Supersymmetry on Graphs and Networks

We show that graphs, networks and other related discrete model systems carry a natural supersymmetric structure, which, apart from its conceptual importance as to possible physical applications, allows to derive a series of spectral properties for a class of graph operators which typically encode relevant graph characteristics.Comment: 11 pages, Latex, no figures, remark 4.1 added, slight alterations in lemma 5.3, a more detailed discussion at beginning of sect.6 (zero eigenspace

Interference effects in the counting statistics of electron transfers through a double quantum dot

We investigate the effect of quantum interferences and Coulomb interaction on the counting statistics of electrons crossing a double quantum dot in a parallel geometry using a generating function technique based on a quantum master equation approach. The skewness and the average residence time of electrons in the dots are shown to be the quantities most sensitive to interferences and Coulomb coupling. The joint probabilities of consecutive electron transfer processes show characteristic temporal oscillations due to interference. The steady-state fluctuation theorem which predicts a universal connection between the number of forward and backward transfer events is shown to hold even in the presence of Coulomb coupling and interference.Comment: 11 pages, 12 figure

Tailoring the frictional properties of granular media

A method of modifying the roughness of soda-lime glass spheres is presented, with the purpose of tuning inter-particle friction. The effect of chemical etching on the surface topography and the bulk frictional properties of grains is systematically investigated. The surface roughness of the grains is measured using white light interferometry and characterised by the lateral and vertical roughness length scales. The underwater angle of repose is measured to characterise the bulk frictional behaviour. We observe that the co-efficient of friction depends on the vertical roughness length scale. We also demonstrate a bulk surface roughness measurement using a carbonated soft drink.Comment: 10 pages, 17 figures, submitted to Phys. Rev.

On the solution of the initial value constraints for general relativity coupled to matter in terms of Ashtekar's variables

The method of solution of the initial value constraints for pure canonical gravity in terms of Ashtekar's new canonical variables due to CDJ is further developed in the present paper. There are 2 new main results : 1) We extend the method of CDJ to arbitrary matter-coupling again for non-degenerate metrics : the new feature is that the 'CDJ-matrix' adopts a nontrivial antisymmetric part when solving the vector constraint and that the Klein-Gordon-field is used, instead of the symmetric part of the CDJ-matrix, in order to satisfy the scalar constraint. 2) The 2nd result is that one can solve the general initial value constraints for arbitrary matter coupling by a method which is completely independent of that of CDJ. It is shown how the Yang-Mills and gravitational Gauss constraints can be solved explicitely for the corresponding electric fields. The rest of the constraints can then be satisfied by using either scalar or spinor field momenta. This new trick might be of interest also for Yang-Mills theories on curved backgrounds.Comment: Latex, 15 pages, PITHA93-1, January 9

Predicting anticancer hyperfoods with graph convolutional networks

Background: Recent efforts in the field of nutritional science have allowed the discovery of disease-beating molecules within foods based on the commonality of bioactive food molecules to FDA-approved drugs. The pioneering work in this field used an unsupervised network propagation algorithm to learn the systemic-wide effect on the human interactome of 1962 FDA-approved drugs and a supervised algorithm to predict anticancer therapeutics using the learned representations. Then, a set of bioactive molecules within foods was fed into the model, which predicted molecules with cancer-beating potential.The employed methodology consisted of disjoint unsupervised feature generation and classification tasks, which can result in sub-optimal learned drug representations with respect to the classification task. Additionally, due to the disjoint nature of the tasks, the employed approach proved cumbersome to optimize, requiring testing of thousands of hyperparameter combinations and significant computational resources.To overcome the technical limitations highlighted above, we represent each drug as a graph (human interactome) with its targets as binary node features on the graph and formulate the problem as a graph classification task. To solve this task, inspired by the success of graph neural networks in graph classification problems, we use an end-to-end graph neural network model operating directly on the graphs, which learns drug representations to optimize model performance in the prediction of anticancer therapeutics. Results: The proposed model outperforms the baseline approach in the anticancer therapeutic prediction task, achieving an F1 score of 67.99%±2.52% and an AUPR of 73.91%±3.49%. It is also shown that the model is able to capture knowledge of biological pathways to predict anticancer molecules based on the molecules’ effects on cancer-related pathways. Conclusions: We introduce an end-to-end graph convolutional model to predict cancer-beating molecules within food. The introduced model outperforms the existing baseline approach, and shows interpretability, paving the way to the future of a personalized nutritional science approach allowing the development of nutrition strategies for cancer prevention and/or therapeutics

Weakly-supervised mesh-convolutional hand reconstruction in the wild

We introduce a simple and effective network architecture for monocular 3D hand pose estimation consisting of an image encoder followed by a mesh convolutional decoder that is trained through a direct 3D hand mesh reconstruction loss. We train our network by gathering a large-scale dataset of hand action in YouTube videos and use it as a source of weak supervision. Our weakly-supervised mesh convolutions-based system largely outperforms state-of-the-art methods, even halving the errors on the in the wild benchmark. The dataset and additional resources are available at https://arielai.com/mesh_hands

Polar magneto-optical Kerr effect for low-symmetric ferromagnets

The polar magneto-optical Kerr effect (MOKE) for low-symmetric ferromagnetic crystals is investigated theoretically based on first-principle calculations of optical conductivities and a transfer matrix approach for the electrodynamics part of the problem. Exact average magneto-optical properties of polycrystals are described, taking into account realistic models for the distribution of domain orientations. It is shown that for low-symmetric ferromagnetic single crystals the MOKE is determined by an interplay of crystallographic birefringence and magnetic effects. Calculations for single and bi-crystal of hcp 11-20 Co and for a polycrystal of CrO_2 are performed, with results being in good agreement with experimental data.Comment: 14 pages, 7 figures, accepted for publication in Phys. Rev.

Renormalization of heavy-light currents in moving NRQCD

Heavy-light decays such as $B \to \pi \ell \nu$, $B \to K^{*} \gamma$ and $B \to K^{(*)} \ell \ell$ can be used to constrain the parameters of the Standard Model and in indirect searches for new physics. While the precision of experimental results has improved over the last years this has still to be matched by equally precise theoretical predictions. The calculation of heavy-light form factors is currently carried out in lattice QCD. Due to its small Compton wavelength we discretize the heavy quark in an effective non-relativistic theory. By formulating the theory in a moving frame of reference discretization errors in the final state are reduced at large recoil. Over the last years the formalism has been improved and tested extensively. Systematic uncertainties are reduced by renormalizing the m(oving)NRQCD action and heavy-light decay operators. The theory differs from QCD only for large loop momenta at the order of the lattice cutoff and the calculation can be carried out in perturbation theory as an expansion in the strong coupling constant. In this paper we calculate the one loop corrections to the heavy-light vector and tensor operator. Due to the complexity of the action the generation of lattice Feynman rules is automated and loop integrals are solved by the adaptive Monte Carlo integrator VEGAS. We discuss the infrared and ultraviolet divergences in the loop integrals both in the continuum and on the lattice. The light quarks are discretized in the ASQTad and highly improved staggered quark (HISQ) action; the formalism is easily extended to other quark actions.Comment: 24 pages, 11 figures. Published in Phys. Rev. D. Corrected a typo in eqn. (51