Canonical forms of self-adjoint boundary conditions for differential operators of order four

Canonical forms of regular self-adjoint boundary conditions for differential operators are well known in the second order i.e. Sturm–Liouville case. In this paper we find canonical forms for fourth order self-adjoint boundary conditions.     

Cellular resolutions of cointerval ideals

Minimal cellular resolutions of the edge ideals of cointerval hypergraphs are constructed. This class of d-uniform hypergraphs coincides with the complements of interval graphs (for the case d?=?2), and strictly contains the class of ‘strongly stable’ hypergraphs corresponding to pure shifted simplicial complexes. The polyhedral complexes supporting the resolutions are described as certain spaces of directed graph homomorphisms, and are realized as subcomplexes of mixed subdivisions of the Minkowski sums of simplices. Resolutions of more general hypergraphs are obtained by considering decompositions into cointerval hypergraphs.     

Limitation of predictive 2-D liquid chromatography in reducing the database search space in shotgun proteomics: in silico studies

A two-dimensional (2-D) liquid chromatography (LC) separation of complex peptide mixtures that combines a normal phase utilizing hydrophilic interactions and a reversed phase offers reportedly the highest level of 2-D LC orthogonality by providing an even spread of peptides across multiple LC fractions. Matching experimental peptide retention times to those predicted by empirical models describing chromatographic separation in each LC dimension leads to a significant reduction in a database search space. In this work, we calculated the retention times of tryptic peptides separated in the C18 reversed phase at different separation conditions (pH 2 and pH 10) and in TSK gel Amide-80 normal phase. We show that retention times calculated for different 2-D LC separation schemes utilizing these phases start to correlate once the mass range of peptides under analysis becomes progressively narrow. This effect is explained by high degree of correlation between retention coefficients in the considered phases.     

Stabilization of Peptide‐Based Vesicles via in situ Oxygen‐Mediated Cross‐Linking

Reversible vesicles from poly(L ‐glutamic acid)₆₅‐block‐poly[(L ‐lysine)‐ran‐(L ‐3,4‐dihydroxyphenylalanine)]₇₅ [PLGA₆₅‐b‐P(LL‐r‐DOPA)₇₅] block copolypeptide adopt different configurations depending on the surrounding pH. At pH = 3, AFM and TEM images show ellipsoidal morphologies, whereas at pH = 12 both TEM and AFM reveal the formation of hollow vesicles. At pH = 12, the P(LL‐r‐DOPA) block forms the internal layer of the vesicle shell and the subsequent oxygen‐mediated oxidation of the phenolic groups of the DOPA lead to the formation of quinonic intermediates, which undergo intermolecular dimerization to stabilize the vesicles via in situ cross‐linking. Consequently, the vesicles maintain their shape even when the pH is reversed back to 3, as confirmed by AFM and TEM.

     

On the utility of predictive chromatography to complement mass spectrometry based intact protein identification

The amino acid sequence determines the individual protein three-dimensional structure and its functioning in an organism. Therefore, “reading” a protein sequence and determining its changes due to mutations or post-translational modifications is one of the objectives of proteomic experiments. The commonly utilized approach is gradient high-performance liquid chromatography (HPLC) in combination with tandem mass spectrometry. While serving as a way to simplify the protein mixture, the liquid chromatography may be an additional analytical tool providing complementary information about the protein structure. Previous attempts to develop “predictive” HPLC for large biomacromolecules were limited by empirically derived equations based purely on the adsorption mechanisms of the retention and applicable to relatively small polypeptide molecules. A mechanism of the large biomacromolecule retention in reversed-phase gradient HPLC was described recently in thermodynamics terms by the analytical model of liquid chromatography at critical conditions (BioLCCC). In this work, we applied the BioLCCC model to predict retention of the intact proteins as well as their large proteolytic peptides separated under different HPLC conditions. The specific aim of these proof-of-principle studies was to demonstrate the feasibility of using “predictive” HPLC as a complementary tool to support the analysis of identified intact proteins in top-down, middle-down, and/or targeted selected reaction monitoring (SRM)-based proteomic experiments.     

The current role of high-resolution mass spectrometry in food analysis

High-resolution mass spectrometry (HRMS), which is used for residue analysis in food, has gained wider acceptance in the last few years. This development is due to the availability of more rugged, sensitive, and selective instrumentation. The benefits provided by HRMS over classical unit-mass-resolution tandem mass spectrometry are considerable. These benefits include the collection of full-scan spectra, which provides greater insight into the composition of a sample. Consequently, the analyst has the freedom to measure compounds without previous compound-specific tuning, the possibility of retrospective data analysis, and the capability of performing structural elucidations of unknown or suspected compounds. HRMS strongly competes with classical tandem mass spectrometry in the field of quantitative multiresidue methods (e.g., pesticides and veterinary drugs). It is one of the most promising tools when moving towards nontargeted approaches. Certain hardware and software issues still have to be addressed by the instrument manufacturers for it to dislodge tandem mass spectrometry from its position as the standard trace analysis tool.     

Analysis and interpretation of the first monochromatic X‐ray tomography data collected at the Australian Synchrotron Imaging and Medical beamline

The first monochromatic X‐ray tomography experiments conducted at the Imaging and Medical beamline of the Australian Synchrotron are reported. The sample was a phantom comprising nylon line, Al wire and finer Cu wire twisted together. Data sets were collected at four different X‐ray energies. In order to quantitatively account for the experimental values obtained for the Hounsfield (or CT) number, it was necessary to consider various issues including the point‐spread function for the X‐ray imaging system and harmonic contamination of the X‐ray beam. The analysis and interpretation of the data includes detailed considerations of the resolution and efficiency of the CCD detector, calculations of the X‐ray spectrum prior to monochromatization, allowance for the response of the double‐crystal Si monochromator used (via X‐ray dynamical theory), as well as a thorough assessment of the role of X‐ray phase‐contrast effects. Computer simulations relating to the tomography experiments also provide valuable insights into these important issues. It was found that a significant discrepancy between theory and experiment for the Cu wire could be largely resolved in terms of the effect of the point‐spread function. The findings of this study are important in respect of any attempts to extract quantitative information from X‐ray tomography data, across a wide range of disciplines, including materials and life sciences.     

Scaling in the diffusion limited aggregation model

We present a self-consistent picture of diffusion limited aggregation (DLA) growth based on the assumption that the probability density P(r,N) for the next particle to be attached within the distance r to the center of the cluster is expressible in the scale-invariant form P[r/R{dep}(N)]. It follows from this assumption that there is no multiscaling issue in DLA and there is only a single fractal dimension D for all length scales. We check our assumption self-consistently by calculating the particle-density distribution with a measured P(r/R{dep}) function on an ensemble with 1000 clusters of 5×10{7} particles each. We also show that a nontrivial multiscaling function D(x) can be obtained only when small clusters (N<10?000) are used to calculate D(x). Hence, multiscaling is a finite-size effect and is not intrinsic to DLA.     

Hopf bifurcation analysis of an aeroelastic model using stochastic normal form

We investigate the effects of parameter uncertainties on the dynamical response of an aeroelastic model representing an oscillating airfoil in pitch and plunge with linear aerodynamics and cubic structural nonlinearities. An approach based on the stochastic normal form is proposed to determine the effects due to the variations in the flow speed and the structural stiffness terms on the stability of the aeroelastic system near the Hopf bifurcation point. This approach allows us to study analytically the bifurcation scenario and to predict the amplitude and frequency of the limit cycle oscillation (LCO). The results show that the amplitude of LCO corresponding to the supercritical Hopf bifurcation increases with the intensity of the noise perturbing the pitch and plunge cubic terms, but there is almost no effect on the LCO frequency. Uncertainties in the flow speed produce a shift in the bifurcation point, and unstable subcritical behavior may occur for values of parameters for which the corresponding deterministic model is stable. The stochastic normal form confirms and extends previously known numerical results regarding the effect of parameter variations, and offers an effective way to perform sensitivity analysis of the system's response.     

Observation of vector solitons with hidden vorticity

This letter reports the first experimental observation, to our knowledge, of optical vector solitons composed of two incoherently coupled vortex components. We employ nematic liquid crystal to generate stable vector solitons with counterrotating vortices and hidden vorticity. In contrast, the solitons with explicit vorticity and corotating vortex components show azimuthal splitting.