Some Information Theoretic Ideas Useful in Statistical Inference

In this paper we discuss four information theoretic ideas and present their implications to statistical inference: (1) Fisher information and divergence generating functions, (2) information optimum unbiased estimators, (3) information content of various statistics, (4) characterizations based on Fisher information. This paper was written while the first author was visiting the University of Cyprus, Department of Mathematics and Statistics.     

Evaluation of Different Turbulent Combustion Models Based on Tabulated Chemistry Using DNS of Heterogeneous Mixtures Under Multi-injection Diesel Engine-Relevant Conditions

Flow, Turbulence and Combustion - This paper assesses the accuracy of partially-premixed turbulent combustion models based on the tabulation of chemical kinetics, under multi-injection diesel...     

Improvement of image quality using BLADE sequences in brain MR imaging

The purpose of this study is to compare two types of sequences in brain magnetic resonance (MR) examinations of uncooperative and cooperative patients. For each group of patients, the pairs of sequences that were compared were two T2-weighted (T2-W) fluid attenuated inversion recovery sequences with different k-space trajectories (conventional Cartesian and BLADE) and two T2-TSE weighted with different k-space trajectories (conventional Cartesian and BLADE). Twenty-three consecutive uncooperative patients and 44 cooperative patients, who routinely underwent brain MR imaging examination, participated in the study. Both qualitative and quantitative analyses were performed based on the signal-to-noise ratio, contrast-to-noise ratio (CNR), and relative contrast (ReCon) measures of normal anatomic structures. The qualitative analysis was performed by experienced radiologists. Also, the presence of motion, other (e.g., Gibbs, susceptibility artifacts, phase encoding from vessels) artifacts and pulsatile flow artifacts was evaluated.     

Different versions of a first countable space without choice

We show that two versions of a first countable topological space which are equivalent in ZFC set theory split in the absence of the Axiom of Choice AC. This answers in the negative a related question from Gutierres “What is a first countable space?”.     

Information in Quantal Response Data and Random Censoring

In this paper we study interesting properties of Fisher and divergence type measures of information for quantal, complete and incomplete random censoring, and not censoring at all. It is shown that, while quantal random censoring is less expensive, it is less informative than complete random censoring. It is also shown that in experiments which are mixtures of quantal and complete random censoring, the information received from these experiments is a convex combination of quantal information and the information in complete random censoring. Finally, the "total information" property is studied, in which the information received by the uncensored experiment can be expressed as the sum of the information provided by random censoring and the loss of information due to censoring. The results for Fisher's measure of information are an extension of already known results to the multiparameter case. The investigation of the previous information properties for divergence type measures is a new element, as well as the comparison of byproducts of Fisher information matrices.     

A simple synthesis of compounds with the benz[h]imidazo[1,2-c]quinazoline ring system

The ureas obtained from 1-amino-3(or 4)-methyl-2-naphthalenecarbonitrile and 2-chloroethyl isocyanate, or ethyl isocyanatoacetate undergo a double cyclization upon thermal decomposition, or treatment with base to yield compounds with the benz[h]imidazo[1,2-c]quinazoline ring system.     

Self-replication vs. reactive binary complexes--manipulating recognition-mediated cycloadditions by simple structural modifications

The rate of reaction and the selectivity of a Diels-Alder cycloaddition between a furan and a maleimide can be enhanced by the introduction of complementary recognition sites on the reactant species. Subtle manipulation of other structural elements allows the generation of the observed rate enhancements and selectivities through either self-replication or formation of a pre-reactive binary complex.     

Mechanical strength of amorphous CaCO3 colloidal spheres

Amorphous glassy CaCO3 colloidal spheres of monomodal size distribution were studied by high-resolution Brillouin light scattering. The Young modulus of 37 GPa and shear modulus of 14 GPa of glassy CaCO3 at a density of 1.9 g/cm3 were extracted from the particle vibration frequencies by employing acoustic wave scattering cross-section calculations. The line shape of the low-frequency modes is a sensitive index of the particle polydispersity.     

Specific autocatalysis in diastereoisomeric replicators

Two diastereoisomeric cycloadducts are capable of accelerating their own formation through the assembly of catalytic ternary complexes. The two cycloadducts do not have any measurable catalytic effect on the rate of formation of their diastereoisomer. [structure: see text]     

No decreasing sequence of cardinals

In set theory without the Axiom of Choice (AC), we investigate the set-theoretic strength of the principle NDS which states that there is no function f on the set ω of natural numbers such that for everyn ∈ ω, f (n + 1) ? f (n), where for sets x and y, x ? y means that there is a one-to-one map g : x → y, but no one-to-one map h : y → x. It is a long standing open problem whether NDS implies AC. In this paper, among other results, we show that NDS is a strong axiom by establishing that AC^LO (AC restricted to linearly ordered sets of non-empty sets, and also equivalent to AC in ZF, the Zermelo–Fraenkel set theory minus AC) ? NDS in ZFA set theory (ZF with the Axiom of Extensionality weakened in order to allow the existence of atoms). The latter result provides a strongly negative answer to the question of whether “every Dedekind-finite set is finite” implies NDS addressed in G. H. Moore “Zermelo’s Axiom of Choice. Its Origins, Development, and Influence” and in P. Howard–J. E. Rubin “Consequences of the Axiom of Choice”. We also prove that AC^WO (AC restricted to well-ordered sets of non-empty sets) ? NDS in ZF (hence, “every Dedekind-finite set is finite” ? NDS in ZF, either) and that “for all infinite cardinals m, m + m = m” ? NDS in ZFA.