The Empirical Bayes Classification Rules for Mixtures of Discrete and Continuous Variables

Let us consider a general population π. Each object belonging to the population π is characterized by a pair of correlated random vectors (X, Y ). Both X and Y may be mixtures of discrete and continuous random variables. It will be assumed that our population π consists of k groups π₁,….,πk, which depend on the value of the random vector Y. A certain object, which is an element of one of the k groups π₁, …, πk, has to be classified into the correct group. The knowledge of the value of the random vector Y would permit its correct classification, but the observation of this vector is difficult or dangerous and we must assign the individual on the basis of the observation of the random vector X . The classification procedure is based on randomized decision function δ* which minimizes the risk function i.e. Bayes decision function. We give also two empirical Bayes classification rules i.e. decision functions based on the sample from population π and having property that their risks converge to Bayes risk when the sample size increases.     

Global analysis of plasticity in turgor loss point,a key drought tolerance trait

Many species face increasing drought under climate change. Plasticity has been predicted to strongly influence species' drought responses, but broad patterns in plasticity have not been examined for key drought tolerance traits, including turgor loss or ‘wilting’ point (π_tlp). As soil dries, plants shift π_tlp by accumulating solutes (i.e. ‘osmotic adjustment’). We conducted the first global analysis of plasticity in Δπ_tlp and related traits for 283 wild and crop species in ecosystems worldwide. Δπ_tlp was widely prevalent but moderate (?0.44 MPa), accounting for 16% of post‐drought π_tlp. Thus, pre‐drought π_tlp was a considerably stronger predictor of post‐drought π_tlp across species of wild plants. For cultivars of certain crops Δπ_tlp accounted for major differences in post‐drought π_tlp. Climate was correlated with pre‐ and post‐drought π_tlp, but not Δπ_tlp. Thus, despite the wide prevalence of plasticity, π_tlp measured in one season can reliably characterise most species' constitutive drought tolerances and distributions relative to water supply.     

Correlation of drought traits and the predictability of osmotic potential at full leaf turgor in vegetation from New Zealand

Scientists do not know precisely how severe will be the impact of climate change on species. Evidence suggests that for some species, their future distributions might be jeopardized by local extinctions and drought‐induced tree mortality. Thus, we require models capable of estimating drought tolerance across many species. We can approach this goal by assessing functional traits. The trait osmotic potential at full turgor, π_O, is potentially a good drought indicator; however, few studies address its importance as a drought‐tolerance predictor and it is difficult to measure in the field with accuracy. In this work, we aim to answer the questions: which drought traits correlate with π_O?; do morpho‐anatomical traits correlate with π_O?; and which trees and shrubs are more (or less) vulnerable to drought? To achieve this aim, we assessed physiological and morpho‐anatomical traits for 14 native species from New Zealand forests. We included leaf‐ and wood‐related traits, π_O, water potential and stomatal conductance. We examined how these traits correlate with π_O and sought to generate models to predict π_O as a function of other traits. We tested 33 different models and evaluated them using Akaike's information criterion. Unfortunately, none of the morpho‐anatomical traits correlated well with π_O. Instead, water potential correlated most strongly with π_O. None of the models using only morpho‐anatomical traits produced plausible results. The model with the best predictive performance incorporated the effects of both morpho‐anatomical and physiological traits: water potential and wood saturated water content. Of the species analysed, and based on their π_O response, Lophozonia menziesii was considered the most vulnerable to drought stress, whereas Plagianthus regius was the least vulnerable. Our findings imply that it is potentially valuable to keep exploring the use of π_O as a drought indicator and that the effort required to measure some physiological traits, such as water potential, may be essential to consider plant drought responses and to predict π_O.     

Inhibierungserscheinungen bei der alkoholishchen Gärung III. Der Einfluß des osmotischen Druckes auf die Lebensfähigkeit von Saccharomyces cerevisiae

The influence of the osmotic pressure on the viability of yeast cells was studied in batch processes. It could be found, that the viability is a function of the total osmotic pressure obtained by adding the partial osmotic values of the principal ingredients saccharose, ethanol and salts dissolved in the medium. At optimum process conditions (pH, T, etc.) the cells can tolerate the osmotic pressure up to fixed value π₁. Above π₁ the viability decreases linearly and upward of a second threshold value π₂ nonlinearly. In the case of the used strain Saccharomyces cerevisiae Hansen Sc 5 the values of the both points are π₁ = 25 atm and π₂ = 47 atm.     

The protonated 2-halogenated imidazolium cation as the noncovalent interaction donor: the σ-hole and π-hole interactions

The σ-hole and π-hole of the protonated 2-halogenated imidazolium cation (XC₃H₄N₂ ⁺; X = F, Cl, Br, I) were investigated and analyzed. The monomers of (CH₃)₃SiY(Y=F, Cl, Br, I), considered as the Lewis base, were combined with the σ-hole and π-hole of XC₃H₄N₂ ⁺ to form the σ-hole and π-hole interactions in the bimolecular complexes (CH₃)₃SiY?·?·?·?XC₃H₄N₂ ⁺ and (CH₃)₃SiY?·?·?·?C₃(X)H₄N₂ ⁺(X/Y=F, Cl, Br, I), respectively. For both the σ-hole and π-hole interactions, the equilibrium geometries of complexes show regular changes according to the sequence of heavy sequence of the noncovalent interaction acceptors and donors. The electrostatic energy is the main contribution in the formation of both kinds of interactions, it has linear relations with the V _S,max values of σ-hole and the V′ _S,max values of π-hole. Both the σ-hole and π-hole interactions belong to the closed-shell and noncovalent interactions. The π-hole interactions are stronger than the σ-hole interactions. For the π-hole interactions, the contribution percents of the dispersion energies are somewhat greater than those of the σ-hole interactions, while it is contrary for the polarization energy.

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Graphical Abstract The protonated 2-halogenated imidazolium cation as the noncovalent interaction donor: the σ-hole and π-hole interactions?

     

Life in Its Uniqueness Remains Difficult to Define in Scientific Terms

Abstract

The crystal structure of the dehydro octapeptide Boc-Val-ΔPhe-Phe-Ala-Leu-Ala-ΔPhe-Leu-OH has been determined to atomic resolution by X-ray crystallographic methods. The crystals grown by slow evaporation of peptide solution in methanol/water are orthorhombic, space group P2₁2₁2₁. The unit cell parameters are a= 8.404 (3), b= 25.598(2) and c = 27.946(3) Å, Z=4. The agreement factor is R= 7.58% for 3636 reflections having (IF₀I) ≥ 3σ (IF₀I). The peptide molecule is characterised by a 3₁₀-helix at the N-terminus and a π-turn at the C-terminus. This conformation is exactly similar to the helix termination features observed in proteins. The π-turn conformation observed in the octapeptide is in good agreement with the conformational features of π-turns seen in some proteins. The α_L-position in the π-turn of the octapeptide is occupied by ΔPhe⁷, which shows that even bulky residues can be accommodated in this position of the π-turns. In proteins, it is generally seen that aL- position is occupied by glycine residue. No intermolecular head-to-tail hydrogen bonds are observed in solid state structure of the octapeptide. A water molecule located in the unit cell of the peptide molecule is mainly used to hold the peptide molecule together in the crystal. The conformation observed for the octapeptide might be useful to understand the helix termination and chain reversal in proteins and to construct helix terminators for denovo protein design.     

Sequential Classification Based on Regression

Let us consider m general populations π₁, …,π_m. Each object belonging to these populations is represented by (p ± 1) characteristics x₁, x₂,…,x_p,y. A certain object, which is an element of one of the m general populations π₁,…,π_m has to be classified into the correct population. It will be assumed that knowledge of the value of the characteristic y would permit its correct classification, but that the observation of this characteristic is expensive, difficult or dangerous, as e.g. in medical applications. y is correlated with a set of p characteristics x₁,x₂,…,x_p, which are observed sequentially. The classification procedure is based on the division of the space of the observed value of characteristics x₁,x₂,…,x_p into nonintersecting areas determined so as to minimize the value of BAYES' risk given by equation (3).     

Synthesis and characterization of Pt(II) and Pt(II)/Ru(II) complexes with the bidentate bridging ligand dipyrido(2,3-a:3′,2′-h)phenazine (dpop)

Three new complexes [Pt(dpop)(Cl)₂], [(Cl)₂Pt(dpop)Pt(Cl)₂] and [(bpy)₂Ru(dpop)Pt(Cl)₂](PF₆)₂ (dpop = dipyrido(2,3-a:3′,2′-h)phenazine) were prepared and studied. The electronic absorption spectra of the complexes display Pt dπ → dpop π* and Ru dπ → dpop π* MLCT transitions at longer wavelengths than for previously reported similar complexes. Results of cyclic voltammograms show reversible dpop centered reductions while for the mixed metal [(bpy)₂Ru(dpop)Pt(Cl)₂]²⁺ an irreversible Pt(II) oxidative wave precedes the Ru(II) oxidation/reduction couple. Spectroelectrochemical results show that all oxidative and reductive processes are completely reversible. The [(Cl)₂Pt(dpop)Pt(Cl)₂] complex cleaves in solution with pseudo-first order kinetics resulting in loss of the Pt dπ → dpop π* MLCT transition at 545 nm.     

Crystal packing driven by metal-ligand interactions, hydrogen bonds, π-π stacking and anion-π stacking

Two polymeric copper(II) compounds have been synthesized with the ligand bis(pyrimidin-2yl)amine (dipm), by means of coordination bonds, Watson-Crick type hydrogen bond interactions and π-π stacking. Both supramolecules hold the same cationic building block, namely [Cu(dipm)₂(H₂O)₂]²⁺. However, their crystal structure significantly differs and this variation apparently arises from the nature of the anion which induces dissimilar crystal packings. The crystal growth is driven by several synergistic intermolecular interactions, i.e., coordination and hydrogen bonds, π-π and anion-π stacks.     

A Robust Method for Large‐Scale Multiple Hypotheses Testing

When drawing large‐scale simultaneous inference, such as in genomics and imaging problems, multiplicity adjustments should be made, since, otherwise, one would be faced with an inflated type I error. Numerous methods are available to estimate the proportion of true null hypotheses π₀, among a large number of hypotheses tested. Many methods implicitly assume that the π₀ is large, that is, close to 1. However, in practice, mid‐range π₀ values are frequently encountered and many of the widely used methods tend to produce highly variable or biased estimates of π₀. As a remedy in such situations, we propose a hierarchical Bayesian model that produces an estimator of π₀ that exhibits considerably less bias and is more stable. Simulation studies seem indicative of good method performance even when low‐to‐moderate correlation exists among test statistics. Method performance is assessed in simulated settings and its practical usefulness is illustrated in an application to a type II diabetes study.     

Photophysical properties, X-ray structures, electrochemistry, and DFT computational chemistry of osmium complexes

We report the synthesis of phosphorescent divalent osmium complexes of the form [Os(N-N)₂(L-L) or Os(L-L)₂(N-N)]²⁺ (PF₆)₂ where N-N is a derivative of 1,10-phenanthroline, and L-L is a diarsine or diphosphine ligand: 1,2-bis(dimethylphosphino)ethane, 1,2-bis(dicyclohexylphosphino)ethane, or 1,2-bis(dimethylarseno)benzene. X-ray structures have been determined, luminescent and electrochemical properties have been measured and DFT calculations have been performed on the complexes. The emission lifetime of complexes of structure Os(II)(L-L)₂(N-N) are longer than the those of Os(II)(N-N)₂(L-L). The DFT calculations show that there is significant mixing of the π−π^∗ into the dπ−π^∗ charge-transfer state for the complexes of the form Os(II)(L-L)₂(N-N) resulting in a longer lived excited state. Through DFT calculations we were able to conclude that the HOMO of the complexes is a d orbital on the osmium while the LUMO is the b₁(ψ) π^∗ system of the phenanthroline. However, we found that the HOMO did not have the correct symmetry to enable strong charge transfer to the phenanthroline to be observed, and the strong MLCT transition observed in the spectra is the metal d HOMO(−1) to the b1 π^∗ LUMO of the phenanthroline.     

Two new supermolecular structures of organic-inorganic hybrid compounds: [Zn(phen)(SO4)(H2O)2]n and [Cu(phen)(H2O)2] · SO4 (phen = 1,10-phenanthroline)

Two new organic-inorganic hybrid compounds [Zn(phen)(SO₄)(H₂O)₂]_n (1) and [Cu(phen)(H₂O)₂] · SO₄ (2) have been prepared by conventional aqueous solution synthesis and characterized by single-crystal X-ray diffraction, IR spectroscopy, thermal gravimetric analysis (TGA) and fluorescent spectroscopy. In compound 1, the sulfate group adopts bidentate mode to coordinate with two Zn(II) ions to form one-dimensional polymer. The one-dimensional polymers are further linked together via the intermolecular hydrogen-bonding and π-π stacking interactions to form a 3D supramolecular framework. Compound 2 is build up of discrete [Cu(phen)(H₂O]²⁺ cations and SO₄²⁻ anions to form a three-dimensional framework via hydrogen-bonding and π-π stacking interactions. Furthermore, the luminescent properties of both 1 and 2 were studied. The complexes 1 and 2 excited at 280 nm wavelength produced characteristic luminescence features, arising maybe due to the π-π transitions.     

The role of protein and porphyrin in the reactivity of horseradish peroxidase toward hydrogen donors.

The electronic ground state of the peroxidase compound I π-cation radical has been changed from ²A_2u to ²A_1u by substituting deuterohemin for the protohemin of the native enzyme. Although the ²A_1u ground state is the same one as that taken by the catalase compound I π-cation radical deuterohemin horseradish peroxidase possesses no catalase activity. It thus appears that the protein and not only the ground state of the compound I π-cation radical determines the reactivities of compounds I of horseradish peroxidase toward hydrogen donors.     

On the electron delocalization in cyclopropenylidenes - An experimental charge-density approach

The extent and nature of cyclic electron delocalization in free and coordinated cyclopropenylidene carbenes has been analyzed by combined experimental and theoretical charge-density studies. The significant asymmetry of the C-C bond lengths in substituted cyclopropenylidene carbenes was identified as cooperative effect which depends on contributions of both σ- and π-bonding. We show that analyses of (i) the topology of the Laplacian of the electron density distribution and (ii) the out-of-plane atomic quadrupole moments - the charge-density analogues of p_π occupation - allow to distinguish between the influence of σ- and π-electrons on cyclic electron delocalization. These studies hint for pronounced electron localization in the carbene lone pair region which dominates the electronic structure of free cyclopropenylidene carbenes and hinders the establishment of true aromaticity. We further investigated the electron donating/withdrawing ability of cyclopropenylidene ligands relative to N-heterocyclic carbenes. The experimental benchmark systems LCr(CO)₅ (L = 2,3-diphenylcyclopropenylidene and 1,2-dimethylimidazol-2-ylidene) show that the cyclopropenylidene ligand clearly displays the higher π-acceptor capability relative to N-heterocyclic carbenes.     

Rhodium paddlewheel dimers containing the π···π stacking, 1,8-naphthalimide supramolecular synthon

The bifunctional ligand 3-(1,8-naphthalimido)propanoate (L_C2⁻), which contains a carboxylate group linked to the robust π···π stacking 1,8-naphthalimide supramolecular synthon, has been used to prepare two new rhodium carboxylate dimer complexes, [Rh₂(L_C2)₄(DMF)₂] (1) and [Rh₂(L_C2)₄(py)₂]·3DMF (2). Both complexes have been structurally characterized and contain the Rh₂(O₂CR)₄ paddlewheel core, but have different axial ligands. The four naphthalimide side arms in the carboxylate ligands are arranged in the square shape imposed by the SBU in complex 1, but are bent in 2. In both cases, the supramolecular structure is organized into one-dimensional chains by strong π···π stacking interactions between only two of the 1,8-naphthalimide moieties on each dimeric unit. In 1, the other naphthalimide units do not interact strongly and in 2 they intramolecularly π···π stack with the adjacent axial pyridine molecules.     

Theoretical π-π* absorption and circular dichroic spectra of polypeptide β-structures

Absorption and circular dichroic (CD) spectra of the π-π* transition near 200 nm are calculated for poly(Gly), poly(Ala), poly(Abu), and poly(Val) in the β_P (paralle) and β_A (antiparallel) pleated-sheet structures using the dipole interaction model and including interactions among all atoms; optical parameters were obtained from previous studies of related molecules. Most of the calculations are for structures with one or three chains of six residues each. The oscillator strength and splitting of the π-π* modes are found to be affected only to a small extent by variations in side-chain structure and conformation, whereas the CD spectrum is very sensitive to these variations. Poly(Gly) and poly(Ala) β-structures in uniform, planar lattices do not show sufficient rotational strength to account for observed CD spectra. Poly(Abu) and poly(Val) β-structures in uniform, planar lattices show rotational strengths comparable to experiment when χ¹ is near ?60° for β_A-structures or in a broad range near 140° for β_P-structures. Poly(Ala) in uniformly twisted β_A- and β_P-structures or in irregular β_A-structures corresponding to regions of the crystal structure of concanavalin A also show enhanced rotational strengths in the principal π-π* CD band. Absorption and CD spectra calculated for poly(Abu) in uniform β_A- and β_P-structures are compared with experimental data on poly(Lys) in the β-form, assuming side-chain conformations in Abu that maximize the intensity of the principal CD band. The calculations for the β_A-form show the better agreement with experiment for both types of spectra.     

Structure-activity relationships in papain and bromelain ligand interactions

The parameters K_m and k_cat were determined for 16 methyl hippurates (CH₃OCOCH₂NHCOC₆H₄-X) hydrolyzed by papain. A simple linear relationship is found between log $\text{1}\text{K}{}_{\mathrm{m}}$ and the hydrophobic substituent constant π. It is found that log k_cat is parabolically related to π. The results with papain are compared with results obtained by Hawkins and Williams with the enzyme bromelain. The two enzymes behave in a similar fashion.     

Theoretical study on <Emphasis Type="Italic">p</Emphasis>-type D-π-A sensitizers with modified π-spacers for dye-sensitized solar cells

Based on a prototype sensitizer W2, we designed triarylamine-based p-type sensitizers W2-1 to W2-7 that contain modified π-spacers (π'), a π-spacer and two anchors. For W2-1 to W2-4, instead of 2,1,3-benzothiadiazole in W2, thieno[3,4-b]-1,4-dioxin, thiophene, thieno[3,4-c][1,2,5]thiadizole, thiazolo[5,4-d]thiazole are π' and thiophene as π-spacer. For W2-5 to W2-8, π' and π are same, with 2,1,3-benzothiadiazole, thieno[3,4-b]-1,4-dioxin, thieno[3,4-c][1,2,5]thiadiazo, thiazolo[5,4-d]thiazole, respectively, as the π'-spacers. Structure optimization, electronic level and absorption characters were calculated with density functional theory (DFT) and time-dependent DFT (TDDFT) at the CAM-B3LYP/6-311G (d,p). The solvent effect was involved using a polarized continuum model in chloroform. The results showed that the highest occupied molecular orbital and the lowest unoccupied molecular orbital guarantee sufficient hole injection (lower than –0.2 eV), and dye regeneration (lower than –0.2 eV). W2-4 has higher light-harvesting efficiency (LHE) (0.994) and larger overlap with the visible light from 400 nm to 600 nm. Finally, the results suggest that the driving force of hole injection, dye regeneration and charge recombination (ΔG_inj, ΔG_reg and ΔG_CR) of W2-4 are the best, with more negative ΔG_inj (–4.33), ΔG_reg (–1.74) and more positive ΔG_CR (1.92). Replacing 2,1,3-benzothiadiazole with thiazolo[5,4-d]thiazole as π'-spacers is a effective way to improve the performance of the dyes. An introduction of thiazolo[5,4-d]thiazole group can improve the absorption ability and hinder charge recombination.

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Graphical abstract Absorption spectra of p-type D-π-A sensitizers with modified π-spacers

     

Synthesis, structure and luminescence study of two cadmium(II) coordination polymers with hetero donor ligands: Expansion of network dimensionality from 2D to 3D through hydrogen bonding

Two coordination polymers of cadmium with formula [Cd(pyp)₂(H₂O)₂]_n (1) and {[Cd₂(pyzca)₃(atr)(H₂O)]·H₂O}_n (2) [pypH = 3-pyridinepropionic acid, pyzcaH = 2-pyrazinecarboxylic acid and atrH = 5-aminotetrazole] have been synthesized and structurally characterized by X-ray single crystal diffraction analysis. Both complexes display 2D structures that extend into a 3D network by means of hydrogen bonding. The crystal packing of both complexes is reinforced by π-π interactions between adjacent aromatic rings. The fluorescence study indicates intraligand π-π* charge transfer, which is the reason for emission in both the complexes.     

Synthesis and crystal structures of mono- and dinuclear silver(I) complexes bearing 1,8-naphthyridine ligand

Mononuclear and dinuclear silver(I) complexes bearing 1,8-naphthyridine (napy) were prepared. The crystal structures of [Ag(napy-κN)₂](PF₆) (1) and [Ag₂(μ-napy)₂](PF₆)₂ · 3CH₃CN (2 · 3CH₃CN) were determined by X-ray diffraction studies. In complex 1, intermolecular π-π interaction of napy ligands between neighboring molecules forms left-handed hexagonal columns in the solid state. On the other hand, two napy ligands bridging two Ag ions in the dinuclear complex 2 shape a face-to-face π-π stacking with those of the neighboring molecule to form the dimeric unit. Besides, two of four napy ligands, which are located in a diagonal position in the dimeric unit, build intermolecular back-to-back π-π stackings with those of the adjacent dimeric unit, and a ladder-like stairway structure is generated in the solid state. Irrespective of such characteristic structures of 1 and 2 in the solid state, both complexes show very rapid dynamic behavior in solutions. No conversion between 1 and 2 took place even in the presence of excess amounts of Ag⁺ or napy in solutions.