Multicriteria decision making under uncertainty

Formalization for problems of multicriteria decision making under uncertainty is constructed in terms of guaranteed and weak estimates. A relevant definition of the vector maximinimax value is given. Parameterization and approximation of maximum, minimax, and maximinimax values based on the inverse logical convolution are suggested. An application for multicommodity networks is considered. Received: December 13, 2000 / Accepted: August 21, 2001?Published online May 8, 2002     

Non-Convex Global Minimization and False Discovery Rate Control for the TREX

The TREX is a recently introduced method for performing sparse high-dimensional regression. Despite its statistical promise as an alternative to the lasso, square-root lasso, and scaled lasso, the TREX is computationally challenging in that it requires solving a nonconvex optimization problem. This article shows a remarkable result: despite the nonconvexity of the TREX problem, there exists a polynomial-time algorithm that is guaranteed to find the global minimum. This result adds the TREX to a very short list of nonconvex optimization problems that can be globally optimized (principal components analysis being a famous example). After deriving and developing this new approach, we demonstrate that (i) the ability of the preexisting TREX heuristic to reach the global minimum is strongly dependent on the difficulty of the underlying statistical problem, (ii) the new polynomial-time algorithm for TREX permits a novel variable ranking and selection scheme, (iii) this scheme can be incorporated into a rule that controls the false discovery rate (FDR) of included features in the model. To achieve this last aim, we provide an extension of the results of Barber and Candes to establish that the knockoff filter framework can be applied to the TREX. This investigation thus provides both a rare case study of a heuristic for nonconvex optimization and a novel way of exploiting nonconvexity for statistical inference.     

Surprisingly slow reaction of dimethylsilylene with dimethylgermane: time-resolved kinetic studies and related quantum chemical calculations

Time-resolved studies of silylene, SiH2, and dimethylsilylene, SiMe2, generated by the 193 nm laser flash photolysis of appropriate precursor molecules have been carried out to obtain rate constants for their bimolecular reactions with dimethylgermane, Me2GeH2, in the gas phase. SiMe2 + Me2GeH2 was studied at five temperatures in the range 299-555 K. Problems of substrate UV absorption at 193 nm at temperatures above 400 K meant that only three temperatures could be used reliably for rate constant measurement. These rate constants gave the Arrhenius parameters log(A/cm3 molecule(-1) s(-1)) = -13.25 +/- 0.16 and E(a) = -(5.01 +/- 1.01) kJ mol(-1). Only room temperature studies of SiH2 were carried out. These gave values of (4.05 +/- 0.06) x 10(-10) cm3 molecule(-1) s(-1) (SiH2 + Me2GeH2 at 295 K) and also (4.41 +/- 0.07) x 10(-10) cm3 molecule(-1) s(-1) (SiH2 + MeGeH3 at 296 K). Rate constant comparisons show the surprising result that SiMe2 reacts 12.5 times slower with Me2GeH2 than with Me2SiH2. Quantum chemical calculations (G2(MP2,SVP)//B3LYP level) of the model Si-H and Ge-H insertion processes of SiMe2 with SiH4/MeSiH3 and GeH4/MeGeH3 support these findings and show that the lower reactivity of SiMe2 with Ge-H bonds is caused by a higher secondary barrier for rearrangement of the initially formed complexes. Full details of the structures of intermediate complexes and the discussion of their stabilities are given in the paper. Other, related, comparisons of silylene reactivity are also presented.     

Synthesis,Structure and Molecular Docking of New 4,5-Dihydrothiazole Derivatives Based on 3,5-Dimethylpyrazole and Cytisine and Salsoline Alkaloids

The interaction results of 1,2-dibromo-3-isothiocyanatopropane with some pyrazoles as well as cytisine and salsoline alkaloids were presented in this paper. It was shown that the reaction resulted in one one-step and rather mild method for the preparation of the corresponding 1,3-thiazoline bromomethyl derivatives. The yield of this reaction was affected by the presence of a base and an order in which reagents were added. Molecular docking of the synthesized 1,3-thiazoline derivatives for putative antibacterial activity was carried out using the penicillin-binding target protein (PBP4) of the bacteria E. coli “Homo sapiens” and S. aureus “Homo sapiens” as an example. Molecular docking demonstrated that the compounds had insignificant binding energies at the level of selected reference drugs (Cephalotin and Chloramphenicol). The presence of natural alkaloids in the structure of thiazoline derivatives somewhat increased the affinity of these substrates for target proteins selected.     

Unexpectedly low affinity of aromatic disulfides for π-stacking interactions of the arene-polyfluoroarene type

1,2,3,4,5-Pentafluorodiphenyl disulfide (1) was synthesized from C₆F₅SCl and C₆H₅SSiMe₃ in quantitative yield. The homo-crystals of disulfide 1 and co-crystals of 1,1′,2,2′,3,3′,4,4′,5,5′-decafluorodiphenyl disulfide (2) with naphthalene (stoichiometry 1:2, complex 4) and diphenyl disulfide (3) with octafluoronaphthalene (stoichiometry 2:1, complex 5) were prepared followed by XRD characterization. In the crystal lattice of 1, face-to-face and face-to-edge Ph_H/Ph_F orientations of neighboring rings were observed together with face-to-edge Ph_F/Ph_F orientations. For the face-to-face Ph_H/Ph_F orientation, the large offset of Ph_H and Ph_F groups excludes their π-stacking interaction which is very non-typical of the field. The crystal lattice of 4 reveals standard π-stacking interactions of the arene-polyfluoroarene type. While in the lattice of 4 each Ph_F ring interacts alternating with naphthalenes, in 5 two disulfides 3 are bridged by one octafluoronaphthalene with only one of the Ph_H rings of each disulfide interacting with the polyfluoroarene π-system. The large offset of neighboring molecules excludes however their π-stacking interactions in complex 5. An attempt to prepare 2/3 co-crystals failed.     

Microwave-assisted three-component synthesis of 7-aryl-2-alkylthio-4,7-dihydro-1,2,4-triazolo[1,5-a]-pyrimidine-6-carboxamides and their selective reduction

Multicomponent reactions (MCRs) and microwave-assisted organic synthesis (MAOS) have been used as key methods for the synthesis of fused dihydropyrimidine derivatives. The three-component condensation of 3-amino-5-alkylthio-1,2,4-triazoles with aromatic aldehydes and acetoacetamides under microwave irradiation was developed as a rapid and efficient solution-phase method for the high-yielding preparation of 7-aryl-2-alkylthio-4,7-dihydro-1,2,4-triazolo[1,5-a]pyrimidine-6-carboxamide libraries. In addition, the selective reduction of the formed dihydrotriazolopyrimidines to trans-trans-2-alkylthio-7-aryl-4,5,6,7-tetrahydro-1,2,4-triazolo[1,5-a]pyrimidine-6-carboxamides was established. The described synthetic protocols provide rapid access to novel and diversely substituted dihydroazolopyrimidine libraries.     

Excited-state absorption properties of platinum(II) terpyridyl acetylides

A comprehensive photophysical study is presented which compares the ground- and excited-state properties of four platinum(II) terpyridyl acetylide compounds of the general formula [Pt(tBu3tpy)(CCR)]+, where tBu3tpy is 4,4',4' '-tri-tert-butyl-2,2':6',2' '-terpyridine and R is an alkyl or aryl group. [Ru(tBu3tpy)3]2+ and the pivotal synthetic precursor [Pt(tBu3tpy)Cl]+ were also investigated in the current work. The latter two complexes possess short excited-state lifetimes and were investigated using ultrafast spectrometry while the other four compounds were evaluated using conventional nanosecond transient-absorption spectroscopy. The original intention of this study was to comprehend the nature of the impressive excited-state absorptions that emanate from this class of transition-metal chromophores. Transient-absorbance-difference spectra across the series contain the same salient features, which are modulated only slightly in wavelength and markedly in intensity as a function of the appended acetylide ligand. More intense absorption transients are observed in the arylacetylide structures relative to those bearing an alkylacetylide, consistent with transitions coupled to the pi system of the ancillary ligand. Reductive spectroelectrochemical measurements successfully generated the electronic spectrum of the tBu3tpy radical anion in all six complexes at room temperature. These measurements confirm that electronic absorptions associated with the tBu3tpy radical anion simply do not account for the intense optical transitions observed in the excited state of the Pt(II) chromophores. Transient-trapping experiments using the spectroscopically silent reductive quencher DABCO clearly demonstrate the loss of most transient-absorption features in the acetylide complexes throughout the UV, visible, and near-IR regions following bimolecular excited-state electron transfer, suggesting that these features are strongly tied to the photogenerated hole which is delocalized across the Pt center and the ancillary acetylide ligand.     

Organometallic complexes as hole-transporting materials in organic light-emitting diodes

The use of metal complexes fac-tris(1-phenylpyrazolato-N,C(2)('))cobalt(III) [fac-Co(ppz)(3)], fac-tris(2-phenylpyridinato-N,C(2)(') cobalt(III) [fac-Co(ppy)(3)], and [tris[2-((pyrrole-2-ylmethylidene)amino)ethyl]amine]gallium(III) [Ga(pma)] as materials for hole-transporting layers (HTL) in organic light-emitting diodes (OLEDs) is reported. Co(ppz)(3) and Co(ppy)(3) were prepared by following literature procedures and isolated as mixtures of facial (fac) and meridional (mer) isomers. The more stable fac isomers were separated from the unstable mer forms via column chromatography and thermal gradient sublimation. Crystals of fac-Co(ppz)(3) are monoclinic, space group P2(1)/c, with a = 13.6121(12) A, b = 15.5600(12) A, c = 22.9603(17) A, beta = 100.5 degrees, V = 4781.3(7) A(3), and Z = 8. [Tris[2-((pyrrol-2-ylmethylidene)amino)ethyl]amine]gallium [Ga(pma)] was prepared by the reaction of gallium(III) nitrate with the pmaH(3) ligand precursor in methanol. Ga(pma) crystallizes in the cubic space group I3d with cell parameters a = 20.2377(4) A, b = 20.2377(4) A, c = 20.2377(4) A, beta = 90.0 degrees, V = 8288.6(3) A(3), and Z = 16. These cobalt and gallium complexes are pale colored to colorless solids, with optical energy gaps ranging 2.6-3.36 eV. A two-layer HTL/ETL (ETL = electron-transporting layer) device structure using fac-Co(ppz)(3) and fac-Co(ppy)(3) as the HTL does not give efficient electroluminescence. However, the introduction of a thin layer of a hole-transporting material (N,N'-bis(1-naphthyl)-N,N'-diphenylbenzidine, NPD) as an energy "stair-step" and electron/exciton-blocker dramatically improves the device performance. Both fac-Co(ppz)(3) and fac-Co(ppy)(3) devices give external quantum efficiencies higher than 1.0%, with brightness 5000 and 7000 Cd/m(2) at 10 V, respectively. Ga(pma) also functions as an efficient interface layer, giving device performances very similar to those of analogous devices using NPD as the interface layer. Stability tests have been carried out for Co(ppz)(3)/NPD/Alq(3) and Co(ppy)(3)/NPD/Alq(3) devices. While fac-Co(ppy)(3) gave stable OLEDs, the fac-Co(ppz)(3)-based devices had very short lifetimes. On the basis of the experimental results of chemical oxidation of fac-Co(ppz)(3), the major cause for the fast decay of the fac-Co(ppz)(3) device is proposed to be the decomposition of fac-Co(ppz)(3)(+) in the HTL layer during the device operation.     

Calculated and experimental geometries and infrared spectra of metal tris-acetylacetonates: vibrational spectroscopy as a probe of molecular structure for ionic complexes. Part II

Following on from our previous work on Sc, Fe, Cr, and Al (Part I; see J. Phys. Chem. A, 105 (2001) 238), the geometries and infrared spectra of the trivalent metal tris-acetylacetonate complexes (M[O2C5H7]3; M = Ti, V, Mn, Co) have been studied both experimentally and theoretically using nonlocal hybrid density functional theory with a split-valence plus polarization basis for the ligand and valence triple-zeta for the metal. Unlike the D3 complexes studied in Part I, those of Ti, V and Mn are candidates for Jahn-Teller distortion due to fractional d-shell occupancy. Using scale factors transferred from Part I, our calculated frequencies are in very good agreement with experimentally observed fundamentals. Our investigation shows that the V and Mn complexes distort to C2 ground states, but D3 Ti tris-acetylacetonate is stable. Further investigation of the weak band observed around 800 cm(-1) in the Fe complex (and present in almost all studied first-row transition metal tris-acetylacetonates), which we were unable to assign theoretically in Part I, supports the argument that this band is not a fundamental but is due to Fermi resonance.