scholarly journals Weighted Tree-Numbers of Matroid Complexes

2015 ◽  
Vol DMTCS Proceedings, 27th... (Proceedings) ◽  
Author(s):  
Woong Kook ◽  
Kang-Ju Lee
Keyword(s):  
High Dimensional ◽  
Weighted Tree ◽  
Key Factor ◽  
International Audience ◽  
New Formula

International audience We give a new formula for the weighted high-dimensional tree-numbers of matroid complexes. This formula is derived from our result that the spectra of the weighted combinatorial Laplacians of matroid complexes consist of polynomials in the weights. In the formula, Crapo’s $\beta$-invariant appears as the key factor relating weighted combinatorial Laplacians and weighted tree-numbers for matroid complexes. Nous présentons une nouvelle formule pour les nombres d’arbres pondérés de grande dimension des matroïdes complexes. Cette formule est dérivée du résultat que le spectre des Laplaciens combinatoires pondérés des matrides complexes sont des polynômes à plusieurs variables. Dans la formule, le $\beta$;-invariant de Crapo apparaît comme étant le facteur clé reliant les Laplaciens combinatoires pondérés et les nombres d’arbres pondérés des matroïdes complexes.

scholarly journals How to visualize high-dimensional data: a roadmap

2020 ◽  
Vol Special issue on... ◽  
Author(s):  
Hermann Moisl
Keyword(s):  
Cluster Analysis ◽  
High Dimensional Data ◽  
Latent Structure ◽  
High Dimensional ◽  
Graphical Methods ◽  
Data Set ◽  
The Third ◽  
Historical Text ◽  
International Audience ◽  
And Cluster Analysis

International audience Discovery of the chronological or geographical distribution of collections of historical text can be more reliable when based on multivariate rather than on univariate data because multivariate data provide a more complete description. Where the data are high-dimensional, however, their complexity can defy analysis using traditional philological methods. The first step in dealing with such data is to visualize it using graphical methods in order to identify any latent structure. If found, such structure facilitates formulation of hypotheses which can be tested using a range of mathematical and statistical methods. Where, however, the dimensionality is greater than 3, direct graphical investigation is impossible. The present discussion presents a roadmap of how this obstacle can be overcome, and is in three main parts: the first part presents some fundamental data concepts, the second describes an example corpus and a high-dimensional data set derived from it, and the third outlines two approaches to visualization of that data set: dimensionality reduction and cluster analysis.

scholarly journals A bijection between planar constellations and some colored Lagrangian trees

2003 ◽  
Vol Vol. 6 no. 1 ◽  
Author(s):  
Cedric Chauve
Keyword(s):  
Generating Functions ◽  
Functional Equations ◽  
Formula One ◽  
Lagrange Formula ◽  
International Audience ◽  
Planar Maps ◽  
New Formula

International audience Constellations are colored planar maps that generalize different families of maps (planar maps, bipartite planar maps, bi-Eulerian planar maps, planar cacti, ...) and are strongly related to factorizations of permutations. They were recently studied by Bousquet-Mélou and Schaeffer who describe a correspondence between these maps and a family of trees, called Eulerian trees. In this paper, we derive from their result a relationship between planar constellations and another family of trees, called stellar trees. This correspondence generalizes a well known result for planar cacti, and shows that planar constellations are colored Lagrangian objects (that is objects that can be enumerated by the Good-Lagrange formula). We then deduce from this result a new formula for the number of planar constellations having a given face distribution, different from the formula one can derive from the results of Bousquet-Mélou and Schaeffer, along with systems of functional equations for the generating functions of bipartite and bi-Eulerian planar maps enumerated according to the partition of faces and vertices.

scholarly journals Partitioned Cacti: a Bijective Approach to the Cycle Factorization Problem

2008 ◽  
Vol DMTCS Proceedings vol. AJ,... (Proceedings) ◽  
Author(s):  
Gilles Schaeffer ◽  
Ekaterina Vassilieva
Keyword(s):  
Factorization Problem ◽  
Long Cycle ◽  
International Audience ◽  
Number Of Cycles ◽  
New Formula

International audience In this paper we construct a bijection for partitioned 3-cacti that gives raise to a new formula for enumeration of factorizations of the long cycle into three permutations with given number of cycles. Dans cet article, nous construisons une bijection pour 3-cacti partitionnés faisant apparaître une nouvelle formule pour l’énumération des factorisations d’un long cycle en trois permutations ayant un nombre donné de cycles.

A ‘Corporate Technology Stock’ Model

1996 ◽  
Vol 10 (6) ◽  
pp. 388-393
Author(s):  
Akio Kameoka
Keyword(s):  
Technology Development ◽  
Corporate Investments ◽  
Market Mechanisms ◽  
Knowledge Based ◽  
Key Factor ◽  
Technology Market ◽  
Stock Model ◽  
New Formula ◽  
Market Infrastructure ◽  
Sophisticated Technology

A concept of ‘corporate technology stock’ (CTS), facilitates understanding of the corporate technological process. A model based on ‘depreciation’ has led to a new formula for determining appropriate corporate investments on research and technology development (RTD), and simulations have revealed the model accords satisfactorily with experience in industry. The model was extended to define corporate RTD productivity, in terms of ‘knowledge productivity’ to clarify the performance of knowledge-based activities. A key factor for collaboration is to activate knowledge exchanges among researchers and engineers. The paper concludes that a sophisticated technology market infrastructure established by introducing new market mechanisms greatly contributes to RTD collaborations.

scholarly journals On trees, tanglegrams, and tangled chains

2020 ◽  
Vol DMTCS Proceedings, 28th... ◽  
Author(s):  
Sara Billey ◽  
Matjaz Konvalinka ◽  
Frderick Matsen IV
Keyword(s):  
Asymptotic Formula ◽  
Computer Science ◽  
Explicit Formula ◽  
Binary Trees ◽  
Biological Research ◽  
Open Problems ◽  
International Audience ◽  
Enumeration Formula ◽  
New Formula ◽  
Simple Asymptotic Formula

International audience Tanglegrams are a class of graphs arising in computer science and in biological research on cospeciation and coevolution. They are formed by identifying the leaves of two rooted binary trees. The embedding of the trees in the plane is irrelevant for this application. We give an explicit formula to count the number of distinct binary rooted tanglegrams with n matched leaves, along with a simple asymptotic formula and an algorithm for choosing a tanglegram uniformly at random. The enumeration formula is then extended to count the number of tangled chains of binary trees of any length. This work gives a new formula for the number of binary trees with n leaves. Several open problems and conjectures are included along with pointers to several followup articles that have already appeared.

scholarly journals Bijective Enumeration of Bicolored Maps of Given Vertex Degree Distribution

2009 ◽  
Vol DMTCS Proceedings vol. AK,... (Proceedings) ◽  
Author(s):  
Alejandro Morales ◽  
Ekaterina Vassilieva
Keyword(s):  
Degree Distribution ◽  
Vertex Degree ◽  
Combinatorial Proof ◽  
Theoretic Approach ◽  
Simple Description ◽  
International Audience ◽  
Number Of Cycles ◽  
The One ◽  
New Formula ◽  
First Time

International audience We derive a new formula for the number of factorizations of a full cycle into an ordered product of two permutations of given cycle types. For the first time, a purely combinatorial argument involving a bijective description of bicolored maps of specified vertex degree distribution is used. All the previous results in the field rely either partially or totally on a character theoretic approach. The combinatorial proof relies on a new bijection extending the one in [G. Schaeffer and E. Vassilieva. $\textit{J. Comb. Theory Ser. A}$, 115(6):903―924, 2008] that focused only on the number of cycles. As a salient ingredient, we introduce the notion of thorn trees of given vertex degree distribution which are recursive planar objects allowing simple description of maps of arbitrary genus. \par Nous démontrons une nouvelle formule exprimant le nombre de factorisations d'un long cycle en produit de deux permutations ayant un type cyclique donné. Pour la première fois, nous utilisons un argument purement combinatoire basé sur une description bijective des cartes bicolores dont la distribution des degrés des sommets est donnée. Tous les résultats précédents dans le domaine se basent soit partiellement soit totalement sur la théorie des caractères de groupe. La preuve combinatoire se fonde sur une nouvelle bijection généralisant celle introduite dans [G. Schaeffer and E. Vassilieva. $\textit{J. Comb. Theory Ser. A}$, 115(6):903―924, 2008] ne s'intéressant qu'au nombre de cycles. L'ingrédient le plus saillant est l'introduction de la notion d'arbre épineux de structure cyclique donnée, des objets récursifs et planaires permettant une description simple des cartes de genus arbitraire.

scholarly journals Non-ambiguous trees: new results and generalization

2020 ◽  
Vol DMTCS Proceedings, 28th... ◽  
Author(s):  
Jean-Christophe Aval ◽  
Adrien Boussicault ◽  
Bérénice Delcroix-Oger ◽  
Florent Hivert ◽  
Patxi Laborde-Zubieta
Keyword(s):  
Binary Trees ◽  
Higher Dimension ◽  
International Audience ◽  
Definition Of ◽  
New Formula ◽  
Ential Equation

International audience We present a new definition of non-ambiguous trees (NATs) as labelled binary trees. We thus get a differ- ential equation whose solution can be described combinatorially. This yield a new formula for the number of NATs. We also obtain q-versions of our formula. And we generalize NATs to higher dimension.

The Research of Generation Algorithm of Frequent Itemsets in High-Dimensional Data

2015 ◽  
Vol 710 ◽  
pp. 127-131
Author(s):  
Qing Chao Jiang
Keyword(s):  
Association Rules ◽  
High Efficiency ◽  
High Dimensional Data ◽  
Frequent Itemsets ◽  
Boolean Matrix ◽  
High Dimensional ◽  
Rule Mining ◽  
Key Factor ◽  
And Performance ◽  
The Times

In the mining of association rules, the generation of frequent itemsets is a key factor that influence the efficiency and performance of the algorithm. With the increase of data dimension, it is obvious that the traditional association rules mining algorithm can’t meet the demand of high dimensional data mining. On the basis of Apriori algorithm, we put forward Split Mtrix _Apriori algorithm in this paper. By generating the Boolean matrix of the database, Split Mtrix _Apriori algorithm decreased the times of scanning database when generating the frequent itemsets. With adopting grouping processing strategy in the Boolean matrix, the algorithm can still keep high efficiency in dealing with high-dimensional data.So Split Mtrix _Apriori improved the efficiency of association rule mining significantly.

scholarly journals Carbon deposition mechanism of molten salt cleaning and optimization of multicomponent molten salt formula for remanufacturing

2021 ◽  
Vol 104 (3) ◽  
pp. 003685042110310
Author(s):  
Shuo Zhang ◽  
Shanguo Zhang ◽  
Jianyong Li ◽  
Jianfeng Li ◽  
Xin Zhou ◽  
...  
Keyword(s):  
Molten Salt ◽  
Adsorption Mechanism ◽  
Carbon Deposition ◽  
Salt Bath ◽  
Storage Medium ◽  
Optimal Process ◽  
Deposition Mechanism ◽  
Low Viscosity ◽  
Key Factor ◽  
New Formula

In remanufacturing engineering, cleaning is the key factor for subsequent blank inspection and parts repair. Molten salt has the characteristics of low viscosity, good fluidity, and strong chemical stability. Salt bath cleaning can be comprehensively applied to remove various organic pollutants. Molten salt has the function of self-cleaning. The dirt in the cleaning pool can be decomposed and reused. Moreover, the waste molten salt is massive, and the waste residue is easy to treat. The formation and adsorption mechanism of carbon deposition was explored, and the formation mechanism of carbon deposition was verified by experiments. Then, the existing formula was improved by mixing experiment and compared with the current cleaning method; the cleaning effect was excellent. A new molten salt formula is proposed on the basis of the research on solar thermal storage medium. The composition percentage and the optimal process parameters of the new molten salt formula were determined on the basis of the experimental design of mixture. The cleaning effect of the new formula is good.

scholarly journals Combinatorics of the PASEP partition function

2010 ◽  
Vol DMTCS Proceedings vol. AN,... (Proceedings) ◽  
Author(s):  
Matthieu Josuat-Vergès
Keyword(s):  
Partition Function ◽  
Closed Formula ◽  
International Audience ◽  
The One ◽  
New Formula

International audience We consider a three-parameter PASEP model on $N$ sites. A closed formula for the partition function was obtained analytically by Blythe et al. We give a new formula which generalizes the one of Blythe et al, and is proved in two combinatorial ways. Moreover the first proof can be adapted to give the moments of Al-Salam-Chihara polynomials. Nous considérons un modèle de PASEP à trois paramètres sur $N$ sites. Une formule close pour la fonction de partition a été obtenue analytiquement par Blythe et al. Nous donnons une formule qui généralise celle de Blythe et al, prouvée combinatoirement de deux manières diffèrentes. Par ailleurs la première preuve peut être adaptée de sorte à obtenir les moments des polynômes d'Al-Salam-Chihara.

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