Minimizing the error of linear separators on linearly inseparable data

Given linearly inseparable sets $R$ of red points and $B$ of blue points, we consider several measures of how far they are from being separable. Intuitively, given a potential separator (“classifier”), we measure its quality (“error”) according to how much work it would take to move the misclassified points across the classifier to yield separated sets. We consider several measures of work and provide algorithms to find linear classifiers that minimize the error under these different measures.     

Micelles in mixtures of sodium dodecyl sulfate and a bolaform surfactant

Mixtures composed of water, sodium dodecyl sulfate (SDS), and a bolaform surfactant with two aza-crown ethers as polar headgroups (termed Bola C-16) were investigated by modulating the mole ratios between the components. The two surfactants have ionic and nonionic, but ionizable, headgroups, respectively. The ionization is due to the complexation of alkali ions by the aza-crown ether unit(s). Structural, thermodynamic, and transport properties of the above mixtures were investigated. Results from surface tension, translational self-diffusion, and small angle neutron scattering (SANS) are reported and discussed. Interactions between the two surfactants to form mixed micelles result in a combination of electrostatic and hydrophobic contributions. These effects are reflected in the size and shape of the aggregates as well as in transport properties. The translational diffusion of the components in mixed micelles, in particular, depends on the Bola C-16/SDS mole ratio. Nonideality of mixing of the two components was inferred from the dependence of the critical micelle concentration, cmc, on the mole fraction of Bola C-16. This behavior is also reflected in surface adsorption and in the area per polar headgroup at the air-water interface. SANS data analysis for the pure components gives results in good agreement with previous findings. An analysis of data relative to mixed systems allows us to compute some structural parameters of the mixed aggregates. The dependence of aggregation numbers, nu(T), on the Bola C-16/SDS mole ratio displays a maximum that depends on the overall surfactant content and is rationalized in terms of the nonideality of mixing. Aggregates grow perpendicularly to the major rotation axis, as formerly observed in the Bola C-16 system, and become progressively ellipsoidal in shape.     

Synthesis of acetimino complexes of Pt(II) and Pt(IV) and the first heteronuclear mu-acetimido complexes

The reactions of [Ag(NH=CMe2)2]ClO4 with cis-[PtCl2L2] in a 1:1 molar ratio give cis-[PtCl(NH=CMe2)(PPh3)2]ClO4 (1cis) or cis-[PtCl(NH=CMe2)2(dmso)]ClO4 (2), and in 2:1 molar ratio, they produce [Pt(NH=CMe2)2L2](ClO4)2 [L = PPh3 (3), L2= tbbpy = 4,4'-di-tert-butyl-2,2'-dipyridyl (4)]. Complex 2 reacts with PPh3 (1:2) to give trans-[PtCl(NH=CMe2)(PPh3)2]ClO(4) (1trans). The two-step reaction of cis-[PtCl2(dmso)2], [Au(NH=CMe2)(PPh3)]ClO4, and PPh3 (1:1:1) gives [SP-4-3]-[PtCl(NH=CMe2)(dmso)(PPh3)]ClO4 (5). The reactions of complexes 2 and 4 with PhICl2 give the Pt(IV) derivatives [OC-6-13]-[PtCl3(NH=CMe2)(2)(dmso)]ClO4 (6) and [OC-6-13]-[PtCl2(NH=CMe2)2(dtbbpy)](ClO4)2 (7), respectively. Complexes 1cis and 1trans react with NaH and [AuCl(PPh3)] (1:10:1.2) to give cis- and trans-[PtCl{mu-N(AuPPh3)=CMe2}(PPh3)2]ClO4 (8cis and 8trans), respectively. The crystal structures of 4.0.5Et2O.0.5Me2CO and 6 have been determined; both exhibit pseudosymmetry.     

Screening for crystalline salts via mechanochemistry

Neat grinding and solvent-drop grinding methods are found to be effective screening tools for indicating the potential for crystalline salt formation involving a given acid-base pair, as demonstrated with two model pharmaceuticals.     

Generation of chemisorbed benzyl radicals on silica nanoparticles

Functionalized silica nanoparticles (NP) were obtained by esterification of the silanol groups of fumed silica nanoparticles with benzyl alcohol. These particles were characterized by Fourier transform infrared spectroscopy, ¹³C and ²⁹Si NMR spectroscopy, thermogravimetry, total organic carbon, Brunauer–Emmett–Teller analysis, UV-visible spectroscopy, and transmission electron microscopy. NP suspensions in water/acetonitrile mixtures were used as quenchers of benzophenone (BP) phosphorescence in time-resolved experiments at the excitation wavelength of 266 nm. The phosphorescence signals obtained in the presence of the nanoparticles were fitted to biexponential decays. Both decays were accelerated in the presence of increasing amounts of NP. A model, including the reversible adsorption of BP on the NP, which was supported by computer simulations accounts for the observed results. Laser flash-photolysis experiments with excitation at 266 nm of NP suspensions in water/acetonitrile in the presence of BP generated benzyl radicals that were attached to the silica surface. These radicals were detected at their absorption maxima (320 nm) by transient optical techniques.     

Role of direct microbial electron transfer in corrosion of steels

It has recently been discovered that many microbial species have the capacity to connect their metabolism to solid electrodes, directly exchanging electrons with them through membrane-bound redox compounds, nevertheless such a direct electron transfer pathway has been evoked rarely in the domain of microbial corrosion. Here was evidenced for the first time that the bacterium Geobacter sulfurreducens is able to increase the free potential of 304 L stainless steel up to 443 mV in only a few hours, which represents a drastic increase in the corrosion risk. In contrast, when the bacterial cells form a locally well-established biofilm, pitting potentials were delayed towards positive values. The microscopy pictures confirmed an intimate correlation between the zones where pitting occurred and the local settlement of cells. Geobacter species must now be considered as key players in the mechanisms of corrosion.     

Theoretical Study on Hydrogen‐Bond Effects in IR Spectra of High‐ and Low‐Temperature Phases of Nitric Acid Dihydrate

The low‐ and high‐temperature phases (α and β, respectively) of solid nitric acid dihydrate (NAD) are studied in depth by DFT methods. Each phase contains two types of complex structures (H₃O⁺) ? (H₂O), designated A and B, with different hydrogen‐bonding (HB) characteristics. The theoretical study reveals that type A complexes are weakly bound and could be described as (H₃O)⁺ and H₂O aggregates, with decoupled vibrational modes, whereas in type B structures the proton is situated close to the centre of the O ??? O bond and induces strong vibrational coupling. The proton‐transfer mode is predicted at quite different wavenumbers in each complex, which provides an important differentiating spectral feature, together with splitting of some bands in β‐NAD. Theoretical spectra are estimated by using two GGA parameterizations, namely, PBE and BLYP. The potential‐energy surface for each type of HB in NAD is also studied, as is the spectral influence of displacement of the shared H atom along the O? O bond. The results are compared to literature infrared spectra recorded by different techniques, namely, transmission and reflection–absorption, with both normal and tilted incident radiation. This work provides a thorough assignment of the observed spectra, and predictions for some spectra not yet available. The usefulness of high‐level theoretical calculations as performed herein to discriminate between two phases of a solid crystal is thus evidenced.     

Chiral Single-Molecule Potentiometers Based on Stapled ortho- Oligo(phenylene)ethynylenes

We report on the chemical design of chiral molecular junctions with stress-dependent conductance, whose helicity is maintained during the stretching of a single molecule junction due to the stapling of both ends of the inner helix. In the reported compounds, different conductive pathways are observed, with clearly different conductance values and plateau-length distributions, attributed to different conformations of the helical structures. The large chiro-optical responses and the potential use of these molecules as unimolecular spin filters have been theoretically proved using state-of-the-art Density Functional Theory (DFT) calculations, including a fully ab-initio estimation of the CISS-originating spin polarization which is done, for the first time, for a realistic molecular system.