N,N′‐Di­methyl‐1,4‐dithiine‐1,2:4,5‐tetracarbox­imide and N,N′‐di­methyl‐1,4‐diselenine‐1,2:4,5‐tetracarbox­imide

The title compounds of sulfur, C₁₀H₆N₂O₄S₂, (I), and selenium, C₁₀H₆N₂O₄Se₂, (II), are isomorphous. The crystallographically centrosymmetric mol­ecules are planar. The bond distances and angles, except for those involving the S and Se atoms, are comparable. The mol­ecules are disposed in layers parallel to the bc plane. The molecular axes differ by 75° for (I) and by 80° for (II) from one layer to the next.     

Impact of DNA Sequence and Oligonucleotide Length on a Polythiophene‐Based Fluorescent DNA Biosensor

DNA hybridization is a universal and specific mechanism for the recognition of biological targets. Some cationic polythiophene transducers sensitive to DNA structure have been previously utilized to detect such biomolecules. Further characterization of these systems indicates that both DNA sequence composition and length modulate the biosensor performance. It appears that different repeated sequence patterns cause different conformational changes of the polythiophene, from a more relaxed form to an extremely rigid one. A length difference between the DNA oligonucleotide probe and target has a detrimental effect on the fluorescent signal, but it can be attenuated by changing the sequence composition of the protruding target sequence. This demonstrates that the nature of DNA can be critical for hybridization‐based detection systems.

     

On the growth of Betti numbers of locally symmetric spaces

We announce new results concerning the asymptotic behavior of the Betti numbers of higher rank locally symmetric spaces as their volumes tend to infinity. Our main theorem is a uniform version of the Lück Approximation Theorem (Lück, 1994 [10]) which is much stronger than the linear upper bounds on Betti numbers given by Gromov in Ballmann et al. (1985) [3].The basic idea is to adapt the theory of local convergence, originally introduced for sequences of graphs of bounded degree by Benjamini and Schramm, to sequences of Riemannian manifolds. Using rigidity theory we are able to show that when the volume tends to infinity, the manifolds locally converge to the universal cover in a sufficiently strong manner that allows us to derive the convergence of the normalized Betti numbers.     

Inequalities between Littlewood-Richardson coefficients

We prove that a conjecture of Fomin, Fulton, Li, and Poon, associated to ordered pairs of partitions, holds for many infinite families of such pairs. We also show that the bounded height case can be reduced to checking that the conjecture holds for a finite number of pairs, for any given height. Moreover, we propose a natural generalization of the conjecture to the case of skew shapes.     

Skew Schubert functions and the Pieri formula for flag manifolds

We show the equivalence of the Pieri formula for flag manifolds with certain identities among the structure constants for the Schubert basis of the polynomial ring. This gives new proofs of both the Pieri formula and of these identities. A key step is the association of a symmetric function to a finite poset with labeled Hasse diagram satisfying a symmetry condition. This gives a unified definition of skew Schur functions, Stanley symmetric functions, and skew Schubert functions (defined here). We also use algebraic geometry to show the coefficient of a monomial in a Schubert polynomial counts certain chains in the Bruhat order, obtainng a combinatorial chain construction of Schubert polynomials.

     

A quantum-mechanical investigation of a collinear model for collision-induced dissociation

Quantum-mechanical wavepacket results are reported for a collinear A + BC → A + B + C dissociation model previously investigated semi-classically by Rusinek and Roberts. The quantum-mechanical and semi-classical probabilities are found to be in very good agreement.     

Saturation transfer double-difference NMR spectroscopy using a dual solenoid microcoil difference probe

An experiment designed to collect a saturation transfer double difference (STDD) NMR spectrum using a solenoid microcoil NMR difference probe is reported. STDD-NMR allows the investigation of ligand-biomolecule binding, with moderate concentration requirements for unlabeled molecular targets and the ability to discern binding events in the presence of non-binding ligands. The NMR difference probe acquires the signals from two different samples at once, and cancels common signals automatically through a mechanism of switching between parallel excitation and serial acquisition of the sample signals. STDD spectra were acquired on a system consisting of human serum albumin and two ligands, octanoic acid and glucose. The non-binding ligand, glucose, was cancelled internally through phase cycling, while the protein signal was subtracted automatically by the difference probe. The proton NMR resonance signal from octanoic acid remained in the double difference spectrum. This work demonstrates that the double difference can be performed both internally and automatically through the utilization of the solenoid microcoil NMR difference probe and STDD-NMR pulse sequence, resulting in a clean signal from the binding ligand with good protein background subtraction and an overall favorable result when compared to the conventional approach.     

The Pieri Rule for Dual Immaculate Quasi-Symmetric Functions

The immaculate basis of the non-commutative symmetric functions was recently introduced by the first and third authors to lift certain structures in the symmetric functions to the dual Hopf algebras of the non-commutative and quasi-symmetric functions. It was shown that immaculate basis satisfies a positive, multiplicity free right Pieri rule. It was conjectured that the left Pieri rule may contain signs but that it would be multiplicity free. Similarly, it was also conjectured that the dual quasi-symmetric basis would also satisfy a signed multiplicity free Pieri rule. We prove these two conjectures here.