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.
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.
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.
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
Negative / Null Result ReportOpen accessMathematics
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.
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
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 $k\geqslant2$.
Negative / Null Result ReportOpen accessMathematics
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.
Negative / Null Result ReportOpen accessComputer Science
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
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.
Negative / Null Result ReportOpen accessMathematics
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.
Negative / Null Result ReportOpen accessComputer Science
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.
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:
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.
Negative / Null Result ReportOpen accessComputer Science
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.
Negative / Null Result ReportOpen accessComputer Science
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
Negative / Null Result ReportOpen accessPhysics
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
Negative / Null Result ReportOpen accessMathematics
Andreas Nordvall Lagerås · 2007 · arXiv
Bertoin and Le Gall (2003) introduced a certain probability measure valued Markov process that describes the evolution of a population, such that a sample from this population would exhibit a genealogy given by the so-called $Λ$-coalescent, or coalescent with multiple collisions, introduced independently by Pitman (1999) and Sagitov (1999). We show how this process can be extended to the case where lineages can experience mutations. Regenerative compositions enter naturally into this model, which is somewhat surprising, considering a negative result by M{ö}hle (2007).
Negative / Null Result ReportOpen accessEngineering
Daniele Gerosa, Thomas Eriksson · 2026 · arXiv
Motivated by recent developments in stochastic modeling of clock jitter in Analog-to-Digital Converters (ADCs) as autoregressive processes of order one (AR(1)), we study the density and stability properties of AR(1)-jittered sampling sets for Paley-Wiener signals. We show that, despite having the correct asymptotic density both on average and almost surely, such sets almost surely fail to be stable sampling sets. We complement this negative result with a finite-dimensional analysis, showing that the corresponding jittered sinc matrices are nonetheless well-conditioned with high probability.
Negative / Null Result ReportOpen accessMathematics
Yemon Choi · 2015 · arXiv
We show that, given a compact Hausdorff space $Ω$, there is a compact group ${\mathbb G}$ and a homeomorphic embedding of $Ω$ into ${\mathbb G}$, such that the restriction map ${\rm A}({\mathbb G})\to C(Ω)$ is a complete quotient map of operator spaces. In particular, this shows that there exist compact groups which contain infinite cb-Helson subsets, answering a question raised in [Choi--Samei, Proc. AMS 2013; cf. http://arxiv.org/abs/1104.2953]. A negative result from the same paper is also improved.
Negative / Null Result ReportOpen accessMathematics
Alexander Reznikov, Oleksandr Vlasiuk · 2018 · arXiv
We investigate properties of minimal $N$-point Riesz $s$-energy on fractal sets of non-integer dimension, as well as asymptotic behavior of $N$-point configurations that minimize this energy. For $s$ bigger than the dimension of the set $A$, we constructively prove a negative result concerning the asymptotic behavior (namely, its nonexistence) of the minimal $N$-point Riesz $s$-energy of $A$, but we show that the asymptotic exists over reasonable sub-sequences of $N$. Furthermore, we give a short proof of a result concerning asymptotic behavior of configurations that minimize the discrete Ries
Failed Experiment ReportOpen accessMathematics
Jake A. Soloff, Adityanand Guntuboyina, Michael I. Jordan · 2020 · arXiv
We study the problem of high-dimensional covariance estimation under the constraint that the partial correlations are nonnegative. The sign constraints dramatically simplify estimation: the Gaussian maximum likelihood estimator is well defined with only two observations regardless of the number of variables. We analyze its performance in the setting where the dimension may be much larger than the sample size. We establish that the estimator is both high-dimensionally consistent and minimax optimal in the symmetrized Stein loss. We also prove a negative result which shows that the sign-constrai
Negative / Null Result ReportOpen accessComputer Science
Paolo Boldi, Flavio Furia, Chiara Prezioso et al. · 2025 · arXiv
Axiomatization of centrality measures often involves proving that something cannot hold by providing a counterexample (i.e., a graph for which that specific centrality index fails to have a given property). In the context of geometric centralities, building such counterexamples requires constructing a graph with specific distance counts between nodes, as expressed by its distance-count matrix. We prove that deciding whether a matrix is the distance-count matrix of a graph is strongly NP-complete. This negative result implies that a brute-force approach to building this kind of counterexample i
Negative / Null Result ReportOpen accessComputer Science
Luca Aceto, Valentina Castiglioni, Anna Ingolfsdottir et al. · 2021 · arXiv
This paper studies the existence of finite equational axiomatisations of the interleaving parallel composition operator modulo the behavioural equivalences in van Glabbeek's linear time-branching time spectrum. In the setting of the process algebra BCCSP over a finite set of actions, we provide finite, ground-complete axiomatisations for various simulation and (decorated) trace semantics. We also show that no congruence over BCCSP that includes bisimilarity and is included in possible futures equivalence has a finite, ground-complete axiomatisation; this negative result applies to all the nest
Failed Experiment ReportOpen accessMathematics
Birgit Richter · 2005 · arXiv
We provide a lower bound for the coherence of the homotopy commutativity of the Brown-Peterson spectrum, BP, at a given prime p and prove that it is at least (2p^2 + 2p - 2)-homotopy commutative. We give a proof based on Dyer-Lashof operations that BP cannot be a Thom spectrum associated to n-fold loop maps to BSF for n=4 at 2 and n=2p+4 at odd primes. Other examples where we obtain estimates for coherence are the Johnson-Wilson spectra, localized away from the maximal ideal and unlocalized. We close with a negative result on Morava-K-theory.
Negative / Null Result ReportOpen accessMathematics
William Minicozzi, Christopher D. Sogge · 1999 · arXiv
We expand on counterxamples of Bourgain showing how Nikodym maximal estimates and oscillatory integral estimates can break down in the non-Euclidean case. Our examples show the role that the non-existence of totally geodesic submanifolds can play in these problems.
Negative / Null Result ReportOpen accessMathematics
Bobby DeMarco, Amanda Redlich · 2012 · arXiv
Motivated by a recent extension of the zero-one law by Kolaitis and Kopparty, we study the distribution of the number of copies of a fixed disconnected graph in the random graph $G(n,p)$. We use an idea of graph decompositions to give a sufficient condition for this distribution to tend to uniform modulo $q$. We determine the asymptotic distribution of all fixed two-component graphs in $G(n,p)$ for all $q$, and we give infinite families of many-component graphs with a uniform asymptotic distribution for all $q$. We also prove a negative result, that no simple proof of uniform asymptotic distri
Negative / Null Result ReportOpen accessComputer Science
Dana Fisman, Hadar Frenkel, Sandra Zilles · 2021 · arXiv
We study the learnability of symbolic finite state automata (SFA), a model shown useful in many applications in software verification. The state-of-the-art literature on this topic follows the query learning paradigm, and so far all obtained results are positive. We provide a necessary condition for efficient learnability of SFAs in this paradigm, from which we obtain the first negative result. The main focus of our work lies in the learnability of SFAs under the paradigm of identification in the limit using polynomial time and data, and its strengthening efficient identifiability, which are c
Negative / Null Result ReportOpen accessComputer Science
Angelos Assos, Yuval Dagan, Constantinos Daskalakis · 2024 · arXiv
Learning algorithms are often used to make decisions in sequential decision-making environments. In multi-agent settings, the decisions of each agent can affect the utilities/losses of the other agents. Therefore, if an agent is good at anticipating the behavior of the other agents, in particular how they will make decisions in each round as a function of their experience that far, it could try to judiciously make its own decisions over the rounds of the interaction so as to influence the other agents to behave in a way that ultimately benefits its own utility. In this paper, we study repeated
Negative / Null Result ReportOpen accessComputer Science
S. M. Bilenky, M. D. Mateev, S. T. Petcov · 2006 · arXiv
We discuss the physics potential of future tritium beta-decay experiments having a sensitivity to a neutrino mass ~\sqrt{|Δm^{2}_{23}|}~5x10^{-2} eV. The case of three-neutrino mixing is analised. A negative result of such an experiment would imply that the neutrino mass spectrum is of normal hierarchical type. The interpretation of a positive result would depend on the value of the lightest neutrino mass; if the lightest neutrino mass satisfies the inequality min(m_j) << \sqrt{|Δm^{2}_{23}|}, it would imply that the neutrino mass spectrum is of the inverted hierarchical type.
