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
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
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.
Negative / Null Result ReportOpen accessMathematics
F. Iavernaro, F. Mazzia, M. S. Mukhametzhanov et al. · 2018 · arXiv
Multi-derivative one-step methods based upon Euler-Maclaurin integration formulae are considered for the solution of canonical Hamiltonian dynamical systems. Despite the negative result that simplecticity may not be attained by any multi-derivative Runge--Kutta methods, we show that the Euler-MacLaurin method of order p is conjugate-symplectic up to order p+2. This feature entitles them to play a role in the context of geometric integration and, to make their implementation competitive with the existing integrators, we explore the possibility of computing the underlying higher order derivative
Negative / Null Result ReportOpen accessMathematics
Andres Gomez, Weijun Xie · 2022 · arXiv
In this paper, we study the mixed-integer nonlinear set given by a separable quadratic constraint on continuous variables, where each continuous variable is controlled by an additional indicator. This set occurs pervasively in optimization problems with uncertainty and in machine learning. We show that optimization over this set is NP-hard. Despite this negative result, we characterize the structure of the convex hull, and show that it can be formally studied using polyhedral theory. Moreover, we show that although perspective relaxation in the literature for this set fails to match the struct
Negative / Null Result ReportOpen accessMathematics
Ingo Steinwart · 2024 · arXiv
We investigate for which Gaussian processes there do or do not exist reproducing kernel Hilbert spaces (RKHSs) that contain almost all of their paths. In particular, we establish a new result that makes it possible to exclude the existence of such RKHSs in many cases. Moreover, we combine this negative result with some known techniques to establish positive results. Here it turns out that for many classical families of Gaussian processes we can fully characterize for which members of these families there exist RKHSs containing the paths. Similar characterizations are obtained for Gaussian proc
Negative / Null Result ReportOpen accessMathematics
Andrey Sarychev · 2011 · arXiv
We study controllability of $d$-dimensional defocusing cubic Schroedinger equation under periodic boundary conditions. The control is applied additively, via a source term, which is a linear combination of few complex exponentials (modes) with time-variant coefficients - controls. We manage to prove that controlling at most $2^d$ modes one can achieve controllability of the equation in any finite-dimensional projection of the evolution space $H^{s}(\mathbb{T}^d), \ s>d/2$, as well as approximate controllability in $H^{s}(\mathbb{T}^d)$. We also present negative result regarding exact controlla
Negative / Null Result ReportOpen accessMathematics
Swagato K. Ray, Rudra P. Sarkar · 2012 · arXiv
Generalizing a result of Roe \cite{Roe} Strichartz proved in \cite{Str} that if a doubly-infinite sequence $\{f_k\}$ of functions on $\R^n$ satisfies $f_{k+1}=Δf_k$ and $|f_{k}(x)|\leq M$ for all $k=0,\pm 1,\pm 2,...$ and $x\in \R^n$, then $Δf_0(x)= -f_0$. Strichartz also showed that the result fails for hyperbolic 3-space. This negative result can be indeed extended to any Riemannian symmetric space of noncompact type. Taking this into account we shall prove that for all Riemannian symmetric spaces of noncompact type the theorem actually holds true when uniform boundedness is modified suitabl
Negative / Null Result ReportOpen accessComputer Science
Marcus Beck · 2009 · arXiv
The KArlsruhe TRitium Neutrino mass experiment, KATRIN, aims to search for the mass of the electron neutrino with a sensitivity of 0.2 eV/c^2 (90% C.L.) and a detection limit of 0.35 eV/c^2 (5 sigma). Both a positive or a negative result will have far reaching implications for cosmology and the standard model of particle physics and will give new input for astroparticle physics and cosmology. The major components of KATRIN are being set up at the Karlsruhe Institut of Technology in Karlsruhe, Germany, and test measurements of the individual components have started. Data taking with tritium is
Negative / Null Result Report
Dharam Vir Singh · 2024 · International Education and Research Journal
Michelson and Morley conducted an experiment in the year 1887 to measure the speed of earth in luminiferous aether. In this experiment Michelson’s interferometer was used in which two waves are superimposed to generate interference…
View details →DOI: 10.21276/ierj24566444797404 Negative / Null Result ReportOpen accessComputer Science
Francesco Bacchiocchi, Matteo Castiglioni, Alberto Marchesi et al. · 2022 · arXiv
We study signaling in Bayesian ad auctions, in which bidders' valuations depend on a random, unknown state of nature. The auction mechanism has complete knowledge of the actual state of nature, and it can send signals to bidders so as to disclose information about the state and increase revenue. For instance, a state may collectively encode some features of the user that are known to the mechanism only, since the latter has access to data sources unaccessible to the bidders. We study the problem of computing how the mechanism should send signals to bidders in order to maximize revenue. While t
Negative / Null Result ReportOpen accessMathematics
Fausto Di Biase, Haguma Gratien, Olof Svensson · 2025 · arXiv
In 1906 Fatou proved that bounded holomorphic functions on the unit disc converge a.e. on the boundary along nontangential approach regions. In 1927 Littlewood proved a negative result, i.e., that a.e. convergence fails for certain approach regions: More precisely, it fails for the rotationally invariant families of tangential approach regions that end curvilinearly at the boundary. The fact that tangential approach regions which end sequentially at the boundary may instead be very well conducive to a.e. convergence was understood more recently by W. Rudin (in 1979) and A. Nagel and E.M. Stein
Negative / Null Result ReportOpen accessMathematics
Antoine Salomon, Jean-Yves Audibert · 2011 · arXiv
This paper studies the deviations of the regret in a stochastic multi-armed bandit problem. When the total number of plays n is known beforehand by the agent, Audibert et al. (2009) exhibit a policy such that with probability at least 1-1/n, the regret of the policy is of order log(n). They have also shown that such a property is not shared by the popular ucb1 policy of Auer et al. (2002). This work first answers an open question: it extends this negative result to any anytime policy. The second contribution of this paper is to design anytime robust policies for specific multi-armed bandit pro
Negative / Null Result ReportOpen accessComputer Science
Nathan Stringham, Fateme Hashemi Chaleshtori, Xinyuan Yan et al. · 2025 · arXiv
People use large language models (LLMs) when they should not. This is partly because they see LLMs compose poems and answer intricate questions, so they understandably, but incorrectly, assume LLMs won't stumble on basic tasks like simple arithmetic. Prior work has tried to address this by clustering instance embeddings into regions where an LLM is likely to fail and automatically describing patterns in these regions. The found failure patterns are taught to users to mitigate their overreliance. Yet, this approach has not fully succeeded. In this analysis paper, we aim to understand why. We fi
Negative / Null Result ReportOpen accessComputer Science
Antonio Bernal · 2016 · arXiv
In this paper we prove that no absolutely maximally entangled, AME, state with minimal support exists with 7 sites and 5 levels. General AME states are pure multipartite states that, when reduced to half or less of the sites, the maximum entropy mixed state is obtained. They have found applications in teleportation and quantum secret sharing, and finding conditions for their existence is a well known open problem. We consider the version of this problem for minimally supported AME states. We single out known both sufficient and necessary conditions in that case. From our negative result, we sh
