On Topological Lower Bounds for Algebraic Computation Trees

We prove that the height of any algebraic computation tree for deciding membership in a semialgebraic set \(\Sigma \subset {\mathbb R}^n\) is bounded from below by

$$\begin{aligned} \frac{c_1\log (\mathrm{b}_m(\Sigma ))}{m+1} -c_2n, \end{aligned}$$

where \(\mathrm{b}_m(\Sigma )\) is the mth Betti number of \(\Sigma \) with respect to “ordinary” (singular) homology and \(c_1,\ c_2\) are some (absolute) positive constants. This result complements the well-known lower bound by Yao (J Comput Syst Sci 55:36–43, 1997) for locally closed semialgebraic sets in terms of the total Borel–Moore Betti number. We also prove that if \(\rho :\> {\mathbb R}^n \rightarrow {\mathbb R}^{n-r}\) is the projection map, then the height of any tree deciding membership in \(\Sigma \) is bounded from below by

$$\begin{aligned} \frac{c_1\log (\mathrm{b}_m(\rho (\Sigma )))}{(m+1)^2} -\frac{c_2n}{m+1} \end{aligned}$$

for some positive constants \(c_1,\ c_2\). We illustrate these general results by examples of lower complexity bounds for some specific computational problems.

     

A boundary quotient diagram for right LCM semigroups

We propose a boundary quotient diagram for right LCM semigroups with property (AR) that generalizes the boundary quotient diagram for \(\mathbb {N}\rtimes \mathbb {N}^\times \). Our approach focuses on two important subsemigroups: the core subsemigroup and the semigroup of core irreducible elements. The diagram is then employed to unify several case studies on KMS-states, and we end with a discussion on K-theoretical aspects of the diagram motivated by recent findings for integral dynamics.     

On the crucial importance of the pH for the formation and self-stabilization of protein microgels and strands

Stable suspensions of protein microgels are formed by heating salt-free β-lactoglobulin solutions at concentrations up to about C = 50 g·L(-1) if the pH is set within a narrow range between 5.75 and 6.1. The internal protein concentration of these spherical particles is about 150 g·L(-1) and the average hydrodynamic radius decreases with increasing pH from 200 to 75 nm. The formation of the microgels leads to an increase of the pH, which is a necessary condition to obtain stable suspensions. The spontaneous increase of the pH during microgel formation leads to an increase of their surface charge density and inhibits secondary aggregation. This self-stabilization mechanism is not sufficient if the initial pH is below 5.75 in which case secondary aggregation leads to precipitation. Microgels are no longer formed above a critical initial pH, but instead short, curved protein strands are obtained with a hydrodynamic radius of about 15-20 nm.     

Controlling chiral organization of molecular rods on Au(111) by molecular design

Chiral self-assembled structures formed from organic molecules adsorbed on surfaces have been the subject of intense investigation in the recent decade, owing both to relevance in applications such as enantiospecific heterogeneous catalysis or chiral separation as well as to fundamental interest, for example, in relation to the origin of biomolecular homochirality. A central target is rational design of molecular building blocks allowing transfer of chirality from the molecular to the supramolecular level. We previously studied the surface self-assembly of a class of linear compounds based on an oligo(phenylene ethynylene) backbone, which were shown to form a characteristic windmill adsorption pattern on the Au(111) surface. However, since these prochiral compounds were intrinsically achiral, domains with oppositely oriented windmill motifs and related conformational surface enantiomers were always realized in equal proportion. Here we report on the enantioselective, high yield chemical synthesis of a structurally related but intrinsically chiral compound in which two peripheral tert-butyl substituents are replaced by sec-butyl groups, each containing an (S) chiral center. Using scanning tunneling microscopy under ultrahigh vacuum conditions, we characterize the adsorption structures formed from this compound on the Au(111) surface. The perturbation introduced by the modified molecular design is found to be sufficiently small so structures form that are closely analogous to those observed for the original tert-butyl substituted compound. However, as demonstrated from careful statistical analysis of high-resolution STM images, the introduction of the two chiral (S)-sec-butyl substituents leads to a strong preference for windmill motifs with one orientation, demonstrating control of the chiral organization of the molecular backbones through rational molecular design.     

Chiral induction by seeding surface assemblies of chiral switches

It is demonstrated by scanning tunneling microscopy that coadsorption of a molecular chiral switch with a complementary, intrinsically chiral induction seed on the Au(111) surface leads to the formation of globally homochiral molecular assemblies.     

Investigation of a fiber optic surface plasmon spectroscopy in conjunction with conductivity as an in situ method for simultaneously monitoring changes in dissolved organic carbon and salinity in coastal waters

A combination surface plasmon resonance (SPR) and conductivity sensor array was developed and implemented to demonstrate the ability to differentiate among changes in dissolved organic carbon (DOC) and salinity in coastal water. The array is capable of achieving sufficient spatial and temporal data density to better understand the cycling and fate of terrestrial DOC in coastal areas. DOC is the second largest source of bioreactive carbon in the environment and plays a key role in mediating microbial activity and generation of atmospheric CO(2). In the coastal areas, the salinity is also an important property in many applications, such as leak detection for landfill liners, saltwater intrusion to drinking water, marine environment monitoring, and seasonal climate prediction. Conductivity sensors are the industry standard for determining salinity in ocean systems. However, both conductivity and refractive index sensors, such as SPR spectroscopy based sensors, respond to salinity and DOC levels. To demonstrate the capability of the SPR sensor and a conductivity sensor to collect complimentary data useful in discrimination of salinity and DOC in coastal zone water, conductivity, SPR, and temperature data were collected during passage from the Juan de Fuca ridge area returning to the University of Washington docks.     

Identification of Nitrotyrosine Containing Peptides using Combined Fractional Diagonal Chromatography (COFRADIC) and Off-Line Nano-LC-MALDI

Protein nitration take place on tyrosine residues under oxidative stress conditions and may influence a number of processes including enzyme activity, protein-protein interactions and phospho-tyrosine signalling pathways. Nitrated proteins have been identified in a number of diseases, however, the study of these proteins has been compromised by the lack of good methods for identifying nitrated proteins, their nitration sites and the level of nitration. Here, we present a method for identification of nitrated peptides that allows the site specific assignment of nitration, is easy to use and reproducible, and opens up for the possibility to quantify the level of nitration of specific peptides as function of different oxidative conditions, namely combined fractional diagonal chromatography (COFRADIC) in combination with off-line nano-LC-MALDI. We identify six nitrated peptides from in vitro nitrated bovine serum albumin and propose that automated COFRADIC using nano-LC and off-line MALDI-MS might be a possibility for identification of tyrosine nitrated proteins and the nitration sites in complex samples.     

Characterization and modeling of nonlinear hydrophobic interaction chromatographic systems

A general rate model was employed in concert with a preferential interaction quadratic adsorption isotherm for the characterization of HIC resins and the prediction of solute behavior in these separation systems. The results indicate that both pore and surface diffusion play an important role in protein transport in HIC resins. The simulated and experimental solute profiles were compared for two model proteins, lysozyme and lectin, for both displacement and gradient modes of chromatography. Our results indicate that a modeling approach using the generate rate model and preferential interaction isotherm can accurately predict the shock layer response in both gradient and displacement chromatography in HIC systems. While pore and surface diffusion played a major role and were limiting steps for proteins, surface diffusion was seen to play less of a role for the displacer. The results demonstrate that this modeling approach can be employed to describe the behavior of these non-linear HIC systems, which may have implications for the development of more efficient preparative HIC separations.     

Characterization of a synthetic peroxodiiron(III) protein model complex by nuclear resonance vibrational spectroscopy

The vibrational spectrum of an η(1),η(1)-1,2-peroxodiiron(III) complex was measured by nuclear resonance vibrational spectroscopy and fit using an empirical force field analysis. Isotopic (18)O(2) labelling studies revealed a feature involving motion of the {Fe(2)(O(2))}(4+) core that was not previously observed by resonance Raman spectroscopy.