Integrating multiple sources of ordinal information in portfolio optimization

Active portfolio management tries to incorporate any source of meaningful information into the asset selection process. In this contribution we consider qualitative views specified as total orders of the expected asset returns and discuss two different approaches for incorporating this input in a mean-variance portfolio optimization model. In the robust optimization approach we first compute a posterior expectation of asset returns for every given total order by an extension of the Black-Litterman (BL) framework. Then these expected asset returns are considered as possible input scenarios for robust optimization variants of the mean-variance portfolio model (max-min robustness, min regret robustness and soft robustness). In the order aggregation approach rules from social choice theory (Borda, Footrule, Copeland, Best-of-k and MC4) are used to aggregate the total order in a single ``consensus total order''. Then expected asset returns are computed for this ``consensus total order'' by the extended BL framework mentioned above. Finally, these expectations are used as an input of the classical mean-variance optimization. Using data from EUROSTOXX 50 and S&P 100 we empirically compare the success of the two approaches in the context of portfolio performance analysis and observe that in general aggregating orders by social choice methods outperforms robust optimization based methods for both data sets

Synthesis and Properties of syn-[2.2](1,6)- and (4,6)Azulenophanes and Macrocyclic Azulenophanes

A regioselective synthesis of syn-[2.2](1,6)azulenophane (9) and syn-[2.2](4,6)azulenophane (12) is described. Azulenophane 9 is prepared by deprotonation of 1,2-bis(6-methylazulen-1-yl)ethane (5), followed by oxidative coupling of the initially formed dilithium salt 8 with iodine under high-dilution conditions in 17% yield, along with the macrocyclic [2.2.2.2](1,6)azulenophane (10) (3%), and [2.2.2.2.2.2](1,6)azulenophane (11) (1.5%). The azulenophane 12 and the macrocyclic [2.2.2.2](4,6)azulenophane (13) are obtained by coupling of the dianion of 1,2-bis(4-methylazulen-6-yl)ethane (14). The structural assignments of the title compounds are based on their spectral data. Protonation of 9 furnishes the mono- and dications 24 and 25, respectively, of which the first exhibits a charge-transfer band in its electronic spectrum, indicating a transannular interaction between the protonated and unprotonated azulene units. Protonation of 12 yields the mono- and dications 26 and 27, respectively. In contrast to 24, no new band due to an intramolecular transannular charge-transfer interaction is observed in the electronic spectrum of 26, and this is due to an insufficient overlap between the protonated and unprotonated azulene decks in 26. Vilsmeier formylation of 9 with 1.5 mol equivalents of phosphoryl chloride in DMF at room temp. yields 3-formyl-syn-[2.2](1,6)azulenophane (28) in 15% yield. Under the same reaction conditions a double formylation of 9 with 3 mol equivalents of phosphoryl chloride leads to 3,3′-diformyl-syn-[2.2](1,6)azulenophane (29) in 42% yield. The aminomethylation of 9 with paraformaldehyde and N, N, N′, N′-tetramethyldiaminomethane in the presence of acetic acid furnishes the Mannich bases 3-N, N-dimethylaminomethyl-syn-[2.2](1,6)azulenophane (30) and 3,3′-bis(N, N-dimethylaminomethyl)-syn-[2.2](1,6)azulenophane (31) in 40% and 46% yields, respectively

Biphasic decay kinetics suggest progressive slowing in turnover of latently HIV-1 infected cells during antiretroviral therapy

BACKGROUND: Mathematical models based on kinetics of HIV-1 plasma viremia after initiation of combination antiretroviral therapy (cART) inferred HIV-infected cells to decay exponentially with constant rates correlated to their strength of virus production. To further define in vivo decay kinetics of HIV-1 infected cells experimentally, we assessed infected cell-classes of distinct viral transcriptional activity in peripheral blood mononuclear cells (PBMC) of five patients during 1 year after initiation of cART RESULTS: In a novel analytical approach patient-matched PCR for unspliced and multiply spliced viral RNAs was combined with limiting dilution analysis at the single cell level. This revealed that HIV-RNA+ PBMC can be stratified into four distinct viral transcriptional classes. Two overlapping cell-classes of high viral transcriptional activity, suggestive of a virion producing phenotype, rapidly declined to undetectable levels. Two cell classes expressing HIV-RNA at low and intermediate levels, presumably insufficient for virus production and occurring at frequencies exceeding those of productively infected cells matched definitions of HIV-latency. These cells persisted during cART. Nevertheless, during the first four weeks of therapy their kinetics resembled that of productively infected cells. CONCLUSIONS: We have observed biphasic decays of latently HIV-infected cells of low and intermediate viral transcriptional activity with marked decreases in cell numbers shortly after initiation of therapy and complete persistence in later phases. A similar decay pattern was shared by cells with greatly enhanced viral transcriptional activity which showed a certain grade of levelling off before their disappearance. Thus it is conceivable that turnover/decay rates of HIV-infected PBMC may be intrinsically variable. In particular they might be accelerated by HIV-induced activation and reactivation of the viral life cycle and slowed down by the disappearance of such feedback-loops after initiation of cART