MA348exam 1998

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MA348exam 1998 pdf

Exam questions and solutions in PDF

Exam 1987

Exam and solutions in LaTex

Exam 1986

Exam and solutions in LaTex

Exam 1988

Exam and solutions in LaTex

Petróleo e indígenas en Colombia. Una mirada desde la seguridad humana

En Colombia las actividades de exploración, explotación, transporte y procesamiento de hidrocarburos que se vienen realizando desde comienzos del siglo XX son responsables de grandes procesos de transformación del territorio y de degradación de los ecosistemas en los que se realizan. Estos procesos han impactado negativamente la seguridad de las comunidades indígenas poniendo en riesgo su cultura y en algunos casos su existencia misma. Aunque históricamente los derechos de estas poblaciones frente a la explotación petrolera, y minera en general, han cambiado y su autonomía e integridad es protegida por la Constitución de 1991, las comunidades siguen teniendo una alta vulnerabilidad frente a la intervención de los ecosistema que habitan.La degradación ambiental producida directamente por las actividades petroleras y por los procesos de colonización que estas impulsan se constituye en una amenaza a la seguridad de las comunidades, cuyos territorios y recursos de subsistencia se ven disminuidos. La colonización y la presión sobre los recursos naturales que esta produce son motivadas principalmente por la pobreza de poblaciones campesinas que buscan nuevas tierras para habitar, a su vez estos dos procesos son causa de degradación ambiental que empobrece a las comunidades étnicas debido a que afecta sus fuentes de sustento, situación que genera inseguridad para los indígenas. Adicionalmente, la degradación ambiental y la disminución de los territorios ponen en riesgo la cultura de estos grupos humanos, pues afecta sus valores, tradiciones, autoridades y, en general, su forma de vida lo que constituye una amenaza a su seguridad.-----In Colombia, the exploration, exploitation, transport, and processing of hydrocarbons since the beginning of the 20th century have caused great territory transformations and ecosystem degradation. These processes have impacted adversely the indigenous communities security, exposing their culture and, in some cases, their existence itself. Even though, facing oil and, in general, mineral exploitation, the rights of this population have changed historically and their autonomy and integrity is protected by the 1991 Constitution, the communities are still highly vulnerable to the intervention on the ecosystem they inhabit.The environmental degradation directly arisen from the oil exploitation activities and the colonization they have driven, has become a threat to the security of the communities whose territories and subsistence resources have been reduced. Colonization and the resulting natural resource pressure are mainly caused by the poverty of the country population that seek new lands to occupy and these two facts cause in turn the environmental degradation that impoverish the ethnic communities by affecting their living sources, thereby causing insecurity to the indigenous population. In addition, environmental degradation and territory reduction risk these human groups’ culture by impacting their values, tradition, authorities and, in general, their way of living, and therefore turn into a threat to their security.

Ecuaciones diferenciales estocásticas con condición final y soluciones de viscosidad de EDPS semilineales de segundo orden

El objetivo de este documento es recopilar algunos resultados clasicos sobre existencia y unicidad ´ de soluciones de ecuaciones diferenciales estocasticas (EDEs) con condici ´ on final (en ingl ´ es´ Backward stochastic differential equations) con particular enfasis en el caso de coeficientes mon ´ otonos, y su cone- ´ xion con soluciones de viscosidad de sistemas de ecuaciones diferenciales parciales (EDPs) parab ´ olicas ´ y el´ıpticas semilineales de segundo orden.

Medical image registration based on random line sampling

One of the key aspects in 3D-image registration is the computation of the joint intensity histogram. We propose a new approach to compute this histogram using uniformly distributed random lines to sample stochastically the overlapping volume between two 3D-images. The intensity values are captured from the lines at evenly spaced positions, taking an initial random offset different for each line. This method provides us with an accurate, robust and fast mutual information-based registration. The interpolation effects are drastically reduced, due to the stochastic nature of the line generation, and the alignment process is also accelerated. The results obtained show a better performance of the introduced method than the classic computation of the joint histogram

Hedging effectiveness of total returns swaps: application to the Japanese market

The development of the real estate swap market offers many opportunities for investors to adjust the exposure of their portfolios to real estate. A number of OTC transactions have been observed in markets around the world. In this paper we examine the Japanese commercial real estate market from the point of view of an investor holding a portfolio of properties seeking to reduce the portfolio exposure to the real estate market by swapping an index of real estate for LIBOR. This paper explores the practicalities of hedging portfolios comprising small numbers of individual properties against an appropriate index. We use the returns from 74 properties owned by Japanese Real Estate Investment Trusts over the period up to September 2007. The paper also discusses and applies the appropriate stochastic processes required to model real estate returns in this application and presents alternative ways of reporting hedging effectiveness. We find that the development of the derivative does provide the capacity for hedging market risk but that the effectiveness of the hedge varies considerably over time. We explore the factors that cause this variability.

Law of large numbers for super-brownian motions with a single point source

We investigate the super-Brownian motion with a single point source in dimensions 2 and 3 as constructed by Fleischmann and Mueller in 2004. Using analytic facts we derive the long time behavior of the mean in dimension 2 and 3 thereby complementing previous work of Fleischmann, Mueller and Vogt. Using spectral theory and martingale arguments we prove a version of the strong law of large numbers for the two dimensional superprocess with a single point source and finite variance.

Evidence of neutral transcriptome evolution in plants

The transcriptome of an organism is its set of gene transcripts (mRNAs) at a defined spatial and temporal locus. Because gene expression is affected markedly by environmental and developmental perturbations, it is widely assumed that transcriptome divergence among taxa represents adaptive phenotypic selection. This assumption has been challenged by neutral theories which propose that stochastic processes drive transcriptome evolution. To test for evidence of neutral transcriptome evolution in plants, we quantified 18 494 gene transcripts in nonsenescent leaves of 14 taxa of Brassicaceae using robust cross-species transcriptomics which includes a two-step physical and in silico-based normalization procedure based on DNA similarity among taxa. Transcriptome divergence correlates positively with evolutionary distance between taxa and with variation in gene expression among samples. Results are similar for pseudogenes and chloroplast genes evolving at different rates. Remarkably, variation in transcript abundance among root-cell samples correlates positively with transcriptome divergence among root tissues and among taxa. Because neutral processes affect transcriptome evolution in plants, many differences in gene expression among or within taxa may be nonfunctional, reflecting ancestral plasticity and founder effects. Appropriate null models are required when comparing transcriptomes in space and time.

Ensemble downscaling in coupled solar wind-magnetosphere modeling for space weather forecasting

Advanced forecasting of space weather requires simulation of the whole Sun-to-Earth system, which necessitates driving magnetospheric models with the outputs from solar wind models. This presents a fundamental difficulty, as the magnetosphere is sensitive to both large-scale solar wind structures, which can be captured by solar wind models, and small-scale solar wind “noise,” which is far below typical solar wind model resolution and results primarily from stochastic processes. Following similar approaches in terrestrial climate modeling, we propose statistical “downscaling” of solar wind model results prior to their use as input to a magnetospheric model. As magnetospheric response can be highly nonlinear, this is preferable to downscaling the results of magnetospheric modeling. To demonstrate the benefit of this approach, we first approximate solar wind model output by smoothing solar wind observations with an 8 h filter, then add small-scale structure back in through the addition of random noise with the observed spectral characteristics. Here we use a very simple parameterization of noise based upon the observed probability distribution functions of solar wind parameters, but more sophisticated methods will be developed in the future. An ensemble of results from the simple downscaling scheme are tested using a model-independent method and shown to add value to the magnetospheric forecast, both improving the best estimate and quantifying the uncertainty. We suggest a number of features desirable in an operational solar wind downscaling scheme.

A moment problem for random discrete measures

Let X be a locally compact Polish space. A random measure on X is a probability measure on the space of all (nonnegative) Radon measures on X. Denote by K(X) the cone of all Radon measures η on X which are of the form η =

The uniqueness of signature problem in the non-Markov setting

We establish a general framework for a class of multidimensional stochastic processes over [0,1] under which with probability one, the signature (the collection of iterated path integrals in the sense of rough paths) is well-defined and determines the sample paths of the process up to reparametrization. In particular, by using the Malliavin calculus we show that our method applies to a class of Gaussian processes including fractional Brownian motion with Hurst parameter H>1/4, the Ornstein–Uhlenbeck process and the Brownian bridge.