Discrete-time mean variance optimal control of linear systems with Markovian jumps and multiplicative noise

In this article, we consider the stochastic optimal control problem of discrete-time linear systems subject to Markov jumps and multiplicative noise under three kinds of performance criterions related to the final value of the expectation and variance of the output. In the first problem it is desired to minimise the final variance of the output subject to a restriction on its final expectation, in the second one it is desired to maximise the final expectation of the output subject to a restriction on its final variance, and in the third one it is considered a performance criterion composed by a linear combination of the final variance and expectation of the output of the system. We present explicit sufficient conditions for the existence of an optimal control strategy for these problems, generalising previous results in the literature. We conclude this article presenting a numerical example of an asset liabilities management model for pension funds with regime switching.

Introduction to fractional linear systems. Part 2: discrete-time case

IEE Proceedings - Vision, Image, and Signal Processing, Vol. 147, nº 1

Studies in Fuzzy Commutative Algebra

The main objective of this thesis was to extend some basic concepts and results in module theory in algebra to the fuzzy setting.The concepts like simple module, semisimple module and exact sequences of R-modules form an important area of study in crisp module theory. In this thesis generalising these concepts to the fuzzy setting we have introduced concepts of ‘simple and semisimple L-modules’ and proved some results which include results analogous to those in crisp case. Also we have defined and studied the concept of ‘exact sequences of L-modules’.Further extending the concepts in crisp theory, we have introduced the fuzzy analogues ‘projective and injective L-modules’. We have proved many results in this context. Further we have defined and explored notion of ‘essential L-submodules of an L-module’. Still there are results in crisp theory related to the topics covered in this thesis which are to be investigated in the fuzzy setting. There are a lot of ideas still left in algebra, related to the theory of modules, such as the ‘injective hull of a module’, ‘tensor product of modules’ etc. for which the fuzzy analogues are not defined and explored.

Wind-tunnel modelling of dispersion from a scalar area source in urban-like roughness

A wind-tunnel study was conducted to investigate ventilation of scalars from urban-like geometries at neighbourhood scale by exploring two different geometries a uniform height roughness and a non-uniform height roughness, both with an equal plan and frontal density of λ p = λ f = 25%. In both configurations a sub-unit of the idealized urban surface was coated with a thin layer of naphthalene to represent area sources. The naphthalene sublimation method was used to measure directly total area-averaged transport of scalars out of the complex geometries. At the same time, naphthalene vapour concentrations controlled by the turbulent fluxes were detected using a fast Flame Ionisation Detection (FID) technique. This paper describes the novel use of a naphthalene coated surface as an area source in dispersion studies. Particular emphasis was also given to testing whether the concentration measurements were independent of Reynolds number. For low wind speeds, transfer from the naphthalene surface is determined by a combination of forced and natural convection. Compared with a propane point source release, a 25% higher free stream velocity was needed for the naphthalene area source to yield Reynolds-number-independent concentration fields. Ventilation transfer coefficients w T /U derived from the naphthalene sublimation method showed that, whilst there was enhanced vertical momentum exchange due to obstacle height variability, advection was reduced and dispersion from the source area was not enhanced. Thus, the height variability of a canopy is an important parameter when generalising urban dispersion. Fine resolution concentration measurements in the canopy showed the effect of height variability on dispersion at street scale. Rapid vertical transport in the wake of individual high-rise obstacles was found to generate elevated point-like sources. A Gaussian plume model was used to analyse differences in the downstream plumes. Intensified lateral and vertical plume spread and plume dilution with height was found for the non-uniform height roughness

Resource allocation analysis of the stochastic diffusion search

The Stochastic Diffusion Search (SDS) was developed as a solution to the best-fit search problem. Thus, as a special case it is capable of solving the transform invariant pattern recognition problem. SDS is efficient and, although inherently probabilistic, produces very reliable solutions in widely ranging search conditions. However, to date a systematic formal investigation of its properties has not been carried out. This thesis addresses this problem. The thesis reports results pertaining to the global convergence of SDS as well as characterising its time complexity. However, the main emphasis of the work, reports on the resource allocation aspect of the Stochastic Diffusion Search operations. The thesis introduces a novel model of the algorithm, generalising an Ehrenfest Urn Model from statistical physics. This approach makes it possible to obtain a thorough characterisation of the response of the algorithm in terms of the parameters describing the search conditions in case of a unique best-fit pattern in the search space. This model is further generalised in order to account for different search conditions: two solutions in the search space and search for a unique solution in a noisy search space. Also an approximate solution in the case of two alternative solutions is proposed and compared with predictions of the extended Ehrenfest Urn model. The analysis performed enabled a quantitative characterisation of the Stochastic Diffusion Search in terms of exploration and exploitation of the search space. It appeared that SDS is biased towards the latter mode of operation. This novel perspective on the Stochastic Diffusion Search lead to an investigation of extensions of the standard SDS, which would strike a different balance between these two modes of search space processing. Thus, two novel algorithms were derived from the standard Stochastic Diffusion Search, ‘context-free’ and ‘context-sensitive’ SDS, and their properties were analysed with respect to resource allocation. It appeared that they shared some of the desired features of their predecessor but also possessed some properties not present in the classic SDS. The theory developed in the thesis was illustrated throughout with carefully chosen simulations of a best-fit search for a string pattern, a simple but representative domain, enabling careful control of search conditions.

Vertical and horizontal processes in the global atmosphere and the maximum entropy production conjecture

The objective of this paper is to reconsider the Maximum Entropy Production conjecture (MEP) in the context of a very simple two-dimensional zonal-vertical climate model able to represent the total material entropy production due at the same time to both horizontal and vertical heat fluxes. MEP is applied first to a simple four-box model of climate which accounts for both horizontal and vertical material heat fluxes. It is shown that, under condition of fixed insolation, a MEP solution is found with reasonably realistic temperature and heat fluxes, thus generalising results from independent two-box horizontal or vertical models. It is also shown that the meridional and the vertical entropy production terms are independently involved in the maximisation and thus MEP can be applied to each subsystem with fixed boundary conditions. We then extend the four-box model by increasing its resolution, and compare it with GCM output. A MEP solution is found which is fairly realistic as far as the horizontal large scale organisation of the climate is concerned whereas the vertical structure looks to be unrealistic and presents seriously unstable features. This study suggest that the thermal meridional structure of the atmosphere is predicted fairly well by MEP once the insolation is given but the vertical structure of the atmosphere cannot be predicted satisfactorily by MEP unless constraints are imposed to represent the determination of longwave absorption by water vapour and clouds as a function of the state of the climate. Furthermore an order-of-magnitude estimate of contributions to the material entropy production due to horizontal and vertical processes within the climate system is provided by using two different methods. In both cases we found that approximately 40 mW m−2 K−1 of material entropy production is due to vertical heat transport and 5–7 mW m−2 K−1 to horizontal heat transport

Success and failure of grassroots innovations for addressing climate change: the case of the Transition Movement

Grassroots innovations emerge as networks generating innovative solutions for climate change adaptation and mitigation. However, it is unclear if grassroots innovations can be successful in responding to climate change. Little evidence exists on replication, international comparisons are rare, and research tends to overlook discontinued responses in favour of successful ones. We take the Transition Movement as a case study of a rapidly spreading transnational grassroots network, and include both active and non-active local transition initiatives. We investigate the replication of grassroots innovations in different contexts with the aim to uncover general patterns of success and failure, and identify questions for future research. An online survey was carried out in 23 countries (N=276). The data analysis entailed testing the effect of internal and contextual factors of success as drawn from the existing literature, and the identification of clusters of transition initiatives with similar internal and contextual factor configurations. Most transition initiatives consider themselves successful. Success is defined along the lines of social connectivity and empowerment, and external environmental impact. We find that less successful transition initiatives might underestimate the importance of contextual factors and material resources in influencing success. We also find that their diffusion is linked to the combination of local-global learning processes, and that there is an incubation period during which a transition initiative is consolidated. Transition initiatives seem capable of generalising organisational principles derived from unique local experiences that seem to be effective in other local contexts. However, the geographical locations matter with regard to where transition initiatives take root and the extent of their success, and ‘place attachment’ may have a role in the diffusion of successful initatives. We suggest that longitudinal comparative studies can advance our understanding in this regard, as well as inform the changing nature of the definition of success at different stages of grassroots innovation development, and the dynamic nature of local and global linkages.

Local power of some tests in exponential family nonlinear models

In this paper we obtain asymptotic expansions up to order n(-1/2) for the nonnull distribution functions of the likelihood ratio, Wald, score and gradient test statistics in exponential family nonlinear models (Cordeiro and Paula, 1989), under a sequence of Pitman alternatives. The asymptotic distributions of all four statistics are obtained for testing a subset of regression parameters and for testing the dispersion parameter, thus generalising the results given in Cordeiro et al. (1994) and Ferrari et al. (1997). We also present Monte Carlo simulations in order to compare the finite-sample performance of these tests. (C) 2010 Elsevier B.V. All rights reserved.

Distribution Of Hydrological Losses For Varying Rainfall And Antecedent Wetness Conditions

Hydrological loss is a vital component in many hydrological models, which are usedin forecasting floods and evaluating water resources for both surface and subsurface flows. Due to the complex and random nature of the rainfall runoff process, hydrological losses are not yet fully understood. Consequently, practitioners often use representative values of the losses for design applications such as rainfall-runoff modelling which has led to inaccurate quantification of water quantities in the resulting applications. The existing hydrological loss models must be revisited and modellers should be encouraged to utilise other available data sets. This study is based on three unregulated catchments situated in Mt. Lofty Ranges of South Australia (SA). The paper focuses on conceptual models for: initial loss (IL), continuing loss (CL) and proportional loss (PL) with rainfall characteristics (total rainfall (TR) and storm duration (D)), and antecedent wetness (AW) conditions. The paper introduces two methods that can be implemented to estimate IL as a function of TR, D and AW. The IL distribution patterns and parameters for the study catchments are determined using multivariate analysis and descriptive statistics. The possibility of generalising the methods and the limitations of this are also discussed. This study will yield improvements to existing loss models and will encourage practitioners to utilise multiple data sets to estimate losses, instead of using hypothetical or representative values to generalise real situations.

REDUCTION OF TODA LATTICE HIERARCHY TO GENERALIZED KDV HIERARCHIES AND THE 2-MATRIX MODEL

Toda lattice hierarchy and the associated matrix formulation of the 2M-boson KP hierarchies provide a framework for the Drinfeld-Sokolov reduction scheme realized through Hamiltonian action within the second KP Poisson bracket. By working with free currents, which Abelianize the second KP Hamiltonian structure, we are able to obtain a unified formalism for the reduced SL(M + 1, M - k) KdV hierarchies interpolating between the ordinary KP and KdV hierarchies. The corresponding Lax operators are given as superdeterminants of graded SL(M + 1, M - k) matrices in the diagonal gauge and we describe their bracket structure and field content. In particular, we provide explicit free field representations of the associated W(M, M - k) Poisson bracket algebras generalising the familiar nonlinear W-M+1 algebra. Discrete Backlund transformations for SL(M + 1, M - k) KdV are generated naturally from lattice translations in the underlying Toda-like hierarchy. As an application we demonstrate the equivalence of the two-matrix string model to the SL(M + 1, 1) KdV hierarchy.

Reactive Co-Radicalization: Religious Extremism as Mutual Dicontent

Extremist rhetoric and behaviour, including violence, emanating from those fearing and opposed to Islamic extremism—and typically generalising that to Islam or Muslims—is undeniable. Equally, there is evidence of Muslim rhetoric that fires up fears of a threatening West and antipathy to religious ‘others’ as damned infidels, including Christians and Jews who are otherwise regarded as co-religionists—as ‘peoples of the Book’. Mutual discontent and antipathy abound. On the one hand, Islamic extremism provokes a reactionary extremism from parts, at least, of the non-Muslim world; on the other hand, Muslim extremism appears often in response to the perception of an aggressive and impositional colonising non-Muslim world. ‘Reactive Co-Radicalization’, I suggest, names this mutual rejection and exclusionary circle currently evident, in particular, with respect to many Muslim and non-Muslim communities. This article discusses reactive co-radicalization as a hermeneutical perspective on religious extremism with particular reference to two European cases.

Drivers in adopting adaptation strategies to face increased water scarcity in agriculture. A case study in Doñana (Spain) and Makueni (Kenya)

La agricultura es uno de los sectores más afectados por el cambio climático. A pesar de haber demostrado a lo largo de la historia una gran capacidad para adaptarse a nuevas situaciones, hoy en día la agricultura se enfrenta a nuevos retos tales como satisfacer un elevado crecimiento en la demanda de alimentos, desarrollar una agricultura sostenible con el medio ambiente y reducir las emisiones de gases de efecto invernadero. El potencial de adaptación debe ser definido en un contexto que incluya el comportamiento humano, ya que éste juega un papel decisivo en la implementación final de las medidas. Por este motivo, y para desarrollar correctamente políticas que busquen influir en el comportamiento de los agricultores para fomentar la adaptación a estas nuevas condiciones, es necesario entender previamente los procesos de toma de decisiones a nivel individual o de explotación, así como los efectos de los factores que determinan las barreras o motivaciones de la implementación de medidas. Esta Tesis doctoral trata de profundizar en el análisis de factores que influyen en la toma de decisiones de los agricultores para adoptar estrategias de adaptación al cambio climático. Este trabajo revisa la literatura actual y desarrolla un marco metodológico a nivel local y regional. Dos casos de estudio a nivel local (Doñana, España y Makueni, Kenia) han sido llevados a cabo con el fin de explorar el comportamiento de los agricultores hacia la adaptación. Estos casos de estudio representan regiones con notables diferencias en climatología, impactos del cambio climático, barreras para la adaptación y niveles de desarrollo e influencia de las instituciones públicas y privadas en la agricultura. Mientras el caso de estudio de Doñana representa un ejemplo de problemas asociados al uso y escasez del agua donde se espera que se agraven en el futuro, el caso de estudio de Makueni ejemplifica una zona fuertemente amenazada por las predicciones de cambio climático, donde adicionalmente la falta de infraestructura y la tecnología juegan un papel crucial para la implementación de la adaptación. El caso de estudio a nivel regional trata de generalizar en África el comportamiento de los agricultores sobre la implementación de medidas. El marco metodológico que se ha seguido en este trabajo abarca una amplia gama de enfoques y métodos para la recolección y análisis de datos. Los métodos utilizados para la toma de datos incluyen la implementación de encuestas, entrevistas, talleres con grupos de interés, grupos focales de discusión, revisión de estudios previos y bases de datos públicas. Los métodos analíticos incluyen métodos estadísticos, análisis multi‐criterio para la toma de decisiones, modelos de optimización de uso del suelo y un índice compuesto calculado a través de indicadores. Los métodos estadísticos se han utilizado con el fin de evaluar la influencia de los factores socio‐económicos y psicológicos sobre la adopción de medidas de adaptación. Dentro de estos métodos se incluyen regresiones logísticas, análisis de componentes principales y modelos de ecuaciones estructurales. Mientras que el análisis multi‐criterio se ha utilizado con el fin de evaluar las opciones de adaptación de acuerdo a las opiniones de las diferentes partes interesadas, el modelo de optimización ha tenido como fin analizar la combinación óptima de medidas de adaptación. El índice compuesto se ha utilizado para evaluar a nivel regional la implementación de medidas de adaptación en África. En general, los resultados del estudio ponen de relieve la gran importancia de considerar diferentes escalas espaciales a la hora de evaluar la implementación de medidas de adaptación al cambio climático. El comportamiento de los agricultores es diferente entre lugares considerados a una escala local relativamente pequeña, por lo que la generalización de los patrones del comportamiento a escalas regionales o globales resulta relativamente compleja. Los resultados obtenidos han permitido identificar factores determinantes tanto socioeconómicos como psicológicos y calcular su efecto sobre la adopción de medidas de adaptación. Además han proporcionado una mejor comprensión del distinto papel que desempeñan los cinco tipos de capital (natural, físico, financiero, social y humano) en la implementación de estrategias de adaptación. Con este trabajo se proporciona información de gran interés en los procesos de desarrollo de políticas destinadas a mejorar el apoyo de la sociedad a tomar medidas contra el cambio climático. Por último, en el análisis a nivel regional se desarrolla un índice compuesto que muestra la probabilidad de adoptar medidas de adaptación en las regiones de África y se analizan las causas que determinan dicha probabilidad de adopción de medidas. ABSTRACT Agriculture is and will continue to be one of the sectors most affected by climate change. Despite having demonstrated throughout history a great ability to adapt, agriculture today faces new challenges such as meeting growing food demands, developing sustainable agriculture and reducing greenhouse gas emissions. Adaptation policies planned on global, regional or local scales are ultimately implemented in decision‐making processes at the farm or individual level so adaptation potentials have to be set within the context of individual behaviour and regional institutions. Policy instruments can play a formative role in the adoption of such policies by addressing incentives/disincentives that influence farmer’s behaviour. Hence understanding farm‐level decision‐making processes and the influence of determinants of adoption is crucial when designing policies aimed at fostering adoption. This thesis seeks to analyse the factors that influence decision‐making by farmers in relation to the uptake of adaptation options. This work reviews the current knowledge and develops a methodological framework at local and regional level. Whilst the case studies at the local level are conducted with the purpose of exploring farmer’s behaviour towards adaptation the case study at the regional level attempts to up‐scale and generalise theory on adoption of farmlevel adaptation options. The two case studies at the local level (Doñana, Spain and Makueni, Kenya) encompass areas with different; climates, impacts of climate change, adaptation constraints and limits, levels of development, institutional support for agriculture and influence from public and private institutions. Whilst the Doñana Case Study represents an area plagued with water‐usage issues, set to be aggravated further by climate change, Makueni Case study exemplifies an area decidedly threatened by climate change where a lack of infrastructure and technology plays a crucial role in the uptake of adaptation options. The proposed framework is based on a wide range of approaches for collecting and analysing data. The approaches used for data collection include the implementation of surveys, interviews, stakeholder workshops, focus group discussions, a review of previous case studies, and public databases. The analytical methods include statistical approaches, multi criteria analysis for decision‐making, land use optimisation models, and a composite index based on public databases. Statistical approaches are used to assess the influence of socio‐economic and psychological factors on the adoption or support for adaptation measures. The statistical approaches used are logistic regressions, principal component analysis and structural equation modelling. Whilst a multi criteria analysis approach is used to evaluate adaptation options according to the different perspectives of stakeholders, the optimisation model analyses the optimal combination of adaptation options. The composite index is developed to assess adoption of adaptation measures in Africa. Overall, the results of the study highlight the importance of considering various scales when assessing adoption of adaptation measures to climate change. As farmer’s behaviour varies at a local scale there is elevated complexity when generalising behavioural patterns for farmers at regional or global scales. The results identify and estimate the effect of most relevant socioeconomic and psychological factors that influence adoption of adaptation measures to climate change. They also provide a better understanding of the role of the five types of capital (natural, physical, financial, social, and human) on the uptake of farm‐level adaptation options. These assessments of determinants help to explain adoption of climate change measures and provide helpful information in order to design polices aimed at enhancing societal support for adaptation policies. Finally the analysis at the regional level develops a composite index which suggests the likelihood of the regions in Africa to adopt farm‐level adaptation measures and analyses the main causes of this likelihood of adoption.