Reactivity of (Bicyclo[5.1.0]octadienyl)iron(1+) Cations: Application to the Synthesis of cis-2-(2’-carboxycyclopropyl)glycines

The addition of carbon and heteroatom nucleophiles to (bicyclo[5.1.0]octadienyl)Fe(CO)2L+ cations 5 or 8 (L = CO, PPh3) generally proceeds via attack at the dienyl terminus on the face of the ligand opposite to iron to generate 6-substituted (bicyclo[5.1.0]octa-2,4-diene)iron complexes (11 or 13). In certain cases, these products are unstable with respect to elimination of a proton and the nucleophilic substituent to afford (cyclooctatetraene)Fe(CO)2L (4 or 7). Decomplexation of 13f, arising from addition of phthalimide to 8, gave N-(bicyclo[5.1.0]octa-3,5-dien-2-yl)phthalimide (19). Oxidative cleavage of 19 (RuCl3/NaIO4) followed by esterification gave the cyclopropane diester 22, which upon hydrolysis gave cis-2-(2‘-carboxycyclopropyl)glycine (CCG-III, 18) (eight steps from 4, 43% overall yield). This methodology was also utilized for preparation of stereospecifically deuterated CCG-III (d-18) and optically enriched (−)-18. Deprotonation of 22 resulted in cyclopropane ring opening to afford the benzoindolizidine (23)

Fast gradient descent for drifting least squares regression, with application to bandits

Online learning algorithms require to often recompute least squares regression estimates of parameters. We study improving the computational complexity of such algorithms by using stochastic gradient descent (SGD) type schemes in place of classic regression solvers. We show that SGD schemes efficiently track the true solutions of the regression problems, even in the presence of a drift. This finding coupled with an $O(d)$ improvement in complexity, where $d$ is the dimension of the data, make them attractive for implementation in the big data settings. In the case when strong convexity in the regression problem is guaranteed, we provide bounds on the error both in expectation and high probability (the latter is often needed to provide theoretical guarantees for higher level algorithms), despite the drifting least squares solution. As an example of this case we prove that the regret performance of an SGD version of the PEGE linear bandit algorithm [Rusmevichientong and Tsitsiklis 2010] is worse that that of PEGE itself only by a factor of $O(\log^4 n)$. When strong convexity of the regression problem cannot be guaranteed, we investigate using an adaptive regularisation. We make an empirical study of an adaptively regularised, SGD version of LinUCB [Li et al. 2010] in a news article recommendation application, which uses the large scale news recommendation dataset from Yahoo! front page. These experiments show a large gain in computational complexity, with a consistently low tracking error and click-through-rate (CTR) performance that is $75\%$ close

Crystal structure of \u3cem\u3ecis\u3c/em\u3e-2-(2-carboxycyclopropyl)-glycine (CCG-III) monohydrate

The title compound, C6H9NO4·H2O [systematic name: (αR,1R,2S)-rel-α-amino-2-carb­oxy­cyclo­propane­acetic acid monohydrate], crystallizes with two organic mol­ecules and two water mol­ecules in the asymmetric unit. The space group is P21 and the organic mol­ecules are enanti­omers, thus this is an example of a `false conglomerate\u27 with two mol­ecules of opposite handedness in the asymmetric unit (r.m.s. overlay fit = 0.056 Å for one mol­ecule and its inverted partner). Each mol­ecule exists as a zwitterion, with proton transfer from the amino acid carb­oxy­lic acid group to the amine group. In the crystal, the components are linked by N-H···O and O-H···O hydrogen bonds, generating (100) sheets. Conformationally restricted glutamate analogs are of inter­est due to their selective activation of different glutamate receptors, and the naturally occurring (+)-CCG-III is an inhibitor of glutamate uptake and the key geometrical parameters are discussed

Comparison of Wechsler Memory Scale–Fourth Edition (WMS–IV) and Third Edition (WMS–III) dimensional structures: Improved ability to evaluate auditory and visual constructs

Dimensional structures underlying the Wechsler Memory Scale–Fourth Edition (WMS–IV) and Wechsler Memory Scale–Third Edition (WMS–III) were compared to determine whether the revised measure has a more coherent and clinically relevant factor structure. Principal component analyses were conducted in normative samples reported in the respective technical manuals. Empirically supported procedures guided retention of dimensions. An invariant two-dimensional WMS–IV structure reflecting constructs of auditory learning/memory and visual attention/memory (C1 = .97; C2 = .96) is more theoretically coherent than the replicable, heterogeneous WMS–III dimension (C1 = .97). This research suggests that the WMS–IV may have greater utility in identifying lateralized memory dysfunction

The correlation space of Gaussian latent tree models and model selection without fitting

We provide a complete description of possible covariance matrices consistent with a Gaussian latent tree model for any tree. We then present techniques for utilising these constraints to assess whether observed data is compatible with that Gaussian latent tree model. Our method does not require us first to fit such a tree. We demonstrate the usefulness of the inverse-Wishart distribution for performing preliminary assessments of tree-compatibility using semialgebraic constraints. Using results from Drton et al. (2008) we then provide the appropriate moments required for test statistics for assessing adherence to these equality constraints. These are shown to be effective even for small sample sizes and can be easily adjusted to test either the entire model or only certain macrostructures hypothesized within the tree. We illustrate our exploratory tetrad analysis using a linguistic application and our confirmatory tetrad analysis using a biological application.Comment: 15 page