Symbolic Encoding of Simultaneities: Re-designing the General Chord Type Representation

2021 ◽  
Author(s):  
Konstantinos Giannos ◽  
Emilios Cambouropoulos
Keyword(s):  
Type Representation

scholarly journals Integrability of Riemann-Type Hydrodynamical Systems and Dubrovin’s Integrability Classification of Perturbed KdV-Type Equations

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 1077
Author(s):  
Yarema A. Prykarpatskyy
Keyword(s):  
Conservation Laws ◽  
Hamiltonian Structure ◽  
Necessary Condition ◽  
Type Representation ◽  
Infinite Hierarchy ◽  
Polynomial Coefficients ◽  
Kdv Type Equations ◽  
Special Case

Dubrovin’s work on the classification of perturbed KdV-type equations is reanalyzed in detail via the gradient-holonomic integrability scheme, which was devised and developed jointly with Maxim Pavlov and collaborators some time ago. As a consequence of the reanalysis, one can show that Dubrovin’s criterion inherits important parts of the gradient-holonomic scheme properties, especially the necessary condition of suitably ordered reduction expansions with certain types of polynomial coefficients. In addition, we also analyze a special case of a new infinite hierarchy of Riemann-type hydrodynamical systems using a gradient-holonomic approach that was suggested jointly with M. Pavlov and collaborators. An infinite hierarchy of conservation laws, bi-Hamiltonian structure and the corresponding Lax-type representation are constructed for these systems.

scholarly journals High energy scattering of Dirac particles on smooth potentials

2016 ◽  
Vol 31 (23) ◽  
pp. 1650126 ◽  
Author(s):  
Nguyen Suan Han ◽  
Le Anh Dung ◽  
Nguyen Nhu Xuan ◽  
Vu Toan Thang
Keyword(s):  
Dirac Equation ◽  
Cross Sections ◽  
Differential Cross ◽  
Scattering Amplitude ◽  
High Energy ◽  
Type Representation ◽  
Dirac Particles ◽  
Energy Scattering ◽  
Two Component ◽  
High Energy Scattering

The derivation of the Glauber type representation for the high energy scattering amplitude of particles of spin 1/2 is given within the framework of the Dirac equation in the Foldy–Wouthuysen (FW) representation and two-component formalism. The differential cross-sections on the Yukawa and Gaussian potentials are also considered and discussed.

scholarly journals Unsupervised integration of single-cell multi-omics datasets with disparities in cell-type representation

2021 ◽  
Author(s):  
Pinar Demetci ◽  
Rebecca Santorella ◽  
Bjorn Sandstede ◽  
Ritambhara Singh
Keyword(s):  
Single Cell ◽  
Optimal Transport ◽  
Integrated Analysis ◽  
Omics Data ◽  
Cell Alignment ◽  
Cell Type ◽  
Type Representation ◽  
Cellular Processes ◽  
Self Tuning ◽  
Unsupervised Algorithms

Integrated analysis of multi-omics data allows the study of how different molecular views in the genome interact to regulate cellular processes; however, with a few exceptions, applying multiple sequencing assays on the same single cell is not possible. While recent unsupervised algorithms align single-cell multi-omic datasets, these methods have been primarily benchmarked on co-assay experiments rather than the more common single-cell experiments taken from separately sampled cell populations. Therefore, most existing methods perform subpar alignments on such datasets. Here, we improve our previous work Single Cell alignment using Optimal Transport (SCOT) by using unbalanced optimal transport to handle disproportionate cell-type representation and differing sample sizes across single-cell measurements. We show that our proposed method, SCOTv2, consistently yields quality alignments on five real-world single-cell datasets with varying cell-type proportions and is computationally tractable. Additionally, we extend SCOTv2 to integrate multiple ($M\geq2$) single-cell measurements and present a self-tuning heuristic process to select hyperparameters in the absence of any orthogonal correspondence information.

scholarly journals Constrained exchangeable partitions

2006 ◽  
Vol DMTCS Proceedings vol. AG,... (Proceedings) ◽  
Author(s):  
Alexander Gnedin
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Random Partitions ◽  
Type Representation ◽  
International Audience ◽  
De Finetti ◽  
Infinite Set ◽  
Special Case

International audience For a class of random partitions of an infinite set a de Finetti-type representation is derived, and in one special case a central limit theorem for the number of blocks is shown.

scholarly journals Examples for an extended Barabási-Albert model with random initial degrees

2020 ◽  
Vol 8 ◽  
pp. 3-13
Author(s):  
Sándor Zsuppán
Keyword(s):  
Representation Formula ◽  
Type Representation ◽  
Lamé Equation ◽  
Linear Elastostatics

We develop a Papkovich-Neuber type representation formula for the solutions of the Navier-Lamé equation of linear elastostatics for spatial star-shaped domains. This representation is compared to the existing ones.

A Hybrid-Type Expert System for the Design of Marine Power Plants Using AI Technique and Design Optimization Method

1987 ◽  
Author(s):  
S. Akagi ◽  
T. Tanaka ◽  
H. Kubonishi
Keyword(s):  
Expert System ◽  
Design Process ◽  
Numerical Optimization ◽  
Power Plants ◽  
Optimization Method ◽  
Design Tool ◽  
Production Rules ◽  
Type Representation ◽  
Cad System ◽  
Hybrid Type

Abstract A hybrid-type expert system is developed for supporting the initial design process of marine power plants. Firstly, discussion is given generally to understand design process in the view point of applying the AI technique effectively to design. Based on the result of the discussion, a hybrid-type expert CAD system with coupling the AI technique and the numerical optimization method is developed. In the system, the design knowledge is represented in the production rules, and the data of machineries consisting the plant are described by the frame-type representation. Through the system execution, it is ascertained that the system is effective not only as the design tool assisting designers but also as the tool instructing inexperienced designers.

scholarly journals Weil type representations and automorphic forms

1980 ◽  
Vol 77 ◽  
pp. 145-166 ◽  
Author(s):  
Toshiaki Suzuki
Keyword(s):  
Dirichlet Series ◽  
Functional Equations ◽  
Theta Series ◽  
Type Representation ◽  
Generalized Poisson ◽  
Summation Formulae ◽  
Reciprocity Law ◽  
Weil Type ◽  
Generalized Theta Series ◽  
Poisson Summation

During 1934-1936, W. L. Ferrar investigated the relation between summation formulae and Dirichlet series with functional equations, inspired by Voronoi’s works (1904) on summation formula with respect to the numbers of divisors. In [11] A. Weil showed that the automorphic properties of theta series are expressed by generalized Poisson summation formulae with respect to the so-called Weil representation. On the other hand, T. Kubota, in his study of the reciprocity law in a number field, defined a generalized theta series and a generalized Weil type representation of SL(2, C) and obtained similar results to those of A. Weil (1970-1976, [5], [6], [7]). The methods, used by W. L. Ferrar and T. Kubota, to obtain (generalized Poisson) summation formulae depend similarly on functional equations of Dirichlet series (attached to the generalized theta series).

scholarly journals Design of problem-solving questions for measuring student’s mathematical thinking type representation

2019 ◽  
Vol 1318 ◽  
pp. 012102 ◽  
Author(s):  
I Irenika ◽  
E Susanti ◽  
C Hiltrimartin ◽  
H Hapizah ◽  
M Meryansumayeka
Keyword(s):  
Problem Solving ◽  
Mathematical Thinking ◽  
Type Representation
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