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Using two-dimensional Projections for Stronger Separation and Propagation of Bilinear Terms [article]

Benjamin Müller, Felipe Serrano, Ambros Gleixner
2020 arXiv   pre-print
One of the most fundamental ingredients in mixed-integer nonlinear programming solvers is the well-known McCormick relaxation for a product of two variables x and y over a box-constrained domain.  ...  We complement this by a new bound tightening procedure that efficiently computes the best possible bounds for x, y, and xy over the available projections.  ...  Acknowledgments This work has received support from the Federal Ministry of Education and Research (BMBF Grant 05M14ZAM, Research Campus MODAL) and from the Federal Ministry for Economic Affairs and Energy  ... 
arXiv:1903.05521v2 fatcat:sy5xzfjc6rachiwd55ljvob5vy

Using Two-Dimensional Projections for Stronger Separation and Propagation of Bilinear Terms

Benjamin Müller, Felipe Serrano, Ambros Gleixner
2020 SIAM Journal on Optimization  
One of the most fundamental ingredients in mixed-integer nonlinear programming solvers is the well-known McCormick relaxation for a product of two variables x and y over a boxconstrained domain.  ...  We complement this by a new bound tightening procedure that efficiently computes the best possible bounds for x, y, and xy over the available projections.  ...  Acknowledgments This work has received support from the Federal Ministry of Education and Research (BMBF Grant 05M14ZAM, Research Campus MODAL) and from the Federal Ministry for Economic Affairs and Energy  ... 
doi:10.1137/19m1249825 fatcat:u32oo65hxbgpxpqhf2sdyxfi7i

New extended interpolating operators for hadron correlation functions [article]

Francesco Scardino, Mauro Papinutto, Stefan Schaefer
2016 arXiv   pre-print
New extended interpolating operators made of quenched three dimensional fermions are introduced in the context of lattice QCD.  ...  Moreover the short distance behaviour of the two point functions built from these operators is greatly improved.  ...  The coupling of B with bilinears allows the quenched three dimensional fermions to propagate in time via the four dimensional ones.  ... 
arXiv:1612.07737v1 fatcat:hxyznqtrtvbj3gwjm36kec5upu

Topology and strong four fermion interactions in four dimensions

Simon Catterall, Nouman Butt
2018 Physical Review D  
We determine the structure of the low energy effective action for the auxiliary field needed to generate the four fermion term and find it has an novel structure that admits topologically non-trivial defects  ...  We study massless fermions interacting through a particular four fermion term in four dimensions. Exact symmetries prevent the generation of bilinear fermion mass terms.  ...  The action for such a configuration depends logarithmically on the separation of the two vortices which hence bind tightly together at low temperatures.  ... 
doi:10.1103/physrevd.97.094502 fatcat:p2tsif2cdfbebntv4uwqdiwwha

The Yukawa2 quantum field theory without cutoffs

James Glimm, Arthur Jaffe
1971 Journal of Functional Analysis  
We construct the Heisenberg picture dynamics for the Yukawa quantum field theory in two-dimensional space-time.  ...  All cutoffs are removed in the field operators, and the fields are formally Lorentz covariant. The fields are local, and commute or anticommute at space-like separated points.  ...  Because of the difficulty in solving the equations of quantum field theory, we have worked mainly in two-dimensional space-time.  ... 
doi:10.1016/0022-1236(71)90039-5 fatcat:e6jmh7hp55du7ncf6fhvlmqsui

The Chiral Magnetic Effect and Axial Anomalies [chapter]

Gökçe Başar, Gerald V. Dunne
2013 Lecture Notes in Physics  
We give an elementary derivation of the chiral magnetic effect based on a strong magnetic field lowest-Landau-level projection in conjunction with the well-known axial anomalies in two- and four-dimensional  ...  We then discuss the competition between spin projection, due to a strong magnetic field, and chirality projection, due to an instanton, for light fermions in QCD and QED.  ...  This is the kinetic term of a two-dimensional Lagrangian.  ... 
doi:10.1007/978-3-642-37305-3_10 fatcat:lpplisoflvcztec4kl5kt53bo4

Cloud Transformers: A Universal Approach To Point Cloud Processing Tasks [article]

Kirill Mazur, Victor Lempitsky
2021 arXiv   pre-print
This building block combines the ideas of spatial transformers and multi-view convolutional networks with the efficiency of standard convolutional layers in two and three-dimensional dense grids.  ...  The new block operates via multiple parallel heads, whereas each head differentiably rasterizes feature representations of individual points into a low-dimensional space, and then uses dense convolution  ...  (we use up to w=128 for two-dimensional grids and up to w=32 for three-dimensional grids).  ... 
arXiv:2007.11679v4 fatcat:kyt3l6f3sjcgrm4y6sj25c6pxi

Staggering towards a calculation of weak amplitudes

Stephen R. Sharpe
1989 Nuclear Physics B - Proceedings Supplements  
An explanation is given of the methods required to calculate hadronic matrix elements of the weak Hamiltonian using lattice QCD with staggered fermions.  ...  . : results are presented for the l-loop perturbative mixing of the weak interaction operators. New numerical techniques designed for staggered fermions are described.  ...  ACKNOWLEDGEMENTS -I would like to thank the organizers for an outstanding workshop, and the  ... 
doi:10.1016/0920-5632(89)90572-0 fatcat:o3efd6uux5hhbhlkpcuavzwk7u

A micromechanical fracture analysis to investigate the effect of healing particles on the overall mechanical response of a self‐healing particulate composite

Sathiskumar A. Ponnusami, Jayaprakash Krishnasamy, Sergio Turteltaub, Sybrand Zwaag
2018 Fatigue & Fracture of Engineering Materials & Structures  
The study can be used as a guiding tool for designing an extrinsic self-healing material and understanding the effect of the healing particles on the overall mechanical properties of the material.  ...  The fracture behaviour in terms of the composite strength and the percentage of fractured particles is reported as a function of the mismatch in fracture properties between the healing particles and the  ...  meshed using two-dimensional three-node plane-strain elements (CPE3) for the particle and the matrix phases, to model their bulk constitutive behaviour.  ... 
doi:10.1111/ffe.12929 fatcat:rmilwussm5gghkw2fau4watmmi

Bilinear Generalized Approximate Message Passing—Part I: Derivation

Jason T. Parker, Philip Schniter, Volkan Cevher
2014 IEEE Transactions on Signal Processing  
In the first part of the paper, we derive our Bilinear G-AMP (BiG-AMP) algorithm as an approximation of the sum-product belief propagation algorithm in the high-dimensional limit, where central-limit theorem  ...  We extend the generalized approximate message passing (G-AMP) approach, originally proposed for high-dimensional generalized-linear regression in the context of compressive sensing, to the generalized-bilinear  ...  ACKNOWLEDGMENT The authors would like to thank Sundeep Rangan, Florent Krzakala, and Lenka Zdeborová for insightful discussions on various aspects of AMP-based inference.  ... 
doi:10.1109/tsp.2014.2357776 fatcat:krwqizxehfbjpcezuiilnpguwm

Nonperturbative renormalization for improved staggered bilinears

Andrew T. Lytle, Stephen R. Sharpe
2013 Physical Review D  
term (for ratios) or of size O(1) \times \alpha^2 (for the bilinears themselves).  ...  We derive the consequences of lattice symmetries for the propagator and vertices.  ...  The two propagators are then tied together with the bilinear.  ... 
doi:10.1103/physrevd.88.054506 fatcat:jdhgf45ttncwdhieesf5k5zkva

Learning Temporal Attention in Dynamic Graphs with Bilinear Interactions [article]

Boris Knyazev, Carolyn Augusta, Graham W. Taylor
2020 arXiv   pre-print
We also propose a bilinear transformation layer for pairs of node features instead of concatenation, typically used in prior work, and demonstrate its superior performance in all cases.  ...  As temporal attention drives between-node feature propagation, using the dynamics of node interactions to learn this key component provides more flexibility while simultaneously avoiding issues associated  ...  The views, opinions and/or findings expressed are those of the author and should not be interpreted as representing the official views or policies of the Department of Defense or the U.S. Government.  ... 
arXiv:1909.10367v2 fatcat:uno6dykq7bckrb35liuakxdbmi

New mixed quantum∕semiclassical propagation method

Dimitri Antoniou, David Gelman, Steven D. Schwartz
2007 Journal of Chemical Physics  
The authors developed a new method for calculating the quantum evolution of multidimensional systems, for cases in which the system can be assumed to consist of a quantum subsystem and a bath subsystem  ...  The method combines two ideas: starting from a simple frozen Gaussian description of the bath subsystem, then calculate quantum corrections to the propagation of the quantum subsystem.  ...  The initial state for the full quantum calculations was chosen to be a product of two one-dimensional Gaussians.  ... 
doi:10.1063/1.2731779 pmid:17508792 fatcat:rbbxne246zdhresyvswu74jtae

Efficient parametrization of the vertex function,Ωscheme, and thet,t′Hubbard model at van Hove filling

C. Husemann, M. Salmhofer
2009 Physical Review B  
The numerical computation of the RG flow of the boson propagators reproduces the leading weak coupling instabilities of the two-dimensional Hubbard model at Van Hove filling, as they were previously obtained  ...  It is based on a decomposition of the effective two-fermion interaction into fermion bilinears that interact via exchange bosons.  ...  The latter two are not of the form of a boson propagator mediating between two fermion bilinears.  ... 
doi:10.1103/physrevb.79.195125 fatcat:indwb4kzdzdkfo44f2xuvvkhs4

Dimension reduction by balanced truncation: Application to light-induced control of open quantum systems

Boris Schäfer-Bung, Carsten Hartmann, Burkhard Schmidt, Christof Schütte
2011 Journal of Chemical Physics  
Generalization of the linear theory have been proposed to cope with the bilinear terms arising from the coupling between the control field and the quantum system.  ...  The accuracy of dimension reduction is investigated by comparing the populations obtained for the truncated system versus those for the original system.  ...  The use of stochastic wave function methods is an alternative way to cope with high dimensionality [22] [23] [24] in density matrix propagation.  ... 
doi:10.1063/1.3605243 pmid:21744893 fatcat:b25f47rs55eqnlgxggq2wcfkx4
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