A Characterization of Uniquely Representable Graphs

The betweenness structure of a finite metric space $M = (X, d)$ is a pair $\mathcal{B}(M) = (X,\beta_M)$ where $\beta_M$ is the so-called betweenness relation of $M$ that consists of point triplets $(x, y, z)$ such that $d(x, z) = d(x, y) + d(y, z)$. The underlying graph of a betweenness structure $\mathcal{B} = (X,\beta)$ is the simple graph $G(\mathcal{B}) = (X, E)$ where the edges are pairs of distinct points with no third point between them. A connected graph $G$ is uniquely representable if there exists a unique metric betweenness structure with underlying graph $G$. It was implied by previous works that trees are uniquely representable. In this paper, we give a characterization of uniquely representable graphs by showing that they are exactly the block graphs. Further, we prove that two related classes of graphs coincide with the class of block graphs and the class of distance-hereditary graphs, respectively. We show that our results hold not only for metric but also for almost-metric betweenness structures.Comment: 16 pages (without references); 3 figures; major changes: simplified proofs, improved notations and namings, short overview of metric graph theor

Two-colorings with many monochromatic cliques in both colors

Color the edges of the n-vertex complete graph in red and blue, and suppose that red k-cliques are fewer than blue k-cliques. We show that the number of red k-cliques is always less than cknk, where ck∈(0, 1) is the unique root of the equation zk=(1-z)k+kz(1-z)k-1. On the other hand, we construct a coloring in which there are at least cknk-O(nk-1) red k-cliques and at least the same number of blue k-cliques. © 2013 Elsevier Inc

Variational wave functions for homogenous Bose systems

We study variational wave functions of the product form, factorizing according to the wave vectors k, for the ground state of a system of bosons interacting via positive pair interactions with a positive Fourier transform. Our trial functions are members of different orthonormal bases in Fock space. Each basis contains a quasiparticle vacuum state and states with an arbitrary finite number of quasiparticles. One of the bases is that of Valatin and Butler (VB), introduced fifty years ago and parametrized by an infinite set of variables determining Bogoliubov's canonical transformation for each k. In another case, inspired by Nozi\`eres and Saint James the canonical transformation for k=0 is replaced by a shift in the creation/annihilation operators. For the VB basis we prove that the lowest energy is obtained in a state with ~sqrt{volume} quasiparticles in the zero mode. The number of k=0 physical particles is of the order of the volume and its fluctuation is anomalously large, resulting in an excess energy. The same fluctuation is normal in the second type of optimized bases, the minimum energy is smaller and is attained in a vacuum state. Associated quasiparticle theories and questions about the gap in their spectrum are also discussed

Mycophenolate mofetil inhibits lymphocyte binding and the upregulation of adhesion molecules in acute rejection of rat kidney allografts.

Mycophenolate mofetil (MMF) interacts with purine metabolism and possibly with the expression of adhesion molecules. In the present study, we analysed the expression of these molecules in transplanted kidney allografts treated with RS LBNF1 kidneys were orthotopically transplanted into Lewis rats and either treated with RS (20 mg/kg/day) or vehicle. Rats were harvested 3, 5 and 7 days following transplantation. For binding studies, fresh-frozen sections of transplanted kidneys were incubated with lymph node lymphocytes (LNL) derived from transplanted rats. Additionally, immunohistology was performed with various monoclonal antibodies. In general, MMF resulted in better preservation of graft structure by 7 days. Cellular infiltration and tubular atrophy were less pronounced. At day 3, macrophages were diminished in MMF-treated animals to a high extent, while the number of T cells was almost identical to that of controls. In addition, the number of cells positive for MHC class II and LFA-1 was reduced in the MMF-treated animals. These findings correlated with the binding results. Three days following engraftment, LNL bound to MMF-treated kidneys to a lesser extent compared to controls. In conclusion, MMF resulted in a markedly reduced leucocytic infiltrate, presumably based on a reduced expression of lymphocytic adhesion molecules and an interaction with macrophages

Learning of Signaling Networks: Molecular Mechanisms

Molecular processes of neuronal learning have been well described. However, learning mechanisms of non-neuronal cells are not yet fully understood at the molecular level. Here, we discuss molecular mechanisms of cellular learning, including conformational memory of intrinsically disordered proteins (IDPs) and prions, signaling cascades, protein translocation, RNAs [miRNA and long noncoding RNA (lncRNA)], and chromatin memory. We hypothesize that these processes constitute the learning of signaling networks and correspond to a generalized Hebbian learning process of single, non-neuronal cells, and we discuss how cellular learning may open novel directions in drug design and inspire new artificial intelligence methods. © 2020 The Author

Evaluation of a High-speed Planter in Soybean Production

Timely and quality planting of soybean is important to achievemaximum yield potential. Wet spring soil conditions and rain frequently shorten the time for farmers to plant crops within optimal soil conditions. New planter technology has been introduced that enables farmers to plant their fields faster and more precisely than with traditional planters. Large plot field studies were conducted in Indiana from 2015 to 2017 to evaluate a high-speed planter at various planting speeds with multiple seeding rates on soybean. Seedling emergence, plant distribution, and final yield were evaluated. Three planting speeds [8, 12, and 16 kilometers per hour (kph)] and two seeding rates (222,000 and 321,000 seeds ha−1) were included in all years, and an additional planting speed and seeding rate were included in 2016 (20 kph and 420,000 seeds ha−1, respectively). Overall, planting speed did not impact soybean seedling emergence. Uniformity of plant spacing decreased slightly as the planting speed increased from 8 to 20 kph in 2016. Cool and wet conditions immediately after planting likely led to inconsistent emergence. Final grain yield was not affected by planting speeds or seeding rate except in 2017 when 12 kph planting speed yielded 0.25 Mg ha−1 higher than the other planting speeds. Increasing planting speed can be achieved without detrimentally affecting plant population, plant spacing, and yield in soybean

Negative radiation pressure exerted on kinks

The interaction of a kink and a monochromatic plane wave in one dimensional scalar field theories is studied. It is shown that in a large class of models the radiation pressure exerted on the kink is negative, i.e. the kink is {\sl pulled} towards the source of the radiation. This effect has been observed by numerical simulations in the $\phi^4$ model, and it is explained by a perturbative calculation assuming that the amplitude of the incoming wave is small. Quite importantly the effect is shown to be robust against small perturbations of the $\phi^4$ model. In the sine-Gordon (sG) model the time averaged radiation pressure acting on the kink turns out to be zero. The results of the perturbative computations in the sG model are shown to be in full agreement with an analytical solution corresponding to the superposition of a sG kink with a cnoidal wave. It is also demonstrated that the acceleration of the kink satisfies Newton's law.Comment: 23 pages, 8 figures, LaTeX/RevTe