Neighbor Distinguishing Edge Colorings Via the Combinatorial Nullstellensatz Revisited

Consider a simple graph and its proper edge coloring c with the elements of the set . We say that c is neighbor set distinguishing (or adjacent strong) if for every edge , the set of colors incident with u is distinct from the set of colors incident with v. Let us then consider a stronger requirement and suppose we wish to distinguishing adjacent vertices by sums of their incident colors. In both problems the challenging conjectures presume that such colorings exist for any graph G containing no isolated edges if only . We prove that in both problems is sufficient. The proof is based on the Combinatorial Nullstellensatz, applied in the “sum environment.” In fact the identical bound also holds if we use any set of k real numbers instead of as edge colors, and the same is true in list versions of the both concepts. In particular, we therefore obtain that lists of length ( in fact) are sufficient for planar graphs.     

Mechanisms of fibrinogen adsorption at solid substrates

Adsorption of fibrinogen, modeled as a linear chain of touching beads of various sizes, was theoretically studied using the random sequential adsorption (RSA) model. The adsorption process was assumed to consist of two steps: (i) formation of an irreversibly bound fibrinogen monolayer under the side-on orientation, which is independent of the bulk protein concentration and (ii) formation of the reversibly bound, end-on monolayer, whose coverage was dependent on the bulk concentration. Calculation based on the RSA model showed that the maximum surface concentration of the end-on (reversible) monolayer equals N(⊥∞) = 6.13 × 10(3) μm(-2) which is much larger than the previously found value for the side-on (irreversible) monolayer, equal to N(∞) = 2.27 × 10(3) μm(-2). Hence, the maximum surface concentration of fibrinogen in both orientations is determined to be 8.40 × 10(3) μm(-2) corresponding to the protein coverage of 5.70 mg m(-2) assuming 20% hydration. Additionally, the surface blocking function (ASF) was determined for the end-on fibrinogen adsorption, approximated for the entire range of coverage by the interpolating polynomial. For the coverage approaching the jamming limit, the surface blocking function (ASF) was shown to vanish proportionally to (θ(⊥∞) - θ(⊥))(2). These calculation allowed one to theoretically predict adsorption isotherms for the end-on regime of fibrinogen and adsorption kinetics under various transport conditions (diffusion and convection). Using these theoretical results, a quantitative interpretation of experimental data obtained by TIRF and ellipsometry was successfully performed. The equilibrium adsorption constant for the end-on adsorption regime was found to be 8.04 × 10(-3) m. On the basis of this value, the depth of the adsorption energy minimum, equal to -17.4 kT, was predicted, which corresponds to ΔG = -41.8 kJ mol(-1). This is in accordance with adsorption energy derived as the sum of the van der Waals and electrostatic interactions. Besides having significance for predicting fibrinogen adsorption, theoretical results derived in this work also have implications for basic science providing information on mechanisms of anisotropic protein molecule adsorption on heterogeneous surfaces.     

The Lattice of Compatible Quasiorders of Acyclic Monounary Algebras

Acyclic monounary algebras are characterized by the property that any compatible partial order r can be extended to a compatible linear order. In the case of rooted monounary algebras A=(A,f){\cal A}=(A,f) we characterize the intersection of compatible linear extensions of r by several equivalent conditions and generalize these results to compatible quasiorders of A{\cal A}. We show that the lattice QuordA{\rm{Quord}}{\cal A} of compatible quasiorders is a disjoint union of semi-intervals whose maximal elements equal the intersection of their compatible quasilinear extensions. We also investigate algebraic properties of the lattices QuordA{\rm{Quord}}{\cal A} and ConA{\rm{Con}}{\cal A}.     

On 2-Connected Spanning Subgraphs with Bounded Degree in K 1,r -Free Graphs

For any integer r > 1, an r-trestle of a graph G is a 2-connected spanning subgraph F with maximum degree Δ(F) ≤ r. A graph G is called K _1,r -free if G has no K _1,r as an induced subgraph. Inspired by the work of Ryjáček and Tkáč, we show that every 2-connected K _1,r -free graph has an r-trestle. The paper concludes with a corollary of this result for the existence of k-walks.     

Single atom hot-spots at Au-Pd nanoalloys for electrocatalytic H2O2 production

A novel strategy to direct the oxygen reduction reaction to preferentially produce H(2)O(2) is formulated and evaluated. The approach combines the inertness of Au nanoparticles toward oxidation, with the improved O(2) sticking probability of isolated transition metal "guest" atoms embedded in the Au "host". DFT modeling was employed to screen for the best alloy candidates. Modeling indicates that isolated alloying atoms of Pd, Pt, or Rh placed within the Au surface should enhance the H(2)O(2) production relative to pure Au. Consequently, Au(1-x)Pd(x) nanoalloys with variable Pd content supported on Vulcan XC-72 were prepared to investigate the predicted selectivity toward H(2)O(2) production for Au alloyed with Pd. It is demonstrated that increasing the Pd concentration to 8% leads to an increase of the electrocatalytic H(2)O(2) production selectivity up to nearly 95%, when the nanoparticles are placed in an environment compatible with that of a proton exchange membrane. Further increase of Pd content leads to a drop in H(2)O(2) selectivity, to below 10% for x = 0.5. It is proposed that the enhancement in H(2)O(2) selectivity is caused by the presence of individual surface Pd atoms surrounded by gold, whereas surface ensembles of contiguous Pd atoms support H(2)O formation. The results are discussed in the context of exergonic electrocatalytic H(2)O(2) synthesis in Polymer Electrolyte Fuel Cells for the simultaneous cogeneration of chemicals and electricity, the latter a credit to production costs.     

Molecular mechanisms of signalling specificity via phosphorelay pathways in Arabidopsis

Multistep phosphorelay (MSP) pathways mediate a wide spectrum of adaptive responses in plants, including hormonal and abiotic stress regulations. Recent genetic evidence suggests both partial redundancy and possible functional cross-talk on the one hand and a certain level of specificity on the other. Here, we discuss recent achievements improving our understanding of possible molecular mechanisms of specificity in MSP. We consider a certain evolutionary conservation of ancestral two-component signalling systems from bacteria in a process of molecular recognition that, as we have recently shown, could be applied also to a certain extent in the case of plant MSP. Furthermore, we discuss possible roles of kinase and phosphatase activities, kinetics of both these enzymatic reactions, and phosphorylation lifetime. We include also recent findings on the expression specificity of individual members of MSP pathways and, finally, based on our recent findings, we speculate about a possible role of magnesium in regulation of MSP pathways in plants. All these mechanisms could significantly influence specificity and signalling output of the MSP pathways.     

Phase transformation in shape memory alloys: a numerical approach for thermomechanical modeling via peridynamics

Meccanica - The work is devoted to the numerical aspects of the modeling tool elaborated to simulate the phenomenon of solid phase transformation in shape memory alloys. Particularly, a nonlocal...     

Assessing Similarity of Random sets via Skeletons

Methodology and Computing in Applied Probability - The paper concerns a method for assessing similarity of realisations of random sets based on a construction of their morphological skeletons and a...