Watson-Crick pairing, the Heisenberg group and Milnor invariants

We study the secondary structure of RNA determined by Watson-Crick pairing without pseudo-knots using Milnor invariants of links. We focus on the first non-trivial invariant, which we call the Heisenber invariant. The Heisenberg invariant, which is an integer, can be interpreted in terms of the Heisenberg group as well as in terms of lattice paths. We show that the Heisenberg invariant gives a lower bound on the number of unpaired bases in an RNA secondary structure. We also show that the Heisenberg invariant can predict allosteric structures for RNA. Namely, if the Heisenberg invariant is large, then there are widely separated local maxima (i.e., allosteric structures) for the number of Watson-Crick pairs found.

Anisotropic Gaussian Schell-model beams: Passage through optical systems and associated invariants

Anisotropic Gaussian Schell-model (AGSM) fields and their transformation by first-order optical systems (FOS’s) forming Sp(4,R) are studied using the generalized pencils of rays. The fact that Sp(4,R), rather than the larger group SL(4,R), is the relevant group is emphasized. A convenient geometrical picture wherein AGSM fields and FOS’s are represented, respectively, by antisymmetric second-rank tensors and de Sitter transformations in a (3+2)-dimensional space is developed. These fields are shown to separate into two qualitatively different families of orbits and the invariants over each orbit, two in number, are worked out. We also develop another geometrical picture in a (2+1)-dimensional Minkowski space suitable for the description of the action of axially symmetric FOS’s on AGSM fields, and the invariants, now seven in number, are derived. Interesting limiting cases forming coherent and quasihomogeneous fields are analyzed.

Localization of handwritten text in documents using moment invariants and Delaunay triangulation

This paper describes an approach based on Zernike moments and Delaunay triangulation for localization of hand-written text in machine printed text documents. The Zernike moments of the image are first evaluated and we classify the text as hand-written using the nearest neighbor classifier. These features are independent of size, slant, orientation, translation and other variations in handwritten text. We then use Delaunay triangulation to reclassify the misclassified text regions. When imposing Delaunay triangulation on the centroid points of the connected components, we extract features based on the triangles and reclassify the text. We remove the noise components in the document as part of the preprocessing step so this method works well on noisy documents. The success rate of the method is found to be 86%. Also for specific hand-written elements such as signatures or similar text the accuracy is found to be even higher at 93%.

Open manifolds, Ozsvath-Szabo invariants and exotic R-4 ` S

We construct an invariant of certain open four-manifolds using the Heegaard Floer theory of Ozsvath and Szabo. We show that there is a manifold X homeomorphic to R-4 for which the invariant is non-trivial,showing that X is an exotic R-4. This is the first invariant that detects exotic R-4' s. (C) 2009 Published by Elsevier GmbH.

Floquet generation of Majorana end modes and topological invariants

We show how Majorana end modes can be generated in a one-dimensional system by varying some of the parameters in the Hamiltonian periodically in time. The specific model we consider is a chain containing spinless electrons with a nearest-neighbor hopping amplitude, a p-wave superconducting term, and a chemical potential; this is equivalent to a spin-1/2 chain with anisotropic XY couplings between nearest neighbors and a magnetic field applied in the (z) over cap direction. We show that varying the chemical potential (or magnetic field) periodically in time can produce Majorana modes at the ends of a long chain. We discuss two kinds of periodic driving, periodic delta-function kicks, and a simple harmonic variation with time. We discuss some distinctive features of the end modes such as the inverse participation ratio of their wave functions and their Floquet eigenvalues which are always equal to +/- 1 for time-reversal-symmetric systems. For the case of periodic delta-function kicks, we use the effective Hamiltonian of a system with periodic boundary conditions to define two topological invariants. The first invariant is a well-known winding number, while the second invariant has not appeared in the literature before. The second invariant is more powerful in that it always correctly predicts the numbers of end modes with Floquet eigenvalues equal to + 1 and -1, while the first invariant does not. We find that the number of end modes can become very large as the driving frequency decreases. We show that periodic delta-function kicks in the hopping and superconducting terms can also produce end modes. Finally, we study the effect of electron-phonon interactions (which are relevant at finite temperatures) and a random noise in the chemical potential on the Majorana modes.

Enantiospecific first total synthesis of (-)-4-thiocyanatoneopupukeanane

The first total synthesis of (-)-4-thiocyanatoneopupukeanane starting from (R)-carvone has been achieved, establishing the relative as well as absolute structure of the natural product.

First donor-acceptor interaction promoted gelation of organic fluids

In recent years there has been considerable interest in developing new types of gelators of organic solvents.1 Despite the recent advances, a priori design of a gelator for gelling a given solvent has remained a challenging task. Various noncovalent interactions like hydrogen-bonding,2 metal coordination3 etc. have been used as the driving force for the gelation process. A special class of cholesterol-based gelators were reported by Weiss,4 and by Shinkai.5 Gels derived from these molecules have been used for chiral recognition/sensing,6 for studying photo- and metal-responsive functions,7 and as templates to make hollow fiber silica.8 Other types of organogels have been used for designing polymerized 9 and reverse aerogels,10 and in molecular imprinting.11 Hanabusa’s group has recently reported organogels with a bile acid derivative.12 This has prompted us to disclose our results on a novel electron donor–acceptor (EDA) interaction mediated two-component13 gelator system based on the bile acid14 backbone.

First principles study of magnetism in divalent Eu perovskites

A comparative first principles study has been carried out for EuLiH3 (ELH) and EuTiO3 (ETO) using the generalized gradient approximation +U approach. While ELH exhibits ferromagnetic ground state for all volumes, the magnetic ground state of ETO has the tendency to switch from G-type antiferromagnetic to a ferromagnetic state with change in volume. The marked difference in magnetic behavior and magnitude of the nearest neighbors exchange interaction of both the compounds are shown to be related to the difference in their respective electronic structure near the Fermi level. The Ti 3d states are shown to play predominant role in weakening the strength of the exchange interaction in ETO.

The first observation of a Na2TiS2 related structure in a 2-D anionic manganese trimesate intercalated by cationic imidazole

A hydrothermal reaction of Mn(OAc)2·4H2O, trimesic acid, imidazole, KOH and water at 75 °C for 24 h gave rise to a 2-D compound, [HImd][Mn(BTC)(H2O)] (Imd = imidazole; BTC = trimesate), with protonated imidazole molecules occupying the inter-lamellar space, and the structure resembles the classic inorganic compound, the sodium intercalated TiS2 (Na2TiS2).

Quantum first-passage problem

Formulation of quantum first passage problem is attempted in terms of a restricted Feynman path integral that simulates an absorbing barrier as in the corresponding classical case. The positivity of the resulting probability density, however, remains to be demonstrated.

First hyperpolarizability of bacteriorhodopsin, retinal and related molecules revisited

The previously reported beta values of BR and retinal based chromophores were very high but subsequent measurements found them to be much less. We have found that the beta values of these compounds do not vary so much with experimental conditions as with the method of analysis. Hyper-Rayleigh scattering measurements at 1543 and 1907 nm produce more realistic beta values close to the intrinsic (static) hyperpolarizability, beta(0) which for BR is still very high (275 x 10 (30) esu). The optical nonlinearity of BR arises entirely due to the protonated retinal Schiff Base (PRSB) which in its isolated form has the same intrinsic hyperpolarizability as that of the rotein.

On the invariants of coloured Petri Nets

In this paper, we develop a theorem that enables computation of the place invariants of the union of a finite collection of coloured Petri Nets when the individual nets satisfy certain conditions and their invariants are known. We consider the illustrative examples of the Readers-Writers problem, a resource sharing system, and a network of databases and show how this theorem is a valuable tool in the analysis of concurrent systems.

X-ray absorption spectra of niobium dichalcogenides and their first-row transition-metal intercalates

X-ra!. K-absorption spectra of niobium in niobium dichalcogenides. namely NbS, and NbSe, and their first-row transition-metal intercalates Mi P 3N bSz (M = Cr. Mn. Fe. Co. Ni) and Ml#,NbSe2 (M = Fe. CO). have been measured together with those in niobium metal. The spectra of these materials are \er? similar to one another. They reflect the transitions to the partially filled niobium d band with some p character. A bariety of x-ray absorption nearedge structures (XASES) associated with the K edges of intercalated atoms are also presented and discussed.

Testing approximate theories of first-order phase transitions on the two-dimensional Potts model

The two-dimensional,q-state (q>4) Potts model is used as a testing ground for approximate theories of first-order phase transitions. In particular, the predictions of a theory analogous to the Ramakrishnan-Yussouff theory of freezing are compared with those of ordinary mean-field (Curie-Wiess) theory. It is found that the Curie-Weiss theory is a better approximation than the Ramakrishnan-Yussouff theory, even though the former neglects all fluctuations. It is shown that the Ramakrishnan-Yussouff theory overestimates the effects of fluctuations in this system. The reasons behind the failure of the Ramakrishnan-Yussouff approximation and the suitability of using the two-dimensional Potts model as a testing ground for these theories are discussed.