Rhapsody in Fractional

This paper studies several topics related with the concept of “fractional” that are not directly related with Fractional Calculus, but can help the reader in pursuit new research directions. We introduce the concept of non-integer positional number systems, fractional sums, fractional powers of a square matrix, tolerant computing and FracSets, negative probabilities, fractional delay discrete-time linear systems, and fractional Fourier transform.

Factorization of elliptic boundary value problems by invariant embedding and application to overdetermined problems

Dissertação para obtenção do Grau de Doutor em Matemática

An intertemporal pricing model for CO2 allowances: The impact of the clean development mechanism

A Work Project, presented as part of the requirements for the Award of a Masters Degree in Finance from the NOVA – School of Business and Economics

Modeling and optimization of extracellular polysaccharides production by Enterobacter A47

Polysaccharides are gaining increasing attention as potential environmental friendly and sustainable building blocks in many fields of the (bio)chemical industry. The microbial production of polysaccharides is envisioned as a promising path, since higher biomass growth rates are possible and therefore higher productivities may be achieved compared to vegetable or animal polysaccharides sources. This Ph.D. thesis focuses on the modeling and optimization of a particular microbial polysaccharide, namely the production of extracellular polysaccharides (EPS) by the bacterial strain Enterobacter A47. Enterobacter A47 was found to be a metabolically versatile organism in terms of its adaptability to complex media, notably capable of achieving high growth rates in media containing glycerol byproduct from the biodiesel industry. However, the industrial implementation of this production process is still hampered due to a largely unoptimized process. Kinetic rates from the bioreactor operation are heavily dependent on operational parameters such as temperature, pH, stirring and aeration rate. The increase of culture broth viscosity is a common feature of this culture and has a major impact on the overall performance. This fact complicates the mathematical modeling of the process, limiting the possibility to understand, control and optimize productivity. In order to tackle this difficulty, data-driven mathematical methodologies such as Artificial Neural Networks can be employed to incorporate additional process data to complement the known mathematical description of the fermentation kinetics. In this Ph.D. thesis, we have adopted such an hybrid modeling framework that enabled the incorporation of temperature, pH and viscosity effects on the fermentation kinetics in order to improve the dynamical modeling and optimization of the process. A model-based optimization method was implemented that enabled to design bioreactor optimal control strategies in the sense of EPS productivity maximization. It is also critical to understand EPS synthesis at the level of the bacterial metabolism, since the production of EPS is a tightly regulated process. Methods of pathway analysis provide a means to unravel the fundamental pathways and their controls in bioprocesses. In the present Ph.D. thesis, a novel methodology called Principal Elementary Mode Analysis (PEMA) was developed and implemented that enabled to identify which cellular fluxes are activated under different conditions of temperature and pH. It is shown that differences in these two parameters affect the chemical composition of EPS, hence they are critical for the regulation of the product synthesis. In future studies, the knowledge provided by PEMA could foster the development of metabolically meaningful control strategies that target the EPS sugar content and oder product quality parameters.

Directed integration of new insulated lentiviral vectors to heterochromatin towards safer gene transfer to stem cells

The need for better gene transfer systems towards improved risk=benefit balance for patients remains a major challenge in the clinical translation of gene therapy (GT). We have investigated the improvement of integrating vectors safety in combining (i) new short synthetic genetic insulator elements (GIE) and (ii) directing genetic integration to heterochromatin. We have designed SIN-insulated retrovectors with two candidate GIEs and could identify a specific combination of insulator 2 repeats which translates into best functional activity, high titers and boundary effect in both gammaretro (p20) and lentivectors (DCaro4) (see Duros et al, abstract ibid). Since GIEs are believed to shield the transgenic cassette from inhibitory effects and silencing, DCaro4 has been further tested with chimeric HIV-1 derived integrases which comprise C-ter chromodomains targeting heterochromatin through either histone H3 (ML6chimera) or methylatedCpGislands (ML10). With DCaro4 only and both chimeras, a homogeneous expression is evidenced in over 20% of the cells which is sustained over time. With control lentivectors, less than 2% of cells express GFP as compared to background using a control double-mutant in both catalytic and ledgf binding-sites; in addition, a two-times increase of expression can be induced with histone deacetylase inhibitors. Our approach could significantly reduce integration into open chromatin sensitive sites in stem cells at the time of transduction, a feature which might significantly decrease subsequent genotoxicity, according to X-SCIDs patients data.Work performed with the support of EC-DG research within the FP6-Network of Excellence, CLINIGENE: LSHB-CT-2006-018933

Sports practice among adolescents with chronic health conditions.

OBJECTIVES: To compare the level of sports practice between adolescents with chronic health conditions (CHCs) and control peers and to examine the reasons given by adolescents with CHCs for not practicing any sports in comparison with the control group. DESIGN: School survey. SETTING: Postmandatory schools. PARTICIPANTS: A total of 6790 students (3275 females) aged 16 to 20 years, grouped as adolescents with CHCs (355 females, 354 males) and control peers (2920 females, 3161 males). MAIN EXPOSURE: Chronic health condition was defined using a noncategorical approach including adolescents with a chronic disease and/or a physical handicap. MAIN OUTCOME MEASURES: Sports practice, barriers to sports practice among individuals not practicing any sports, and biological, psychological, socioeducative, and physical activity characteristics. RESULTS: Males with CHCs were less likely than control males to practice sports, whereas no significant difference was observed for females. Chronically ill youth were significantly more likely to report having a CHC as a barrier for not practicing sports. However, the most frequently reported barrier was preference for other activities for males with CHCs and lack of time for control males and for females with and without CHCs. CONCLUSIONS: Having a CHC seems to influence sports practice among males but not females. We recommend that practitioners dealing with adolescents remember to take into account sports practice as part of the care of young patients with CHCs.

The Emperor Has New Clothes: Empirical Tests of Mainstream Theories of Economic Growth

Modern macroeconomic theory utilises optimal control techniques to model the maximisation of individual well-being using a lifetime utility function. Agents face choices over current and future consumption (with resultant implied savings decisions) seeking to maximise the present value of current plus future well-being. However, such inter-temporal welfare-maximising assumptions remain empirically untested. In the work presented here we test whether welfare was in (historical) fact maximised in the US between 1870-2000 and find empirical support for the optimising basis of growth theory, but only once a comprehensive view of what constitutes a country’s wealth or capital is taken into account.

Prognostic importance of anaemia in patients with acute pulmonary embolism.

Although associated with adverse outcomes in other cardiopulmonary diseases, limited evidence exists on the prognostic value of anaemia in patients with acute pulmonary embolism (PE). We sought to examine the associations between anaemia and mortality and length of hospital stay in patients with PE. We evaluated 14,276 patients with a primary diagnosis of PE from 186 hospitals in Pennsylvania, USA. We used random-intercept logistic regression to assess the association between anaemia at the time of presentation and 30-day mortality and discrete-time logistic hazard models to assess the association between anaemia and time to hospital discharge, adjusting for patient (age, gender, race, insurance type, clinical and laboratory variables) and hospital (region, size, teaching status) factors. Anaemia was present in 38.7% of patients at admission. Patients with anaemia had a higher 30-day mortality (13.7% vs. 6.3%; p <0.001) and a longer length of stay (geometric mean, 6.9 vs. 6.6 days; p <0.001) compared to patients without anaemia. In multivariable analyses, anaemia remained associated with an increased odds of death (OR 1.82, 95% CI: 1.60-2.06) and a decreased odds of discharge (OR 0.85, 95% CI: 0.82-0.89). Anaemia is very common in patients presenting with PE and is independently associated with an increased short-term mortality and length of stay.

An anonymous reputation mechanism for cloud computing networks using volunteer resources

One of the major problems when using non-dedicated volunteer resources in adistributed network is the high volatility of these hosts since they can go offlineor become unavailable at any time without control. Furthermore, the use ofvolunteer resources implies some security issues due to the fact that they aregenerally anonymous entities which we know nothing about. So, how to trustin someone we do not know?.Over the last years an important number of reputation-based trust solutionshave been designed to evaluate the participants' behavior in a system.However, most of these solutions are addressed to P2P and ad-hoc mobilenetworks that may not fit well with other kinds of distributed systems thatcould take advantage of volunteer resources as recent cloud computinginfrastructures.In this paper we propose a first approach to design an anonymous reputationmechanism for CoDeS [1], a middleware for building fogs where deployingservices using volunteer resources. The participants are reputation clients(RC), a reputation authority (RA) and a certification authority (CA). Users needa valid public key certificate from the CA to register to the RA and obtain thedata needed to participate into the system, as now an opaque identifier thatwe call here pseudonym and an initial reputation value that users provide toother users when interacting together. The mechanism prevents not only themanipulation of the provided reputation values but also any disclosure of theusers' identities to any other users or authorities so the anonymity isguaranteed.

Modeling of hybrid systems by piecewise decomposition

Piecewise linear models systems arise as mathematical models of systems in many practical applications, often from linearization for nonlinear systems. There are two main approaches of dealing with these systems according to their continuous or discrete-time aspects. We propose an approach which is based on the state transformation, more particularly the partition of the phase portrait in different regions where each subregion is modeled as a two-dimensional linear time invariant system. Then the Takagi-Sugeno model, which is a combination of local model is calculated. The simulation results show that the Alpha partition is well-suited for dealing with such a system

Automatic generation of active coordinates for quantum dynamics calculations: application to the dynamics of benzene photochemistry

A new practical method to generate a subspace of active coordinates for quantum dynamics calculations is presented. These reduced coordinates are obtained as the normal modes of an analytical quadratic representation of the energy difference between excited and ground states within the complete active space self-consistent field method. At the Franck-Condon point, the largest negative eigenvalues of this Hessian correspond to the photoactive modes: those that reduce the energy difference and lead to the conical intersection; eigenvalues close to 0 correspond to bath modes, while modes with large positive eigenvalues are photoinactive vibrations, which increase the energy difference. The efficacy of quantum dynamics run in the subspace of the photoactive modes is illustrated with the photochemistry of benzene, where theoretical simulations are designed to assist optimal control experiments

When mothers work and fathers care. Joint household fertility decisions in Denmark and Spain

We analyze second birth decisions within the theoretical framework of joint household decision making, comparing two countires that represent the international extremes in terms of women's career behaviour, Denmark and Spain. Using all 8 ECHP panels we apply discrete time estimations of the likelihood of a second birth and show that in Spain, fertility behaviour continues to conform to the classic "Becker model" while in Denmark we identify a radically new behavioral pattern according to which career-women's fertility is conditional of their partners' contribution to care for the children.

Randomized observation periods for the compound Poisson risk model: Dividends

In the framework of the classical compound Poisson process in collective risk theory, we study a modification of the horizontal dividend barrier strategy by introducing random observation times at which dividends can be paid and ruin can be observed. This model contains both the continuous-time and the discrete-time risk model as a limit and represents a certain type of bridge between them which still enables the explicit calculation of moments of total discounted dividend payments until ruin. Numerical illustrations for several sets of parameters are given and the effect of random observation times on the performance of the dividend strategy is studied.

Improved multiexponential transient spectroscopy by iterative deconvolution

The analysis of multiexponential decays is challenging because of their complex nature. When analyzing these signals, not only the parameters, but also the orders of the models, have to be estimated. We present an improved spectroscopic technique specially suited for this purpose. The proposed algorithm combines an iterative linear filter with an iterative deconvolution method. A thorough analysis of the noise effect is presented. The performance is tested with synthetic and experimental data.

Can we identify Walrasian allocations?

[eng] We consider a discrete time, pure exchange infinite horizon economy with two or more consumers and at least one concumption good per period. Within the framework of decentralized mechanisms, we show that for a given consumption trade at any period of time, say at time one, the consumers will need, in general, an infinite dimensional (informational) space to identigy such a trade as an intemporal Walrasian one. However, we show and characterize a set of enviroments where the Walrasian trades at each period of time can be achieved as the equilibrium trades of a sequence of decentralized competitive mechanisms, using only both current prices and quantities to coordinate decisions.