scholarly journals Quantitative and Algorithmic aspects of Barrier Synchronization in Concurrency

2021 ◽  
Vol vol. 22 no. 3, Computational... (Special issues) ◽  
Author(s):  
OLivier Bodini ◽  
Matthieu Dien ◽  
Antoine Genitrini ◽  
Frédéric Peschanski
Keyword(s):  
Integral Formula ◽  
Explicit Construction ◽  
Point Of View ◽  
Combinatorial Explosion ◽  
Control Graph ◽  
International Audience ◽  
Sampling Algorithms ◽  
Generate Process ◽  
Quantitative Results ◽  
Combinatorial Point

International audience In this paper we address the problem of understanding Concurrency Theory from a combinatorial point of view. We are interested in quantitative results and algorithmic tools to refine our understanding of the classical combinatorial explosion phenomenon arising in concurrency. This paper is essentially focusing on the the notion of synchronization from the point of view of combinatorics. As a first step, we address the quantitative problem of counting the number of executions of simple processes interacting with synchronization barriers. We elaborate a systematic decomposition of processes that produces a symbolic integral formula to solve the problem. Based on this procedure, we develop a generic algorithm to generate process executions uniformly at random. For some interesting sub-classes of processes we propose very efficient counting and random sampling algorithms. All these algorithms have one important characteristic in common: they work on the control graph of processes and thus do not require the explicit construction of the state-space.

scholarly journals A new combinatorial identity for unicellular maps, via a direct bijective approach.

2009 ◽  
Vol DMTCS Proceedings vol. AK,... (Proceedings) ◽  
Author(s):  
Guillaume Chapuy
Keyword(s):  
Closed Form ◽  
Point Of View ◽  
Catalan Number ◽  
Combinatorial Identity ◽  
International Audience ◽  
Combinatorial Point ◽  
Closed Form Formula

International audience We give a bijective operation that relates unicellular maps of given genus to unicellular maps of lower genus, with distinguished vertices. This gives a new combinatorial identity relating the number $\epsilon_g(n)$ of unicellular maps of size $n$ and genus $g$ to the numbers $\epsilon _j(n)$'s, for $j \lt g$. In particular for each $g$ this enables to compute the closed-form formula for $\epsilon_g(n)$ much more easily than with other known identities, like the Harer-Zagier formula. From the combinatorial point of view, we give an explanation to the fact that $\epsilon_g(n)=R_g(n) \mathrm{Cat}(n)$, where $\mathrm{Cat}(n$) is the $n$-th Catalan number and $R_g$ is a polynomial of degree $3g$, with explicit interpretation. On décrit une opération bijective qui relie les cartes à une face de genre donné à des cartes à une face de genre inférieur, portant des sommets marqués. Cela conduit à une nouvelle identité combinatoire reliant le nombre $\epsilon_g(n)$ de cartes à une face de taille $n$ et genre $g$ aux nombres $\epsilon _j(n)$, pour $j \lt g$. En particulier, pour tout $g$, cela permet de calculer la formule close donnant $\epsilon_g(n)$ bien plus facilement qu'à l'aide des autres identités connues, comme la formule d'Harer-Zagier. Du point de vue combinatoire, nous donnons une explication au fait que $\epsilon _g(n)=R_g(n) \mathrm{Cat}(n)$, où $\mathrm{Cat}(n)$ est le $n$ième nombre de Catalan et $R_g$ est un polynôme de degré $3g$, à l'interprétation explicite.

scholarly journals A Quantitative Study of Pure Parallel Processes

10.37236/3977 ◽  
2016 ◽  
Vol 23 (1) ◽  
Author(s):  
O. Bodini ◽  
A. Genitrini ◽  
F. Peschanski
Keyword(s):  
Quantitative Study ◽  
Random Sampling ◽  
Linear Time ◽  
Time Algorithm ◽  
Point Of View ◽  
Total Size ◽  
Combinatorial Explosion ◽  
Analytic Combinatorics ◽  
Parallel Processes ◽  
Uniform Random Sampling

In this paper, we study the interleaving – or pure merge – operator that most often characterizes parallelism in concurrency theory. This operator is a principal cause of the so-called combinatorial explosion that makes the analysis of process behaviours e.g. by model-checking, very hard – at least from the point of view of computational complexity. The originality of our approach is to study this combinatorial explosion phenomenon on average, relying on advanced analytic combinatorics techniques. We study various measures that contribute to a better understanding of the process behaviours represented as plane rooted trees: the number of runs (corresponding to the width of the trees), the expected total size of the trees as well as their overall shape. Two practical outcomes of our quantitative study are also presented: (1) a linear-time algorithm to compute the probability of a concurrent run prefix, and (2) an efficient algorithm for uniform random sampling of concurrent runs. These provide interesting responses to the combinatorial explosion problem.

Software for XRF

1993 ◽  
Vol 37 ◽  
pp. 13-20
Author(s):  
Michael Mantler
Keyword(s):  
Spectral Data ◽  
Point Of View ◽  
Data Evaluation ◽  
Raw Data ◽  
X Ray ◽  
Fluorescent Analysis ◽  
Qualitative Interpretation ◽  
Large Numbers ◽  
Instrument Control ◽  
Quantitative Results

As in other fields of spectroscopy, software for x-ray fluorescent analysis has to assist the user in instrument control, raw data refinement, qualitative interpretation of spectral data, and computations for obtaining quantitative results. From a historical point of view, instrument automation and data evaluation routines tor large numbers of samples have been a most important incentive for the introduction of computers into x-ray analysis.

scholarly journals Graphs and complete intersection toric ideals

2015 ◽  
Vol 14 (09) ◽  
pp. 1540011 ◽  
Author(s):  
I. Bermejo ◽  
I. García-Marco ◽  
E. Reyes
Keyword(s):  
Complete Intersection ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Point Of View ◽  
Toric Ideals ◽  
Induced Subgraphs ◽  
Toric Ideal ◽  
Vertex Set ◽  
Combinatorial Point ◽  
Ring Graph

Our purpose is to study the family of simple undirected graphs whose toric ideal is a complete intersection from both an algorithmic and a combinatorial point of view. We obtain a polynomial time algorithm that, given a graph G, checks whether its toric ideal PG is a complete intersection or not. Whenever PG is a complete intersection, the algorithm also returns a minimal set of generators of PG. Moreover, we prove that if G is a connected graph and PG is a complete intersection, then there exist two induced subgraphs R and C of G such that the vertex set V(G) of G is the disjoint union of V(R) and V(C), where R is a bipartite ring graph and C is either the empty graph, an odd primitive cycle, or consists of two odd primitive cycles properly connected. Finally, if R is 2-connected and C is connected, we list the families of graphs whose toric ideals are complete intersection.

scholarly journals A stochastic modelling of phytoplankton aggregation

2006 ◽  
Vol Volume 5, Special Issue TAM... ◽  
Author(s):  
Nadjia El Saadi ◽  
Ovide Arino
Keyword(s):  
Differential Equation ◽  
Stochastic Partial Differential Equation ◽  
Stochastic Modelling ◽  
Point Of View ◽  
Modèle Mathématique ◽  
Initial Number ◽  
Microscopic Description ◽  
Random Dispersal ◽  
International Audience ◽  
Number Of Cells

International audience The aim of this work is to provide a stochastic mathematical model of aggregation in phytoplankton, from the point of view of modelling a system of a large but finite number of phytoplankton cells that are subject to random dispersal, mutual interactions allowing the cell motions some dependence and branching (cell division or death). We present the passage from the ''microscopic'' description to the ''macroscopic'' one, when the initial number of cells tends to infinity (large phytoplankton populations). The limit of the system is an extension of the Dawson-Watanabe superprocess: it is a superprocess with spatial interactions which can be described by a nonlinear stochastic partial differential equation. L'objectif de ce travail est de fournir un modèle mathématique stochastique qui décrit l'aggrégation du hytoplancton,à partir de la modélisation d'un système de grande taille, mais finie, de cellules de phytoplancton sujettes à une dispersion aléatoire, des interactions spatiales qui donnent aux mouvements des cellules une certaine dépendance et un branchement (division cellulaire ou mort). Nous présentons le passage de la description microscopique à une description macroscopique, lorsque le nombre de cellules devient très grand (grandes populations de phytoplancton). La limite du système est une extension du superprocessus de Dawson-Watanabe: c'est un superprocessus avec interactions qui peut être décrit par une équation aux dérivées partielles stochastique non linéaire.

scholarly journals Tangible interaction on tabletop, an illustrated federating framework

2017 ◽  
Vol Volume 5, Number 1 (Research articles) ◽  
Author(s):  
Sophie Lepreux ◽  
Julien Castet ◽  
Nadine Couture ◽  
Emmanuel Dubois ◽  
Christophe Kolski ◽  
...  
Keyword(s):  
User Interfaces ◽  
Point Of View ◽  
Tangible Interaction ◽  
Tangible User Interfaces ◽  
Complex Part ◽  
The Everyday ◽  
Tangible Object ◽  
International Audience ◽  
Coffee Table ◽  
The One

International audience Since many years, the Human-Computer Interaction community is interested in the tangible user interfaces (TUI). A part of these TUI focuses on the interaction performed with one or several objects. The domain is in extension by the development of contactless objects (using NFC, RFID technology, etc.). In the system, tangible objects could represent data, action, or complex part. Interaction on a table, which is a common furniture in the everyday life and used in multiple activities (desktop, coffee table, kitchen table, etc.), opens a new way for the research and development in HCI. This article proposes to use a framework, previously proposed in a conjunct article, to characterize applications supported by the couple <interactive tabletop, tangible object>. These applications aim at supporting complex business tasks; they are described from a technological point of view on the one hand, and from an applicative point of view on the other hand. These applications show the benefit brought by the couple <interactive tabletop, tangible object> to the interaction and they are immersed in the framework. The framework shows with these instantiations that it is generic and supports such descriptions. Depuis plusieurs années, les interfaces tangibles impliquant des interactions réalisées via un ou plusieurs objets prennent une importance grandissante en interaction homme-machine. Ce domaine est en extension grâce au développement d'objets exploitant des technologies sans contact (NFC, RFID, etc.). L'objet tangible représente un sujet ou une action ; cet objet agit sur le système, telle une action sur une interface « classique ». L'interaction sur table, c'est-à-dire sur un meuble présent dans la vie courante et utilisé à diverses fins (bureau, table à manger, table de salon, table bar, etc.), ouvre un champ nouveau de recherche et de développement. Nous proposons d'illustrer un cadre proposé dans un article conjoint, en positionnant des applications mettant en oeuvre le couple <table, objet tangible>. Plusieurs applications, visant à supporter chacune une tâche métier complexe, sont décrites à la fois d'un point de vue technologique et d'un point de vue applicatif. Ces applications montrent les apports de l'association <table, objet tangible> à l'interaction et sont caractérisées selon les dimensions du cadre de conception présenté dans un article conjoint, montrant ainsi la généricité et le pouvoir descriptif du cadre proposé.

Numerical Simulation of the Transient Three-Dimensional Gas-Liquid Flow in a Cylindrical Bubble Column

2006 ◽  
Author(s):  
Santiago Lai´n Beatove ◽  
Martin Sommerfeld
Keyword(s):  
Liquid Flow ◽  
Bubble Column ◽  
Three Dimensional ◽  
Dynamic Structure ◽  
Point Of View ◽  
Pressure Drag ◽  
Eddy Simulation ◽  
Discrete Phase ◽  
Quantitative Results ◽  
Gas Liquid Flow

In this paper the transient three-dimensional flow developing in a cylindrical laboratory bubble column is addressed from a numerical point of view. The simulation scheme combines a Large Eddy Simulation (LES) for describing the liquid phase and a Lagragian approach for the gas (discrete) phase. The bubble equation of motion considers all the relevant forces, i.e., buoyancy, pressure, drag, added mass and transverse lift. From the calculations, the transverse lift in combination with the drag is identified as the main mechanism allowing the bubbles to spread over the column cross-section. The liquid and gas velocity profiles obtained are compared with the experimental data and k–ε results presented in Lai´n et al. (2001). As a matter of fact, the dynamic structure of the liquid flow induced by the rising bubbles is well reproduced and also good quantitative results for all measured variables of both phases, gas and liquid, are obtained.

scholarly journals The combinatorics of minimal unsatisfiability: connecting to graph theory

2021 ◽  
Author(s):  
◽  
Hoda Abbasizanjani
Keyword(s):  
Graph Theory ◽  
Building Blocks ◽  
Point Of View ◽  
New Class ◽  
Strongly Connected ◽  
Combinatorial Point ◽  
Minimal Unsatisfiability ◽  
Full Classification ◽  
New Framework

Minimally Unsatisfiable CNFs (MUs) are unsatisfiable CNFs where removing any clause destroys unsatisfiability. MUs are the building blocks of unsatisfia-bility, and our understanding of them can be very helpful in answering various algorithmic and structural questions relating to unsatisfiability. In this thesis we study MUs from a combinatorial point of view, with the aim of extending the understanding of the structure of MUs. We show that some important classes of MUs are very closely related to known classes of digraphs, and using arguments from logic and graph theory we characterise these MUs.Two main concepts in this thesis are isomorphism of CNFs and the implica-tion digraph of 2-CNFs (at most two literals per disjunction). Isomorphism of CNFs involves renaming the variables, and flipping the literals. The implication digraph of a 2-CNF F has both arcs (¬a → b) and (¬b → a) for every binary clause (a ∨ b) in F .In the first part we introduce a novel connection between MUs and Minimal Strong Digraphs (MSDs), strongly connected digraphs, where removing any arc destroys the strong connectedness. We introduce the new class DFM of special MUs, which are in close correspondence to MSDs. The known relation between 2-CNFs and implication digraphs is used, but in a simpler and more direct way, namely that we have a canonical choice of one of the two arcs. As an application of this new framework we provide short and intuitive new proofs for two im-portant but isolated characterisations for nonsingular MUs (every literal occurs at least twice), both with ingenious but complicated proofs: Characterising 2-MUs (minimally unsatisfiable 2-CNFs), and characterising MUs with deficiency 2 (two more clauses than variables).In the second part, we provide a fundamental addition to the study of 2-CNFs which have efficient algorithms for many interesting problems, namely that we provide a full classification of 2-MUs and a polytime isomorphism de-cision of this class. We show that implication digraphs of 2-MUs are “Weak Double Cycles” (WDCs), big cycles of small cycles (with possible overlaps). Combining logical and graph-theoretical methods, we prove that WDCs have at most one skew-symmetry (a self-inverse fixed-point free anti-symmetry, re-versing the direction of arcs). It follows that the isomorphisms between 2-MUs are exactly the isomorphisms between their implication digraphs (since digraphs with given skew-symmetry are the same as 2-CNFs). This reduces the classifi-cation of 2-MUs to the classification of a nice class of digraphs.Finally in the outlook we discuss further applications, including an alter-native framework for enumerating some special Minimally Unsatisfiable Sub-clause-sets (MUSs).

Sign in / Sign up

Export Citation Format

Share Document