479,338 research outputs found
Color-flow decomposition of QCD amplitudes
We introduce a new color decomposition for multi-parton amplitudes in QCD,
free of fundamental-representation matrices and structure constants. This
decomposition has a physical interpretation in terms of the flow of color,
which makes it ideal for merging with shower Monte-Carlo programs. The
color-flow decomposition allows for very efficient evaluation of amplitudes
with many quarks and gluons, many times faster than the standard color
decomposition based on fundamental-representation matrices. This will increase
the speed of event generators for multi-jet processes, which are the principal
backgrounds to signals of new physics at colliders.Comment: 23 pages, 11 figures, version to appear on Phys. Rev.
A practical fpt algorithm for Flow Decomposition and transcript assembly
The Flow Decomposition problem, which asks for the smallest set of weighted
paths that "covers" a flow on a DAG, has recently been used as an important
computational step in transcript assembly. We prove the problem is in FPT when
parameterized by the number of paths by giving a practical linear fpt
algorithm. Further, we implement and engineer a Flow Decomposition solver based
on this algorithm, and evaluate its performance on RNA-sequence data.
Crucially, our solver finds exact solutions while achieving runtimes
competitive with a state-of-the-art heuristic. Finally, we contextualize our
design choices with two hardness results related to preprocessing and weight
recovery. Specifically, -Flow Decomposition does not admit polynomial
kernels under standard complexity assumptions, and the related problem of
assigning (known) weights to a given set of paths is NP-hard.Comment: Introduces software package Toboggan: Version 1.0.
http://dx.doi.org/10.5281/zenodo.82163
Applying Machine Based Decomposition in 2-Machine Flow Shops
The Shifting Bottleneck (SB) heuristic is among the most successful approximation methods for solving the Job Shop problem. It is essentially a machine based decomposition procedure where a series of One Machine Sequencing Problems (OMSPs) are solved. However, such a procedure has been reported to be highly ineffective for the Flow Shop problems (Jain and Meeran 2002). In particular, we show that for the 2-machine Flow Shop problem, the SB heurisitc will deliver the optimal solution in only a small number of instances. We examine the reason behind the failure of the machine based decomposition method for the Flow Shop. An optimal machine based decomposition procedure is formulated for the 2-machine Flow Shop, the time complexity of which is worse than that of the celebrated Johnsons Rule. The contribution of the present study lies in showing that the same machine based decomposition procedures which are so successful in solving complex Job Shops can also be suitably modified to optimally solve the simpler Flow Shops.
Decomposition of Optical Flow on the Sphere
We propose a number of variational regularisation methods for the estimation
and decomposition of motion fields on the -sphere. While motion estimation
is based on the optical flow equation, the presented decomposition models are
motivated by recent trends in image analysis. In particular we treat
decomposition as well as hierarchical decomposition. Helmholtz decomposition of
motion fields is obtained as a natural by-product of the chosen numerical
method based on vector spherical harmonics. All models are tested on time-lapse
microscopy data depicting fluorescently labelled endodermal cells of a
zebrafish embryo.Comment: The final publication is available at link.springer.co
Investigation of flow structures involved in sound generation by two- and three-dimensional cavity flows
Proper Orthogonal Decomposition and Stochastic Estimation are combined to shed some light on the link between organized flow structures and noise generation by turbulent flows. Proper Orthogonal Decomposition (POD) is firstly used to extract selected flow events. Based on the knowledge of these structures, the Quadratic Stochastic Estimation of the acoustic pressure field is secondly performed. Both procedures are successively applied to two- and three-dimensional numerical databases of a flow over a cavity. It is demonstrated that POD can extract selected aerodynamic events which can be associated with selected frequencies in the acoustic spectra. Reconstructed acoustic fields also indicate the aerodynamic events which are responsible of the main energy of the noise emission. Such mathematical tools offer new perspectives in analysing flow structures involved in sound generation by turbulent flows and in the experimental design of a flow control strategy
The triple decomposition of a fluctuating velocity field in a multiscale flow
A new method for the triple decomposition of a multiscale flow, which is based on the novel optimal mode decomposition (OMD) technique, is presented. OMD provides low order linear dynamics, which fits a given data set in an optimal way and is used to distinguish between a coherent (periodic) part of a flow and a stochastic fluctuation. The method needs no external phase indication since this information, separate for coherent structures associated with each length scale introduced into the flow, appears as the output. The proposed technique is compared against two traditional methods of the triple decomposition, i.e., bin averaging and proper orthogonal decomposition. This is done with particle image velocimetry data documenting the near wake of a multiscale bar array. It is shown that both traditional methods are unable to provide a reliable estimation for the coherent fluctuation while the proposed technique performs very well. The crucial result is that the coherence peaks are not observed within the spectral properties of the stochastic fluctuation derived with the proposed method; however, these properties remain unaltered at the residual frequencies. This proves the method’s capability of making a distinction between both types of fluctuations. The sensitivity to some prescribed parameters is checked revealing the technique’s robustness. Additionally, an example of the method application for analysis of a multiscale flow is given, i.e., the phase conditioned transverse integral length is investigated in the near wake region of the multiscale object array
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