Iteration of closed geodesics in stationary Lorentzian manifolds

Following the lines of Bott in (Commun Pure Appl Math 9:171-206, 1956), we study the Morse index of the iterates of a closed geodesic in stationary Lorentzian manifolds, or, more generally, of a closed Lorentzian geodesic that admits a timelike periodic Jacobi field. Given one such closed geodesic gamma, we prove the existence of a locally constant integer valued map Lambda(gamma) on the unit circle with the property that the Morse index of the iterated gamma(N) is equal, up to a correction term epsilon(gamma) is an element of {0,1}, to the sum of the values of Lambda(gamma) at the N-th roots of unity. The discontinuities of Lambda(gamma) occur at a finite number of points of the unit circle, that are special eigenvalues of the linearized Poincare map of gamma. We discuss some applications of the theory.

Microstructure evolution and softening processes in hot deformed austenitic and duplex stainless steels

The microstructure evolution and softening processes occurring in 22Cr-19Ni-3Mo austenitic and 21Cr-10Ni-3Mo duplex stainless steels deformed in torsion at 900 and 1200 °C were studied in the present work. Austenite was observed to soften in both steels via dynamic recovery (DRV) and dynamic recrystallisation (DRX) for the low and high deformation temperatures, respectively. At 900 °C, an "organised", self-screening austenite deformation substructure largely comprising microbands, locally accompanied by micro-shear bands, was formed. By contrast, a "random", accommodating austenite deformation substructure composed of equiaxed subgrains formed at 1200 °C. In the single-phase steel, DRX of austenite largely occurred through straininduced grain boundary migration accompanied by (multiple) twinning. In the duplex steel, this softening mechanism was complemented by the formation of DRX grains through subgrain growth in the austenite/ferrite interface regions and by large-scale subgrain coalescence. At 900 °C, the duplex steel displayed limited stress-assisted phase transformations between austenite and ferrite, characterised by the dissolution of the primary austenite, formation of Widmanstätten secondary austenite and gradual globularisation of the transformed regions with strain. The softening process within ferrite was classified as "extended DRV", characterised by a continuous increase in misorientations across the sub-boundaries with strain, for both deformation temperatures.

Nonparametric rank tests for non-stationary panels

We develop a set of nonparametric rank tests for non-stationary panels based on multivariate variance ratios which use untruncated kernels. As such, the tests do not require the choice of tuning parameters associated with bandwidth or lag length and also do not require choices with respect to numbers of common factors. The tests allow for unrestricted cross-sectional dependence and dynamic heterogeneity among the units of the panel, provided simply that a joint functional central limit theorem holds for the panel of differenced series. We provide a discussion of the relationships between our setting and the settings for which first- and second generation panel unit root tests are designed. In Monte Carlo simulations we illustrate the small-sample performance of our tests when they are used as panel unit root tests under the more restrictive DGPs for which panel unit root tests are typically designed, and for more general DGPs we also compare the small-sample performance of our nonparametric tests to parametric rank tests. Finally, we provide an empirical illustration by testing for income convergence among countries.

A new perspective on the PPP hypothesis

This paper the stastistical properties of the real exchange rates of G-5 countries for the Bretton-Woods peiod, and draw implications on the purchasing power parity (PPP) hypothesis. In contrast to most previous studies that consider only unit root and stationary process to describe the real exchange tae, this paper also considers two in-between processes, the locally persistent process ans the fractionally integrated process, to complement past studies. Seeking to be consistent with tha ample evidence of near unit in the real exchange rate movements very well. This finding implies that: 1) the real exchange movement is more persistent than the stationary case but less persistent than the unit root case; 2) the real exchange rate is non-stationary but the PPP reversion occurs and the PPP holds in the long run; 3) the real exchange rate does not exhibit the secular dependence of the fractional integration; 4) the real exchange rate evolves over time in a way that there is persistence over a range of time, but the effect of shocks will eventually disappear over time horizon longer than order O (nd), that is, at finite time horizon; 5) shocks dissipation is fasters than predicted by the fractional integracion, and the total sum of the effects of a unit innovation is finite, implying that a full PPP reversion occurs at finite horizons. These results may explain why pasrt empirical estudies could not provide a clear- conclusion on the real exchange rate processes and the PPP hypothesis.

Nonparametric entropy-based tests of independence between stochastic processes

This paper develops nonparametric tests of independence between two stationary stochastic processes. The testing strategy boils down to gauging the closeness between the joint and the product of the marginal stationary densities. For that purpose, I take advantage of a generalized entropic measure so as to build a class of nonparametric tests of independence. Asymptotic normality and local power are derived using the functional delta method for kernels, whereas finite sample properties are investigated through Monte Carlo simulations.

Diamondiferous deposits in the Jequitai area (Minas Gerais, Brazil): a consequence of neotectonic processes

Diamonds obtained from small scale mining near Jequitai and surrounding villages are extracted from Tertiary conglomerates and Quaternary gravels of the Rio Jequitai. Eocretaceous conglomerates, which are locally poorly diamondiferous, cover parts of the Serra da Agua Fria and Serra do Cabral. They are of no economic importance. Analyses of neotectonic, post-Miocene features support a transpressive regime that gave rise to N-S to N25° E transcurrent faults, and WNW normal faults. The main evidence for neotectonic processes are inclined Tertiary sediments, drainage captures, striated laterites of Miocene age, and tilting of blocks that form the Rio Jequitai graben. Diamonds in the Tertiary terraces derived from the Eocretaceous conglomerates, which were affected by neotectonic processes, followed by erosion and concentration during redeposition of sediments.

Non-Markovian stochastic processes and their applications: from anomalous diffusion to time series analysis

This work provides a forward step in the study and comprehension of the relationships between stochastic processes and a certain class of integral-partial differential equation, which can be used in order to model anomalous diffusion and transport in statistical physics. In the first part, we brought the reader through the fundamental notions of probability and stochastic processes, stochastic integration and stochastic differential equations as well. In particular, within the study of H-sssi processes, we focused on fractional Brownian motion (fBm) and its discrete-time increment process, the fractional Gaussian noise (fGn), which provide examples of non-Markovian Gaussian processes. The fGn, together with stationary FARIMA processes, is widely used in the modeling and estimation of long-memory, or long-range dependence (LRD). Time series manifesting long-range dependence, are often observed in nature especially in physics, meteorology, climatology, but also in hydrology, geophysics, economy and many others. We deepely studied LRD, giving many real data examples, providing statistical analysis and introducing parametric methods of estimation. Then, we introduced the theory of fractional integrals and derivatives, which indeed turns out to be very appropriate for studying and modeling systems with long-memory properties. After having introduced the basics concepts, we provided many examples and applications. For instance, we investigated the relaxation equation with distributed order time-fractional derivatives, which describes models characterized by a strong memory component and can be used to model relaxation in complex systems, which deviates from the classical exponential Debye pattern. Then, we focused in the study of generalizations of the standard diffusion equation, by passing through the preliminary study of the fractional forward drift equation. Such generalizations have been obtained by using fractional integrals and derivatives of distributed orders. In order to find a connection between the anomalous diffusion described by these equations and the long-range dependence, we introduced and studied the generalized grey Brownian motion (ggBm), which is actually a parametric class of H-sssi processes, which have indeed marginal probability density function evolving in time according to a partial integro-differential equation of fractional type. The ggBm is of course Non-Markovian. All around the work, we have remarked many times that, starting from a master equation of a probability density function f(x,t), it is always possible to define an equivalence class of stochastic processes with the same marginal density function f(x,t). All these processes provide suitable stochastic models for the starting equation. Studying the ggBm, we just focused on a subclass made up of processes with stationary increments. The ggBm has been defined canonically in the so called grey noise space. However, we have been able to provide a characterization notwithstanding the underline probability space. We also pointed out that that the generalized grey Brownian motion is a direct generalization of a Gaussian process and in particular it generalizes Brownain motion and fractional Brownain motion as well. Finally, we introduced and analyzed a more general class of diffusion type equations related to certain non-Markovian stochastic processes. We started from the forward drift equation, which have been made non-local in time by the introduction of a suitable chosen memory kernel K(t). The resulting non-Markovian equation has been interpreted in a natural way as the evolution equation of the marginal density function of a random time process l(t). We then consider the subordinated process Y(t)=X(l(t)) where X(t) is a Markovian diffusion. The corresponding time-evolution of the marginal density function of Y(t) is governed by a non-Markovian Fokker-Planck equation which involves the same memory kernel K(t). We developed several applications and derived the exact solutions. Moreover, we considered different stochastic models for the given equations, providing path simulations.

Beyond simple proton transfer processes: domino reactions between 4-substituted indoles and nitroethene as a new gateway to ergot alkaloids

The multimodal biology activity of ergot alkaloids is known by humankind since middle ages. Synthetically modified ergot alkaloids are used for the treatment of various medical conditions. Despite the great progress in organic syntheses, the total synthesis of ergot alkaloids remains a great challenge due to the complexity of their polycyclic structure with multiple stereogenic centres. This project has developed a new domino reaction between indoles bearing a Michael acceptor at the 4 position and nitroethene, leading to potential ergot alkaloid precursors in highly enantioenriched form. The reaction was optimised and applied to a large variety of substrate with good results. Even if unfortunately all attempts to further modify the obtained polycyclic structure failed, it was found a reaction able to produce the diastereoisomer of the polycyclic product in excellent yields. The compounds synthetized were characterized by NMR and ESIMS analysis confirming the structure and their enantiomeric excess was determined by chiral stationary phase HPLC. The mechanism of the reaction was evaluated by DFT calculations, showing the formation of a key bicoordinated nitronate intermediate, and fully accounting for the results observed with all substrates. The relative and absolute configuration of the adducts were determined by a combination of NMR, ECD and computational methods.

Stationary states in random walks on networks

In this thesis we dealt with the problem of describing a transportation network in which the objects in movement were subject to both finite transportation capacity and finite accomodation capacity. The movements across such a system are realistically of a simultaneous nature which poses some challenges when formulating a mathematical description. We tried to derive such a general modellization from one posed on a simplified problem based on asyncronicity in particle transitions. We did so considering one-step processes based on the assumption that the system could be describable through discrete time Markov processes with finite state space. After describing the pre-established dynamics in terms of master equations we determined stationary states for the considered processes. Numerical simulations then led to the conclusion that a general system naturally evolves toward a congestion state when its particle transition simultaneously and we consider one single constraint in the form of network node capacity. Moreover the congested nodes of a system tend to be located in adjacent spots in the network, thus forming local clusters of congested nodes.

Continuum percolation for Gibbs point processes

We consider percolation properties of the Boolean model generated by a Gibbs point process and balls with deterministic radius. We show that for a large class of Gibbs point processes there exists a critical activity, such that percolation occurs a.s. above criticality. For locally stable Gibbs point processes we show a converse result, i.e. they do not percolate a.s. at low activity.

Bounds for the probability generating functional of a Gibbs point process

We derive explicit lower and upper bounds for the probability generating functional of a stationary locally stable Gibbs point process, which can be applied to summary statistics such as the F function. For pairwise interaction processes we obtain further estimates for the G and K functions, the intensity, and higher-order correlation functions. The proof of the main result is based on Stein's method for Poisson point process approximation.

Running the Gauntlet: Inhibitory Effects of Algal Turfs on the Processes of Coral Recruitment

Mortality of corals is increasing due to bleaching, disease and algal overgrowth. In the Caribbean, low rates of coral recruitment contribute to the slow or undetectable rates of recovery in reef ecosystems. Although algae have long been suspected to interfere with coral recruitment, the mechanisms of that interaction remain unclear. We experimentally tested the effects of turf algal abundance on 3 sequential factors important to recruitment of corals: the biophysical delivery of planktonic coral larvae, their propensity to settle, and the availability of microhabitats where they survive. We deployed coral settlement plates inside and outside damselfish Stegastes spp. gardens and cages. Damselfish aggression reduced herbivory from fishes, and cages became fouled with turf algae, both locally increasing algal biomass surrounding the plates. This reduced flushing rates in nursery microhabitats on the plate underside, limiting larvae available for settlement. Coral spat settled preferentially on an early successional crustose coralline alga Titanoderma prototypum but also on or near other coralline algae, biofilms, and calcareous polychaete worm tubes. Post-settlement survival was highest in the fully grazed, lowest algal biomass treatment, and after 27 mo 'spat' densities were 73 % higher in this treatment. The 'gauntlet' refers to the sequence of ecological processes through which corals must survive to recruit. The highest proportion of coral spat successfully running the gauntlet did so under conditions of low algal biomass resulting from increased herbivory. If coral recruitment is heavily controlled at very local scales by this gauntlet, then coral reef managers could improve a reef's recruitment potential by managing for reduced algal biomass.

Characteristics, Distribution and Persistence of Thin Layers Over a 48 Hour Period

The biological and physical processes contributing to planktonic thin layer dynamics were examined in a multidisciplinary study conducted in East Sound, Washington, USA between June 10 and June 25, 1998. The temporal and spatial scales characteristic of thin layers were determined using a nested sampling strategy utilizing 4 major types of platforms: (1) an array of 3 moored acoustical instrument packages and 2 moored optical instrument packages that recorded distributions and intensities of thin layers; (2) additional stationary instrumentation deployed outside the array comprised of meteorological stations, wave-tide gauges, and thermistor chains; (3) a research vessel anchored 150 m outside the western edge of the array; (4) 2 mobile vessels performing basin-wide surveys to define the spatial extent of thin layers and the physical hydrography of the Sound. We observed numerous occurrences of thin layers that contained locally enhanced concentrations of material; many of the layers persisted for intervals of several hours to a few days. More than one persistent thin layer may be present at any one time, and these spatially distinct thin layers often contain distinct plankton assemblages. The results suggest that the species or populations comprising each distinct thin layer have responded to different sets of biological and/or physical processes. The existence and persistence of planktonic thin layers generates extensive biological heterogeneity in the water column and may be important in maintaining species diversity and overall community structure.

Regularity conditions in the realisability problem in applications to point processes and random closed sets

We study existence of random elements with partially specified distributions. The technique relies on the existence of a positive ex-tension for linear functionals accompanied by additional conditions that ensure the regularity of the extension needed for interpreting it as a probability measure. It is shown in which case the extens ion can be chosen to possess some invariance properties. The results are applied to the existence of point processes with given correlation measure and random closed sets with given two-point covering function or contact distribution function. It is shown that the regularity condition can be efficiently checked in many cases in order to ensure that the obtained point processes are indeed locally finite and random sets have closed realisations.

Stationary Markovian Equilibrium in Overlapping Generation Models with Stochastic Nonclassical Production

This paper provides new sufficient conditions for the existence, computation via successive approximations, and stability of Markovian equilibrium decision processes for a large class of OLG models with stochastic nonclassical production. Our notion of stability is existence of stationary Markovian equilibrium. With a nonclassical production, our economies encompass a large class of OLG models with public policy, valued fiat money, production externalities, and Markov shocks to production. Our approach combines aspects of both topological and order theoretic fixed point theory, and provides the basis of globally stable numerical iteration procedures for computing extremal Markovian equilibrium objects. In addition to new theoretical results on existence and computation, we provide some monotone comparative statics results on the space of economies.