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Papers by Estíbaliz Fraca

This paper presents the case study of an intervention called Numberfit that aims at capturing pri... more This paper presents the case study of an intervention called Numberfit that aims at capturing primarily students’ interest in mathematics by combining team games and physical activity. We describe the hybrid learning space that is created through this approach that includes an online platform that allows the teachers and facilitators to design a lesson plan, input student scores and visualise a leaderboard. At the same time, various digital and tangible resources engage students in group (collaborative or competitive) activities while practising a range of topics in mathematics. We examine the changing role of the teacher and provide some methodological insights for conducting research in relation to student’s affect, motivation and behaviour in this context.

Proceedings of the 18th IFAC World Congress, 2011

Petri nets (PN) represent a well known family of formalisms for the modeling and analysis of Disc... more Petri nets (PN) represent a well known family of formalisms for the modeling and analysis of Discrete Event Systems (DES). As most formalisms for DES, PNs suffer from the state explosion problem. A way to overcome this difficulty is to relax the original discrete model and deal with a fully or partially continuous model. In contrast to continuous Petri nets that consider a full continuous firing of transitions, what can lead to the loss some properties of the original discrete model, this paper deals with Hybrid Adaptive Petri nets (HAPNs), that consider partially continuous firings. In an HAPN, a threshold is associated with each transition: if the load of the transition is higher than its threshold, it behaves as continuous; if it is lower, it behaves as discrete. This way, transitions adapt dynamically to their load. The reachability space and the deadlock-freeness property of HAPNs are studied and compared to those of discrete and continuous Petri nets.

The analysis of Discrete Event Systems suffer from the well known state explosion problem. A clas... more The analysis of Discrete Event Systems suffer from the well known state explosion problem. A classical technique to overcome this problem is to relax the behaviour by partially removing the integrality constraints, thus dealing with hybrid or continuous systems. In the Petri nets framework, continuous net systems (technically hybrid systems) are the result of removing the integrality constraint in the firing of transitions. This relaxation may highly reduce the complexity of analysis techniques but may not preserve important properties of the original system. This paper deals with the basic operation of fluidization. More precisely, it aims at establishing conditions that a discrete system must satisfy so that a given property is preserved by the continuous system. These conditions will be mainly based on the here introduced marking homothetic behaviours of the system. The focus will be on logical properties as boundedness, deadlock-freeness, liveness and reversibility. Furthermore, testing homothetic montonicity of some properties in the discrete systems will be considered.

Discrete Event Dynamic Systems

Fluidization is an appealing relaxation technique based on the removal of integrality constraints... more Fluidization is an appealing relaxation technique based on the removal of integrality constraints in order to ease the analysis of discrete Petri nets. The result of fluidifying discrete Petri nets are the so called Fluid or Continuous Petri nets. As with any relaxation technique, discrepancies among the behaviours of the discrete and the relaxed model may appear. Moreover, such discrepancies may have a comparatively bigger effect when the population of the system, the marking in Petri net terms, is "relatively" small. This paper proposes two complementary approaches to obtain a better fluid approximation of discrete Petri nets. The first one focuses on untimed systems and is based on the addition of places that are implicit in the untimed discrete system but not in the continuous. The idea is to cut undesired spurious solutions whose existence worsens the fluidization. The second one focuses on a particular situation that can severely affect the quality of fluidization in timed systems. Namely, such a situation arises when the enabling degree of a transition is equal to 1. This last approach aims to alleviate such a state of affairs, which is termed the bound reaching problem, on systems under infinite servers semantics.

Nonlinear Analysis: Hybrid Systems, 2014

ABSTRACT Petri Nets (PNs) constitute a well known family of formalisms for the modelling and anal... more ABSTRACT Petri Nets (PNs) constitute a well known family of formalisms for the modelling and analysis of Discrete Event Dynamic Systems (DEDS). As general formalisms for DEDS, PNs suffer from the state explosion problem. A way to alleviate this difficulty is to relax the original discrete model and deal with a fully or partially continuous model. In Hybrid Petri Nets (HPNs), transitions can be either discrete or continuous, but not both. In Hybrid Adaptive Petri Nets (HAPNs), each transition commutes between discrete and continuous behaviour depending on a threshold: if its load is higher than its threshold, it behaves as continuous; otherwise, it behaves as discrete. This way, transitions adapt their behaviour dynamically to their load. This paper proposes a method to compute the Reachability Graph (RG) of HPNs and HAPNs.

12th International Workshop on Discrete Event Systems (2014), 2014

Lecture Notes in Computer Science, 2013

This paper presents the case study of an intervention called Numberfit that aims at capturing pri... more This paper presents the case study of an intervention called Numberfit that aims at capturing primarily students’ interest in mathematics by combining team games and physical activity. We describe the hybrid learning space that is created through this approach that includes an online platform that allows the teachers and facilitators to design a lesson plan, input student scores and visualise a leaderboard. At the same time, various digital and tangible resources engage students in group (collaborative or competitive) activities while practising a range of topics in mathematics. We examine the changing role of the teacher and provide some methodological insights for conducting research in relation to student’s affect, motivation and behaviour in this context.

Proceedings of the 18th IFAC World Congress, 2011

Petri nets (PN) represent a well known family of formalisms for the modeling and analysis of Disc... more Petri nets (PN) represent a well known family of formalisms for the modeling and analysis of Discrete Event Systems (DES). As most formalisms for DES, PNs suffer from the state explosion problem. A way to overcome this difficulty is to relax the original discrete model and deal with a fully or partially continuous model. In contrast to continuous Petri nets that consider a full continuous firing of transitions, what can lead to the loss some properties of the original discrete model, this paper deals with Hybrid Adaptive Petri nets (HAPNs), that consider partially continuous firings. In an HAPN, a threshold is associated with each transition: if the load of the transition is higher than its threshold, it behaves as continuous; if it is lower, it behaves as discrete. This way, transitions adapt dynamically to their load. The reachability space and the deadlock-freeness property of HAPNs are studied and compared to those of discrete and continuous Petri nets.

The analysis of Discrete Event Systems suffer from the well known state explosion problem. A clas... more The analysis of Discrete Event Systems suffer from the well known state explosion problem. A classical technique to overcome this problem is to relax the behaviour by partially removing the integrality constraints, thus dealing with hybrid or continuous systems. In the Petri nets framework, continuous net systems (technically hybrid systems) are the result of removing the integrality constraint in the firing of transitions. This relaxation may highly reduce the complexity of analysis techniques but may not preserve important properties of the original system. This paper deals with the basic operation of fluidization. More precisely, it aims at establishing conditions that a discrete system must satisfy so that a given property is preserved by the continuous system. These conditions will be mainly based on the here introduced marking homothetic behaviours of the system. The focus will be on logical properties as boundedness, deadlock-freeness, liveness and reversibility. Furthermore, testing homothetic montonicity of some properties in the discrete systems will be considered.

Discrete Event Dynamic Systems

Fluidization is an appealing relaxation technique based on the removal of integrality constraints... more Fluidization is an appealing relaxation technique based on the removal of integrality constraints in order to ease the analysis of discrete Petri nets. The result of fluidifying discrete Petri nets are the so called Fluid or Continuous Petri nets. As with any relaxation technique, discrepancies among the behaviours of the discrete and the relaxed model may appear. Moreover, such discrepancies may have a comparatively bigger effect when the population of the system, the marking in Petri net terms, is "relatively" small. This paper proposes two complementary approaches to obtain a better fluid approximation of discrete Petri nets. The first one focuses on untimed systems and is based on the addition of places that are implicit in the untimed discrete system but not in the continuous. The idea is to cut undesired spurious solutions whose existence worsens the fluidization. The second one focuses on a particular situation that can severely affect the quality of fluidization in timed systems. Namely, such a situation arises when the enabling degree of a transition is equal to 1. This last approach aims to alleviate such a state of affairs, which is termed the bound reaching problem, on systems under infinite servers semantics.

Nonlinear Analysis: Hybrid Systems, 2014

ABSTRACT Petri Nets (PNs) constitute a well known family of formalisms for the modelling and anal... more ABSTRACT Petri Nets (PNs) constitute a well known family of formalisms for the modelling and analysis of Discrete Event Dynamic Systems (DEDS). As general formalisms for DEDS, PNs suffer from the state explosion problem. A way to alleviate this difficulty is to relax the original discrete model and deal with a fully or partially continuous model. In Hybrid Petri Nets (HPNs), transitions can be either discrete or continuous, but not both. In Hybrid Adaptive Petri Nets (HAPNs), each transition commutes between discrete and continuous behaviour depending on a threshold: if its load is higher than its threshold, it behaves as continuous; otherwise, it behaves as discrete. This way, transitions adapt their behaviour dynamically to their load. This paper proposes a method to compute the Reachability Graph (RG) of HPNs and HAPNs.

12th International Workshop on Discrete Event Systems (2014), 2014

Lecture Notes in Computer Science, 2013