Miettinen, Jari; Nordhausen, Klaus; Oja, Hannu; Taskinen, Sara(Academic Press, 2014)
In this paper we assume that the observed pp time series are linear combinations of pp latent uncorrelated weakly stationary time series. The problem is then to find an estimate for an unmixing matrix that transforms the ...
We show the existence of the local dimension of an invariant probability measure on an infinitely generated self-affine set, for almost all translations. This implies that an ergodic probability measure is exactly dimensional. ...
Sampo, Jouni; Takalo, Jouni; Siltanen, Samuli; Miettinen, Arttu; Lassas, Matti; Timonen, Jussi(S P I E - International Society for Optical Engineering, 2014)
A method based on the curvelet transform is introduced to estimate the orientation distribution from
two-dimensional images of small anisotropic particles. Orientation of fibers in paper is considered as a particular
application ...
Paternain, Gabriel P.; Salo, Mikko; Uhlmann, Gunther(Oxford University Press, 2015)
We describe the range of the attenuated ray transform of a unitary
connection on a simple surface acting on functions and 1-forms. We use this description
to determine the range of the ray transform acting on symmetric ...
Le Donne, Enrico; Rajala, Tapio(Indiana University, 2015)
We study the Assouad dimension and the Nagata dimension
of metric spaces. As a general result, we prove that the Nagata
dimension of a metric space is always bounded from above by the
Assouad dimension. Most of the paper ...
We show that in any infinitesimally Hilbertian CD
.K; N /-space at almost
every point there exists a Euclidean weak tangent, i.e., there exists a sequence of dilations
of the space that converges to a Euclidean space ...
In a prior work of the first two authors with Savar´e, a new Riemannian
notion of a lower bound for Ricci curvature in the class of metric measure
spaces (X, d, m) was introduced, and the corresponding class of spaces ...
We study optimal transportation with the quadratic cost function
in geodesic metric spaces satisfying suitable non-branching assumptions. We
introduce and study the notions of slope along curves and along geodesics and
we ...
We prove that in metric measure spaces where the entropy functional is Kconvex
along every Wasserstein geodesic any optimal transport between two absolutely continuous
measures with finite second moments lives on a ...
Magnani, Valentino; Rajala, Tapio(Oxford University Press, 2014)
We prove a Rademacher-type theorem for Lipschitz mappings from a subset
of a Carnot group to a Banach homogeneous group, equipped with a suitably weakened
Radon-Nikodym property. We provide a metric area formula that ...