Parallel arrays of geometric nanowells for assembling curtains of DNA with controlled lateral dispersion

The analysis of individual molecules is evolving into an important tool for biological research, and presents conceptually new ways of approaching experimental design strategies. However, more robust methods are required if these technologies are to be made broadly available to the biological research community. To help achieve this goal we have combined nanofabrication techniques with single-molecule optical microscopy for assembling and visualizing curtains comprised of thousands of individual DNA molecules organized at engineered diffusion barriers on a lipid bilayer-coated surface. Here we present an important extension of this technology that implements geometric barrier patterns comprised of thousands of nanoscale wells that can be loaded with single molecules of DNA. We show that these geometric nanowells can be used to precisely control the lateral distribution of the individual DNA molecules within curtains assembled along the edges of the engineered barrier patterns. The individual molecules making up the DNA curtain can be separated from one another by a user-defined distance dictated by the dimensions of the nanowells. We demonstrate the broader utility of these patterned DNA curtains in a novel, real time restriction assay that we refer to as dynamic optical restriction mapping, which can be used to rapidly identify entire sets of cleavage sites within a large DNA molecule.     

Polymeric Carbon Nitride with Chirality Inherited from Supramolecular Assemblies

The facile synthesis of chiral materials is of paramount importance for various applications. Supramolecular preorganization of monomers for thermal polymerization has been proven as an effective tool to synthesize carbon and carbon nitride-based (CN) materials with ordered morphology and controlled properties. However, the transfer of an intrinsic chemical property, such as chirality from supramolecular assemblies to the final material after thermal condensation, was not shown. Here, we report the large-scale synthesis of chiral CN materials capable of enantioselective recognition. To achieve this, we designed supramolecular assemblies with a chiral center that remains intact at elevated temperatures. The optimized chiral CN demonstrates an enantiomeric preference of ca. 14 %; CN electrodes were also prepared and show stereoselective interactions with enantiomeric probes in electrochemical measurements. By adding chirality to the properties transferrable from monomers to the final product of a thermal polymerization, this study confirms the potential of using supramolecular precursors to produce carbon and CN materials and electrodes with designed chemical properties.     

Compression modes and the nuclear matter incompressibility coefficient

We review the current status of the nuclear matter (N=Z and no Coulomb interaction) incompressibility coefficient, K _nm , and describe the theoretical and the experimental methods used to determine K _nm from properties of compression modes in nuclei. In particular we consider the long standing problem of the conflicting results obtained for K _nm , deduced from experimental data on excitation cross sections for the isoscalar giant monopole resonance (ISGMR) and data for the isoscalar giant dipole resonance (ISGDR).     

Dependence of transmission of conjugation through cyclopropane ring into vinyl group on electron demand of substituent

The placement of a methoxycarbonyl or a cyano group on the cyclopropane ring in spiro-vinylcyclopropanes ($\text{7a}$, $\text{7b}$) causes a drain of electrons from the vinyl group through the ring into the electron demanding substituent, precluding their [2+2]cycloaddition with TCNE but not with the stronger electrophilic olefin CSI ($\text{7}$ → $\text{8}$), whereas the placement of a hydroxymethyl group renders the vinyl group reactive toward TCNE ($\text{9}$ → $\text{13}$).     

Expanding graphs and invariant means

All the known explicit constructions of expander families are essentially obtained by considering a sequence of finite index normal subgroupsN _i , and taking the Cayley graphs of /N _i w.r. to the projection of aglobal finite set of generators of . For many of these examples (e.g. =SL ₂, /N _i SL ₂( ) we present first constructions of new, different, sets of generators for the finite quotients, which make the Cayley graphs an expander family. An intrinsic connection between the expanding property and uniqueness of the Haar measure on an appropriate compact group, as an invariant mean, is established and used in the construction of such generators.Partially sponsored by the Edmund Landau Center for research in Mathematical Analysis, supported by the Minerva Foundation (Germany).     

Approximating the traffic grooming problem

The problem of grooming is central in studies of optical networks. In graph-theoretic terms, this can be viewed as assigning colors to the lightpaths so that at most g of them (g being the grooming factor) can share one edge. The cost of a coloring is the number of optical switches (ADMs); each lightpath uses two ADMs, one at each endpoint, and in case g lightpaths of the same wavelength enter through the same edge to one node, they can all use the same ADM (thus saving g−1 ADMs). The goal is to minimize the total number of ADMs. This problem was shown to be NP-complete for g=1 and for a general g. Exact solutions are known for some specific cases, and approximation algorithms for certain topologies exist for g=1. We present an approximation algorithm for this problem. For every value of g the running time of the algorithm is polynomial in the input size, and its approximation ratio for a wide variety of network topologies—including the ring topology—is shown to be 2lng+o(lng). This is the first approximation algorithm for the grooming problem with a general grooming factor g.     

A chiral SU(4) × SU(4) gauge theory of weak and electromagnetic interactions

A lepton hadron analogy is considered based on the gauge group SU(4)_L × SU(4)_R × U(1), which is broken entirely spontaneously. The model satisfies the physical requirements of the V-A theory, muon-electron universality, no neutral strangeness changing currents, the Cabibbo structure for the SU(3) currents, and triangle anomalies can be avoided. The contribution of the existing neutral currents to various neutrino processes are calculated.