Age of information (AoI) has been widely accepted as a measure quantifying freshness status in real-time update systems. In many such systems, multiple sources share limited network resource and therefore the AoIs defined for individual should be correlated with each other. However, there are not found any results literature studying correlation two or more system sources. this work, we conside...

We define a construction operation on hypergraphs based on a colimit and show that its expressiveness is equal to the graph expressions of Bauderon and Courcelle. We also demonstrate that by closing a set of rewrite rules under graph construction we obtain a notion of rewriting equivalent to the double-pushout approach of Ehrig. The usefulness of our approach for the compositional modelling of ...

We introduce a simple logic that allows to quantify over the subobjects of a categorical object. We subsequently show that, for the category of graphs, this logic is equally expressive as second-order monadic graph logic (msogl). Furthermore we show that for the more general setting of hereditary pushout categories, a class of categories closely related to adhesive categories, we can recover Co...

Reconfigurable place/transition systems are Petri nets with initial markings and a set of rules which allow the modification of the net during runtime in order to adapt the net to new requirements of the environment. In this paper we use transformation rules for place/transition systems in the sense of the double pushout approach for graph transformation. The main problem in this context is to ...

This note presents a new formalization of graph rewritings which generalizes traditional graph rewritings. Relational notions of graphs and their rewritings are introduced and several properties about graph rewritings are discussed using relational calculus (theory of binary relations). Single pushout approaches to graph rewritings proposed by Raoult and Kennaway are compared with our rewriting...

This paper gives a truly concurrent semantics with sharing of resources for the K semantic framework, an executable (term-)rewritingbased formalism for defining programming languages and calculi. Akin to graph rewriting rules, the K (rewrite) rules explicitly state what can be concurrently shared with other rules. The desired true concurrency is obtained by translating the K rules into a novel ...

A recent result of ours [GM] shows that all Hopf algebra liftings of a given diagram in the sense of Andruskiewitsch and Schneider are cocycle deformations of each other. Here we develop a ‘non-abelian’ cohomology theory, which gives a method for an explicit description of cocycles relevant to the lifting process. 0. Introduction The Nichols algebra B(V ) of a crossed kG-module V is a connected...

In this paper we study the problem of the optimal design of bu er management policies for a shared memory ATM switch or demultiplexer fed by tra c containing two different space priorities. We present the properties of the optimal policy within the class of pushout and expelling policies that minimizes total weighted cell loss. A numerical study of the optimal policies for small bu er sizes bas...

We obtain some explicit calculations of crossed Q modules induced from a crossed module over a normal subgroup P of Q By virtue of theorems of Brown and Higgins this enables the computation of the homotopy types and second homotopy modules of certain homotopy pushouts of maps of classifying spaces of discrete groups Introduction A crossed module M M P has a classifying space BM see for example ...

We propose a new diagrammatic modeling language, DML. The paradigm used is that of the category theory and in particular of the pushout tool. We show that most of the object-oriented structures can be described with this tool and have many examples in C++, ranging from virtual inheritance and polymorphism to template genericity. With this powerful tool, we propose a quite simple description of ...