From static to dynamic: escaping kinetic traps in hydrazone-based dynamic combinatorial libraries

Thermodynamic control over kinetically-trapped mixtures of hydrazone-based macrocycles is achieved by addition of an aromatic monohydrazide to generate dynamic combinatorial libraries (DCLs) of linear and macrocyclic oligomers.     

The binding of CNA35 contrast agents to collagen fibrils

CryoTEM demonstrates that a CNA35-bearing liposomal MRI contrast agent selectively binds to poorly assembled collagen type I as opposed to well-assembled collagen fibrils, whereas monomeric CNA35 binds to all forms of collagen. It is shown that upon conjugation to liposomes and micelles CNA35 loses its ability to dissociate ordered collagen fibrils and thereby to create its own binding sites.     

Some new analysis results for a class of interface problems

Interface problems modeled by differential equations have many applications in mathematical biology, fluid mechanics, material sciences, and many other areas. Typically, interface problems are characterized by discontinuities in the coefficients and/or the Dirac delta function singularities in the source term. Because of these irregularities, solutions to the differential equations are not smooth or discontinuous. In this paper, some new results on the jump conditions of the solution across the interface are derived using the distribution theory and the theory of weak solutions. Some theoretical results on the boundary singularity in which the singular delta function is at the boundary are obtained. Finally, the proof of the convergency of the immersed boundary (IB) method is presented. The IB method is shown to be first‐order convergent in L ^∞ norm. Copyright © 2013 John Wiley & Sons, Ltd.     

Reverse Mathematics and parameter-free Transfer

Recently, conservative extensions of Peano and Heyting arithmetic in the spirit of Nelson's axiomatic approach to Nonstandard Analysis, have been proposed. In this paper, we study the Transfer axiom of Nonstandard Analysis restricted to formulas without parameters. Based on this axiom, we formulate a base theory for the Reverse Mathematics of Nonstandard Analysis and prove some natural reversals, and show that most of these equivalences do not hold in the absence of parameter-free Transfer.     

Characterizing plant cell wall derived oligosaccharides using hydrophilic interaction chromatography with mass spectrometry detection

Analysis of complex mixtures of plant cell wall derived oligosaccharides is still challenging and multiple analytical techniques are often required for separation and characterization of these mixtures. In this work it is demonstrated that hydrophilic interaction chromatography coupled with evaporative light scattering and mass spectrometry detection (HILIC-ELSD-MS(n)) is a valuable tool for identification of a wide range of neutral and acidic cell wall derived oligosaccharides. The separation potential for acidic oligosaccharides observed with HILIC is much better compared to other existing techniques, like capillary electrophoresis, reversed phase and porous-graphitized carbon chromatography. Important structural information, such as presence of methyl esters and acetyl groups, is retained during analysis. Separation of acidic oligosaccharides with equal charge yet with different degrees of polymerization can be obtained. The efficient coupling of HILIC with ELSD and MS(n)-detection enables characterization and quantification of many different oligosaccharide structures present in complex mixtures. This makes HILIC-ELSD-MS(n) a versatile and powerful additional technique in plant cell wall analysis.     

Dynamic combinatorial donor-acceptor catenanes in water: access to unconventional and unexpected structures

We describe here the assembly of new types of donor-acceptor [2]catenanes from dynamic combinatorial libraries (DCL) in water. These new catenanes contain both the donor and acceptor components in at least one of the interlocked rings, thereby possessing unusual and unexpected DAAD or DADD stacking sequences of the π units in their structures. The efficiency of the catenane assembly process can be enhanced by manipulating the DCL equilibrium in a variety of ways: adding a guest, changing the building block stoichiometries, or increasing the library concentration or the ionic strength of the solvent. The formation of catenanes and their constitutions are found to be dependent on subtle differences in the geometry, dimension, and flexibility of the donor building blocks.     

On the Geometric Distance Between Quantum States with Positive Partial Transposition and Private States

We prove an analytic positive lower bound for the geometric distance between entangled positive partial transpose (PPT) states of a broad class and any private state that delivers one secure key bit. Our proof holds for any Hilbert space of finite dimension. Although our result is proven for a specific class of PPT states, we show that our bound nonetheless holds for all known entangled PPT states with non-zero distillable key rates, irrespective of whether they are in our special class or not. Thus, our result naturally leads to the conjecture of impossibility of using PPT-bound entangled state in physical implementation of quantum key distribution.     

Empirical State Determination of Entangled Two-Level Systems and Its Relation to Information Theory

Theoretical methods for empirical state determination of entangled two-level systems are analyzed in relation to information theory. We show that hidden variable theories would lead to a Shannon index of correlation between the entangled subsystems which is larger than that predicted by quantum mechanics. Canonical representations which have maximal correlations are treated by the use of Schmidt and Hilbert-Schmidt decomposition of the entangled states, including especially the Bohm singlet state and the GHZ entangled states. We show that quantum mechanics does not violate locality, but does violate realism.