A Wiener-Hopf type factorization for the exponential functional of Levy processes

For a Lévy process ξ=(ξt)t≥0 drifting to −∞, we define the so-called exponential functional as follows: Formula Under mild conditions on ξ, we show that the following factorization of exponential functionals: Formula holds, where × stands for the product of independent random variables, H− is the descending ladder height process of ξ and Y is a spectrally positive Lévy process with a negative mean constructed from its ascending ladder height process. As a by-product, we generate an integral or power series representation for the law of Iξ for a large class of Lévy processes with two-sided jumps and also derive some new distributional properties. The proof of our main result relies on a fine Markovian study of a class of generalized Ornstein–Uhlenbeck processes, which is itself of independent interest. We use and refine an alternative approach of studying the stationary measure of a Markov process which avoids some technicalities and difficulties that appear in the classical method of employing the generator of the dual Markov process.

Evaluation of boundary-layer type in a weather forecast model utilising long-term Doppler lidar observations

Many studies evaluating model boundary-layer schemes focus either on near-surface parameters or on short-term observational campaigns. This reflects the observational datasets that are widely available for use in model evaluation. In this paper we show how surface and long-term Doppler lidar observations, combined in a way to match model representation of the boundary layer as closely as possible, can be used to evaluate the skill of boundary-layer forecasts. We use a 2-year observational dataset from a rural site in the UK to evaluate a climatology of boundary layer type forecast by the UK Met Office Unified Model. In addition, we demonstrate the use of a binary skill score (Symmetric Extremal Dependence Index) to investigate the dependence of forecast skill on season, horizontal resolution and forecast leadtime. A clear diurnal and seasonal cycle can be seen in the climatology of both the model and observations, with the main discrepancies being the model overpredicting cumulus capped and decoupled stratocumulus capped boundary-layers and underpredicting well mixed boundary-layers. Using the SEDI skill score the model is most skillful at predicting the surface stability. The skill of the model in predicting cumulus capped and stratocumulus capped stable boundary layer forecasts is low but greater than a 24 hr persistence forecast. In contrast, the prediction of decoupled boundary-layers and boundary-layers with multiple cloud layers is lower than persistence. This process based evaluation approach has the potential to be applied to other boundary-layer parameterisation schemes with similar decision structures.

Toward a theory of semantic representation

We present an account of semantic representation that focuses on distinct types of information from which word meanings can be learned. In particular, we argue that there are at least two major types of information from which we learn word meanings. The first is what we call experiential information. This is data derived both from our sensory-motor interactions with the outside world, as well as from our experience of own inner states, particularly our emotions. The second type of information is language-based. In particular, it is derived from the general linguistic context in which words appear. The paper spells out this proposal, summarizes research supporting this view and presents new predictions emerging from this framework.

Exact vortex solutions in a CP(N) Skyrme-Faddeev type model

We consider a four dimensional field theory with target space being CP(N) which constitutes a generalization of the usual Skyrme-Faddeev model defined on CP(1). We show that it possesses an integrable sector presenting an infinite number of local conservation laws, which are associated to the hidden symmetries of the zero curvature representation of the theory in loop space. We construct an infinite class of exact solutions for that integrable submodel where the fields are meromorphic functions of the combinations (x(1) + i x(2)) and (x(3) + x(0)) of the Cartesian coordinates of four dimensional Minkowski space-time. Among those solutions we have static vortices and also vortices with waves traveling along them with the speed of light. The energy per unity of length of the vortices show an interesting and intricate interaction among the vortices and waves.

Infrared degrees of freedom of Yang-Mills theory in the Schrodinger representation

We set up a new calculational framework for the Yang-Mills vacuum transition amplitude in the Schrodinger representation. After integrating out hard-mode contributions perturbatively and performing a gauge-invariant gradient expansion of the ensuing soft-mode action, a manageable saddle-point expansion for the vacuum overlap can be formulated. In combination with the squeezed approximation to the vacuum wave functional this allows for an essentially analytical treatment of physical amplitudes. Moreover, it leads to the identification of dominant and gauge-invariant classes of gauge field orbits which play the role of gluonic infrared (IR) degrees of freedom. The latter emerge as a diverse set of saddle-point solutions and are represented by unitary matrix fields. We discuss their scale stability, the associated virial theorem and other general properties including topological quantum numbers and action bounds. We then find important saddle-point solutions (most of them solitons) explicitly and examine their physical impact. While some are related to tunneling solutions of the classical Yang-Mills equation, i.e. to instantons and merons, others appear to play unprecedented roles. A remarkable new class of IR degrees of freedom consists of Faddeev-Niemi type link and knot solutions, potentially related to glueballs.

Szego type polynomials and para-orthogonal polynomials

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Type-II defects in the super-Liouville theory

The introduction of type-II defects is discussed under the Lagrangian formalism and Lax representation for the N = 1 super-Liouville model. We derive a new kind of super-Backlund transformation for the model and show explicitly the conservation of the modified energy and momentum, as well as supercharge.

Representation of the Weddell Sea deep water masses in the ocean component of the NCAR-CCSM model

We examine Weddell Sea deep water mass distributions with respect to the results from three different model runs using the oceanic component of the National Center for Atmospheric Research Community Climate System Model (NCAR-CCSM). One run is inter-annually forced by corrected NCAR/NCEP fluxes, while the other two are forced with the annual cycle obtained from the same climatology. One of the latter runs includes an interactive sea-ice model. Optimum Multiparameter analysis is applied to separate the deep water masses in the Greenwich Meridian section (into the Weddell Sea only) to measure the degree of realism obtained in the simulations. First, we describe the distribution of the simulated deep water masses using observed water type indices. Since the observed indices do not provide an acceptable representation of the Weddell Sea deep water masses as expected, they are specifically adjusted for each simulation. Differences among the water masses` representations in the three simulations are quantified through their root-mean-square differences. Results point out the need for better representation (and inclusion) of ice-related processes in order to improve the oceanic characteristics and variability of dense Southern Ocean water masses in the outputs of the NCAR-CCSM model, and probably in other ocean and climate models.

An analysis of variance type method to describe and compare steady states in clinical data

Identifying and comparing different steady states is an important task for clinical decision making. Data from unequal sources, comprising diverse patient status information, have to be interpreted. In order to compare results an expressive representation is the key. In this contribution we suggest a criterion to calculate a context-sensitive value based on variance analysis and discuss its advantages and limitations referring to a clinical data example obtained during anesthesia. Different drug plasma target levels of the anesthetic propofol were preset to reach and maintain clinically desirable steady state conditions with target controlled infusion (TCI). At the same time systolic blood pressure was monitored, depth of anesthesia was recorded using the bispectral index (BIS) and propofol plasma concentrations were determined in venous blood samples. The presented analysis of variance (ANOVA) is used to quantify how accurately steady states can be monitored and compared using the three methods of measurement.

Explicit description of generic representations for quivers of type An or Dn

We describe explicitly a generic representation for Dynkin quivers of type An or Dn for any dimension vector.

Sized Type Analysis for Logic Programs (Technical Communication)

We present a novel analysis for relating the sizes of terms and subterms occurring at diferent argument positions in logic predicates. We extend and enrich the concept of sized type as a representation that incorporates structural (shape) information and allows expressing both lower and upper bounds on the size of a set of terms and their subterms at any position and depth. For example, expressing bounds on the length of lists of numbers, together with bounds on the values of all of their elements. The analysis is developed using abstract interpretation and the novel abstract operations are based on setting up and solving recurrence relations between sized types. It has been integrated, together with novel resource usage and cardinality analyses, in the abstract interpretation framework in the Ciao preprocessor, CiaoPP, in order to assess both the accuracy of the new size analysis and its usefulness in the resource usage estimation application. We show that the proposed sized types are a substantial improvement over the previous size analyses present in CiaoPP, and also benefit the resource analysis considerably, allowing the inference of equal or better bounds than comparable state of the art systems.

Assessing forest response-type diversity to natural disturbances in Peninsular Spain and the Balearic Islands = Evaluación de la diversidad de tipos de respuesta a perturbaciones naturales en la España peninsular e Islas Baleares

Disturbances shape forest ecosystems by influencing their composition, structure, and processes. In the Mediterranean Basin, changes in the disturbance regimes have been predicted to occur in the next future with a higher occurrence of extreme events of drought, wildfire, and – to a lesser extent – windstorm. Woody species are the main elements defining the structure and functioning of forest ecosystems. Recently, response-type diversity has been pointed out as an appropriate indicator of ecosystems resilience. For this, we have elaborated a complete response-trait database for the tree and shrubby species considered in the Third Spanish National Forest Inventory (3SNFI). In the database, the presence or absence of nine response traits associated to drought, fire, and wind were assigned to each species. The database reflected the lack of information about some important traits (in particular for shrubby species) and allowed to determine those traits most widely distributed. The information contained in the database was then used to assess a relative index of forest resilience to these disturbances calculated from the abundance of response traits and the species redundancy for each plot of the 3SNFI; considering both tree and shrubby species. In general, few plots showed high values of the resilience index, probably because some traits were scarcely presented in the species and also because most plots presented very few species. The cartographic representation of the index showed low values for the stands located in mountainous ranges, which are mostly composed by species typical from central Europe. In the other side, Eucalyptus plantations in Galicia appeared as one thee the most resilient ecosystems, due to its higher adaptive capacity to persist after the occurrence of drought, fire, and windstorm events. We conclude that the response traits database can constitute a useful tool for forest management and planning and for future research to enhance the forest resilience.

Representation and parameterisation issues in genetic algorithms

A multi-chromosome GA (Multi-GA) was developed, based upon concepts from the natural world, allowing improved flexibility in a number of areas including representation, genetic operators, their parameter rates and real world multi-dimensional applications. A series of experiments were conducted, comparing the performance of the Multi-GA to a traditional GA on a number of recognised and increasingly complex test optimisation surfaces, with promising results. Further experiments demonstrated the Multi-GA's flexibility through the use of non-binary chromosome representations and its applicability to dynamic parameterisation. A number of alternative and new methods of dynamic parameterisation were investigated, in addition to a new non-binary 'Quotient crossover' mechanism. Finally, the Multi-GA was applied to two real world problems, demonstrating its ability to handle mixed type chromosomes within an individual, the limited use of a chromosome level fitness function, the introduction of new genetic operators for structural self-adaptation and its viability as a serious real world analysis tool. The first problem involved optimum placement of computers within a building, allowing the Multi-GA to use multiple chromosomes with different type representations and different operators in a single individual. The second problem, commonly associated with Geographical Information Systems (GIS), required a spatial analysis location of the optimum number and distribution of retail sites over two different population grids. In applying the Multi-GA, two new genetic operators (addition and deletion) were developed and explored, resulting in the definition of a mechanism for self-modification of genetic material within the Multi-GA structure and a study of this behaviour.

An investigation into the use of knowledge representation in computer-integrated manufacturing

In a certain automobile factory, batch-painting of the body types in colours is controlled by an allocation system. This tries to balance production with orders, whilst making optimally-sized batches of colours. Sequences of cars entering painting cannot be optimised for easy selection of colour and batch size. `Over-production' is not allowed, in order to reduce buffer stocks of unsold vehicles. Paint quality is degraded by random effects. This thesis describes a toolkit which supports IKBS in an object-centred formalism. The intended domain of use for the toolkit is flexible manufacturing. A sizeable application program was developed, using the toolkit, to test the validity of the IKBS approach in solving the real manufacturing problem above, for which an existing conventional program was already being used. A detailed statistical analysis of the operating circumstances of the program was made to evaluate the likely need for the more flexible type of program for which the toolkit was intended. The IKBS program captures the many disparate and conflicting constraints in the scheduling knowledge and emulates the behaviour of the program installed in the factory. In the factory system, many possible, newly-discovered, heuristics would be awkward to represent and it would be impossible to make many new extensions. The representation scheme is capable of admitting changes to the knowledge, relying on the inherent encapsulating properties of object-centres programming to protect and isolate data. The object-centred scheme is supported by an enhancement of the `C' programming language and runs under BSD 4.2 UNIX. The structuring technique, using objects, provides a mechanism for separating control of expression of rule-based knowledge from the knowledge itself and allowing explicit `contexts', within which appropriate expression of knowledge can be done. Facilities are provided for acquisition of knowledge in a consistent manner.