Leggett–Williams theorems for coincidences of multivalued operators

We study the existence of positive solutions to the operator equation Lx∈Nx$Lx\in Nx$, where L$L$ is a linear Fredholm mapping of index zero and N$N$ is a nonlinear multivalued operator.     

Automated,feature-based image alignment for high-resolution imaging mass spectrometry of large biological samples

High-resolution imaging mass spectrometry of large biological samples is the goal of several research groups. In mosaic imaging, the most common method, the large sample is divided into a mosaic of small areas that are then analyzed with high resolution. Here we present an automated alignment routine that uses principal component analysis to reduce the uncorrelated noise in the imaging datasets, which previously obstructed automated image alignment. An additional signal quality metric ensures that only those regions with sufficient signal quality are considered. We demonstrate that this algorithm provides superior alignment performance than manual stitching and can be used to automatically align large imaging mass spectrometry datasets comprising many individual mosaic tiles.     

Positive solutions for second-order superlinear repulsive singular Neumann boundary value problems

In this paper we establish the multiplicity of positive solutions to second-order superlinear repulsive singular Neumann boundary value problems. It is proved that such a problem has at least two positive solutions under reasonable conditions. Our nonlinearity may be repulsive singular in its dependent variable and superlinear at infinity. The proof relies on a nonlinear alternative of Leray-Schauder type and on Krasnoselskii fixed point theorem on compression and expansion of cones.      

The extinction and persistence of the stochastic SIS epidemic model with vaccination

In this paper, we discuss the dynamics of a stochastic SIS epidemic model with vaccination. When the noise is large, the infective decays exponentially to zero regardless of the magnitude of _R0$R_0$. When the noise is small, sufficient conditions for extinction exponentially and persistence in the mean are established. The results are illustrated by computer simulations.     

Secondary ligands enhance affinity at a designed metal-binding site.

BACKGROUND: Specific interactions of metal ions with proteins are central to all life processes. The varied functions enabled by this cooperation are a consequence of strict control of the binding-site environment, particularly the number, type and geometry of metal-coordinating sidechains. Attempts to mimic these characteristics in the de novo design of metal-binding sites have thus far concentrated primarily on metal recruitment and not on affecting site function through systematic fine-tuning of the metal environment. RESULTS: A designed tetrahedral Zn(II)-binding site in a variant of the B1 domain of IgG-binding protein G has been expanded by introducing 'secondary ligands'. These interactions were engineered to stabilize the positions of the metal-coordinating histidine residues while retaining the desired coordination geometry. Each mutation increased the protein's affinity for metal, and combining two secondary ligands demonstrated that these enhancements are additive. These results mimic the effects of altering similar interactions observed in the native Zn(II)-binding site of carbonic anhydrase. In the B1 system, this enhanced affinity for metal is observed despite a substantial decrease in protein secondary structure. CONCLUSIONS: The intended effects of secondary ligand addition on metal affinity were observed in each mutant and demonstrated to be additive. Addition of metal also stabilized the protein's structure, partially offsetting the destabilizing effect of the mutations. These results represent a successful first attempt at designing an extended metal-binding site environment and illustrate the importance of including secondary interactions in the design of metal-binding sites.     

Temperature measurement through detailed balance in x-ray Thomson scattering

The plasma conditions in isochorically heated beryllium are measured by collective x-ray Thomson scattering. The collectively scattered Cl Ly-α x-ray line at 2.96 keV shows up- and down-shifted plasmon signals. From the detailed balance relation, i.e., the ratio of the up-shifted to the down-shifted plasmon intensities, the plasma temperature can be determined independent of model assumptions. Results are shown for an experiment in which a temperature of 18 eV was measured. Using detailed balance for temperature measurement will be important to validate models that calculate the static ion–ion structure factor S_ii(k).     

Fractional boundary value problems with singularities in space variables

We are concerned with the existence of solutions for the singular fractional boundary value problem $^{c}\kern-1pt D^{\alpha}u = f(t,u)$ , u(0)+u(1)=0, u′(0)=0, where α∈(1,2), f∈C([0,1]×(??{0})) and lim _x→0 f(t,x)=∞ for all t∈[0,1]. Here, $^{c}\kern-1pt D$ is the Caputo fractional derivative. Increasing solutions of the problem vanish at points of (0,1), that is, they “pass through” the singularity of f inside of (0,1). The results are based on combining regularization and sequential techniques with a nonlinear alternative. In limit processes, the Vitali convergence theorem is used.