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On the complexity of evaluating highest weight vectors [article]

Markus Bläser, Julian Dörfler, Christian Ikenmeyer
2021 arXiv   pre-print
However, fundamental theorems of algebraic geometry and representation theory grant that every lower bound in GCT can be proved by the use of so-called highest weight vectors (HWVs).  ...  In the setting of interest in GCT (namely in the setting of polynomials) we prove the NP-hardness of the evaluation of HWVs in general, and we give efficient algorithms if the treewidth of the corresponding  ...  Our contributions To our best knowledge, we systematically study the complexity of evaluating highest weight vectors for the first time.  ... 
arXiv:2002.11594v2 fatcat:a2eslzwjw5gr5acapxa3kel6eu

On the Complexity of Evaluating Highest Weight Vectors

Markus Bläser, Julian Dörfler, Christian Ikenmeyer, Valentine Kabanets
2021
However, fundamental theorems of algebraic geometry and representation theory grant that every lower bound in GCT can be proved by the use of so-called highest weight vectors (HWVs).  ...  In the setting of interest in GCT (namely in the setting of polynomials) we prove the NP-hardness of the evaluation of HWVs in general, and we give efficient algorithms if the treewidth of the corresponding  ...  C C C 2 0 2 1 29:6 On the Complexity of Evaluating Highest Weight Vectors The proof uses a power series argument.  ... 
doi:10.4230/lipics.ccc.2021.29 fatcat:ws3dlfrhwzgqzc4xgrt4qpqlum

A new method of weight multiplicities evaluation for semi-simple Lie algebras [article]

Anatoli Loutsiouk
2018 arXiv   pre-print
In most applications of semi-simple Lie groups and algebras representation theory, calculating weight multiplicities is one of the most often used and effort consuming operations.  ...  The celebrated Kostant weight multiplicity formula uses summation over the Weyl group of values of Kostant partition function, and the Freudenthal formula is recurrent.  ...  The program has 3 subroutines, which evaluate the polytopes k depending on the type of the highest weight: (p=q, p<q, p>q).  ... 
arXiv:1809.04837v1 fatcat:ygulym2p2jh4dpq75r7oc36nqa

Viral Vector Mimicking And Nucleus Targeted Nanoparticles Based On Dexamethasone Conjugated Polyethylenimine Nano-Liposomes: Preparation And Evaluation Of Transfection Efficiency

Reza Kazemi Oskuee
2016 Zenodo  
Complexes containing liposome, PEI 10 kDa and dexamethasone had the highest transfection activity. Furthermore, non-viral vectors described in this study showed low cytotoxicity.  ...  Mean particle size of prepared complexes was less than 200 nm and there was no significant difference in size by increasing molecular weight of PEIs. All complexes had positive surface charge.  ...  Complexes containing liposome, PEI 10 kDa and dexamethasone had the highest transfection activity.  ... 
doi:10.5281/zenodo.155376 fatcat:7idwzuajjrel3a2huauggiipwi

On representations of the elliptic quantum groupE τ,η(sl 2)

Giovanni Felder, Alexander Varchenko
1996 Communications in Mathematical Physics  
We describe representation theory of the elliptic quantum group E_τ,η(sl_2).  ...  It turns out that the representation theory is parallel to the representation theory of the Yangian Y(sl_2) and the quantum loop group U_q( sl _2).  ...  The highest weight is of one of the following three types.  ... 
doi:10.1007/bf02101296 fatcat:ofepytkm7nbxjbplulud6h5lye

Classification of irreducible quasifinite modules over map Virasoro algebras

Alistair Savage
2012 Transformation groups  
over the complex numbers.  ...  It is shown that all such modules are tensor products of generalized evaluation modules. We also give an explicit sufficient condition for a Verma module of Vir \otimes A to be reducible.  ...  So we get a complete characterization of the highest weight modules that are quasifinite (this problem is trivial for the usual Virasoro algebra). algebra of polynomial vector fields on the circle.  ... 
doi:10.1007/s00031-012-9182-9 fatcat:mv4v33u7hja7bjpuuh3euealvu

Statistical Pattern Recognition Using the Normalized Complex Moment Components Vector [chapter]

Stavros Paschalakis, Peter Lee
2000 Lecture Notes in Computer Science  
This paper presents a new feature vector for statistical pattern recognition based on the theory of moments, namely the Normalized Complex Moment Components (NCMC).  ...  vector, the Hu moment invariants.  ...  In this implementation, the reference vector for each group is the complex moment of the highest order p+q within the group.  ... 
doi:10.1007/3-540-44522-6_55 fatcat:nystpfgw2zgaxpqfobpopwijti

Algebraic Bethe ansatz for the elliptic quantum group Eτ,η(sl2)

Giovanni Felder, Alexander Varchenko
1996 Nuclear Physics B  
The latter is a q-deformation of Hermite's solution of the Lamé equation.  ...  To each representation of the elliptic quantum group E_τ,η(sl_2) is associated a family of commuting transfer matrices. We give common eigenvectors by a version of the algebraic Bethe ansatz method.  ...  We are grateful to the organizers of the program on "Conformal and integrable quantum field theory", K. Gawȩdzki and I. Todorov, for giving us this opportunity.  ... 
doi:10.1016/s0550-3213(96)00461-0 fatcat:wsf23wba4rd25h37kt725ne3fm

The Six-Vertex Model at Roots of Unity and some Highest Weight Representations of the sl2 Loop Algebra

Tetsuo Deguchi
2006 Annales de l'Institute Henri Poincare. Physique theorique  
We discuss irreducible highest weight representations of the sl(2) loop algebra and reducible indecomposable ones in association with the sl(2) loop algebra symmetry of the six-vertex model at roots of  ...  We formulate an elementary proof that every highest weight representation with distinct evaluation parameters is irreducible.  ...  He would also like to thank many participants of the conference for useful comments and discussions. This work is partially supported by the Grant-in-Aid (No. 17540351).  ... 
doi:10.1007/s00023-006-0290-8 fatcat:vzd2zb6rdfdildpanha737jt7a

Subsumptive reflection in SNOMED CT: a large description logic-based terminology for diagnosis [article]

A.M. Mohan Rao
2015 arXiv   pre-print
We also use a 50-million medical word corpus for estimating the vectors of disease-feature links.  ...  Logical implications of PAIRS data on SNOMED CT include 70% of the links do not share any common system while 18% share organ and 12% share both system and organ.  ...  Performance of PAIRS is evaluated and results are available publicly.  ... 
arXiv:1512.03516v1 fatcat:a45jbwjv2zh3bkeucrmosmze7e

All Singular Vectors of the N=2 Superconformal Algebra via the Algebraic Continuation Approach [article]

A M Semikhatov, I Yu Tipunin
1998 arXiv   pre-print
Our construction is based on continuing the extremal diagrams of N=2 Verma modules to the states satisfying the twisted conditions with complex twists.  ...  The method of 'continued products' of fermions is a counterpart of the method of complex powers used in the constructions of singular vectors for affine Lie algebras.  ...  The work of AMS was supported in part by grant #93-0633 from the European Community and the work of IYT, by the RFFI grant 96-01-00725. The work of IYT is also supported by a Landau grant.  ... 
arXiv:hep-th/9604176v3 fatcat:35mpyyfm6jdyphf3a6mxqtbzda

Equations for GL invariant families of polynomials [article]

Paul Breiding, Christian Ikenmeyer, Mateusz Michałek, Reuven Hodges
2021 arXiv   pre-print
The algorithm relies on a database of specific Young tableaux and highest weight polynomials. We provide the database and the implementation of the database construction algorithm.  ...  It outputs the ideal of that family intersected with the space of homogeneous polynomials of degree d.  ...  These questions not only inspired us, but also revealed bottlenecks of our algorithms. We also thank anonymous referees, whose suggestions helped us to improve the exposition of the paper.  ... 
arXiv:2110.06608v1 fatcat:dpddnpsjzfcffbd3aq7rkbq5ru

Design and evaluation of medical ultrasonic adaptive beamforming algorithm implementation on heterogeneous embedded computing platform

Junying Chen, Jinhui Chen, Huaqing Min
2017 EURASIP Journal on Embedded Systems  
Recently, because of the needs of portable and mobile medical ultrasonic diagnoses, the development of real-time medical ultrasonic imaging algorithms on embedded computing platforms is a rising research  ...  Furthermore, platform power consumptions, computation energy efficiency, and platform cost efficiency of the experimental heterogeneous embedded platforms were also evaluated, which demonstrated that the  ...  For example, the input data delay calculation had a computational complexity of O(n), the covariance matrix calculation had a computational complexity of O(n 2 ), and the adaptive weight calculation had  ... 
doi:10.1186/s13639-017-0069-7 fatcat:757woct4f5av7gm4b666fsxjqi

Page 795 of Mathematical Reviews Vol. , Issue 98B [page]

1998 Mathematical Reviews  
The au- thors show that under certain conditions any irreducible highest- weight module of finite type is isomorphic to a tensor product of evaluation modules and a one-dimensional module.  ...  This very long paper is devoted to computing the highest coefficient of det H,, where H, is a contravariant form defined on highest weight modules.  ... 

Scaling techniques for parallel ant colony optimization on large problem instances

Joshua Peake, Martyn Amos, Paraskevas Yiapanis, Huw Lloyd
2019 Proceedings of the Genetic and Evolutionary Computation Conference on - GECCO '19  
Using a combination of these techniques we achieve, in a reasonable time, the best solution qualities recorded by ACO on the Art TSP Traveling Salesman Problem instances, and the first evaluation of a  ...  In this paper we propose a restricted variant of the pheromone matrix with linear memory complexity, which stores pheromone values only for members of a candidate set of next moves.  ...  A highest weights vector is maintained, storing the highest weight from each lane of the vector.  ... 
doi:10.1145/3321707.3321832 dblp:conf/gecco/PeakeAYL19 fatcat:ezdwdvytpfhbhamwovj6eihcg4
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