238 research outputs found
AGING OF SCARCELY SOLUBLE PHOSPHATES DURING LONG PERIODS AND ITS INFLUENCE ON AVAILABILITY IV. STUDIES ON THE CONSTITUTION AND MANURIAL EFFECT OF SCARCELY SOLUBLE PHOSPHATE
EFFECTS OF HEATING AND DEHYDRATION ON THE CONSTITUTION AND AVAILABILITY OF SCARCELY SOLUBLE PHOSPHATES III. STUDIES ON THE CONSTITUTIONS AND MANURIAL EFFECTS OF SCARCELY SOLUBLE PHOSPHATES
CHEMICAL CONSTITUTION AND AVAILABILITY OF IRON AND ALUMINUM PHOSPHATES I. STUDIES ON THE CONSTITUTIONS AND MANURIAL EFFECTS OF SCARCELY SOLUBLE PHOSPHATES
Quantum local asymptotic normality based on a new quantum likelihood ratio
We develop a theory of local asymptotic normality in the quantum domain based
on a novel quantum analogue of the log-likelihood ratio. This formulation is
applicable to any quantum statistical model satisfying a mild smoothness
condition. As an application, we prove the asymptotic achievability of the
Holevo bound for the local shift parameter.Comment: Published in at http://dx.doi.org/10.1214/13-AOS1147 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Autoparallelity of Quantum Statistical Manifolds in The Light of Quantum Estimation Theory
In this paper we study the autoparallelity w.r.t. the e-connection for an
information-geometric structure called the SLD structure, which consists of a
Riemannian metric and mutually dual e- and m-connections, induced on the
manifold of strictly positive density operators. Unlike the classical
information geometry, the e-connection has non-vanishing torsion, which brings
various mathematical difficulties. The notion of e-autoparallel submanifolds is
regarded as a quantum version of exponential families in classical statistics,
which is known to be characterized as statistical models having efficient
estimators (unbiased estimators uniformly achieving the equality in the
Cramer-Rao inequality). As quantum extensions of this classical result, we
present two different forms of estimation-theoretical characterizations of the
e-autoparallel submanifolds. We also give several results on the
e-autoparallelity, some of which are valid for the autoparallelity w.r.t. an
affine connection in a more general geometrical situation
BIOCHEMICAL STUDIES OF MICROELEMENTS IN GREEN PLANTS 1. DEFICIENCY SYMPTOMS OF MICROELEMENTS ON BARLEY PLANTS AND CHANGES OF INDOLACETIC ACID OXIDASE ACTIVITY
PHYSIOLOGICAL STUDIES OF PLANT ROOTS II. RELATIONS BETWEEN CONCENTRATIONS OF INORGANlC IONS IN THE MEDIUM AND GROWTH OF THE ISOLATED WHEAT ROOTS
BIOCHEMICAL AND NUTRITIONAL STUDIES ON POTASSIUM III. ON THE LEACHING EXTRACTION OF POTASSIUM FROM THE HIGHER PLANTS
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