β-Amino alcohol selectors for enantioselective separation of amino acids by ligand-exchange capillary zone electrophoresis in a low molecular weight organogel

A new family of copper ligand-exchange selectors, L- or D-β-amino alcohols, is employed for the chiral separation of D,L-dansyl-amino acids, unmodified amino acid racemates, phenylalanine and tryptophan, and β-blocker L,D-propranolol by SDS-micellar electrokinetic chromatography and by electrophoretic chromatography in a low molecular weight organogel (LMOG)-filled capillary. The LMOG comprised a self-assembled fibrillar gel of trans-(1S,2S)-1,2-bis-(dodecylamido) cyclohexane in methanol. The di-L-valinol-copper complex exhibited the best performance on LMOG-CE compared with all other β-amino alcohol-copper selectors. The dependence of chiral resolution on the pH*, the ratio between the copper and the L-valinol ligand and the concentration of added selector complex in the run buffer were investigated revealing a marked difference between the activity of the copper-valinol and the previously studied copper-valine selector. The optimal separation conditions were achieved using a 2:1 valinol/copper ratio, in accordance with the 2:1 structure of the complex, which was proven by single crystal and powder X-ray diffractions and by elemental analysis. Unlike the copper-valine selectors that could be used only under acidic conditions (pH* 3.5), the copper-valinol selectors could be used under near-neutral conditions and even at pH* 9.1. A comparison between SDS-micellar electrokinetic chromatography and LMOG-CE under otherwise identical conditions revealed a significant superior separation on the LMOG-filled capillaries.     

N-fold integer programming and nonlinear multi-transshipment

The multi-transshipment problem is NP-hard already for two commodities over bipartite networks. Nonetheless, using our recent theory of n-fold integer programming and extensions developed herein, we are able to establish the polynomial time solvability of the problem in two broad situations. First, for any fixed number of commodities and number of suppliers, we solve the problem over bipartite networks with variable number of consumers in polynomial time. This is very natural in operations research applications where few facilities serve many customers. Second, for every fixed network, we solve the problem with variable number of commodities in polynomial time.     

Stabilizing stick-slip friction

Even the most regular stick-slip frictional sliding is always stochastic, with irregularity in both the intervals between slip events and the sizes of the associated stress drops. Applying small-amplitude oscillations to the shear force, we show, experimentally and theoretically, that the stick-slip periods synchronize. We further show that this phase locking is related to the inhibition of slow rupture modes which forces a transition to fast rupture, providing a possible mechanism for observed remote triggering of earthquakes. Such manipulation of collective modes may be generally relevant to extended nonlinear systems driven near to criticality.     

Kilohertz laser frequency sensing with Brillouin mutually modulated cross-gain modulation

Using mutually modulated cross-gain modulation, Stokes optical frequency changes are converted into modulation phase changes with high sensitivity. In the slow-light transition regime, we demonstrate kilohertz sensitivity to the Stokes optical carrier frequency. The sensitivity is inversely proportional to the modulation frequency of the pump and Stokes beams.     

Transition from the ballistic to the diffusive regime in a turbid medium

By varying the absorption coefficient and width of an intralipid-India ink solution in a quasi-one-dimensional experiment, we investigate the transition between the ballistic and the diffusive regimes. The medium's attenuation coefficient changes abruptly between two different values within a single mean free path. This problem is analyzed both experimentally and theoretically, and it is demonstrated that the transition location depends on the scattering coefficient as well as on the measuring solid angle.     

Robust integer programming

We provide a complexity classification of four variants of robust integer programming when the underlying Graver basis is given. We discuss applications to robust multicommodity flows and multiway statistical table problems, and describe an effective parametrization of robust integer programming.     

Improved Alignment-Based Algorithm for Multilingual Text Compression

Multilingual text compression exploits the existence of the same text in several languages to compress the second and subsequent copies by reference to the first. This is done based on bilingual text alignment, a mapping of words and phrases in one text to their semantic equivalents in the translation. A new multilingual text compression scheme is suggested, which improves over an immediate generalization of bilingual algorithms. The idea is to store the necessary markup data within the source language text; the incurred compression loss due to this overhead is smaller than the savings in the compressed target language texts, for a large enough number of the latter. Experimental results are presented for a parallel corpus in six languages extracted from the EUR-Lex website of the European Union. These results show the superiority of the new algorithm as a function of the number of languages.     

The higher lower central series

The Baer invariants Γ _n (G) of a group are central extensions of the elementsγ _n (G) of the lower central series. We show that the inclusionsγ _n +1 ⊂γ _n can be lifted to functor morphisms Γ _n+1→Γ _n and a canonical Lie algebra, analogous to Lazard’s Lie algebra, can be constructed which is explicitly computable. This is applied in various ways.     

The Novikov Conjecture for Linear Groups

Let K be a field. We show that every countable subgroup of GL(n,K) is uniformly embeddable in a Hilbert space. This implies that Novikov’s higher signature conjecture holds for these groups. We also show that every countable subgroup of GL(2,K) admits a proper, affine isometric action on a Hilbert space. This implies that the Baum-Connes conjecture holds for these groups. Finally, we show that every subgroup of GL(n,K) is exact, in the sense of C^*-algebra theory.