Branching processes and computational collapse of discretized unimodal mappings

In computer simulations of smooth dynamical systems, the original phase space is replaced by machine arithmetic, which is a finite set. The resulting spatially discretized dynamical systems do not inherit all functional properties of the original systems, such as surjectivity and existence of absolutely continuous invariant measures. This can lead to computational collapse to fixed points or short cycles. The paper studies loss of such properties in spatial discretizations of dynamical systems induced by unimodal mappings of the unit interval. The problem reduces to studying set-valued negative semitrajectories of the discretized system. As the grid is refined, the asymptotic behavior of the cardinality structure of the semitrajectories follows probabilistic laws corresponding to a branching process. The transition probabilities of this process are explicitly calculated. These results are illustrated by the example of the discretized logistic mapping.

Transformation processes, pathways, and possible sources of distinctive polychlorinated dibenzo-p-dioxin signatures in sink environments

In recent years, studies on environmental samples with unusual dibenzo-p-dioxin (PCDD) congener profiles were reported from a range of countries. These profiles, characterized by a dominance of octachlorinated dibenzodioxin (OCDD) and relatively low in dibenzofuran (PCDF) concentrations, could not be attributed to known sources or formation processes. In the present study, the processes that result in these unusual profiles were assessed using the concentrations and isomer signatures of PCDDs from dated estuarine sediment cores in Queensland, Australia. Increases in relative concentrations of lower chlorinated PODS and a relative decrease of OCDD were correlated with time of sediment deposition. Preferred lateral, anaerobic dechlorination of OCDD represents a likely pathway for these changes. In Queensland sediments, these transformations result in a distinct dominance of isomers fully chlorinated in the 1,4,6,9-positions (1,4-patterns), and similar 1,4-patterns were observed in sediments from elsewhere. Consequently, these environmental samples may not reflect the signatures of the original source, and a reevaluation of source inputs was undertaken. Natural formation of PCDDs, which has previously been suggested, is discussed; however, based on the present results and literature comparisons, we propose an alternative scenario. This scenario hypothesizes that an anthropogenic PCDD precursor input (e.g. pentachlorophenol) results in the contamination. These results and hypothesis imply further investigations are warrented into possible anthropogenic sources in areas where natural PCDD formation has been suggested.

Robust model-order reduction of complex biological processes

This paper addresses robust model-order reduction of a high dimensional nonlinear partial differential equation (PDE) model of a complex biological process. Based on a nonlinear, distributed parameter model of the same process which was validated against experimental data of an existing, pilot-scale BNR activated sludge plant, we developed a state-space model with 154 state variables in this work. A general algorithm for robustly reducing the nonlinear PDE model is presented and based on an investigation of five state-of-the-art model-order reduction techniques, we are able to reduce the original model to a model with only 30 states without incurring pronounced modelling errors. The Singular perturbation approximation balanced truncating technique is found to give the lowest modelling errors in low frequency ranges and hence is deemed most suitable for controller design and other real-time applications. (C) 2002 Elsevier Science Ltd. All rights reserved.

A note on quasi-stationary distributions of birth-death processes and the SIS logistic epidemic

For Markov processes on the positive integers with the origin as an absorbing state, Ferrari, Kesten, Martinez and Picco studied the existence of quasi-stationary and limiting conditional distributions by characterizing quasi-stationary distributions as fixed points of a transformation Phi on the space of probability distributions on {1, 2,.. }. In the case of a birth-death process, the components of Phi(nu) can be written down explicitly for any given distribution nu. Using this explicit representation, we will show that Phi preserves likelihood ratio ordering between distributions. A conjecture of Kryscio and Lefevre concerning the quasi-stationary distribution of the SIS logistic epidemic follows as a corollary.

Using the flexibility index to compare batch and continuous activated sludge processes

This paper considers the question of which is better: the batch or the continuous activated sludge processes? It is an important question because dissension still exists in the wastewater industry as to the relative merits of each of the processes. A review of perceived differences in the processes from the point of view of two related disciplines, process engineering and biotechnology, is presented together with the results of previous comparative studies. These reviews highlight possible areas where more understanding is required. This is provided in the paper by application of the flexibility index to two case studies. The flexibility index is a useful process design tool that measures the ability of the process to cope with long term changes in operation.

The Lake Tekapo experiment (LTEX): An investigation of atmospheric boundary layer processes in complex terrain

A research program on atmospheric boundary layer processes and local wind regimes in complex terrain was conducted in the vicinity of Lake Tekapo in the southern Alps of New Zealand, during two 1-month field campaigns in 1997 and 1999. The effects of the interaction of thermal and dynamic forcing were of specific interest, with a particular focus on the interaction of thermal forcing of differing scales. The rationale and objectives of the field and modeling program are described, along with the methodology used to achieve them. Specific research aims include improved knowledge of the role of surface forcing associated with varying energy balances across heterogeneous terrain, thermal influences on boundary layer and local wind development, and dynamic influences of the terrain through channeling effects. Data were collected using a network of surface meteorological and energy balance stations, radiosonde and pilot balloon soundings, tethered balloon and kite-based systems, sodar, and an instrumented light aircraft. These data are being used to investigate the energetics of surface heat fluxes, the effects of localized heating/cooling and advective processes on atmospheric boundary layer development, and dynamic channeling. A complementary program of numerical modeling includes application of the Regional Atmospheric Modeling System (RAMS) to case studies characterizing typical boundary layer structures and airflow patterns observed around Lake Tekapo. Some initial results derived from the special observation periods are used to illustrate progress made to date. In spite of the difficulties involved in obtaining good data and undertaking modeling experiments in such complex terrain, initial results show that surface thermal heterogeneity has a significant influence on local atmospheric structure and wind fields in the vicinity of the lake. This influence occurs particularly in the morning. However, dynamic channeling effects and the larger-scale thermal effect of the mountain region frequently override these more local features later in the day.

Model-based analysis of anaerobic acetate uptake by a mixed culture of polyphosphate-accumulating and glycogen-accumulating organisms

An increasing number of studies shows that the glycogen-accumulating organisms (GAOs) can survive and may indeed proliferate under the alternating anaerobic/aerobic conditions found in EBPR systems, thus forming a strong competitor of the polyphosphate-accumulating organisms (PAOs). Understanding their behaviors in a mixed PAO and GAO culture under various operational conditions is essential for developing operating strategies that disadvantage the growth of this group of unwanted organisms. A model-based data analysis method is developed in this paper for the study of the anaerobic PAO and GAO activities in a mixed PAO and GAO culture. The method primarily makes use of the hydrogen ion production rate and the carbon dioxide transfer rate resulting from the acetate uptake processes by PAOs and GAOs, measured with a recently developed titration and off-gas analysis (TOGA) sensor. The method is demonstrated using the data from a laboratory-scale sequencing batch reactor (SBR) operated under alternating anaerobic and aerobic conditions. The data analysis using the proposed method strongly indicates a coexistence of PAOs and GAOs in the system, which was independently confirmed by fluorescent in situ hybridization (FISH) measurement. The model-based analysis also allowed the identification of the respective acetate uptake rates by PAOs and GAOs, along with a number of kinetic and stoichiometric parameters involved in the PAO and GAO models. The excellent fit between the model predictions and the experimental data not involved in parameter identification shows that the parameter values found are reliable and accurate. It also demonstrates that the current anaerobic PAO and GAO models are able to accurately characterize the PAO/GAO mixed culture obtained in this study. This is of major importance as no pure culture of either PAOs or GAOs has been reported to date, and hence the current PAO and GAO models were developed for the interpretation of experimental results of mixed cultures. The proposed method is readily applicable for detailed investigations of the competition between PAOs and GAOs in enriched cultures. However, the fermentation of organic substrates carried out by ordinary heterotrophs needs to be accounted for when the method is applied to the study of PAO and GAO competition in full-scale sludges. (C) 2003 Wiley Periodicals, Inc.

Online titrimetric and off-gas analysis for examining nitrification processes in wastewater treatment

The two steps of nitrification, namely the oxidation of ammonia to nitrite and nitrite to nitrate, often need to be considered separately in process studies. For a detailed examination, it is desirable to monitor the two-step sequence using online measurements. In this paper, the use of online titrimetric and off-gas analysis (TOGA) methods for the examination of the process is presented. Using the known reaction stoichiometry, combination of the measured signals (rates of hydrogen ion production, oxygen uptake and carbon dioxide transfer) allows the determination of the three key process rates, namely the ammonia consumption rate, the nitrite accumulation rate and the nitrate production rate. Individual reaction rates determined with the TOGA sensor under a number of operation conditions are presented. The rates calculated directly from the measured signals are compared with those obtained from offline liquid sample analysis. Statistical analysis confirms that the results from the two approaches match well. This result could not have been guaranteed using alternative online methods. As a case study, the influences of pH and dissolved oxygen (DO) on nitrite accumulation are tested using the proposed method. It is shown that nitrite accumulation decreased with increasing DO and pH. Possible reasons for these observations are discussed. (C) 2003 Elsevier Science Ltd. All rights reserved.

Use of confocal microscopy to follow the development of penetrative hyphae during growth of Rhizopus oligosporus in an artificial solid-state fermentation system

Two methods were compared for determining the concentration of penetrative biomass during growth of Rhizopus oligosporus on an artificial solid substrate consisting of an inert gel and starch as the sole source of carbon and energy. The first method was based on the use of a hand microtome to make sections of approximately 0.2- to 0.4-mm thickness parallel to the substrate surface and the determination of the glucosamine content in each slice. Use of glucosamine measurements to estimate biomass concentrations was shown to be problematic due to the large variations in glucosamine content with mycelial age. The second method was a novel method based on the use of confocal scanning laser microscopy to estimate the fractional volume occupied by the biomass. Although it is not simple to translate fractional volumes into dry weights of hyphae due to the lack of experimentally determined conversion factors, measurement of the fractional volumes in themselves is useful for characterizing fungal penetration into the substrate. Growth of penetrative biomass in the artificial model substrate showed two forms of growth with an indistinct mass in the region close to the substrate surface and a few hyphae penetrating perpendicularly to the surface in regions further away from the substrate surface. The biomass profiles against depth obtained from the confocal microscopy showed two linear regions on log-linear plots, which are possibly related to different oxygen availability at different depths within the substrate. Confocal microscopy has the potential to be a powerful tool in the investigation of fungal growth mechanisms in solid-state fermentation. (C) 2003 Wiley Periodicals, Inc.

Mid- to Late-Holocene estuarine infilling processes studied by radiocarbon dates, high resolution seismic and biofacies at Vitoria Bay, Espirito Santo, Southeastern Brazil

A Baía de Vitória é um estuário com 20 km de comprimento, morfologicamente estreito, com um regime de micromaré e, como outros estuários modernos, formado durante a última transgressão pós-glacial. A morfologia de fundo do estrato estuarino é caracterizada por um canal natural principal limitado por planícies de maré com manguezais desenvolvidos. Datações de radiocarbono originais foram obtidas para a área. Cinco idades de radiocarbono estendendo-se de 1.010 a 7.240 anos AP foram obtidas através de dois testemunhos de sedimento, representando uma sequência estratigráfica de 5 m de espessura. Os resultados indicam que até aproximadamente 4.000 anos cal. AP, as condições ambientais da Baía de Vitória eram ainda de uma baía aberta, com uma conexão livre e aberta com águas marinhas. Durante os últimos 4.000 anos a baía experimentou uma fase de regressão importante, tornando-se mais restrita em termos de circulação da água do mar e provavelmente aumentando a energia de marés. Três superfícies estratigráficas principais foram reconhecidas, limitando fácies transgressiva, transgressiva/nível de mar alto e regressiva. A morfologia do canal atual representa um diastema de maré, mostrando fácies regressivas truncadas e erodidas. Biofácies de foraminíferos, passando de ambiente marinho para ambiente salobro e de manguezais em planície de maré confirmam a interpretação sismoestratigráfica. A ausência de biofácies de mangue em um dos dois testemunhos é tambémuma indicação de ravinamento de maré atual.

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On the discovery of business processes orchestration patterns

COORDINSPECTOR is a Software Tool aiming at extracting the coordination layer of a software system. Such a reverse engineering process provides a clear view of the actually invoked services as well as the logic behind such invocations. The analysis process is based on program slicing techniques and the generation of, System Dependence Graphs and Coordination Dependence Graphs. The tool analyzes Common Intermediate Language (CIL), the native language of the Microsoft .Net Framework, thus making suitable for processing systems developed in any .Net Framework compilable language. COORDINSPECTOR generates graphical representations of the coordination layer together with business process orchestrations specified in WSBPEL 2.0