Renormalized field theory of collapsing directed randomly branched polymers

We present a dynamical field theory for directed randomly branched polymers and in particular their collapse transition. We develop a phenomenological model in the form of a stochastic response functional that allows us to address several interesting problems such as the scaling behavior of the swollen phase and the collapse transition. For the swollen phase, we find that by choosing model parameters appropriately, our stochastic functional reduces to the one describing the relaxation dynamics near the Yang-Lee singularity edge. This corroborates that the scaling behavior of swollen branched polymers is governed by the Yang-Lee universality class as has been known for a long time. The main focus of our paper lies on the collapse transition of directed branched polymers. We show to arbitrary order in renormalized perturbation theory with $\varepsilon$-expansion that this transition belongs to the same universality class as directed percolation.Comment: 18 pages, 7 figure

An Extracellular Interactome of Immunoglobulin and LRR Proteins Reveals Receptor-Ligand Networks

Extracellular domains of cell surface receptors and ligands mediate cell-cell communication, adhesion, and initiation of signaling events, but most existing protein-protein “interactome” data sets lack information for extracellular interactions. We probed interactions between receptor extracellular domains, focusing on a set of 202 proteins composed of the Drosophila melanogaster immunoglobulin superfamily (IgSF), fibronectin type III (FnIII), and leucine-rich repeat (LRR) families, which are known to be important in neuronal and developmental functions. Out of 20,503 candidate protein pairs tested, we observed 106 interactions, 83 of which were previously unknown. We “deorphanized” the 20 member subfamily of defective-in-proboscis-response IgSF proteins, showing that they selectively interact with an 11 member subfamily of previously uncharacterized IgSF proteins. Both subfamilies interact with a single common “orphan” LRR protein. We also observed interactions between Hedgehog and EGFR pathway components. Several of these interactions could be visualized in live-dissected embryos, demonstrating that this approach can identify physiologically relevant receptor-ligand pairs

The collapse transition of randomly branched polymers -renormalized field theory

We present a minimal dynamical model for randomly branched isotropic polymers, and we study this model in the framework of renormalized field theory. For the swollen phase, we show that our model provides a route to understand the well established dimensional-reduction results from a different angle. For the collapse $\theta$-transition, we uncover a hidden Becchi-Rouet-Stora super-symmetry, signaling the sole relevance of tree-configurations. We correct the long-standing 1-loop results for the critical exponents, and we push these results on to 2-loop order. For the collapse $\theta^{\prime}$-transition, we find a runaway of the renormalization group flow, which lends credence to the possibility that this transition is a fluctuation-induced first-order transition. Our dynamical model allows us to calculate for the first time the fractal dimension of the shortest path on randomly branched polymers in the swollen phase as well as at the collapse transition and related fractal dimensions.Comment: 23 pages, 14 figure

Finite-size scaling of directed percolation in the steady state

Recently, considerable progress has been made in understanding finite-size scaling in equilibrium systems. Here, we study finite-size scaling in non-equilibrium systems at the instance of directed percolation (DP), which has become the paradigm of non-equilibrium phase transitions into absorbing states, above, at and below the upper critical dimension. We investigate the finite-size scaling behavior of DP analytically and numerically by considering its steady state generated by a homogeneous constant external source on a d-dimensional hypercube of finite edge length L with periodic boundary conditions near the bulk critical point. In particular, we study the order parameter and its higher moments using renormalized field theory. We derive finite-size scaling forms of the moments in a one-loop calculation. Moreover, we introduce and calculate a ratio of the order parameter moments that plays a similar role in the analysis of finite size scaling in absorbing nonequilibrium processes as the famous Binder cumulant in equilibrium systems and that, in particular, provides a new signature of the DP universality class. To complement our analytical work, we perform Monte Carlo simulations which confirm our analytical results.Comment: 21 pages, 6 figure

Transport on Directed Percolation Clusters

We study random lattice networks consisting of resistor like and diode like bonds. For investigating the transport properties of these random resistor diode networks we introduce a field theoretic Hamiltonian amenable to renormalization group analysis. We focus on the average two-port resistance at the transition from the nonpercolating to the directed percolating phase and calculate the corresponding resistance exponent $\phi$ to two-loop order. Moreover, we determine the backbone dimension $D_B$ of directed percolation clusters to two-loop order. We obtain a scaling relation for $D_B$ that is in agreement with well known scaling arguments.Comment: 4 page

Noisy random resistor networks: renormalized field theory for the multifractal moments of the current distribution

We study the multifractal moments of the current distribution in randomly diluted resistor networks near the percolation treshold. When an external current is applied between to terminals $x$ and $x^\prime$ of the network, the $l$th multifractal moment scales as $M_I^{(l)} (x, x^\prime) \sim | x - x^\prime |^{\psi_l /\nu}$, where $\nu$ is the correlation length exponent of the isotropic percolation universality class. By applying our concept of master operators [Europhys. Lett. {\bf 51}, 539 (2000)] we calculate the family of multifractal exponents $\{\psi_l \}$ for $l \geq 0$ to two-loop order. We find that our result is in good agreement with numerical data for three dimensions.Comment: 30 pages, 6 figure

International Society of Sports Nutrition Position Stand: Nutritional recommendations for single-stage ultra-marathon; training and racing

Background. In this Position Statement, the International Society of Sports Nutrition (ISSN) provides an objective and critical review of the literature pertinent to nutritional considerations for training and racing in single-stage ultra-marathon. Recommendations for Training. i) Ultra-marathon runners should aim to meet the caloric demands of training by following an individualized and periodized strategy, comprising a varied, food-first approach; ii) Athletes should plan and implement their nutrition strategy with sufficient time to permit adaptations that enhance fat oxidative capacity; iii) The evidence overwhelmingly supports the inclusion of a moderate-to-high carbohydrate diet (i.e., ~60% of energy intake, 5 – 8 g⸱kg−1·d−1) to mitigate the negative effects of chronic, training-induced glycogen depletion; iv) Limiting carbohydrate intake before selected low-intensity sessions, and/or moderating daily carbohydrate intake, may enhance mitochondrial function and fat oxidative capacity. Nevertheless, this approach may compromise performance during high-intensity efforts; v) Protein intakes of ~1.6 g·kg−1·d−1 are necessary to maintain lean mass and support recovery from training, but amounts up to 2.5 g⸱kg−1·d−1 may be warranted during demanding training when calorie requirements are greater; Recommendations for Racing. vi) To attenuate caloric deficits, runners should aim to consume 150 - 400 kcal⸱h−1 (carbohydrate, 30 – 50 g⸱h−1; protein, 5 – 10 g⸱h−1) from a variety of calorie-dense foods. Consideration must be given to food palatability, individual tolerance, and the increased preference for savory foods in longer races; vii) Fluid volumes of 450 – 750 mL⸱h−1 (~150 – 250 mL every 20 min) are recommended during racing. To minimize the likelihood of hyponatraemia, electrolytes (mainly sodium) may be needed in concentrations greater than that provided by most commercial products (i.e., >575 mg·L−1 sodium). Fluid and electrolyte requirements will be elevated when running in hot and/or humid conditions; viii) Evidence supports progressive gut-training and/or low-FODMAP diets (fermentable oligosaccharide, disaccharide, monosaccharide and polyol) to alleviate symptoms of gastrointestinal distress during racing; ix) The evidence in support of ketogenic diets and/or ketone esters to improve ultra-marathon performance is lacking, with further research warranted; x) Evidence supports the strategic use of caffeine to sustain performance in the latter stages of racing, particularly when sleep deprivation may compromise athlete safety

Free and inexpensive materials on computing in teaching and learning activities : An informal appraisal

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/21775/1/0000169.pd