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.
View details →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,
View details →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.
View details →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.
View details →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
View details →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.
View details →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
View details →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
View details →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.
View details →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.
View details →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.
View details →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.
View details →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
View details →Negative / Null Result ReportOpen accessMathematics
Jack Hall, Amnon Neeman, David Rydh · 2014 · arXiv
Let $X$ be a quasi-compact and quasi-separated scheme. There are two fundamental and pervasive facts about the unbounded derived category of $X$: (1) $\mathsf{D}_{\mathrm{qc}}(X)$ is compactly generated by perfect complexes and (2) if $X$ is noetherian or has affine diagonal, then the functor $Ψ_X \colon \mathsf{D}(\mathsf{QCoh}(X)) \to \mathsf{D}_{\mathrm{qc}}(X)$ is an equivalence. Our main results are that for algebraic stacks in positive characteristic, the assertions (1) and (2) are typically false.
View details →Negative / Null Result ReportOpen accessMathematics
Michael Edward Hill · 2021 · arXiv
In a pervious paper Weidmann shows that there a bound on the number of orbits of edges in a tree on which a finitely generated group acts $(k,C)$-acylindrically. In this paper we extend this result to actions which are $k$-acylindrical except on a family of groups with "finite height". We also give an example which gives a negative result to a conjecture of Weidmann from the same paper and produce a sharp bound for groups acting $k$--acylindrically.
View details →Negative / Null Result ReportOpen accessComputer Science
Binhai Zhu · 2007 · arXiv
We show that given $m$ proteins (or protein backbones, which are modeled as 3D polygonal chains each of length O(n)) the problem of protein local structure alignment under the discrete Fréchet distance is as hard as Independent Set. So the problem does not admit any approximation of factor $n^{1-ε}$. This is the strongest negative result regarding the protein local structure alignment problem. On the other hand, if $m$ is a constant, then the problem can be solved in polygnomial time.
View details →Negative / Null Result ReportOpen accessPhysics
Joao Magueijo, Ali Mozaffari · 2011 · arXiv
We quantify the potential for testing MOdified Newtonian Dynamics (MOND) with LISA Pathfinder (LPF), should a saddle point flyby be incorporated into the mission. We forecast the expected signal to noise ratio (SNR) for a variety of instrument noise models and trajectories past the saddle. For standard theoretical parameters the SNR reaches middle to high double figures even with modest assumptions about instrument performance and saddle approach. Obvious concerns, like systematics arising from LPF self-gravity, or the Newtonian background, are examined and shown not to be a problem. We also i
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Peter Oswald · 2006 · arXiv
For the L_2-orthogonal projector P onto spaces of linear splines over simplicial partitions of polyhedral domains in R^d, d>1, we show that the L_infty norm of P cannot be bounded uniformly with respect to the partition. This is in contrast to d=1, where these norms are bounded by 3 independently of the partition. This negative result is folklore among specialists in finite element methods and approximation theory but seemingly has never been formally proved.
View details →Negative / Null Result ReportOpen accessComputer Science
Damian Andrew Tamburri, Francesca Arcelli Fontana, Riccardo Roveda et al. · 2023 · arXiv
Technical debt occurs in many different forms across software artifacts. One such form is connected to software architectures where debt emerges in the form of structural anti-patterns across architecture elements, namely, architecture smells. As defined in the literature, ``Architecture smells are recurrent architectural decisions that negatively impact internal system quality", thus increasing technical debt. In this paper, we aim at exploring whether there exist manifestations of architectural technical debt beyond decreased code or architectural quality, namely, whether there is a relation
View details →Negative / Null Result ReportOpen accessMathematics
Yan Zhang · 2023 · arXiv
This paper presents a study of the finite axiomatizability of transitive logics of finite depth and finite weak width. We prove the finite axiomatizability of each transitive logic of finite depth and of weak width $1$ that is characterized by rooted transitive frames in which all antichains contain at most $n$ irreflexive points. As a negative result, we show that there are non-finitely-axiomatizable transitive logics of depth $n$ and of weak width $k$ for each $n\geqslant3$ and $k\geqslant2$.
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Raf Cluckers · 2002 · arXiv
We prove a cell decomposition theorem for Presburger sets and introduce a dimension theory for Z-groups with the Presburger structure. Using the cell decomposition theorem we obtain a full classification of Presburger sets up to definable bijection. We also exhibit a tight connection between the definable sets in an arbitrary p-minimal field and Presburger sets in its value group. We give a negative result about expansions of Presburger structures and prove uniform elimination of imaginaries for Presburger structures within the Presburger language.
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Kanstantsin Pashkovich, Thomas Snow · 2026 · arXiv
We study online algorithms for maximum cardinality matchings with edge arrivals in graphs of low degree. Buchbinder, Segev, and Tkach showed that no online algorithm for maximum cardinality fractional matchings can achieve a competitive ratio larger than $4/(9-\sqrt 5)\approx 0.5914$ even for graphs of maximum degree three. The negative result of Buchbinder et al. holds even when the graph is bipartite and edges are revealed according to vertex arrivals, i.e. once a vertex arrives, all edges are revealed that include the newly arrived vertex and one of the previously arrived vertices. In this
View details →Negative / Null Result ReportOpen accessComputer Science
J. Orloff, A. Rozanov, C. Santoni · 2002 · arXiv
Limits at 90 % c.l. on the square of the mixing strength |U_tau4|^2 between nu_tau and a mostly isosinglet heavy neutrino with mass in the range 10-290 MeV/c^2 are reported. The results were derived using the negative result of a search for neutral particles decaying into two electrons conducted by the CHARM collaboration in a neutrino beam dump experiment. Upper limits ~10^-4 were obtained for neutrino masses larger than 160 MeV/c^2.
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Philip Herrmann · 2013 · arXiv
In this paper we study a model structure on a category of schemes with a group action and the resulting unstable and stable equivariant motivic homotopy theories. The new model structure introduced here samples a comparison to the one by Voevodsky and Hu-Kriz-Ormsby. We show that it allows to detect equivariant motivic weak equivalences on fixed points and how this property leads to a topologically convenient behavior of stable equivalences. We also prove a negative result concerning descent for equivariant algebraic K-theory.
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Brian Swingle · 2009 · arXiv
I compute the entanglement entropy of a strongly coupled 2+1d quantum field theory containing fermions at finite density using gauge/gravity duality. The dual geometry is an extremal black hole in 3+1d Einstein-Maxwell theory. This system was recently shown to exhibit non-Fermi liquid behavior, but the leading geometrical contribution to the entanglement entropy does not produce an expected violation of the boundary law. I discuss this negative result in the context of attempts to find highly entangled states of quantum matter.
View details →Negative / Null Result ReportOpen accessComputer Science
Maya Dotan, Saar Tochner · 2020 · arXiv
Many blockchain systems today, including Bitcoin, rely on Proof of Work (PoW). Proof of work is crucial to the liveness and security of cryptocurrencies. The assumption when using PoW is that a lot of trial and error is required on average before a valid block is generated. One of the main concerns raised with regard to this kind of system is the inherent need to "waste" energy on "meaningless" problems. In fact, the Bitcoin system is believed to consume more electricity than several small countries. In this work we formally define three properties that are necessary for wasteless PoW systems:
View details →Negative / Null Result ReportOpen accessMathematics
Bjørn Kjos-Hanssen · 2026 · arXiv
Carmo and Jones have presented a sequence of candidate axiom systems for conditional obligation between 1997 and 2022. For their most recent system we demonstrate a limited form of deontic explosion: given that a student does not get the highest possible grade on a test, any other passing grade is acceptable. In addition to that negative result, we give a positive one: revisiting the strongest version of Carmo and Jones' 1997 system, we provide a surprising classification of all satisfying models in terms of a single forbidden possible world.
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Anand Ganesh, Babhrubahan Bose, Anand Rajagopalan · 2025 · arXiv
We construct four Schauder bases for the space $C[0,1]$, one using ReLU functions, another using Softplus functions, and two more using sigmoidal versions of the ReLU and Softplus functions. This establishes the existence of a basis using these functions for the first time, and improves on the universal approximation property associated with them. We also show an $O(\frac{1}{n})$ approximation bound based on our ReLU basis, and a negative result on constructing multivariate functions using finite combinations of ReLU functions.
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Brieuc Pinon, Raphaël Jungers, Jean-Charles Delvenne · 2025 · arXiv
Reinforcement Learning algorithms designed for high-dimensional spaces often enforce the Bellman equation on a sampled subset of states, relying on generalization to propagate knowledge across the state space. In this paper, we identify and formalize a fundamental limitation of this common approach. Specifically, we construct counterexample problems with a simple structure that this approach fails to exploit. Our findings reveal that such algorithms can neglect critical information about the problems, leading to inefficiencies. Furthermore, we extend this negative result to another approach fr
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Ali Mozaffari · 2011 · arXiv
Building on previous work, we re-examine the possibility of testing MOdified Newtonian Dynamics near the saddle points of gravitational potentials in the Solar System, through an extension of the forthcoming LISA Pathfinder mission. We extend present analysis to include quasi-linear formulations of these theories, resulting from fully relativistic modified gravity theories. Using similar quantitative and qualitative tools, we demonstrate that in general, both the instrumental response and typical Signal to Noise Ratios for such a test will be different. Finally we investigate constraints from
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