian pair correlations. This result covers a broad class of sequences, e.g., Kronecker sequences,
Negative / Null Result ReportOpen accessMathematics
Enrique Fernández-Cara, José Lucas F. Machado, Diego A. Souza · 2018 · arXiv
In this paper, we study the null controllability of the three-dimensional Stokes equations with a memory term. For any positive final time $T>0$, we construct initial conditions such that the null controllability does not hold even if the controls act on the whole boundary. Moreover, we also prove that this negative result holds for distributed controls.
Negative / Null Result ReportOpen accessComputer Science
Hayato Takahashi · 2010 · arXiv
A new negative result for nonparametric estimation of binary ergodic processes is shown. I The problem of estimation of distribution with any degree of accuracy is studied. Then it is shown that for any countable class of estimators there is a zero-entropy binary ergodic process that is inconsistent with the class of estimators. Our result is different from other negative results for universal forecasting scheme of ergodic processes.
Failed Experiment ReportOpen accessPhysics
A. Yu. Samarin · 2017 · arXiv
It is described a nonlocal interaction between entangled quantum objects, which is initiated by a process different from the reduction of the wave function. The scheme of an experiment realizing a deterministic nonlocal quantum evolution is proposed. In the case of the negative result of the experiment, the universal character of the integral wave equation with a kernel in the form of a path integral is questionable, otherwise faster-then-light communication is possible
Negative / Null Result ReportOpen accessMathematics
Alexander Lemmens · 2018 · arXiv
We study a combinatorial notion where given a set of lattice points one takes the set of all sums of subsets of a fixed size, and we ask if the given set comes from a convex lattice polytope whether the resulting set also comes from a convex lattice polytope. We obtain a positive result in dimension 2 and a negative result in higher dimensions. We apply this to the corner cut polyhedron.
Negative / Null Result ReportOpen accessComputer Science
Raphaël Berthon, Nathanaël Fijalkow, Emmanuel Filiot et al. · 2020 · arXiv
We study alternating automata with qualitative semantics over infinite binary trees: alternation means that two opposing players construct a decoration of the input tree called a run, and the qualitative semantics says that a run of the automaton is accepting if almost all branches of the run are accepting. In this paper we prove a positive and a negative result for the emptiness problem of alternating automata with qualitative semantics. The positive result is the decidability of the emptiness problem for the case of Büchi acceptance condition. An interesting aspect of our approach is that we
Negative / Null Result ReportOpen accessMathematics
Matthew D. Kvalheim · 2026 · arXiv
We study whether second-order systems can be made to behave like prescribed first-order dynamical systems through feedback control. More precisely, we study whether prescribed vector fields on compact smooth manifolds, viewed geometrically as sections of the tangent bundle, can be asymptotically stabilized in a strong sense by second-order control systems on the base manifold. Our class of second-order systems includes most Lagrangian systems, and we obtain both positive and negative results. The positive result asserts that, for fully actuated systems, the section corresponding to any smooth
Negative / Null Result ReportOpen accessMathematics
László Csató · 2017 · arXiv
It has been shown recently that the Eigenvector Method may lead to strong rank reversal in group decision making, that is, the alternative with the highest priority according to all individual vectors may lose its position when evaluations are derived from the aggregated group comparison matrix. We give a minimal counterexample and prove that this negative result is a consequence of the difference of the rankings induced by the right and inverse left eigenvectors.
Negative / Null Result ReportOpen accessComputer Science
Maryam Aliakbarpour, Rose Silver, Thomas Steinke et al. · 2023 · arXiv
We construct differentially private estimators with low sample complexity that estimate the median of an arbitrary distribution over $\mathbb{R}$ satisfying very mild moment conditions. Our result stands in contrast to the surprising negative result of Bun et al. (FOCS 2015) that showed there is no differentially private estimator with any finite sample complexity that returns any non-trivial approximation to the median of an arbitrary distribution.
Negative / Null Result ReportOpen accessComputer Science
Hayato Takahashi · 2011 · arXiv
A new negative result for nonparametric distribution estimation of binary ergodic processes is shown. The problem of estimation of distribution with any degree of accuracy is studied. Then it is shown that for any countable class of estimators there is a zero-entropy binary ergodic process that is inconsistent with the class of estimators. Our result is different from other negative results for universal forecasting scheme of ergodic processes. We also introduce a related result by B. Weiss.
Negative / Null Result ReportOpen accessMathematics
Geivison Ribeiro · 2024 · arXiv
This note presents an extension of a result within the concept of [S]-lineability, originally developed in 2019 by L. Bernal-González, J.A. Conejero, M. Murillo-Arcila, and J.B. Seoane-Sepúlveda . Additionally, we provide a characterization in terms of lineability in the context of complements of unions of closed subspaces in F-spaces, and finally, we present a negative result in both normed spaces and p-Banach spaces. These findings contribute to the understanding of linearity in exotic settings in topological vector spaces.
Negative / Null Result ReportOpen accessComputer Science
Pierre-Étienne Meunier, Matthew J. Patitz, Scott M. Summers et al. · 2013 · arXiv
We prove a negative result on the power of a model of algorithmic self-assembly for which it has been notoriously difficult to find general techniques and results. Specifically, we prove that Winfree's abstract Tile Assembly Model, when restricted to use noncooperative tile binding, is not intrinsically universal. This stands in stark contrast to the recent result that, via cooperative binding, the abstract Tile Assembly Model is indeed intrinsically universal. Noncooperative self-assembly, also known as "temperature 1", is where tiles bind to each other if they match on one or more sides, whe