On Generalized Models and Singular Products of Distributions in Colombeau Algebra G(R)

MSC 2010: 46F30, 46F10

The Soft Budget Constraint. An introductory study to volume IV of the Life’s Work series

The author’s ideas on the soft budget constraint (SBC) were first expressed in 1976. Much progress has been made in understanding the problem over the ensuing four decades. The study takes issue with those who confine the concept to the process of bailing out loss-making socialist firms. It shows how the syndrome can appear in various organizations and forms in many spheres of the economy and points to the various means available for financial rescue. Single bailouts do not as such generate the SBC syndrome. It develops where the SBC becomes built into expectations. Special heed is paid to features generated by the syndrome in rescuer and rescuee organizations. The study reports on the spread of the syndrome in various periods of the socialist and the capitalist system, in various sectors. The author expresses his views on normative questions and on therapies against the harmful effects. He deals first with actual practice, then places the theory of the SBC in the sphere of ideas and models, showing how it relates to other theoretical trends, including institutional and behavioural economics and theories of moral hazard and inconsistency in time. He shows how far the intellectual apparatus of the SBC has spread in theoretical literature and where it has reached in the process of “canonization” by the economics profession. Finally, he reviews the main research tasks ahead.

Improving the predictability of time series by chaotic parameter estimation

Limited literature regarding parameter estimation of dynamic systems has been identified as the central-most reason for not having parametric bounds in chaotic time series. However, literature suggests that a chaotic system displays a sensitive dependence on initial conditions, and our study reveals that the behavior of chaotic system: is also sensitive to changes in parameter values. Therefore, parameter estimation technique could make it possible to establish parametric bounds on a nonlinear dynamic system underlying a given time series, which in turn can improve predictability. By extracting the relationship between parametric bounds and predictability, we implemented chaos-based models for improving prediction in time series. ^ This study describes work done to establish bounds on a set of unknown parameters. Our research results reveal that by establishing parametric bounds, it is possible to improve the predictability of any time series, although the dynamics or the mathematical model of that series is not known apriori. In our attempt to improve the predictability of various time series, we have established the bounds for a set of unknown parameters. These are: (i) the embedding dimension to unfold a set of observation in the phase space, (ii) the time delay to use for a series, (iii) the number of neighborhood points to use for avoiding detection of false neighborhood and, (iv) the local polynomial to build numerical interpolation functions from one region to another. Using these bounds, we are able to get better predictability in chaotic time series than previously reported. In addition, the developments of this dissertation can establish a theoretical framework to investigate predictability in time series from the system-dynamics point of view. ^ In closing, our procedure significantly reduces the computer resource usage, as the search method is refined and efficient. Finally, the uniqueness of our method lies in its ability to extract chaotic dynamics inherent in non-linear time series by observing its values. ^

Space-for-Time Substitution Works in Everglades Ecological Forecasting Models

Space-for-time substitution is often used in predictive models because long-term time-series data are not available. Critics of this method suggest factors other than the target driver may affect ecosystem response and could vary spatially, producing misleading results. Monitoring data from the Florida Everglades were used to test whether spatial data can be substituted for temporal data in forecasting models. Spatial models that predicted bluefin killifish (Lucania goodei) population response to a drying event performed comparably and sometimes better than temporal models. Models worked best when results were not extrapolated beyond the range of variation encompassed by the original dataset. These results were compared to other studies to determine whether ecosystem features influence whether space-for-time substitution is feasible. Taken in the context of other studies, these results suggest space-for-time substitution may work best in ecosystems with low beta-diversity, high connectivity between sites, and small lag in organismal response to the driver variable.

Space-for-Time Substitution Works in Everglades Ecological Forecasting Models

Space-for-time substitution is often used in predictive models because long-term time-series data are not available. Critics of this method suggest factors other than the target driver may affect ecosystem response and could vary spatially, producing misleading results. Monitoring data from the Florida Everglades were used to test whether spatial data can be substituted for temporal data in forecasting models. Spatial models that predicted bluefin killifish (Lucania goodei) population response to a drying event performed comparably and sometimes better than temporal models. Models worked best when results were not extrapolated beyond the range of variation encompassed by the original dataset. These results were compared to other studies to determine whether ecosystem features influence whether space-for-time substitution is feasible. Taken in the context of other studies, these results suggest space-fortime substitution may work best in ecosystems with low beta-diversity, high connectivity between sites, and small lag in organismal response to the driver variable.

Surface velocity fields, digital elevation models, ice front positions and grounding line derived from remote sensing data at Dinsmoor-Bombardier-Edgeworth glacier system, Antarctic Peninsula (1992-2014)

The northern Antarctic Peninsula is one of the fastest changing regions on Earth. The disintegration of the Larsen-A Ice Shelf in 1995 caused tributary glaciers to adjust by speeding up, surface lowering, and overall increased ice-mass discharge. In this study, we investigate the temporal variation of these changes at the Dinsmoor-Bombardier-Edgeworth glacier system by analyzing dense time series from various spaceborne and airborne Earth observation missions. Precollapse ice shelf conditions and subsequent adjustments through 2014 were covered. Our results show a response of the glacier system some months after the breakup, reaching maximum surface velocities at the glacier front of up to 8.8 m/d in 1999 and a subsequent decrease to ~1.5 m/d in 2014. Using a dense time series of interferometrically derived TanDEM-X digital elevation models and photogrammetric data, an exponential function was fitted for the decrease in surface elevation. Elevation changes in areas below 1000 m a.s.l. amounted to at least 130±15 m130±15 m between 1995 and 2014, with change rates of ~3.15 m/a between 2003 and 2008. Current change rates (2010-2014) are in the range of 1.7 m/a. Mass imbalances were computed with different scenarios of boundary conditions. The most plausible results amount to -40.7±3.9 Gt-40.7±3.9 Gt. The contribution to sea level rise was estimated to be 18.8±1.8 Gt18.8±1.8 Gt, corresponding to a 0.052±0.005 mm0.052±0.005 mm sea level equivalent, for the period 1995-2014. Our analysis and scenario considerations revealed that major uncertainties still exist due to insufficiently accurate ice-thickness information. The second largest uncertainty in the computations was the glacier surface mass balance, which is still poorly known. Our time series analysis facilitates an improved comparison with GRACE data and as input to modeling of glacio-isostatic uplift in this region. The study contributed to a better understanding of how glacier systems adjust to ice shelf disintegration.

Bayesian estimation in generalized autoregressive conditional heteroskedasticity models

Esta tesis doctoral nace con el propósito de entender, analizar y sobre todo modelizar el comportamiento estadístico de las series financieras. En este sentido, se puede afirmar que los modelos que mejor recogen las especiales características de estas series son los modelos de heterocedasticidad condicionada en tiempo discreto,si los intervalos de tiempo en los que se recogen los datos lo permiten, y en tiempo continuo si tenemos datos diarios o datos intradía. Con esta finalidad, en esta tesis se proponen distintos estimadores bayesianos para la estimación de los parámetros de los modelos GARCH en tiempo discreto (Bollerslev (1986)) y COGARCH en tiempo continuo (Kluppelberg et al. (2004)). En el capítulo 1 se introducen las características de las series financieras y se presentan los modelos ARCH, GARCH y COGARCH, así como sus principales propiedades. Mandelbrot (1963) destacó que las series financieras no presentan estacionariedad y que sus incrementos no presentan autocorrelación, aunque sus cuadrados sí están correlacionados. Señaló también que la volatilidad que presentan no es constante y que aparecen clusters de volatilidad. Observó la falta de normalidad de las series financieras, debida principalmente a su comportamiento leptocúrtico, y también destacó los efectos estacionales que presentan las series, analizando como se ven afectadas por la época del año o el día de la semana. Posteriormente Black (1976) completó la lista de características especiales incluyendo los denominados leverage effects relacionados con como las fluctuaciones positivas y negativas de los precios de los activos afectan a la volatilidad de las series de forma distinta.

Multilevel structural equation models for longitudinal data where predictors are measured more frequently than outcomes : an application to the effects of stress on the cognitive function of nurses

Funded by Chief Scientist Office, Scotland. Grant Number: CZH/4/394 Economic and Social Research Council grant as part of the National Centre for Research Methods. Grant Number: RES-576-25-0032

Gaussian Process Kernels for Cross-Spectrum Analysis in Electrophysiological Time Series

Multi-output Gaussian processes provide a convenient framework for multi-task problems. An illustrative and motivating example of a multi-task problem is multi-region electrophysiological time-series data, where experimentalists are interested in both power and phase coherence between channels. Recently, the spectral mixture (SM) kernel was proposed to model the spectral density of a single task in a Gaussian process framework. This work develops a novel covariance kernel for multiple outputs, called the cross-spectral mixture (CSM) kernel. This new, flexible kernel represents both the power and phase relationship between multiple observation channels. The expressive capabilities of the CSM kernel are demonstrated through implementation of 1) a Bayesian hidden Markov model, where the emission distribution is a multi-output Gaussian process with a CSM covariance kernel, and 2) a Gaussian process factor analysis model, where factor scores represent the utilization of cross-spectral neural circuits. Results are presented for measured multi-region electrophysiological data.

Middle Eocene Fe and Ca counts, Ca/Fe ratios, revised splices and astronomical age models form different Sites of IODP Exp342

Accurate age models are a tool of utmost important in paleoclimatology. Constraining the rate and pace of past climate change are at the core of paleoclimate research, as such knowledge is crucial to our understanding of the climate system. Indeed, it allows for the disentanglement of the various drivers of climate change. The scarcity of highly resolved sedimentary records from the middle Eocene (Bartonian - Lutetian Stages; 47.8 - 37.8 Ma) has led to the existence of the "Eocene astronomical time scale gap" and hindered the establishment of a comprehensive astronomical time scale (ATS) for the entire Cenozoic. Sediments from the Newfoundland Ridge drilled during Integrated Ocean Drilling Program (IODP) Expedition 342 span the Eocene gap at an unprecedented stratigraphic resolution with carbonate bearing sediments. Moreover, these sediments exhibit cyclic lithological changes that allow for an astronomical calibration of geologic time. In this study, we use the dominant obliquity imprint in XRF-derived calcium-iron ratio series (Ca/Fe) from three sites drilled during IODP Expedition 342 (U1408, U1409, U1410) to construct a floating astrochronology. We then anchor this chronology to numerical geological time by tuning 173-kyr cycles in the amplitude modulation pattern of obliquity to an astronomical solution. This study is one of the first to use the 173-kyr obliquity amplitude cycle for astrochronologic purposes, as previous studies primarily use the 405-kyr long eccentricity cycle as a tuning target to calibrate the Paleogene geologic time scale. We demonstrate that the 173-kyr cycles in obliquity's amplitude are stable between 40 and 50 Ma, which means that one can use the 173-kyr cycle for astrochronologic calibration in the Eocene. Our tuning provides new age estimates for magnetochron reversals C18n.1n - C21r and a stratigraphic framework for key sites from Expedition 342 for the Eocene. Some disagreements emerge when we compare our tuning for the interval between C19r and C20r with previous tuning attempts from the South Atlantic. We therefore present a revision of the original astronomical interpretations for the latter records, so that the various astrochronologic age models for the middle Eocene in the North- and South-Atlantic are consistent.

Holocene precipitation change in different monsoon sub-regions (time-slices and transient data) simulated by different global climate models, with links to model results

The recently proposed global monsoon hypothesis interprets monsoon systems as part of one global-scale atmospheric overturning circulation, implying a connection between the regional monsoon systems and an in-phase behaviour of all northern hemispheric monsoons on annual timescales (Trenberth et al., 2000). Whether this concept can be applied to past climates and variability on longer timescales is still under debate, because the monsoon systems exhibit different regional characteristics such as different seasonality (i.e. onset, peak, and withdrawal). To investigate the interconnection of different monsoon systems during the pre-industrial Holocene, five transient global climate model simulations have been analysed with respect to the rainfall trend and variability in different sub-domains of the Afro-Asian monsoon region. Our analysis suggests that on millennial timescales with varying orbital forcing, the monsoons do not behave as a tightly connected global system. According to the models, the Indian and North African monsoons are coupled, showing similar rainfall trend and moderate correlation in rainfall variability in all models. The East Asian monsoon changes independently during the Holocene. The dissimilarities in the seasonality of the monsoon sub-systems lead to a stronger response of the North African and Indian monsoon systems to the Holocene insolation forcing than of the East Asian monsoon and affect the seasonal distribution of Holocene rainfall variations. Within the Indian and North African monsoon domain, precipitation solely changes during the summer months, showing a decreasing Holocene precipitation trend. In the East Asian monsoon region, the precipitation signal is determined by an increasing precipitation trend during spring and a decreasing precipitation change during summer, partly balancing each other. A synthesis of reconstructions and the model results do not reveal an impact of the different seasonality on the timing of the Holocene rainfall optimum in the different sub-monsoon systems. They rather indicate locally inhomogeneous rainfall changes and show, that single palaeo-records should not be used to characterise the rainfall change and monsoon evolution for entire monsoon sub-systems.

Potassium and Argon data for dating the core, and radiochemical data of a series of measurements made on layers inside various manganese nodules from the Pacific Ocean

Although various models have been proposed to explain the origin of manganese nodules (see Goldberg and Arrhenius), two major hypotheses have received extensive attention. One concept suggests that manganese nodules form as the result of interaction between submarine volcanic products and sea water. The common association of manganese nodules with volcanic materials constitutes the main evidence for this theory. The second theory involves a direct inorganic precipitation of manganese from sea water. Goldberg and Arrhenius view this process as the oxidation of divalent manganese to tetravalent manganese by oxygen under the catalytic action of particulate iron hydroxides. Manganese accumulation by the Goldberg and Arrhenius theory would be a relatively slow and comparatively steady process, whereas Bonatti and Nayudu believe manganese nodule formation takes place subsequent to the eruption of submarine volcanoes by the acidic leaching of lava.

Evaluating demographic models for goat domestication using mtDNA sequences

Routes of migration and exchange are important factors in the debate about how the Neolithic transition spread into Europe. Studying the genetic diversity of livestock can help in tracing back some of these past events. Notably, domestic goat (Capra hircus) did not have any wild progenitors (Capra aegagrus) in Europe before their arrival from the Near East. Studies of mitochondrial DNA have shown that the diversity in European domesticated goats is a subset of that in the wild, underlining the ancestral relationship between both populations. Additionally, an ancient DNA study on Neolithic goat remains has indicated that a high level of genetic diversity was already present early in the Neolithic in northwestern Mediterranean sites. We used coalescent simulations and approximate Bayesian computation, conditioned on patterns of modern and ancient mitochondrial DNA diversity in domesticated and wild goats, to test a series of simplified models of the goat domestication process. Specifically, we ask if domestic goats descend from populations that were distinct prior to domestication. Although the models we present require further analyses, preliminary results indicate that wild and domestic goats are more likely to descend from a single ancestral wild population that was managed 11,500 years before present, and that serial founding events characterise the spread of Capra hircus into Europe.

Models of the user: designers’ perspectives on influencing sustainable behaviour

Influencing more environmentally friendly and sustainable behaviour is a current focus of many projects, ranging from government social marketing campaigns, education and tax structures to designers’ work on interactive products, services and environments. There is a wide variety of techniques and methods used, intended to work via different sets of cognitive and environmental principles. These approaches make different assumptions about ‘what people are like’: how users will respond to behavioural interventions, and why, and in the process reveal some of the assumptions that designers and other stakeholders, such as clients commissioning a project, make about human nature. This paper discusses three simple models of user behaviour – the pinball, the shortcut and the thoughtful – which emerge from user experience designers’ statements about users while focused on designing for behaviour change. The models are characterised using systems terminology and the application of each model to design for sustainable behaviour is examined via a series of examples.