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.     

Planar elongation of soft polymeric networks

A new test fixture for the filament stretch rheometer (FSR) has been developed to measure planar elongation of soft polymeric networks with application towards pressure-sensitive adhesives (PSAs). The concept of this new geometry is to elongate a tube-like sample by keeping the perimeter constant. To validate this new technique, soft polymeric networks of poly(propylene oxide) (PPO) were investigated during deformation. Particle tracking and video recording were used to detect to what extent the imposed strain rate and the sample perimeter remained constant. It was observed that, by using an appropriate choice of initial sample height, perimeter, and thickness, the planar stretch ratio will follow l(t) = h(t)/h₀ = exp([(e)\dot] t)\lambda(t) = h(t)/h_0= \exp({\dot{\varepsilon}} t), with h(t) being the height at time t and [(e)\dot]{\dot{\varepsilon}} the imposed constant strain rate. The perimeter would decrease by a few percent only, which is found to be negligible. The ideal planar extension in this new fixture was confirmed by finite element simulations. Analysis of the stress difference, σ _zz  − σ _xx , showed a network response similar to that of the classical neo-Hookean model. As the Deborah number was increased, the stress difference deviated more from the classical prediction due to the dynamic structures in the material. A modified Lodge model using characteristic parameters from linear viscoelastic measurements gave very good stress predictions at all Deborah numbers used in the quasi-linear regime.     

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.

     

Interaction-induced resonance in conductance and thermopower of quantum wires

We study the effect of electron-electron interaction on the transport properties of short clean quantum wires adiabatically connected to reservoirs. Interactions lead to resonances in a multichannel wire at particular values of the Fermi energy. We investigate in detail the resonance in a two-channel wire. The (negative) conductance correction peaks at the resonance, and decays exponentially as the Fermi energy is tuned away, the resonance width being given by the temperature. Likewise, the thermopower shows a characteristic structure, which is surprisingly well approximated by the so-called Mott formula. Finally, fourfold splitting of the resonance in a magnetic field provides a unique signature of the effect.     

Analytical approach to continuous and intermittent bottleneck flows

We propose a many-particle-inspired theory for granular outflows from a hopper and for the escape dynamics through a bottleneck based on a continuity equation in polar coordinates. If the inflow is below the maximum outflow, we find an asymptotic stationary solution. If the inflow is above this value, we observe queue formation, which can be described by a shock wave equation. We also address the experimental observation of intermittent outflows, taking into account the lack of space in the merging zone by a minimum function and coordination problems by a stochastic variable. This results in avalanches of different sizes even if friction, force networks, inelastic collapse, or delay-induced stop-and-go waves are not assumed. Our intermittent flows result from a random alternation between particle propagation and gap propagation. Erratic flows in congested merging zones of vehicle traffic may be explained in a similar way.     

Low-energy dynamics of the two-dimensional S=1/2 Heisenberg antiferromagnet on percolating clusters

We investigate the quantum dynamics of site diluted S=1/2 Heisenberg antiferromagnetic clusters at the 2D percolation threshold. We use Lanczos diagonalization to calculate the lowest excitation gap Delta and, to reach larger sizes, use quantum Monte Carlo simulations to study an upper bound for Delta obtained from sum rules involving the staggered structure factor and susceptibility. Scaling the gap distribution with the cluster length L, Delta approximately L(-), we obtain a dynamic exponent z approximately 2D(f), where D(f)=91/48 is the fractal dimensionality of the percolating cluster. This is in contrast with previous expectations of z=D(f). We argue that the low-energy excitations are due to weakly coupled effective moments formed due to local imbalance in sublattice occupation.