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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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.
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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
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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
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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.
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P. F. Tupper · 2006 · arXiv
We consider the numerical simulation of Hamiltonian systems of ordinary differential equations. Two features of Hamiltonian systems are that energy is conserved along trajectories and phase space volume is preserved by the flow. We want to determine if there are integration schemes that preserve these two properties for all Hamiltonian systems, or at least for all systems in a wide class. This paper provides provides a negative result in the case of two dimensional (one degree of freedom) Hamiltonian systems, for which phase space volume is identical to area. Our main theorem shows that there
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Karine Beauchard, Frédéric Marbach, Thomas Perrin · 2025 · arXiv
We study the small-time local controllability (STLC) of a bilinear Schrödinger equation with Neumann boundary conditions near its ground state. We focus on the degenerate case where the linearized system is not controllable, necessitating a second-order analysis. We prove two complementary results. The negative result provides a new PDE instance of Sussmann's classical quadratic obstruction, corresponding to a non-vanishing Lie bracket. The positive result appears to be the first to establish STLC at the quadratic order for a physical PDE with a single scalar control. Both proofs rely on a Fou
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