An Entropy-Based Tool to Help the Interpretation of Common-Factor Spaces in Factor Analysis

This paper proposes a method for deriving interpretable common factors based on canonical correlation analysis applied to the vectors of common factors and manifest variables in the factor analysis model. First, an entropy-based method for measuring factor contributions is reviewed. Second, the entropy-based contribution measure of the common-factor vector is decomposed into those of canonical common factors, and it is also shown that the importance order of factors is that of their canonical correlation coefficients. Third, the method is applied to derive interpretable common factors. Numerical examples are provided to demonstrate the usefulness of the present approach.     

The Quantum Regularization of Singular Black-Hole Solutions in Covariant Quantum Gravity

An excruciating issue that arises in mathematical, theoretical and astro-physics concerns the possibility of regularizing classical singular black hole solutions of general relativity by means of quantum theory. The problem is posed here in the context of a manifestly covariant approach to quantum gravity. Provided a non-vanishing quantum cosmological constant is present, here it is proved how a regular background space-time metric tensor can be obtained starting from a singular one. This is obtained by constructing suitable scale-transformed and conformal solutions for the metric tensor in which the conformal scale form factor is determined uniquely by the quantum Hamilton equations underlying the quantum gravitational field dynamics.     

EEG Fractal Analysis Reflects Brain Impairment after Stroke

Stroke is the commonest cause of disability. Novel treatments require an improved understanding of the underlying mechanisms of recovery. Fractal approaches have demonstrated that a single metric can describe the complexity of seemingly random fluctuations of physiological signals. We hypothesize that fractal algorithms applied to electroencephalographic (EEG) signals may track brain impairment after stroke. Sixteen stroke survivors were studied in the hyperacute (<48 h) and in the acute phase (∼1 week after stroke), and 35 stroke survivors during the early subacute phase (from 8 days to 32 days and after ∼2 months after stroke): We compared resting-state EEG fractal changes using fractal measures (i.e., Higuchi Index, Tortuosity) with 11 healthy controls. Both Higuchi index and Tortuosity values were significantly lower after a stroke throughout the acute and early subacute stage compared to healthy subjects, reflecting a brain activity which is significantly less complex. These indices may be promising metrics to track behavioral changes in the very early stage after stroke. Our findings might contribute to the neurorehabilitation quest in identifying reliable biomarkers for a better tailoring of rehabilitation pathways.     

New insights into the seleniranium ion promoted cyclization of prenyl and propenylbenzene aryl ethers

The chromane core is widely represented in nature being part of a wide array of secondary metabolites of plant, fungal, and bacterial origin. In this paper an improved method for the chemical synthesis of differently substituted chromanes is described. Substituted 2H-1-benzopyrans have been synthesized in good to excellent yields (52–81%) by treatment of 3,3-dimethylallyl and propenylbenzene ethers of differently substituted phenols with phenylselenyl chloride.     

High-pressure investigations under CO/H2 of rhodium complexes containing hemispherical diphosphites

The two rhodium complexes [Rh(acac)(L(R))] (L(R)=(S,S)-5,11,17,23-tetra-tert-butyl-25,27-di(OR)-26,28-bis(1,1'-binaphthyl-2,2'-dioxyphosphanyloxy)calix[4]arene; 6: R=benzyl, 7: R=fluorenyl), each based on a hemispherical chelator forming a pocket about the metal centre upon chelation, are active in the hydroformylation of 1-octene and styrene. As expected for this family of diphosphanes, both complexes resulted in remarkably high selectivity towards the linear aldehyde in the hydroformylation of 1-octene (l/b≈15 for both complexes). Linear aldehyde selectivity was also observed when using styrene, but surprisingly only 6 displayed a marked preference for the linear product (l/b=12.4 (6) vs. 1.9 (7)). A detailed study of the structure of the complexes under CO or CO/H(2) in toluene was performed by high-pressure NMR (HP NMR) and FT-IR (HP-IR) spectroscopies. The spectroscopic data revealed that treatment of 6 with CO gave [Rh(acac)(CO)(η(1)-L(benzyl))] (8), in which the diphosphite behaves as a unidentate ligand. Subsequent addition of H(2) to the solution resulted in a well-defined chelate complex with the formula [RhH(CO)(2)(L(benzyl))] (9). Unlike 6, treatment of complex 7 with CO only led to ligand dissociation and concomitant formation of [Rh(acac)(CO)(2)], but upon addition of H(2) a chelate complex analogous to 9 was formed quantitatively. In both [RhH(CO)(2)(L(R))] complexes the diphosphite adopts the bis-equatorial coordination mode, a structural feature known to favour the formation of linear aldehydes. As revealed by variable-temperature NMR spectroscopy, these complexes show the typical fluxionality of trigonal bipyramidal [RhH(CO)(2)(diphosphane)] complexes. The lower linear selectivity of 7 versus 6 in the hydroformylation of styrene was assigned to steric effects, due to the pocket in which the catalysis takes place being less adapted to accommodate CO or larger olefins and, therefore, possibly leading to facile ligand decoordination. This interpretation was corroborated by an X-ray structure determination carried out for 7.     

Catalytic reaction mechanism of Mn-doped nanoporous aluminophosphates for the aerobic oxidation of hydrocarbons

In this work we apply state-of-the-art electronic-structure-based computational methods based on hybrid-exchange density functional theory to study the mechanism of the aerobic oxidation of hydrocarbons catalysed by Mn-doped nanoporous aluminophosphates (Mn-AlPOs). We compare our results with available experimental data. We show that the catalytic efficiency of Mn-AlPOs in oxidation reactions is intrinsically linked to 1) the Mn redox activity, in particular between 2+ and 3+ oxidation states, and 2) the coordinative insaturation of tetrahedral Mn embedded in AlPO frameworks, which facilitates the reaction by stabilising oxo-type radicals through the formation of Mn complexes. Our mechanism demonstrates the crucial role of both Mn(III) and Mn(II) in the reaction mechanism: Mn(III) sites undergo an initial reaction cycle that leads to the production of the alkyl hydroperoxide intermediate, which can only be transformed into the oxidative products (alcohol, aldehyde and acid) by Mn(II). A preactivation step is required to yield the reduced Mn(II) sites able to decompose the hydroperoxide intermediates; this step takes place through a transformation of the hydrocarbon into the corresponding peroxo-derivative, stabilised by forming a complex with Mn(III) and yielding at the same time reduced Mn(II) sites. Both species enter a subsequent propagation cycle in which Mn(II) catalyses the dissociation of the hydroperoxide that proceeds until the formation of the oxidative products by two parallel pathways, through alkoxy- or hydroxy-radical-like intermediates, whilst the Mn(III)-peroxo complex enables further production of the hydroperoxide intermediate.     

Solid-state (15)N CPMAS NMR and computational analysis of ligand hapticity in rhodium(η-diene) poly(pyrazolyl)borate complexes

Novel [Rh(η-diene)Tp(x)] complexes of sterically encumbered Tp(x) ligands (Tp(x) = Tp(4Bo), diene = cod, 1; nbd, 2; Tp(x) = Tp(4Bo,5Me), diene = cod, 3; nbd, 4; Tp(x) = Tp(a,3Me), diene = cod, 5; nbd, 6; Tp(x) = Tp(a*,3Me), diene = cod, 7; nbd, 8) have been prepared by treatment of [Rh(η-diene)(μ-Cl)](2) with TlTp(x) (Tp(x) in general, in detail: Tp(4Bo) = hydrotris(indazol-1-yl)borate, Tp(4Bo,5Me) = hydrotris(5-methyl-indazol-1-yl)borate, Tp(a,3Me) = hydrotris(3-methyl-2H-benz[g]-4,5-dihydroindazol-2-y1)borate, Tp(a*,3Me) = hydrotris(3-methyl-2H-benz[g]indazol-2-yl)borate), and characterized by analytical and spectral data (IR, (1)H, (11)B, and (13)C NMR solution). The structures adopted by [Rh(nbd)Tp(4Bo)] 2, [Rh(cod)Tp(4Bo,5Me)] 3, [Rh(nbd)Tp(a,3Me)] 6, [Rh(nbd)Tp(a*,3Me)] 8, and [Rh(nbd)Tp(a*,3Me*)] 8* (incorporating a borotropomeric ligand), have been investigated. Low steric hindrance between the ligands in 2 and 3 permits κ(3) coordination of the pyrazolylborate while the high steric encumbrance present in 6, 8, and 8* results in κ(2) ligands. The coordination modes of the ligands to the metal have also been established by (15)N CPMAS studies of selected ligands and their corresponding Rh complexes. These spectroscopic data are in agreement with the (15)N chemical shifts obtained by using quantum-chemical methods to assist reliable assignments of the experimental values, affording new insights into the extraction of structural information concerning the hapticity (κ(2) or κ(3)) of the poly(pyrazolyl)borate ligands to the Rh metal.     

Photo-induced pyridine substitution in cis-[Ru(bpy)(2)(py)(2)]Cl(2): a snapshot by time-resolved X-ray solution scattering

Determination of transient structures in light-induced processes is a challenging goal for time-resolved techniques. Such techniques are becoming successful in detecting ultrafast structural changes in molecules and do not require the presence of probe-like groups. Here, we demonstrate that TR-WAXS (Time-Resolved Wide Angle X-ray Scattering) can be successfully employed to study the photochemistry of cis-[Ru(bpy)(2)(py)(2)]Cl(2), a mononuclear ruthenium complex of interest in the field of photoactivatable anticancer agents. TR-WAXS is able to detect the release of a pyridine ligand and the coordination of a solvent molecule on a faster timescale than 800 ns of laser excitation. The direct measurement of the photodissociation of pyridine is a major advance in the field of time-resolved techniques allowing detection, for the first time, of the release of a multiatomic ligand formed by low Z atoms. These data demonstrate that TR-WAXS is a powerful technique for studying rapid ligand substitution processes involving photoactive metal complexes of biological interest.     

Characterization of Acacia mangium polyflavonoid tannins by MALDI-TOF mass spectrometry and CP-MAS C NMR

The MALDI-TOF mass spectrometry (MS) and solid state CP-MAS ¹³C Nuclear Magnetic Resonance (NMR) spectroscopic technique were introduced to characterize Acacia mangium tannin (condensed tannins). The MALDI-TOF MS illustrated a series of peaks corresponding to oligomers of condensed tannins of up to 11 flavonoid units (3200 Da). A. mangium condensed tannins were found to consist predominantly of prorobinetinidin combined with profisetinidin and prodelphinidin. Both the MALDI-TOF mass spectra and the solid state CP-MAS ¹³C NMR indicated that the A. mangium tannins obtained from Kudat, had an almost completely linear structure; In addition, Lembah Beringin, consist of “angular” polymer structure; and Tawau, has included “twice-angular” polymer structures present in oligomers type of up to 7 flavonoid units. The high degree of polymerization of linear, angular type, twice-angular structures and longer oligomer (3200 Da) chains have not been observed in previous studies of condensed tannins. The spectra also indicated that A. mangium tannins are more heavily branched and have higher degree of polymerization (>7.0) compared to commercial mimosa (A. mearnsii) tannin (4.9). Because tannins are phenolic, it was expected that they can be used to replace phenol-formaldehyde (PF) adhesives.