Supervisory control of (max,+) automata: extensions towards applications

International audience

Determinization of timed Petri nets behaviors

International audience

A study on semigroup action on fuzzy subsets, inverse fuzzy automata and related topics

This thesis comprises five chapters including the introductory chapter. This includes a brief introduction and basic definitions of fuzzy set theory and its applications, semigroup action on sets, finite semigroup theory, its application in automata theory along with references which are used in this thesis. In the second chapter we defined an S-fuzzy subset of X with the extension of the notion of semigroup action of S on X to semigroup action of S on to a fuzzy subset of X using Zadeh's maximal extension principal and proved some results based on this. We also defined an S-fuzzy morphism between two S-fuzzy subsets of X and they together form a category S FSETX. Some general properties and special objects in this category are studied and finally proved that S SET and S FSET are categorically equivalent. Further we tried to generalize this concept to the action of a fuzzy semigroup on fuzzy subsets. As an application, using the above idea, we convert a _nite state automaton to a finite fuzzy state automaton. A classical automata determine whether a word is accepted by the automaton where as a _nite fuzzy state automaton determine the degree of acceptance of the word by the automaton. 1.5. Summary of the Thesis 17 In the third chapter we de_ne regular and inverse fuzzy automata, its construction, and prove that the corresponding transition monoids are regular and inverse monoids respectively. The languages accepted by an inverse fuzzy automata is an inverse fuzzy language and we give a characterization of an inverse fuzzy language. We study some of its algebraic properties and prove that the collection IFL on an alphabet does not form a variety since it is not closed under inverse homomorphic images. We also prove some results based on the fact that a semigroup is inverse if and only if idempotents commute and every L-class or R-class contains a unique idempotent. Fourth chapter includes a study of the structure of the automorphism group of a deterministic faithful inverse fuzzy automaton and prove that it is equal to a subgroup of the inverse monoid of all one-one partial fuzzy transformations on the state set. In the fifth chapter we define min-weighted and max-weighted power automata study some of its algebraic properties and prove that a fuzzy automaton and the fuzzy power automata associated with it have the same transition monoids. The thesis ends with a conclusion of the work done and the scope of further study.

Chlamydial infection and spatial ascension of the female genital tract : a novel hybrid cellular automata and continuum mathematical model

Sexually transmitted chlamydial infection initially establishes in the endocervix in females, but if the infection ascends the genital tract, significant disease, including infertility, can result. Many of the mechanisms associated with chlamydial infection kinetics and disease ascension are unknown. We attempt to elucidate some of these processes by developing a novel mathematical model, using a cellular automata–partial differential equation model. We matched our model outputs to experimental data of chlamydial infection of the guinea-pig cervix and carried out sensitivity analyses to determine the relative influence of model parameters. We found that the rate of recruitment and action of innate immune cells to clear extracellular chlamydial particles and the rate of passive movement of chlamydial particles are the dominant factors in determining the early course of infection, magnitude of the peak chlamydial time course and the time of the peak. The rate of passive movement was found to be the most important factor in determining whether infection would ascend to the upper genital tract. This study highlights the importance of early innate immunity in the control of chlamydial infection and the significance of motility-diffusive properties and the adaptive immune response in the magnitude of infection and in its ascension.

Max Dupain and the photography of Australian architecture

This thesis considers Max Dupain (1911-1992) and his contribution to the development of architectural photography in Australia. Through his continuous and prolific output over six decades of professional photography Dupain greatly stimulated awareness of and interest in Australian architecture. Before Dupain began specialising in the field, little consistent professional architectural photography had been practised in Australia. He and some of his close associates subsequently developed architectural photography as both a specialised branch of photography and - perhaps more significantly - as a necessary adjunct to architectural practice. In achieving these dual accomplishments, Dupain and like-minded practitioners succeeded in elevating architectural photography to the status of a discipline in its own right. They also gave Australians generally a deeper understanding of the heritage represented by the nation's built environment. At the same time, some of the photographic images he created became firmly fixed in the public imagination as historical icons within the development of a distinctive Australian tradition in the visual arts. Within his chosen field Dupain was the dominant Australian figure of his time. He was instrumental in breaking the link with Pictorialism by bringing Modernist and Documentary perspectives to Australian architectural photography. He was an innovator in the earlier decades of his professional career, however, his photographic techniques and practice did not develop beyond that. By the end of the 1980s he had largely lost touch with the technology and techniques of contemporary practice. Dupain's reputation, which has continued growing since his death in 1992, therefore arises from reasons other than his photographic images alone. It reflects his accomplishment in raising his fellow citizens' awareness of a worthwhile home-grown artistic tradition.

Exponentiated gradient algorithms for conditional random fields and max-margin Markov Networks

Log-linear and maximum-margin models are two commonly-used methods in supervised machine learning, and are frequently used in structured prediction problems. Efficient learning of parameters in these models is therefore an important problem, and becomes a key factor when learning from very large data sets. This paper describes exponentiated gradient (EG) algorithms for training such models, where EG updates are applied to the convex dual of either the log-linear or max-margin objective function; the dual in both the log-linear and max-margin cases corresponds to minimizing a convex function with simplex constraints. We study both batch and online variants of the algorithm, and provide rates of convergence for both cases. In the max-margin case, O(1/ε) EG updates are required to reach a given accuracy ε in the dual; in contrast, for log-linear models only O(log(1/ε)) updates are required. For both the max-margin and log-linear cases, our bounds suggest that the online EG algorithm requires a factor of n less computation to reach a desired accuracy than the batch EG algorithm, where n is the number of training examples. Our experiments confirm that the online algorithms are much faster than the batch algorithms in practice. We describe how the EG updates factor in a convenient way for structured prediction problems, allowing the algorithms to be efficiently applied to problems such as sequence learning or natural language parsing. We perform extensive evaluation of the algorithms, comparing them to L-BFGS and stochastic gradient descent for log-linear models, and to SVM-Struct for max-margin models. The algorithms are applied to a multi-class problem as well as to a more complex large-scale parsing task. In all these settings, the EG algorithms presented here outperform the other methods.

Combining influence maps and cellular automata for reactive game agents

Agents make up an important part of game worlds, ranging from the characters and monsters that live in the world to the armies that the player controls. Despite their importance, agents in current games rarely display an awareness of their environment or react appropriately, which severely detracts from the believability of the game. Some games have included agents with a basic awareness of other agents, but they are still unaware of important game events or environmental conditions. This paper presents an agent design we have developed, which combines cellular automata for environmental modeling with influence maps for agent decision-making. The agents were implemented into a 3D game environment we have developed, the EmerGEnT system, and tuned through three experiments. The result is simple, flexible game agents that are able to respond to natural phenomena (e.g. rain or fire), while pursuing a goal.

An approximate Bayesian computation approach for estimating parameters of complex environmental processes in a cellular automata

Modelling an environmental process involves creating a model structure and parameterising the model with appropriate values to accurately represent the process. Determining accurate parameter values for environmental systems can be challenging. Existing methods for parameter estimation typically make assumptions regarding the form of the Likelihood, and will often ignore any uncertainty around estimated values. This can be problematic, however, particularly in complex problems where Likelihoods may be intractable. In this paper we demonstrate an Approximate Bayesian Computational method for the estimation of parameters of a stochastic CA. We use as an example a CA constructed to simulate a range expansion such as might occur after a biological invasion, making parameter estimates using only count data such as could be gathered from field observations. We demonstrate ABC is a highly useful method for parameter estimation, with accurate estimates of parameters that are important for the management of invasive species such as the intrinsic rate of increase and the point in a landscape where a species has invaded. We also show that the method is capable of estimating the probability of long distance dispersal, a characteristic of biological invasions that is very influential in determining spread rates but has until now proved difficult to estimate accurately.

Exploring Rhythmic Automata

The use of Cellular Automata (CA) for musical purposes has a rich history. In general the mapping of CA states to note-level music representations has focused on pitch mapping and downplayed rhythm. This paper reports experiments in the application of one-dimensional cellular automata to the generation and evolution of rhythmic patterns. A selection of CA tendencies are identified that can be used as compositional tools to control the rhythmic coherence of monophonic passages and the polyphonic texture of musical works in broad-brush, rather than precisely deterministic, ways. This will provide the composer and researcher with a clearer understanding of the useful application of CAs for generative music.

Automata modeling for cognitive interference in users' relevance judgement

Quantum theory has recently been employed to further advance the theory of information retrieval (IR). A challenging research topic is to investigate the so called quantum-like interference in users’ relevance judgement process, where users are involved to judge the relevance degree of each document with respect to a given query. In this process, users’ relevance judgement for the current document is often interfered by the judgement for previous documents, due to the interference on users’ cognitive status. Research from cognitive science has demonstrated some initial evidence of quantum-like cognitive interference in human decision making, which underpins the user’s relevance judgement process. This motivates us to model such cognitive interference in the relevance judgement process, which in our belief will lead to a better modeling and explanation of user behaviors in relevance judgement process for IR and eventually lead to more user-centric IR models. In this paper, we propose to use probabilistic automaton(PA) and quantum finite automaton (QFA), which are suitable to represent the transition of user judgement states, to dynamically model the cognitive interference when the user is judging a list of documents.

Timed and Probabilistic Automata for Automatic Animal Call Recognition

Automatic Call Recognition is vital for environmental monitoring. Patten recognition has been applied in automatic species recognition for years. However, few studies have applied formal syntactic methods to species call structure analysis. This paper introduces a novel method to adopt timed and probabilistic automata in automatic species recognition based upon acoustic components as the primitives. We demonstrate this through one kind of birds in Australia: Eastern Yellow Robin.