Higher su(N) tensor products

We extend our recent results on ordinary su(N) tensor product multiplicities to higher su(N) tensor products. Particular emphasis is put on four-point couplings where the tensor product of four highest weight modules is considered. The number of times the singlet occurs in the decomposition is the associated multiplicity. In this framework, ordinary tensor products correspond to three-point couplings. As in that case, the four-point multiplicity may be expressed explicitly as a multiple sum measuring the discretised volume of a convex polytope. This description extends to higher-point couplings as well. We also address the problem of determining when a higher-point coupling exists, i.e., when the associated multiplicity is non-vanishing. The solution is a set of inequalities in the Dynkin labels.Comment: 17 pages, LaTe

Adaptive, cautious, predictive control with Gaussian process priors

Nonparametric Gaussian Process models, a Bayesian statistics approach, are used to implement a nonlinear adaptive control law. Predictions, including propagation of the state uncertainty are made over a k-step horizon. The expected value of a quadratic cost function is minimised, over this prediction horizon, without ignoring the variance of the model predictions. The general method and its main features are illustrated on a simulation example

Leucine supplementation differentially enhances pancreatic cancer growth in lean and overweight mice

Kristyn A Liu1†, Laura M Lashinger1†, Audrey J Rasmussen1† and Stephen D Hursting12* Author Affiliations 1 Department of Nutritional Sciences, University of Texas at Austin, Austin, TX 78723, USA 2 Department of Molecular Carcinogenesis, University of Texas M.D. Anderson Cancer Center, 1808 Park Road 1c, Smithville, TX 78957, USABackground: The risk of pancreatic cancer, the 4th deadliest cancer for both men and women in the United States, is increased by obesity. Calorie restriction (CR) is a well-known dietary regimen that prevents or reverses obesity and suppresses tumorigenesis in a variety of animal models, at least in part via inhibition of mammalian target of rapamycin (mTOR) signaling. Branched-chain amino acids (BCAA), especially leucine, activate mTOR and enhance growth and proliferation of myocytes and epithelial cells, which is why leucine is a popular supplement among athletes. Leucine is also increasingly being used as a treatment for pancreatic cancer cachexia, but the effects of leucine supplementation on pancreatic tumor growth have not been elucidated. Results: Supplementation with leucine increased pancreatic tumor growth in both lean (104 ± 17 mm3 versus 46 ± 13 mm3; P <0.05) and overweight (367 ± 45 mm3 versus 230 ± 39 mm3; P <0.01) mice, but tumor enhancement was associated with different biological outcomes depending on the diet. In the lean mice, leucine increased phosphorylation of mTOR and downstream effector S6 ribosomal protein, but in the overweight mice, leucine reduced glucose clearance and thus increased the amount of circulating glucose available to the tumor. Conclusion: These findings show that leucine supplementation enhances tumor growth in both lean and overweight mice through diet-dependent effects in a murine model of pancreatic cancer, suggesting caution against the clinical use of leucine supplementation for the purposes of skeletal muscle enhancement in cachectic patients.Nutritional Science

Guidelines for physical weed control research: flame weeding, weed harrowing and intra-row cultivation

A prerequisite for good research is the use of appropriate methodology. In order to aggregate sound research methodology, this paper presents some tentative guidelines for physical weed control research in general, and flame weeding, weed harrowing and intra-row cultivation in particular. Issues include the adjustment and use of mechanical weeders and other equipment, the recording of impact factors that affect weeding performance, methods to assess effectiveness, the layout of treatment plots, and the conceptual models underlying the experimental designs (e.g. factorial comparison, dose response). First of all, the research aims need to be clearly defined, an appropriate experimental design produced and statistical methods chosen accordingly. Suggestions on how to do this are given. For assessments, quantitative measures would be ideal, but as they require more resources, visual classification may in some cases be more feasible. The timing of assessment affects the results and their interpretation. When describing the weeds and crops, one should list the crops and the most abundantly present weed species involved, giving their density and growth stages at the time of treatment. The location of the experimental field, soil type, soil moisture and amount of fertilization should be given, as well as weather conditions at the time of treatment. The researcher should describe the weed control equipment and adjustments accurately, preferably according to the prevailing practice within the discipline. Things to record are e.g. gas pressure, burner properties, burner cover dimensions and LPG consumption in flame weeding; speed, angle of tines, number of passes and direction in weed harrowing. The authors hope this paper will increase comparability among experiments, help less experienced scientists to prevent mistakes and essential omissions, and foster the advance of knowledge on non-chemical weed management

Novel and holistic approaches are required to realise allelopathic potential for weed management

Allelopathy, i.e. plant-plant inhibition via the release of secondary metabolites into the environment, has potential for the management of weeds by circumventing herbicide resistance. However, mechanisms underpinning allelopathy are notoriously difficult to elucidate, hindering real-world application either in the form of commercial bioherbicides or allelopathic crops. Such limited application is exemplified by evidence of limited knowledge of the potential benefits of allelopathy among end-users. Here, we examine potential applications of this phenomenon, paying attention to novel approaches and influential factors requiring greater consideration, with the intention of improving the reputation and uptake of allelopathy. Avenues to facilitate more effective allelochemical discovery are also considered, with a view to stimulating the identification of new compounds and allelopathic species. Synthesis and Applications: We conclude that tackling increasing weed pressure on agricultural productivity would benefit from greater integration of the phenomenon of allelopathy, which in turn would be greatly served by a multi-disciplinary and exhaustive approach, not just through more effective isolation of the interactions involved, but through greater consideration of factors which may influence them in the field, facilitating optimisation of their benefits for weed management

Parallel Batch-Dynamic Graph Connectivity

In this paper, we study batch parallel algorithms for the dynamic connectivity problem, a fundamental problem that has received considerable attention in the sequential setting. The most well known sequential algorithm for dynamic connectivity is the elegant level-set algorithm of Holm, de Lichtenberg and Thorup (HDT), which achieves $O(\log^2 n)$ amortized time per edge insertion or deletion, and $O(\log n / \log\log n)$ time per query. We design a parallel batch-dynamic connectivity algorithm that is work-efficient with respect to the HDT algorithm for small batch sizes, and is asymptotically faster when the average batch size is sufficiently large. Given a sequence of batched updates, where $\Delta$ is the average batch size of all deletions, our algorithm achieves $O(\log n \log(1 + n / \Delta))$ expected amortized work per edge insertion and deletion and $O(\log^3 n)$ depth w.h.p. Our algorithm answers a batch of $k$ connectivity queries in $O(k \log(1 + n/k))$ expected work and $O(\log n)$ depth w.h.p. To the best of our knowledge, our algorithm is the first parallel batch-dynamic algorithm for connectivity.Comment: This is the full version of the paper appearing in the ACM Symposium on Parallelism in Algorithms and Architectures (SPAA), 201

Singlet-Triplet Physics and Shell Filling in Carbon Nanotube Double Quantum Dots

An artifcial two-atomic molecule, also called a double quantum dot (DQD), is an ideal system for exploring few electron physics. Spin-entanglement between just two electrons can be explored in such systems where singlet and triplet states are accessible. These two spin-states can be regarded as the two states in a quantum two-state system, a so-called singlet-triplet qubit. A very attractive material for realizing spin based qubits is the carbon nanotube (CNT), because it is expected to have a very long spin coherence time. Here we show the existence of a gate-tunable singlet-triplet qubit in a CNT DQD. We show that the CNT DQD has clear shell structures of both four and eight electrons, with the singlet-triplet qubit present in the four-electron shells. We furthermore observe inelastic cotunneling via the singlet and triplet states, which we use to probe the splitting between singlet and triplet, in good agreement with theory.Comment: Supplement available at: http://www.fys.ku.dk/~hij/public/singlet-triple_supp.pd

Discrete Nonlinear Schrodinger Equations with arbitrarily high order nonlinearities

A class of discrete nonlinear Schrodinger equations with arbitrarily high order nonlinearities is introduced. These equations are derived from the same Hamiltonian using different Poisson brackets and include as particular cases the saturable discrete nonlinear Schrodinger equation and the Ablowitz-Ladik equation. As a common property, these equations possess three kinds of exact analytical stationary solutions for which the Peierls-Nabarro barrier is zero. Several properties of these solutions, including stability, discrete breathers and moving solutions, are investigated

Probing the mechanical unzipping of DNA

A study of the micromechanical unzipping of DNA in the framework of the Peyrard-Bishop-Dauxois model is presented. We introduce a Monte Carlo technique that allows accurate determination of the dependence of the unzipping forces on unzipping speed and temperature. Our findings agree quantitatively with experimental results for homogeneous DNA, and for $\lambda$-phage DNA we reproduce the recently obtained experimental force-temperature phase diagram. Finally, we argue that there may be fundamental differences between {\em in vivo} and {\em in vitro} DNA unzipping