Excessive functions, Appell polynomials and optimal stopping

The main topic of the thesis is optimal stopping. This is treated in two research articles. In the first article we introduce a new approach to optimal stopping of general strong Markov processes. The approach is based on the representation of excessive functions as expected suprema. We present a variety of examples, in particular, the Novikov-Shiryaev problem for Lévy processes. In the second article on optimal stopping we focus on differentiability of excessive functions of diffusions and apply these results to study the validity of the principle of smooth fit. As an example we discuss optimal stopping of sticky Brownian motion. The third research article offers a survey like discussion on Appell polynomials. The crucial role of Appell polynomials in optimal stopping of Lévy processes was noticed by Novikov and Shiryaev. They described the optimal rule in a large class of problems via these polynomials. We exploit the probabilistic approach to Appell polynomials and show that many classical results are obtained with ease in this framework. In the fourth article we derive a new relationship between the generalized Bernoulli polynomials and the generalized Euler polynomials.

Implementation of educational change in Finland: The case of the undivided basic education reform

For the past decades, educational large-scale reforms have been elaborated and implemented in many countries and often resulted in partial or complete failure. These results brought researchers to study policy processes in order to address this particular challenge. Studies on implementation processes brought to light an existing causal relationship between the implementation process and the effectiveness of a reform. This study aims to describe the implementation process of educational change in Finland, who produced efficient educational reforms over the last 50 years. The case study used for the purpose of this study is the national reform of undivided basic education (yhtenäinen peruskoulu) implemented in the end of the 1990s. Therefore, this research aims to describe how the Finnish undivided basic education reform was implemented. This research was carried out using a pluralist and structuralist approach of policy process and was analyzed according to the hybrid model of implementation process. The data were collected using a triangulation of methods, i.e. documentary research, interviews and questionnaires. The data were qualitative and were analyzed using content analysis methods. This study concludes that the undivided basic education reform was applied in a very decentralized manner, which is a reflection of the decentralized system present in Finland. Central authorities provided a clear vision of the purpose of the reform, but did not control the implementation process. They rather provided extensive support in the form of transmission of information and development of collaborative networks. Local authorities had complete autonomy in terms of decision-making and implementation process. Discussions, debates and decisions regarding implementation processes took place at the local level and included the participation of all actors present on the field. Implementation methods differ from a region to another, with is the consequence of the variation of the level of commitment of local actors but also the diversity of local realities. The reform was implemented according to existing structures and values, which means that it was in cohesion with the context in which it was implemented. These results cannot be generalized to all implementation processes of educational change in Finland but give a great insight of what could be the model used in Finland. Future studies could intent to confirm the model described here by studying other reforms that took place in Finland.

Implementation of educational change in Finland: The case of the undivided basic education reform

For the past decades, educational large-scale reforms have been elaborated and implemented in many countries and often resulted in partial or complete failure. These results brought researchers to study policy processes in order to address this particular challenge. Studies on implementation processes brought to light an existing causal relationship between the implementation process and the effectiveness of a reform. This study aims to describe the implementation process of educational change in Finland, who produced efficient educational reforms over the last 50 years. The case study used for the purpose of this study is the national reform of undivided basic education (yhtenäinen peruskoulu) implemented in the end of the 1990s. Therefore, this research aims to describe how the Finnish undivided basic education reform was implemented. This research was carried out using a pluralist and structuralist approach of policy process and was analyzed according to the hybrid model of implementation process. The data were collected using a triangulation of methods, i.e. documentary research, interviews and questionnaires. The data were qualitative and were analyzed using content analysis methods. This study concludes that the undivided basic education reform was applied in a very decentralized manner, which is a reflection of the decentralized system present in Finland. Central authorities provided a clear vision of the purpose of the reform, but did not control the implementation process. They rather provided extensive support in the form of transmission of information and development of collaborative networks. Local authorities had complete autonomy in terms of decision-making and implementation process. Discussions, debates and decisions regarding implementation processes took place at the local level and included the participation of all actors present on the field. Implementation methods differ from a region to another, with is the consequence of the variation of the level of commitment of local actors but also the diversity of local realities. The reform was implemented according to existing structures and values, which means that it was in cohesion with the context in which it was implemented. These results cannot be generalized to all implementation processes of educational change in Finland but give a great insight of what could be the model used in Finland. Future studies could intent to confirm the model described here by studying other reforms that took place in Finland.

Discrete commutative difference operator theory

The object of this thesis is to formulate a basic commutative difference operator theory for functions defined on a basic sequence, and a bibasic commutative difference operator theory for functions defined on a bibasic sequence of points, which can be applied to the solution of basic and bibasic difference equations. in this thesis a brief survey of the work done in this field in the classical case, as well as a review of the development of q~difference equations, q—analytic function theory, bibasic analytic function theory, bianalytic function theory, discrete pseudoanalytic function theory and finally a summary of results of this thesis

Properties of Equilibrium Distributions of Order n

The present work is intended to discuss various properties and reliability aspects of higher order equilibrium distributions in continuous, discrete and multivariate cases, which contribute to the study on equilibrium distributions. At first, we have to study and consolidate the existing literature on equilibrium distributions. For this we need some basic concepts in reliability. These are being discussed in the 2nd chapter, In Chapter 3, some identities connecting the failure rate functions and moments of residual life of the univariate, non-negative continuous equilibrium distributions of higher order and that of the baseline distribution are derived. These identities are then used to characterize the generalized Pareto model, mixture of exponentials and gamma distribution. An approach using the characteristic functions is also discussed with illustrations. Moreover, characterizations of ageing classes using stochastic orders has been discussed. Part of the results of this chapter has been reported in Nair and Preeth (2009). Various properties of equilibrium distributions of non-negative discrete univariate random variables are discussed in Chapter 4. Then some characterizations of the geo- metric, Waring and negative hyper-geometric distributions are presented. Moreover, the ageing properties of the original distribution and nth order equilibrium distribu- tions are compared. Part of the results of this chapter have been reported in Nair, Sankaran and Preeth (2012). Chapter 5 is a continuation of Chapter 4. Here, several conditions, in terms of stochastic orders connecting the baseline and its equilibrium distributions are derived. These conditions can be used to rede_ne certain ageing notions. Then equilibrium distributions of two random variables are compared in terms of various stochastic orders that have implications in reliability applications. In Chapter 6, we make two approaches to de_ne multivariate equilibrium distribu- tions of order n. Then various properties including characterizations of higher order equilibrium distributions are presented. Part of the results of this chapter have been reported in Nair and Preeth (2008). The Thesis is concluded in Chapter 7. A discussion on further studies on equilib- rium distributions is also made in this chapter.

Time Discretization of the SST-generalized Navier-Stokes Equations: Positive and Negative Results

In the theory of the Navier-Stokes equations, the proofs of some basic known results, like for example the uniqueness of solutions to the stationary Navier-Stokes equations under smallness assumptions on the data or the stability of certain time discretization schemes, actually only use a small range of properties and are therefore valid in a more general context. This observation leads us to introduce the concept of SST spaces, a generalization of the functional setting for the Navier-Stokes equations. It allows us to prove (by means of counterexamples) that several uniqueness and stability conjectures that are still open in the case of the Navier-Stokes equations have a negative answer in the larger class of SST spaces, thereby showing that proof strategies used for a number of classical results are not sufficient to affirmatively answer these open questions. More precisely, in the larger class of SST spaces, non-uniqueness phenomena can be observed for the implicit Euler scheme, for two nonlinear versions of the Crank-Nicolson scheme, for the fractional step theta scheme, and for the SST-generalized stationary Navier-Stokes equations. As far as stability is concerned, a linear version of the Euler scheme, a nonlinear version of the Crank-Nicolson scheme, and the fractional step theta scheme turn out to be non-stable in the class of SST spaces. The positive results established in this thesis include the generalization of classical uniqueness and stability results to SST spaces, the uniqueness of solutions (under smallness assumptions) to two nonlinear versions of the Euler scheme, two nonlinear versions of the Crank-Nicolson scheme, and the fractional step theta scheme for general SST spaces, the second order convergence of a version of the Crank-Nicolson scheme, and a new proof of the first order convergence of the implicit Euler scheme for the Navier-Stokes equations. For each convergence result, we provide conditions on the data that guarantee the existence of nonstationary solutions satisfying the regularity assumptions needed for the corresponding convergence theorem. In the case of the Crank-Nicolson scheme, this involves a compatibility condition at the corner of the space-time cylinder, which can be satisfied via a suitable prescription of the initial acceleration.

Describing long-term trends in precipitation using generalized additive models

With the current concern over climate change, descriptions of how rainfall patterns are changing over time can be useful. Observations of daily rainfall data over the last few decades provide information on these trends. Generalized linear models are typically used to model patterns in the occurrence and intensity of rainfall. These models describe rainfall patterns for an average year but are more limited when describing long-term trends, particularly when these are potentially non-linear. Generalized additive models (GAMS) provide a framework for modelling non-linear relationships by fitting smooth functions to the data. This paper describes how GAMS can extend the flexibility of models to describe seasonal patterns and long-term trends in the occurrence and intensity of daily rainfall using data from Mauritius from 1962 to 2001. Smoothed estimates from the models provide useful graphical descriptions of changing rainfall patterns over the last 40 years at this location. GAMS are particularly helpful when exploring non-linear relationships in the data. Care is needed to ensure the choice of smooth functions is appropriate for the data and modelling objectives. (c) 2008 Elsevier B.V. All rights reserved.

Generalized honeycomb torus is Hamiltonian

Generalized honeycomb torus is a candidate for interconnection network architectures, which includes honeycomb torus, honeycomb rectangular torus, and honeycomb parallelogramic torus as special cases. Existence of Hamiltonian cycle is a basic requirement for interconnection networks since it helps map a "token ring" parallel algorithm onto the associated network in an efficient way. Cho and Hsu [Inform. Process. Lett. 86 (4) (2003) 185-190] speculated that every generalized honeycomb torus is Hamiltonian. In this paper, we have proved this conjecture. (C) 2004 Elsevier B.V. All rights reserved.

Response theory for equilibrium and non-equilibrium statistical mechanics: causality and generalized Kramers-Kronig relations

We consider the general response theory recently proposed by Ruelle for describing the impact of small perturbations to the non-equilibrium steady states resulting from Axiom A dynamical systems. We show that the causality of the response functions entails the possibility of writing a set of Kramers-Kronig (K-K) relations for the corresponding susceptibilities at all orders of nonlinearity. Nonetheless, only a special class of directly observable susceptibilities obey K-K relations. Specific results are provided for the case of arbitrary order harmonic response, which allows for a very comprehensive K-K analysis and the establishment of sum rules connecting the asymptotic behavior of the harmonic generation susceptibility to the short-time response of the perturbed system. These results set in a more general theoretical framework previous findings obtained for optical systems and simple mechanical models, and shed light on the very general impact of considering the principle of causality for testing self-consistency: the described dispersion relations constitute unavoidable benchmarks that any experimental and model generated dataset must obey. The theory exposed in the present paper is dual to the time-dependent theory of perturbations to equilibrium states and to non-equilibrium steady states, and has in principle similar range of applicability and limitations. In order to connect the equilibrium and the non equilibrium steady state case, we show how to rewrite the classical response theory by Kubo so that response functions formally identical to those proposed by Ruelle, apart from the measure involved in the phase space integration, are obtained. These results, taking into account the chaotic hypothesis by Gallavotti and Cohen, might be relevant in several fields, including climate research. In particular, whereas the fluctuation-dissipation theorem does not work for non-equilibrium systems, because of the non-equivalence between internal and external fluctuations, K-K relations might be robust tools for the definition of a self-consistent theory of climate change.

A new family of generalized distributions

Kumaraswamy [Generalized probability density-function for double-bounded random-processes, J. Hydrol. 462 (1980), pp. 79-88] introduced a distribution for double-bounded random processes with hydrological applications. For the first time, based on this distribution, we describe a new family of generalized distributions (denoted with the prefix `Kw`) to extend the normal, Weibull, gamma, Gumbel, inverse Gaussian distributions, among several well-known distributions. Some special distributions in the new family such as the Kw-normal, Kw-Weibull, Kw-gamma, Kw-Gumbel and Kw-inverse Gaussian distribution are discussed. We express the ordinary moments of any Kw generalized distribution as linear functions of probability weighted moments (PWMs) of the parent distribution. We also obtain the ordinary moments of order statistics as functions of PWMs of the baseline distribution. We use the method of maximum likelihood to fit the distributions in the new class and illustrate the potentiality of the new model with an application to real data.

Dependence of Response Functions and Orbital Functionals on Occupation Numbers

Explicitly orbital-dependent approximations to the exchange-correlation energy functional of density functional theory typically not only depend on the single-particle Kohn-Sham orbitals but also on their occupation numbers in the ground-state Slater determinant. The variational calculation of the corresponding exchange-correlation potentials with the optimized effective potential (OEP) method therefore also requires a variation of the occupation numbers with respect to a variation in the effective single-particle potential, which is usually not taken into account. Here it is shown under which circumstances this procedure is justified.

Regular Derivations in Basic Superposition-Based Calculi

We prove the completeness of the regular strategy of derivations for superposition-based calculi. The regular strategy was pioneered by Kanger in [Kan63], who proposed that all equality inferences take place before all other steps in the proof. We show that the strategy is complete with the elimination of tautologies. The implication of our result is the completeness of non-standard selection functions by which in non-relational clauses only equality literals (and all of them) are selected.

Seguimento clinoceletrográfico de criançcas e adolescentes com crise epiléptica única não-provocada

Os fenômenos convulsivos despertaram o interesse de estudiosos e pensadores já na Antigüidade, quando aspectos mágicos e sobrenaturais eram a eles associados. No século XIX foram lançadas as bases dos conceitos atuais sobre a desestruturação funcional cerebral na epilepsia, e Berger, em 1929, marcou definitivamente a história com a descoberta dos ritmos cerebrais. Crise epiléptica e epilepsia não são sinônimos, já que o último termo refere-se a crises recorrentes espontâneas. Ela costuma iniciar na infância, daí a preocupação com o risco de repetição do primeiro episódio e com a decisão de instituir tratamento medicamentoso. Fatores prognósticos são apontados, mas não há consenso. No Brasil existem poucas pesquisas nesta linha, tanto de prevalência da epilepsia como de fatores envolvidos na recorrência de crises. Este estudo teve como objetivo geral avaliar aspectos clinicoeletrográficos capazes de auxiliar no prognóstico e no manejo da epilepsia da criança e do adolescente. Foram objetivos específicos determinar a incidência de crise epiléptica não provocada recorrente; identificar fatores remotos implicados na ocorrência de crise epiléptica; relacionar tipo de crise com achados eletrencefalográficos; relacionar tipo de crise, duração da crise, estado vigília/sono no momento da crise e achados eletrencefalográficos com possibilidade de recorrência; e identificar os fatores de risco para epilepsia. Foram acompanhados 109 pacientes com idades entre 1 mês e 16 anos, com primeira crise não-provocada, em média por 24 meses, a intervalos trimestrais, no Hospital de Clínicas de Porto Alegre (HCPA). Foram realizados eletrencefalogramas (EEG) após a primeira crise; depois, solicitados anualmente. Não foram incluídos casos com epilepsia ou síndrome epiléptica bem definida, ou que fizeram uso prévio de drogas antiepilépticas. A média de idade foi 6 anos, com predomínio da faixa etária de 6 a 12 anos. Setenta eram meninos e 39, meninas. Os indivíduos brancos eram 92, e os não-brancos, 17. O nível de escolaridade dos casos esteve de acordo com a distribuição da idade e, entre os responsáveis, predominaram 8 anos de escolaridade. Foi possível concluir que as crises únicas não-provocadas mais freqüentes foram generalizadas, e sem predomínio significativo do tipo de EEG. A incidência de crise não-provocada recorrente foi 51,4%. História de intercorrências pré-natais maternas aumentou em 2 vezes o risco de repetição de crises. Via de nascimento, escore de Apgar no 5º minuto, relação peso ao nascer/idade gestacional, intercorrências no período pós-natal imediato e desenvolvimento neuropsicomotor não tiveram influência na recorrência. História familiar de crises mostrou tendência à significância estatística para repetição dos episódios, com risco de 1,7. Não foi encontrada associação entre tipo de crise e achado eletrencefalográfico. A maioria das crises foi de curta duração (até 5 minutos), mas este dado não esteve relacionado com a recorrência. Estado de vigília teve efeito protetor na recorrência. Se a primeira crise foi parcial, o risco de repetição foi 1,62, com tendência à significância. Quando o primeiro EEG foi alterado, houve relação significativa com primeira crise tanto generalizada como parcial. O primeiro EEG com alterações paroxísticas focais apontou risco de repetição de 2,90. Quando as variáveis envolvidas na repetição de crises foram ajustadas pelo modelo de regressão de Cox, EEG alterado mostrou risco de 2,48, com riscos acumulados de 50%, 60%, 62% e 68%; com EEG normal, os riscos foram 26%, 32%, 34% e 36% em 6, 12, 18 e 24 meses respectivamente.

Operational functions for innovative startups in France

Nessa tese, é buscado um maior entendimento sobre a importância das funções operacionais nas startups francesas. Uma grande flexibilidade das tarefas a ser coberta e uma gestão horizontal caracterizam as startups. Desse jeito, não é muito comum para as empresas recentemente criadas como as startups ter uma politica clara de recursos humanos. Na verdade, cada participante na start-up pode ser levado a pensar de forma diferente em termos de vendas desenvolvimento de negócios, comercialização, marketing, tecnologia ou desenvolvimento de produto. Essa tese não vai explorar cada uma dessas tarefas. Mas vai procurar para identifcar a percepção sobre a alocação ótima de recursos para cada função chave da nova empresa. Qualquer seja o setor de mercado em consideração ou o estágio de amadurecimento da startup, funções chaves que são percebidas como sendo a base para start-ups bem sucedidas são pesquisa & desenvolvimento e comercialização. Funções de liderança não são tão importantes. Somente a startup focada na tecnologia tem uma "função de chefe executivo" com maior importância do que as startups médias. Além disso, empreendedores em série, bem sucedidos ou não, focam predominantemente aspectos relacionados ao marketing e à captação de recursos em detrimento de aspectos ligados à gestão do negócio. No final, os empresários, muitas vezes tem um preconceito ao respeito da sua formação acadêmica porque ele sobrestimam funções que eles pensam poder fazer em comparação das funções que eles são capazes de fazer. Nessa tese, intent-se demonstrar a relação entre as funções ocupadas por um sócio e as ações que ele possui na startup. Essa relação depende do número de sócios (conhecido como acionistas), o tipo de sócios (acionistas principais ou acionistas segundarias) e o impacto na administração corporativa a respeito da distribuição do capital próprio.

Generalized linear mixed models for the genetic evaluation of binary reproductive traits: a simulation study

The objective of this study was to evaluate the use of probit and logit link functions for the genetic evaluation of early pregnancy using simulated data. The following simulation/analysis structures were constructed: logit/logit, logit/probit, probit/logit, and probit/probit. The percentages of precocious females were 5, 10, 15, 20, 25 and 30% and were adjusted based on a change in the mean of the latent variable. The parametric heritability (h²) was 0.40. Simulation and genetic evaluation were implemented in the R software. Heritability estimates (ĥ²) were compared with h² using the mean squared error. Pearson correlations between predicted and true breeding values and the percentage of coincidence between true and predicted ranking, considering the 10% of bulls with the highest breeding values (TOP10) were calculated. The mean ĥ² values were under- and overestimated for all percentages of precocious females when logit/probit and probit/logit models used. In addition, the mean squared errors of these models were high when compared with those obtained with the probit/probit and logit/logit models. Considering ĥ², probit/probit and logit/logit were also superior to logit/probit and probit/logit, providing values close to the parametric heritability. Logit/probit and probit/logit presented low Pearson correlations, whereas the correlations obtained with probit/probit and logit/logit ranged from moderate to high. With respect to the TOP10 bulls, logit/probit and probit/logit presented much lower percentages than probit/probit and logit/logit. The genetic parameter estimates and predictions of breeding values of the animals obtained with the logit/logit and probit/probit models were similar. In contrast, the results obtained with probit/logit and logit/probit were not satisfactory. There is need to compare the estimation and prediction ability of logit and probit link functions.