A Second-Order Distributed Trotter-Suzuki Solver with a Hybrid Kernel

The Trotter-Suzuki approximation leads to an efficient algorithm for solving the time-dependent Schr\"odinger equation. Using existing highly optimized CPU and GPU kernels, we developed a distributed version of the algorithm that runs efficiently on a cluster. Our implementation also improves single node performance, and is able to use multiple GPUs within a node. The scaling is close to linear using the CPU kernels, whereas the efficiency of GPU kernels improve with larger matrices. We also introduce a hybrid kernel that simultaneously uses multicore CPUs and GPUs in a distributed system. This kernel is shown to be efficient when the matrix size would not fit in the GPU memory. Larger quantum systems scale especially well with a high number nodes. The code is available under an open source license.Comment: 11 pages, 10 figure

Quantum Monte Carlo scheme for frustrated Heisenberg antiferromagnets

When one tries to simulate quantum spin systems by the Monte Carlo method, often the 'minus-sign problem' is encountered. In such a case, an application of probabilistic methods is not possible. In this paper the method has been proposed how to avoid the minus sign problem for certain class of frustrated Heisenberg models. The systems where this method is applicable are, for instance, the pyrochlore lattice and the $J_1-J_2$ Heisenberg model. The method works in singlet sector. It relies on expression of wave functions in dimer (pseudo)basis and writing down the Hamiltonian as a sum over plaquettes. In such a formulation, matrix elements of the exponent of Hamiltonian are positive.Comment: 19 LaTeX pages, 6 figures, 1 tabl

Human Body Shape Classification Based on a Single Image

There is high demand for online fashion recommender systems that incorporate the needs of the consumer's body shape. As such, we present a methodology to classify human body shape from a single image. This is achieved through the use of instance segmentation and keypoint estimation models, trained only on open-source benchmarking datasets. The system is capable of performing in noisy environments owing to to robust background subtraction. The proposed methodology does not require 3D body recreation as a result of classification based on estimated keypoints, nor requires historical information about a user to operate - calculating all required measurements at the point of use. We evaluate our methodology both qualitatively against existing body shape classifiers and quantitatively against a novel dataset of images, which we provide for use to the community. The resultant body shape classification can be utilised in a variety of downstream tasks, such as input to size and fit recommendation or virtual try-on systems

A Gray Code for the Shelling Types of the Boundary of a Hypercube

We consider two shellings of the boundary of the hypercube equivalent if one can be transformed into the other by an isometry of the cube. We observe that a class of indecomposable permutations, bijectively equivalent to standard double occurrence words, may be used to encode one representative from each equivalence class of the shellings of the boundary of the hypercube. These permutations thus encode the shelling types of the boundary of the hypercube. We construct an adjacent transposition Gray code for this class of permutations. Our result is a signed variant of King's result showing that there is a transposition Gray code for indecomposable permutations

Efficient numerical integrators for stochastic models

The efficient simulation of models defined in terms of stochastic differential equations (SDEs) depends critically on an efficient integration scheme. In this article, we investigate under which conditions the integration schemes for general SDEs can be derived using the Trotter expansion. It follows that, in the stochastic case, some care is required in splitting the stochastic generator. We test the Trotter integrators on an energy-conserving Brownian model and derive a new numerical scheme for dissipative particle dynamics. We find that the stochastic Trotter scheme provides a mathematically correct and easy-to-use method which should find wide applicability.Comment: v

Stochastic Light-Cone CTMRG: a new DMRG approach to stochastic models

We develop a new variant of the recently introduced stochastic transfer-matrix DMRG which we call stochastic light-cone corner-transfer-matrix DMRG (LCTMRG). It is a numerical method to compute dynamic properties of one-dimensional stochastic processes. As suggested by its name, the LCTMRG is a modification of the corner-transfer-matrix DMRG (CTMRG), adjusted by an additional causality argument. As an example, two reaction-diffusion models, the diffusion-annihilation process and the branch-fusion process, are studied and compared to exact data and Monte-Carlo simulations to estimate the capability and accuracy of the new method. The number of possible Trotter steps of more than 10^5 shows a considerable improvement to the old stochastic TMRG algorithm.Comment: 15 pages, uses IOP styl

Bayesian Strong Gravitational-Lens Modeling on Adaptive Grids: Objective Detection of Mass Substructure in Galaxies

We introduce a new adaptive and fully Bayesian grid-based method to model strong gravitational lenses with extended images. The primary goal of this method is to quantify the level of luminous and dark-mass substructure in massive galaxies, through their effect on highly-magnified arcs and Einstein rings. The method is adaptive on the source plane, where a Delaunay tessellation is defined according to the lens mapping of a regular grid onto the source plane. The Bayesian penalty function allows us to recover the best non-linear potential-model parameters and/or a grid-based potential correction and to objectively quantify the level of regularization for both the source and the potential. In addition, we implement a Nested-Sampling technique to quantify the errors on all non-linear mass model parameters -- ... -- and allow an objective ranking of different potential models in terms of the marginalized evidence. In particular, we are interested in comparing very smooth lens mass models with ones that contain mass-substructures. The algorithm has been tested on a range of simulated data sets, created from a model of a realistic lens system. One of the lens systems is characterized by a smooth potential with a power-law density profile, twelve include a NFW dark-matter substructure of different masses and at different positions and one contains two NFW dark substructures with the same mass but with different positions. Reconstruction of the source and of the lens potential for all of these systems shows the method is able, in a realistic scenario, to identify perturbations with masses >=10^7 solar mass when located on the Einstein ring. For positions both inside and outside of the ring, masses of at least 10^9 solar mass are required (...).Comment: 21 pages, 15 figures, 4 tables; accepted for publication in MNRA

Brownian Dynamics Simulation of Polydisperse Hard Spheres

Standard algorithms for the numerical integration of the Langevin equation require that interactions are slowly varying during to the integration timestep. This in not the case for hard-body systems, where there is no clearcut between the correlation time of the noise and the timescale of the interactions. Starting from a short time approximation of the Smoluchowsky equation, we introduce an algorithm for the simulation of the overdamped Brownian dynamics of polydisperse hard-spheres in absence of hydrodynamics interactions and briefly discuss the extension to the case of external drifts

Neutron-Neutron Fusion

The neutron-neutron fusion process, $nn\to de\nu$, at very low neutron energies is studied in the framework of pionless effective field theory that incorporates dibaryon fields. The cross section and electron energy spectrum for this process are calculated up to next-to-leading order. We include the radiative corrections of ${\cal O}(\alpha)$ calculated for the one-body transition amplitude. The precision of our theoretical estimates is found to be governed essentially by the accuracy with which the empirical values of the neutron-neutron scattering length and effective range are currently known. Also discussed is the precision of theoretical estimates of the transition rates of related electroweak processes in few-nucleon systems.Comment: 14 pages, 4 figures, minor correction, accepted for publication in Phys. Lett.