Probably certifiably correct <Emphasis Type="Italic">k</Emphasis>-means clustering

Recently, Bandeira (C R Math, 2015) introduced a new type of algorithm (the so-called probably certifiably correct algorithm) that combines fast solvers with the optimality certificates provided by convex relaxations. In this paper, we devise such an algorithm for the problem of k-means clustering. First, we prove that Peng and Wei’s semidefinite relaxation of k-means Peng and Wei (SIAM J Optim 18(1):186–205, 2007) is tight with high probability under a distribution of planted clusters called the stochastic ball model. Our proof follows from a new dual certificate for integral solutions of this semidefinite program. Next, we show how to test the optimality of a proposed k-means solution using this dual certificate in quasilinear time. Finally, we analyze a version of spectral clustering from Peng and Wei (SIAM J Optim 18(1):186–205, 2007) that is designed to solve k-means in the case of two clusters. In particular, we show that this quasilinear-time method typically recovers planted clusters under the stochastic ball model.     

γ-Hydroxyacetylenic Acid Derivatives: Generation from Propiolic Acid and Ester Anions and Their Use in Butenolide Synthesis

γ-Hydroxyacetylenic acids and esters have been found to be conveniently prepared in our laboratory by the addition of the propiolic acid dianion¹ or the acetylide of methylpropiolate² to an aldehyde or to a ketone (Scheme I, Table I). These polyfunctional compounds have been shown previously to be useful synthetic intermediates in route to such compounds as 1,3-dienes,² carbohydrates³ and butenolides.^4–7     

α-Styrylarsines

The compounds (1) formed by the addition of arsenic trichloride to phenylacetylenes contain several reactive sites and hence are useful synthetic intermediates. We have prepared these compounds in high yield by this route and have examined certain of their properties. The vinylic chlorine, generally stable to reduction, may be quantitatively and readily reduced using a lithium aluminium hydride-lithium hydride mixture. The chlorine atoms attached to arsenic are extremely reactive and readily hydrolysed and hence precautions must be taken to exclude atmospheric moisture from the reaction system. The chlorine atoms will also react on treatment with a Grignard reagent to give the diphenylstyrylarsine (2)     

Efficient synthesis of 5′-O(N)-carbamyl and -polycarbamyl nucleosides

A simple and efficient method for the preparation of 5′-O(N)-carbamyl and 5′-O(N)-polycarbamyl nucleoside derivatives is reported. The method consisted of treatment of 2′,3′-O-protected purine (Ado, Ino) or pyrimidine nucleosides (Thd, Urd) with trichloroacetylisocyanate, followed by cleavage of the trichloroacetyl moiety by silica-gel promoted methanolysis during column chromatography. Iterative application of this method gave mono, di, and tricarbamyl derivatives in good to excellent yields (ave = 80%).     

Brighter‐ and Longer‐Burning Barium‐Free Illuminants for Military and Civilian Pyrotechnics

The development of barium‐free pyrotechnic illuminants is described. Heavy metal barium nitrate oxidizer and strontium nitrate oxidizer were replaced with sodium nitrate to adequately address environmental concerns while providing the brightest possible illuminant. The new formulations further address environmental concerns and mitigate single‐point‐of‐failure through the replacement of polyester‐based Laminac 4116/Lupersol binder system with the epoxy‐based Epon 813/Versamid 140 binder system. The new formulations were found to burn longer and brighter than the control with a low sensitivity to various ignition stimuli.     

HNO and NO release from a primary amine-based diazeniumdiolate as a function of pH

The growing evidence that nitroxyl (HNO) has a rich pharmacological potential that differs from that of nitric oxide (NO) has intensified interest in HNO donors. Recently, the diazeniumdiolate (NONOate) based on isopropylamine (IPA/NO; Na[(CH(3))(2)CHNH(N(O)NO)]) was demonstrated to function under physiological conditions as an organic analogue to the commonly used HNO donor Angeli's salt (Na(2)N(2)O(3)). The decomposition mechanism of Angeli's salt is dependent on pH, with transition from an HNO to an NO donor occurring abruptly near pH 3. Here, pH is shown to also affect product formation from IPA/NO. Chemical analysis of HNO and NO production led to refinement of an earlier, quantum mechanically based prediction of the pH-dependent decomposition mechanisms of primary amine NONOates such as IPA/NO. Under basic conditions, the amine proton of IPA/NO is able to initiate decomposition to HNO by tautomerization to the nitroso nitrogen (N(2)). At lower pH, protonation activates a competing pathway to NO production. At pH 8, the donor properties of IPA/NO and Angeli's salt are demonstrated to be comparable, suggesting that at or above this pH, IPA/NO is primarily an HNO donor. Below pH 5, NO is the major product, while IPA/NO functions as a dual donor of HNO and NO at intermediate pH. This pH-dependent variability in product formation may prove useful in examination of the chemistry of NO and HNO. Furthermore, primary amine NONOates may serve as a tunable class of nitrogen oxide donor.     

Accurate predictions of the energetics of silicon compounds using the multireference correlation consistent composite approach

Theoretical studies, using the multireference correlation consistent composite approach (MR-ccCA), have been carried out on the ground and lowest lying spin-forbidden excited states of a series of silicon-containing systems. The MR-ccCA method is the multireference equivalent of the successful single reference ccCA method that has been shown to produce chemically accurate (within ±1.0 kcal mol(-1) of reliable, well-established experiment) results. The percentage contributions of the SCF configurations to complete active space self-consistent field wave functions together with the Frobenius norm of the t(1) vectors and related D(1) diagnostics of the coupled-cluster single double wave function with the cc-pVTZ basis set have been utilized to illustrate the multi-configurational characteristics of the compounds considered. MR-ccCA incorporates additive terms to account for relativistic effects, atomic spin-orbit coupling, scalar relativistic effects, and core-valence correlation. MR-ccCA has been utilized to predict the atomization energies, enthalpies of formation, and the lowest energy spin-forbidden transitions for Si(n)X(m) (2 ≤ n + m ≥ 3 where n ≠ 0 and X = B, C, N, Al, P), silicon hydrides, and analogous compounds of carbon. The energetics of small silicon aluminides and phosphorides are predicted for the first time.     

Fiber containment for improved laboratory handling and uniform nanocoating of milligram quantities of carbon nanotubes by atomic layer deposition

The presence of nanostructured materials in the workplace is bringing attention to the importance of safe practices for nanomaterial handling. We explored novel fiber containment methods to improve the handling of carbon nanotube (CNT) powders in the laboratory while simultaneously allowing highly uniform and controlled atomic layer deposition (ALD) coatings on the nanotubes, down to less than 4 nm on some CNT materials. Moreover, the procedure yields uniform coatings on milligram quantities of nanotubes using a conventional viscous flow reactor system, circumventing the need for specialized fluidized bed or rotary ALD reactors for laboratory-scale studies. We explored both fiber bundles and fiber baskets as possible containment methods and conclude that the baskets are more suitable for coating studies. An extended precursor and reactant dose and soak periods allowed the gases to diffuse through the fiber containment, and the ALD coating thickness scaled linearly with the number of ALD cycles. The extended dose period produced thicker coatings compared to typical doses on CNT controls not encased in the fibers, suggesting some effects due to the extended reactant dose. Film growth was compared on a range of single-walled NTs, double-walled NTs, and acid-functionalized multiwalled NTs, and we found that ultrathin coatings were most readily controlled on the multiwalled NTs.