Interpreting Kullback-Leibler divergence with the Neyman-Pearson lemma

Kullback-Leibler divergence and the Neyman-Pearson lemma are two fundamental concepts in statistics. Both are about likelihood ratios: Kullback-Leibler divergence is the expected log-likelihood ratio, and the Neyman-Pearson lemma is about error rates of likelihood ratio tests. Exploring this connection gives another statistical interpretation of the Kullback-Leibler divergence in terms of the loss of power of the likelihood ratio test when the wrong distribution is used for one of the hypotheses. In this interpretation, the standard non-negativity property of the Kullback-Leibler divergence is essentially a restatement of the optimal property of likelihood ratios established by the Neyman-Pearson lemma. The asymmetry of Kullback-Leibler divergence is overviewed in information geometry.     

Pressure and temperature effects on the excess deuteron and proton conductance

The limiting molar conductances ° of deuterium chloride DCl in D₂O were determined as a function of pressure and temperature in order to examine the proton-jump mechanism in detail. The excess deuteron conductances °_E(D ⁺), as estimated by the equation [°_E(D ⁺) = °(DCl/D ₂ O) – °(KCl/D ₂ O)], increases with an increase in the pressure and temperature as well as the excess proton conductance [°_E(H ⁺) = °(HCl/H ₂ O) – °(KCl/H ₂ O)]. The isotope effect on the excess conductances, however, depends on the pressure and temperature contrary to the model proposed by Conway et al.: °_E(H ⁺)/°_E(D ⁺) decreases with increasing pressure and temperature. The magnitude of the decrease with pressure becomes more prominent at lower temperature. These results are discussed in terms of the pre-rotation of adjacent water molecules, the bending of hydrogen bonds with pressure, and the difference in strength of hydrogen bonds between D₂O and H₂O.     

Characteristics of hyaluronate-hydroxyethyl acrylate blend gel and release of cationic amphiphilic solutes

Hyaluronate-hydroxyethyl acrylate blend gel (HA-PHEA) were prepared to modify the brittleness of hyaluronate gel (HA) and the characteristics of HA-PHEA gel were compared with those of HA and polyhydroxyethyl acrylate (PHEA) gels. These gels were high in water content and transparent. HA-PHEA gel was improved in viscoelastic properties due to the elasticity and the high affinity with water of PHEA, and the drying-swelling cycles became reversible. The effective charge densities theta of the gels estimated from membrane potentials were -0.002, -0.008 and 0 mol dm(-3) for HA-PHEA, HA and PHEA gels. Effects of electro- static and nonelectrostatic interactions on absorptions and releases were studied using sodium benzoate (NaBA) as an anionic solute, and methylene blue (MB), chlorpromazine (CPHCl) and benzethonium chloride (BZTCl) as cationic solutes, in which CPHCl and BZTCl are cationic amphiphilic solutes. The releases of MB, CPHCl and BZTCl from HA-PHEA and HA gels were suppressed comparing with those of NaBA. By adding salts, the releases of MB and CPHCl were enhanced but those of BZTCl were suppressed due to enhancement of the intra- and intermicelle formation. In the releases of the cationic solutes from HA-PHEA gel, electrostatic and nonelectrostatic interactions with HA were found to play important roles. Behaviors of the releases from HA-PHEA gel were found to possess the features of HA gel.     

Importance of the isopropylidene terminal of geranylgeranyl group for the formation of tetraether lipid in methanogenic archaea

Labeling experiments using several deuterated lipids were pursued to study the biosynthesis of macrocyclic isoprenoidal lipids of thermophilic methanogenic archaea, Methanothermobacter thermautotrophicus. The isopropylidene terminal of geranylgeranyl group of monomeric precursor appeared to be important for the CC bond formation at the hydrophobic end in the macrocyclic lipids. A mechanism involving a radical trigger at the allylic methyl group is proposed for this CC bond formation.     

Cu(I)-catalyzed direct enantioselective cross aldol-type reaction of acetonitrile

Direct catalytic enantioselective cross aldol-type reaction of an acetate surrogate was developed using Cu alkoxide-chiral phosphine complexes as catalysts. Chemoselective activation and deprotonation of the donor substrate (acetonitrile) by the soft metal alkoxide in a strongly donating solvent (HMPA) are key to success in this reaction. Useful chemical yields and promising enantioselectivities are produced using either DTBM-SEGPHOS or a tuned BIPHEP as a chiral ligand. [reaction: see text]     

Generation of 6-(Trifluoromethyl)-4,5-dihydro-2(3H)-pyridone and the Application to Synthesis of Some Fused Nitrogen Heterocycles Carrying a Trifluoromethyl Group on the Bridgehead Position via Radical Cyclization of Dihydropyridones

Staudinger/aza-Wittig reaction of 6,6,6-trifluoro-5-oxohexanoyl azide with PPh(3) or PBu(3) was examined. A reactive intermediate acyl imine 1 was trapped by methanol. Without nucleophile, isomerized enamide form 3 was obtained. N-Iodobenzoylation and N-haloalkylation of 3 and following radical cyclization via the 5-exo or 6-exo mode gave benzoindolizidinone, indolizidinone, and quinolizidinone derivatives 10-14, which have a trifluoromethyl group at the bridgehead position adjacent to nitrogen. Although LiAlH(4) reduction of 10 and 11 gave a mixture of saturated benzoindolizidine 15 and amino alcohol 16, reduction with BH(3)/THF selectively gave the desired 15 and indolizidine 17 from 13.     

Formal catalytic asymmetric total synthesis of fostriecin

The common synthetic intermediate of a potent and promising anticancer agent, fostriecin, was synthesized using a unique method that combines four catalytic asymmetric reactions as shown above.     

Surface structures of adsorption layers of sodium hyaluronate and bovine serum albumin complexes on poly(γ-methyl-l-glutamate) film and their surface properties

Two-dimensional structures and characteristics of the complexes between sodium hyaluronate (NaHA) and bovine serum albumin (BSA) were studied by using a quartz crystal microbalance method and an atomic force microscope (AFM). NaHA did not adsorb on poly(-methyl-l-glutamate) (PMLG) film. On the other hand, the complexes adsorbed on it and the adsorption behaviors were found to be Langmuir types. With increasing weight ratio of BSA to NaHA, W _BSA, the adsorption constants K decreased and the saturated adsorption masses increased. The adsorbed complexes were spherical particles and at saturated adsorption states they covered compactly on the PMLG film. The mean diameters d _AFM estimated from the topographic images decreased from 70 to 54 nm with increasing W _BSA. The adhesion force F _ad and the frictional force F _f between the complex layers and the AFM tip were obtained by using the contact mode of the AFM. With increasing W _BSA, the values of F _ad decreased and the values of F _f increased. Compared with the frictional coefficient of the NaHA adsorption layer on the BSA monolayer, the values for the NaHA–BSA complex layer were found to be much higher.     

A convenient synthesis of 1-bromoolefins and acetylenes by a chain extension of aldehydes

Aldehydes are easily converted to 1-bromoolefins or terminal acetylenes by the use of Wittig reaction of bromomethylenetriphenylphosphorane which is prepared from bromomethyltriphenylphosphonium bromide with potassium tert-butoxide.