SELF-SIMILARITY AND LAMPERTI CONVERGENCE FOR FAMILIES OF STOCHASTIC PROCESSES

We define a new type of self-similarity for one-parameter families of stochastic processes, which applies to certain important families of processes that are not self-similar in the conventional sense. This includes Hougaard Levy processes such as the Poisson processes, Brownian motions with drift and the inverse Gaussian processes, and some new fractional Hougaard motions defined as moving averages of Hougaard Levy process. Such families have many properties in common with ordinary self-similar processes, including the form of their covariance functions, and the fact that they appear as limits in a Lamperti-type limit theorem for families of stochastic processes.

Evaluating the efficiency of fractional integration parameter estimators

This article deals with the efficiency of fractional integration parameter estimators. This study was based on Monte Carlo experiments involving simulated stochastic processes with integration orders in the range]-1,1[. The evaluated estimation methods were classified into two groups: heuristics and semiparametric/maximum likelihood (ML). The study revealed that the comparative efficiency of the estimators, measured by the lesser mean squared error, depends on the stationary/non-stationary and persistency/anti-persistency conditions of the series. The ML estimator was shown to be superior for stationary persistent processes; the wavelet spectrum-based estimators were better for non-stationary mean reversible and invertible anti-persistent processes; the weighted periodogram-based estimator was shown to be superior for non-invertible anti-persistent processes.

Microgranitic Enclaves as Products of Self-mixing Events: a Study of Open-system Processes in the Maua Granite, Sao Paulo, Brazil, Based on in situ Isotopic and Trace Elements in Plagioclase

Felsic microgranular enclaves with structures indicating that they interacted in a plastic state with their chemically similar host granite are abundant in the Maua Pluton, SE Brazil. Larger plagioclase xenocrysts are in textural disequilibrium with the enclave groundmass and show complex zoning patterns with partially resorbed An-rich cores (locally with patchy textures) surrounded by more sodic rims. In situ laser ablation-(multi-collector) inductively coupled plasma mass spectrometry trace element and Sr isotopic analyses performed on the plagioclase xenocrysts indicate open-system crystallization; however, no evidence of derivation from more primitive basic melts is observed. The An-rich cores have more radiogenic initial Sr isotopic ratios that decrease towards the outermost part of the rims, which are in isotopic equilibrium with the matrix plagioclase. These profiles may have been produced by either (1) diffusional re-equilibration after rim crystallization from the enclave-forming magma, as indicated by relatively short calculated residence times, or (2) episodic contamination with a decrease of the contaminant ratio proportional to the extent to which the country rocks were isolated by the crystallization front. Profiles of trace elements with high diffusion coefficients would require unrealistically long residence times, and can be modeled in terms of fractional crystallization. A combination of trace element and Sr isotope data suggests that the felsic microgranular enclaves from the Maua Pluton are the products of interaction between end-member magmas that had similar compositions, thus recording `self-mixing` events.

Scavenging processes of atmospheric particulate matter: a numerical modeling of case studies

Below cloud scavenging processes have been investigated considering a numerical simulation, local atmospheric conditions and particulate matter (PM) concentrations, at different sites in Germany. The below cloud scavenging model has been coupled with bulk particulate matter counter TSI (Trust Portacounter dataset, consisting of the variability prediction of the particulate air concentrations during chosen rain events. The TSI samples and meteorological parameters were obtained during three winter Campaigns: at Deuselbach, March 1994, consisting in three different events; Sylt, April 1994 and; Freiburg, March 1995. The results show a good agreement between modeled and observed air concentrations, emphasizing the quality of the conceptual model used in the below cloud scavenging numerical modeling. The results between modeled and observed data have also presented high square Pearson coefficient correlations over 0.7 and significant, except the Freiburg Campaign event. The differences between numerical simulations and observed dataset are explained by the wind direction changes and, perhaps, the absence of advection mass terms inside the modeling. These results validate previous works based on the same conceptual model.

Biogeochemical processes and the diversity of Nhecolândia lakes, Brazil

The Pantanal of Nhecolândia, the world's largest and most diversified field of tropical lakes, comprises approximately 10,000 lakes, which cover an area of 24,000 km² and vary greatly in salinity, pH, alkalinity, colour, physiography and biological activity. The hyposaline lakes have variable pHs, low alkalinity, macrophytes and low phytoplankton densities. The saline lakes have pHs above 9 or 10, high alkalinity, a high density of phytoplankton and sand beaches. The cause of the diversity of these lakes has been an open question, which we have addressed in our research. Here we propose a hybrid process, both geochemical and biological, as the main cause, including (1) a climate with an important water deficit and poverty in Ca2+ in both superficial and phreatic waters; and (2) an elevation of pH during cyanobacteria blooms. These two aspects destabilise the general tendency of Earth's surface waters towards a neutral pH. This imbalance results in an increase in the pH and dissolution of previously precipitated amorphous silica and quartzose sand. During extreme droughts, amorphous silica precipitates in the inter-granular spaces of the lake bottom sediment, increasing the isolation of the lake from the phreatic level. This paper discusses this biogeochemical problem in the light of physicochemical, chemical, altimetric and phytoplankton data.

Learning processes and the neural analysis of conditioning

Classical and operant conditioning principles, such as the behavioral discrepancy-derived assumption that reinforcement always selects antecedent stimulus and response relations, have been studied at the neural level, mainly by observing the strengthening of neuronal responses or synaptic connections. A review of the literature on the neural basis of behavior provided extensive scientific data that indicate a synthesis between the two conditioning processes based mainly on stimulus control in learning tasks. The resulting analysis revealed the following aspects. Dopamine acts as a behavioral discrepancy signal in the midbrain pathway of positive reinforcement, leading toward the nucleus accumbens. Dopamine modulates both types of conditioning in the Aplysia mollusk and in mammals. In vivo and in vitro mollusk preparations show convergence of both types of conditioning in the same motor neuron. Frontal cortical neurons are involved in behavioral discrimination in reversal and extinction procedures, and these neurons preferentially deliver glutamate through conditioned stimulus or discriminative stimulus pathways. Discriminative neural responses can reliably precede operant movements and can also be common to stimuli that share complex symbolic relations. The present article discusses convergent and divergent points between conditioning paradigms at the neural level of analysis to advance our knowledge on reinforcement.

Stability and ergodicity of piecewise deterministic Markov processes

The main goal of this paper is to establish some equivalence results on stability, recurrence, and ergodicity between a piecewise deterministic Markov process ( PDMP) {X( t)} and an embedded discrete-time Markov chain {Theta(n)} generated by a Markov kernel G that can be explicitly characterized in terms of the three local characteristics of the PDMP, leading to tractable criterion results. First we establish some important results characterizing {Theta(n)} as a sampling of the PDMP {X( t)} and deriving a connection between the probability of the first return time to a set for the discrete-time Markov chains generated by G and the resolvent kernel R of the PDMP. From these results we obtain equivalence results regarding irreducibility, existence of sigma-finite invariant measures, and ( positive) recurrence and ( positive) Harris recurrence between {X( t)} and {Theta(n)}, generalizing the results of [ F. Dufour and O. L. V. Costa, SIAM J. Control Optim., 37 ( 1999), pp. 1483-1502] in several directions. Sufficient conditions in terms of a modified Foster-Lyapunov criterion are also presented to ensure positive Harris recurrence and ergodicity of the PDMP. We illustrate the use of these conditions by showing the ergodicity of a capacity expansion model.

AVERAGE CONTINUOUS CONTROL OF PIECEWISE DETERMINISTIC MARKOV PROCESSES

This paper deals with the long run average continuous control problem of piecewise deterministic Markov processes (PDMPs) taking values in a general Borel space and with compact action space depending on the state variable. The control variable acts on the jump rate and transition measure of the PDMP, and the running and boundary costs are assumed to be positive but not necessarily bounded. Our first main result is to obtain an optimality equation for the long run average cost in terms of a discrete-time optimality equation related to the embedded Markov chain given by the postjump location of the PDMP. Our second main result guarantees the existence of a feedback measurable selector for the discrete-time optimality equation by establishing a connection between this equation and an integro-differential equation. Our final main result is to obtain some sufficient conditions for the existence of a solution for a discrete-time optimality inequality and an ordinary optimal feedback control for the long run average cost using the so-called vanishing discount approach. Two examples are presented illustrating the possible applications of the results developed in the paper.

Weighted S-Asymptotically omega-Periodic Solutions of a Class of Fractional Differential Equations

We study the existence of weighted S-asymptotically omega-periodic mild solutions for a class of abstract fractional differential equations of the form u' = partial derivative (alpha vertical bar 1)Au + f(t, u), 1 < alpha < 2, where A is a linear sectorial operator of negative type.

Polar organic marker compounds in atmospheric aerosols during the LBA-SMOCC 2002 biomass burning experiment in Rondonia, Brazil: sources and source processes, time series, diel variations and size distributions

Measurements of polar organic marker compounds were performed on aerosols that were collected at a pasture site in the Amazon basin (Rondonia, Brazil) using a high-volume dichotomous sampler (HVDS) and a Micro-Orifice Uniform Deposit Impactor (MOUDI) within the framework of the 2002 LBA-SMOCC (Large-Scale Biosphere Atmosphere Experiment in Amazonia - Smoke Aerosols, Clouds, Rainfall, and Climate: Aerosols From Biomass Burning Perturb Global and Regional Climate) campaign. The campaign spanned the late dry season (biomass burning), a transition period, and the onset of the wet season (clean conditions). In the present study a more detailed discussion is presented compared to previous reports on the behavior of selected polar marker compounds, including levoglucosan, malic acid, isoprene secondary organic aerosol (SOA) tracers and tracers for fungal spores. The tracer data are discussed taking into account new insights that recently became available into their stability and/or aerosol formation processes. During all three periods, levoglucosan was the most dominant identified organic species in the PM(2.5) size fraction of the HVDS samples. In the dry period levoglucosan reached concentrations of up to 7.5 mu g m(-3) and exhibited diel variations with a nighttime prevalence. It was closely associated with the PM mass in the size-segregated samples and was mainly present in the fine mode, except during the wet period where it peaked in the coarse mode. Isoprene SOA tracers showed an average concentration of 250 ng m(-3) during the dry period versus 157 ng m(-3) during the transition period and 52 ng m(-3) during the wet period. Malic acid and the 2-methyltetrols exhibited a different size distribution pattern, which is consistent with different aerosol formation processes (i.e., gas-to-particle partitioning in the case of malic acid and heterogeneous formation from gas-phase precursors in the case of the 2-methyltetrols). The 2-methyltetrols were mainly associated with the fine mode during all periods, while malic acid was prevalent in the fine mode only during the dry and transition periods, and dominant in the coarse mode during the wet period. The sum of the fungal spore tracers arabitol, mannitol, and erythritol in the PM(2.5) fraction of the HVDS samples during the dry, transition, and wet periods was, on average, 54 ng m(-3), 34 ng m(-3), and 27 ng m(-3), respectively, and revealed minor day/night variation. The mass size distributions of arabitol and mannitol during all periods showed similar patterns and an association with the coarse mode, consistent with their primary origin. The results show that even under the heavy smoke conditions of the dry period a natural background with contributions from bioaerosols and isoprene SOA can be revealed. The enhancement in isoprene SOA in the dry season is mainly attributed to an increased acidity of the aerosols, increased NO(x) concentrations and a decreased wet deposition.

Emergent and reentrant fractional quantum Hall effect in trilayer systems in a tilted magnetic field

Magnetotransport measurements in triple-layer electron systems with high carrier density reveal fractional quantum Hall effect at total filling factors nu>2. With an in-plane magnetic field we are able to control the suppression of interlayer tunneling which causes a collapse of the integer quantum Hall plateaus at nu=2 and nu=4, and an emergence of fractional quantum Hall states with increasing tilt angles. The nu=4 state is replaced by three fractional quantum Hall states with denominator 3. The state nu=7/3 demonstrates reentrant behavior and the emergent state at nu=12/5 has a nonmonotonic behavior with increasing in-plane field. We attribute the observed fractional quantum Hall plateaus to correlated states in a trilayer system.

High-order fractional microwave-induced resistance oscillations in two-dimensional systems

We report on the observation of microwave-induced resistance oscillations associated with the fractional ratio n/m of the microwave irradiation frequency to the cyclotron frequency for m up to 8 in a two-dimensional electron system with high electron density. The features are quenched at high microwave frequencies independent of the fractional order m. We analyze temperature, power, and frequency dependencies of the magnetoresistance oscillations and discuss them in connection with existing theories.

Shared information in stationary states of stochastic processes

We present four estimators of the shared information (or interdepency) in ground states given that the coefficients appearing in the wave function are all real non-negative numbers and therefore can be interpreted as probabilities of configurations. Such ground states of Hermitian and non-Hermitian Hamiltonians can be given, for example, by superpositions of valence bond states which can describe equilibrium but also stationary states of stochastic models. We consider in detail the last case, the system being a classical not a quantum one. Using analytical and numerical methods we compare the values of the estimators in the directed polymer and the raise and peel models which have massive, conformal invariant and nonconformal invariant massless phases. We show that like in the case of the quantum problem, the estimators verify the area law with logarithmic corrections when phase transitions take place.

Collision probabilities in the rarefaction fan of asymmetric exclusion processes

We consider the one-dimensional asymmetric simple exclusion process (ASEP) in which particles jump to the right at rate p is an element of (1/2, 1.] and to the left at rate 1 - p, interacting by exclusion. In the initial state there is a finite region such that to the left of this region all sites are occupied and to the right of it all sites are empty. Under this initial state, the hydrodynamical limit of the process converges to the rarefaction fan of the associated Burgers equation. In particular suppose that the initial state has first-class particles to the left of the origin, second-class particles at sites 0 and I, and holes to the right of site I. We show that the probability that the two second-class particles eventually collide is (1 + p)/(3p), where a collision occurs when one of the particles attempts to jump over the other. This also corresponds to the probability that two ASEP processes. started from appropriate initial states and coupled using the so-called ""basic coupling,"" eventually reach the same state. We give various other results about the behaviour of second-class particles in the ASEP. In the totally asymmetric case (p = 1) we explain a further representation in terms of a multi-type particle system, and also use the collision result to derive the probability of coexistence of both clusters in a two-type version of the corner growth model.

Random perturbations of stochastic processes with unbounded variable length memory

We consider binary infinite order stochastic chains perturbed by a random noise. This means that at each time step, the value assumed by the chain can be randomly and independently flipped with a small fixed probability. We show that the transition probabilities of the perturbed chain are uniformly close to the corresponding transition probabilities of the original chain. As a consequence, in the case of stochastic chains with unbounded but otherwise finite variable length memory, we show that it is possible to recover the context tree of the original chain, using a suitable version of the algorithm Context, provided that the noise is small enough.