Proper‐walk connection number of graphs

This paper studies the problem of proper‐walk connection number: given an undirected connected graph, our aim is to colour its edges with as few colours as possible so that there exists a properly coloured walk between every pair of vertices of the graph, that is, a walk that does not use consecutively two edges of the same colour. The problem was already solved on several classes of graphs but still open in the general case. We establish that the problem can always be solved in polynomial time in the size of the graph and we provide a characterization of the graphs that can be properly connected with $k$ colours for every possible value of $k$.     

Labelling and targeted ablation of specific bipolar cell types in the zebrafish retina

Background  

Development of a functional retina depends on regulated differentiation of several types of neurons and generation of a highly complex network between the different types of neurons. In addition, each type of retinal neuron includes several distinct morphological types. Very little is known about the mechanisms responsible for generating this diversity of retinal neurons, which may also display specific patterns of regional distribution.     

Coarse-Grained Langevin Approximations and Spatiotemporal Acceleration for Kinetic Monte Carlo Simulations of Diffusion of Interacting Particles

Kinetic Monte Carlo methods provide a powerful computational tool for the simulation of microscopic processes such as the diffusion of interacting particles on a surface, at a detailed atomistic level. However such algorithms are typically computationatly expensive and are restricted to fairly small spatiotemporal scales. One approach towards overcoming this problem was the development of coarse-grained Monte Carlo algorithms. In recent literature, these methods were shown to be capable of efficiently describing much larger length scales while still incorporating information on microscopic interactions and fluctuations. In this paper, a coarse-grained Langevin system of stochastic differential equations as approximations of diffusion of interacting particles is derived, based on these earlier coarse-grained models. The authors demonstrate the asymptotic equivalence of transient and long time behavior of the Langevin approximation and the underlying microscopic process, using asymptotics methods such as large deviations for interacting particles systems, and furthermore, present corresponding numerical simulations, comparing statistical quantities like mean paths, auto correlations and power spectra of the microscopic and the approximating Langevin processes. Finally, it is shown that the Langevin approximations presented here are much more computationally efficient than conventional Kinetic Monte Carlo methods, since in addition to the reduction in the number of spatial degrees of freedom in coarse-grained Monte Carlo methods, the Langevin system of stochastic differential equations allows for multiple particle moves in a single timestep.     

On the two-phase membrane problem with coefficients below the Lipschitz threshold

We study the regularity of the two-phase membrane problem, with coefficients below the Lipschitz threshold. For the Lipschitz coefficient case one can apply a monotonicity formula to prove the C1,1$C^{1,1}$-regularity of the solution and that the free boundary is, near the so-called branching points, the union of two C¹$C^1$-graphs. In our case, the same monotonicity formula does not apply in the same way. In the absence of a monotonicity formula, we use a specific scaling argument combined with the classification of certain global solutions to obtain C1,1$C^{1,1}$-estimates. Then we exploit some stability properties with respect to the coefficients to prove that the free boundary is the union of two Reifenberg vanishing sets near so-called branching points.     

Not-all-equal 3-SAT and 2-colorings of 4-regular 4-uniform hypergraphs

In this paper, we continue our study of 2-colorings in hypergraphs (see, Henning and Yeo, 2013). A hypergraph is 2-colorable if there is a 2-coloring of the vertices with no monochromatic hyperedge. It is known (see Thomassen, 1992) that every 4-uniform 4-regular hypergraph is 2-colorable. Our main result in this paper is a strengthening of this result. For this purpose, we define a vertex in a hypergraph $H$ to be a free vertex in $H$ if we can 2-color $V\left(H\right)?\left\{v\right\}$ such that every hyperedge in $H$ contains vertices of both colors (where $v$ has no color). We prove that every 4-uniform 4-regular hypergraph has a free vertex. This proves a conjecture in Henning and Yeo (2015). Our proofs use a new result on not-all-equal 3-SAT which is also proved in this paper and is of interest in its own right.     

Hydrogen‐bonded network structures in dipyridinium,bis(2‐methylpyridinium), bis(3‐methylpyridinium) and bis(4‐methylpyridinium) dioxidobis(oxydiacetato)uranate(VI)

Four complexes containing the [UO₂(oda)₂]²⁻ anion (oda is oxydiacetate) are reported, namely dipyridinium dioxidobis(oxydiacetato)uranate(VI), (C₅H₆N)₂[U(C₄H₄O₅)₂O₂], (I), bis(2‐methylpyridinium) dioxidobis(oxydiacetato)uranate(VI), (C₈H₈N)₂[U(C₄H₄O₅)₂O₂], (II), bis(3‐methylpyridinium) dioxidobis(oxydiacetato)uranate(VI), (C₈H₈N)₂[U(C₄H₄O₅)₂O₂], (III), and bis(4‐methylpyridinium) dioxidobis(oxydiacetato)uranate(VI), (C₈H₈N)₂[U(C₄H₄O₅)₂O₂], (IV). The anions are achiral and are located on a mirror plane in (I) and on inversion centres in (II)–(IV). The four complexes are assembled into three‐dimensional structures via N—H...O and C—H...O interactions. Compounds (III) and (IV) are isomorphous; the [UO₂(oda)₂]²⁻ anions form a porous matrix which is nearly identical in the two structures, and the cations are located in channels formed in this matrix. Compounds (I) and (II) are very different from (III) and (IV): (I) forms a layered structure, while (II) forms ribbons.     

Diastereoisomeric β‐ethyl aspartate–cobalt(III) complexes: Λ(+)578‐ and Δ(−)578‐bis(ethane‐1,2‐diamine)[β‐ethyl (S)‐aspartato]cobalt(III) bis(perchlorate) monohydrate

The structures of the diastereoisomers Λ(+)₅₇₈‐, (I), and Δ(−)₅₇₈‐bis(ethane‐1,2‐diamine)[β‐ethyl (S)‐aspartato‐κ²N,O¹]cobalt(III) bis(perchlorate) monohydrate, (II), both [Co(C₆H₁₀N₂O₄)(C₂H₈N₂)₂](ClO₄)₂·H₂O, are compared. In both structures, the ester group of the amino acid side chain is engaged only in intramolecular hydrogen bonding to coordinated amine groups. This interaction is stronger in (I) and correlates with previously observed diastereoisomeric equilibrium ratios for related metal complex systems in aqueous media. The two perchlorate anions of (II) are located on twofold axes. Both perchlorates in (I) and one of the perchlorates in (II) are affected by disorder. Both structures exhibit extensive three‐dimensional hydrogen‐bonding networks.     

Plasma protein fractions in healthy blood donors quantitated by an automated multicapillary electrophoresis system

During the last decade, capillary electrophoresis (CE) has emerged as an important alternative to traditional analysis of serum and plasma proteins by agarose or celluloseacetate electrophoresis. CE analysis of plasma proteins can now be fully automated and also includes bar-code identification of samples, preseparation steps, and direct post-separation quantitation of individual peaks, which permits short assay times and high throughput. For laboratory work, it is important to have reference values from healthy individuals. Therefore, plasma samples from 156 healthy blood donors (79 females and 77 males) have been analyzed with the Capillarys instrument and the new high resolution buffer, which yields higher resolution than the beta1-beta2+ buffer. Albumin concentrations in samples are measured using nephelometry in order to assign protein concentrations to each peak. The 2.5 and 97.5 percentiles for both the percentages of different peaks and the protein concentrations in the peaks are calculated according to the recommendations of the International Federation of Clinical Chemistry on the statistical treatment of reference values. The Capillarys instrument is a reliable system for plasma protein analysis, combining advantages of full automation with high analytical performances and throughput.     

Multivariate analysis of fMRI data by oriented partial least squares

Partial least squares (PLS) has been used in multivariate analysis of functional magnetic resonance imaging (fMRI) data as a way of incorporating information about the underlying experimental paradigm. In comparison, principal component analysis (PCA) extracts structure merely by summarizing variance and with no assurance that individual component structures are directly interpretable or that they represent salient and useful features. Oriented partial least squares (OrPLS) is a new PLS-like analysis paradigm in which extracted components can be oriented away from undesirable noise or confounds in the data and toward a desired targeted structure reflecting the fMRI experiment.     

Generalized interpolation in with a complexity constraint

In a seminal paper, Sarason generalized some classical interpolation problems for functions on the unit disc to problems concerning lifting onto of an operator that is defined on ( is an inner function) and commutes with the (compressed) shift . In particular, he showed that interpolants (i.e., such that ) having norm equal to exist, and that in certain cases such an is unique and can be expressed as a fraction with . In this paper, we study interpolants that are such fractions of functions and are bounded in norm by (assuming that , in which case they always exist). We parameterize the collection of all such pairs and show that each interpolant of this type can be determined as the unique minimum of a convex functional. Our motivation stems from the relevance of classical interpolation to circuit theory, systems theory, and signal processing, where is typically a finite Blaschke product, and where the quotient representation is a physically meaningful complexity constraint.