Random diffusion and leverage effect in financial markets

We prove that Brownian market models with random diffusion coefficients provide an exact measure of the leverage effect [J-P. Bouchaud et al., Phys. Rev. Lett. 87, 228701 (2001)]. This empirical fact asserts that past returns are anticorrelated with future diffusion coefficient. Several models with random diffusion have been suggested but without a quantitative study of the leverage effect. Our analysis lets us to fully estimate all parameters involved and allows a deeper study of correlated random diffusion models that may have practical implications for many aspects of financial markets.

Self and cross-velocity correlation functions and diffusion coefficients in liquids: a molecular dynamics study of binary mixtures of soft spheres

Molecular dynamics simulation is applied to the study of the diffusion properties in binary liquid mixtures made up of soft-sphere particles with different sizes and masses. Self- and distinct velocity correlation functions and related diffusion coefficients have been calculated. Special attention has been paid to the dynamic cross correlations which have been computed through recently introduced relative mean molecular velocity correlation functions which are independent on the reference frame. The differences between the distinct velocity correlations and diffusion coefficients in different reference frames (mass-fixed, number-fixed, and solvent-fixed) are discussed.

Generalized Langevin equations: Anomalous diffusion and probability distributions

We study the motion of a particle governed by a generalized Langevin equation. We show that, when no fluctuation-dissipation relation holds, the long-time behavior of the particle may be from stationary to superdiffusive, along with subdiffusive and diffusive. When the random force is Gaussian, we derive the exact equations for the joint and marginal probability density functions for the position and velocity of the particle and find their solutions.

Organic Matter Fractions and Quality of the Surface Layer of a Constructed and Vegetated Soil After Coal Mining. I - Humic Substances and Chemical Characterization

After open coal mining, soils are “constructed”, which usually contain low levels and quality of organic matter (OM). Therefore, the use of plant species for revegetation and reclamation of degraded areas is essential. This study evaluated the distribution of carbon (C) in the chemical fractions as well as the chemical characteristics and humification degree of OM in a soil constructed after coal mining under cultivation of perennial grasses. The experiment was established in 2003 with the following treatments: Hemarthria altissima (T1), Paspalum notatum (T2), Cynodon dactilon (T3), Urochloa brizantha (T4), bare constructed soil (T5), and natural soil (T6). In 2009, soil samples were collected from the 0.00-0.03 m layer and the total organic carbon stock (TOC) and C stock in the chemical fractions: acid extract (CHCl), fulvic acid (CFA), humic acid (CHA), and humin (CHU) were determined. The humic acid (HA) fraction was characterized by infrared spectroscopy and the laser-induced fluorescence index (ILIF) of OM was also calculated. After six years, differences were only observed in the CHA stocks, which were highest in T1 (0.89 Mg ha-1) and T4 (1.06 Mg ha-1). The infrared spectra of HA in T1, T2 and T4 were similar to T6, with greater contribution of aliphatic organic compounds than in the other treatments. In this way, ILIF decreased in the sequence T5>T3>T4>T1>T2>T6, indicating higher OM humification in T3 and T5 and more labile OM in the other treatments. Consequently, the potential of OM quality recovery in the constructed soil was greatest in treatments T1 and T4.

Organic Matter Fractions and Quality of the Surface Layer of a Constructed and Vegetated Soil After Coal Mining. II - Physical Compartments and Carbon Management Index

Soils constructed after mining often have low carbon (C) stocks and low quality of organic matter (OM). Cover crops are decisive for the recovery process of these stocks, improving the quality of constructed soils. Therefore, the goal of this study was to evaluate the effect of cover crops on total organic C (TOC) stocks, C distribution in physical fractions of OM and the C management index (CMI) of a soil constructed after coal mining. The experiment was initiated in 2003 with six treatments: Hemarthria altissima (T1), Paspalum notatum (T2), Cynodon dactylon (T3), Urochloa brizantha (T4), bare constructed soil (T5), and natural soil (T6). Soil samples were collected in 2009 from the 0.00-0.03 m layer, and the TOC and C stocks in the physical particle size fractions (carbon in the coarse fraction - CCF, and mineral-associated carbon - MAC) and density fractions (free light fraction - FLF; occluded light fraction - OLF, and heavy fraction - HF) of OM were determined. The CMI components: carbon pool index (CPI), lability (L) and lability index (LI) were estimated by both fractionation methods. No differences were observed between TOC, CCF and MAC stocks. The lowest C stocks in FLF and OLF fractions were presented by T2, 0.86 and 0.61 Mg ha-1, respectively. The values of TOC stock, C stock in physical fractions and CMI were intermediate, greater than T5 and lower than T6 in all treatments, indicating the partial recovery of soil quality. As a result of the better adaptation of the species Hemarthria and Brizantha, resulting in greater accumulation of labile organic material, the CPI, L, LI and CMI values were higher in these treatments, suggesting a greater potential of these species for recovery of constructed soils.

Estimation of jump-diffusion processes via empirical characteristic functions

Preface The starting point for this work and eventually the subject of the whole thesis was the question: how to estimate parameters of the affine stochastic volatility jump-diffusion models. These models are very important for contingent claim pricing. Their major advantage, availability T of analytical solutions for characteristic functions, made them the models of choice for many theoretical constructions and practical applications. At the same time, estimation of parameters of stochastic volatility jump-diffusion models is not a straightforward task. The problem is coming from the variance process, which is non-observable. There are several estimation methodologies that deal with estimation problems of latent variables. One appeared to be particularly interesting. It proposes the estimator that in contrast to the other methods requires neither discretization nor simulation of the process: the Continuous Empirical Characteristic function estimator (EGF) based on the unconditional characteristic function. However, the procedure was derived only for the stochastic volatility models without jumps. Thus, it has become the subject of my research. This thesis consists of three parts. Each one is written as independent and self contained article. At the same time, questions that are answered by the second and third parts of this Work arise naturally from the issues investigated and results obtained in the first one. The first chapter is the theoretical foundation of the thesis. It proposes an estimation procedure for the stochastic volatility models with jumps both in the asset price and variance processes. The estimation procedure is based on the joint unconditional characteristic function for the stochastic process. The major analytical result of this part as well as of the whole thesis is the closed form expression for the joint unconditional characteristic function for the stochastic volatility jump-diffusion models. The empirical part of the chapter suggests that besides a stochastic volatility, jumps both in the mean and the volatility equation are relevant for modelling returns of the S&P500 index, which has been chosen as a general representative of the stock asset class. Hence, the next question is: what jump process to use to model returns of the S&P500. The decision about the jump process in the framework of the affine jump- diffusion models boils down to defining the intensity of the compound Poisson process, a constant or some function of state variables, and to choosing the distribution of the jump size. While the jump in the variance process is usually assumed to be exponential, there are at least three distributions of the jump size which are currently used for the asset log-prices: normal, exponential and double exponential. The second part of this thesis shows that normal jumps in the asset log-returns should be used if we are to model S&P500 index by a stochastic volatility jump-diffusion model. This is a surprising result. Exponential distribution has fatter tails and for this reason either exponential or double exponential jump size was expected to provide the best it of the stochastic volatility jump-diffusion models to the data. The idea of testing the efficiency of the Continuous ECF estimator on the simulated data has already appeared when the first estimation results of the first chapter were obtained. In the absence of a benchmark or any ground for comparison it is unreasonable to be sure that our parameter estimates and the true parameters of the models coincide. The conclusion of the second chapter provides one more reason to do that kind of test. Thus, the third part of this thesis concentrates on the estimation of parameters of stochastic volatility jump- diffusion models on the basis of the asset price time-series simulated from various "true" parameter sets. The goal is to show that the Continuous ECF estimator based on the joint unconditional characteristic function is capable of finding the true parameters. And, the third chapter proves that our estimator indeed has the ability to do so. Once it is clear that the Continuous ECF estimator based on the unconditional characteristic function is working, the next question does not wait to appear. The question is whether the computation effort can be reduced without affecting the efficiency of the estimator, or whether the efficiency of the estimator can be improved without dramatically increasing the computational burden. The efficiency of the Continuous ECF estimator depends on the number of dimensions of the joint unconditional characteristic function which is used for its construction. Theoretically, the more dimensions there are, the more efficient is the estimation procedure. In practice, however, this relationship is not so straightforward due to the increasing computational difficulties. The second chapter, for example, in addition to the choice of the jump process, discusses the possibility of using the marginal, i.e. one-dimensional, unconditional characteristic function in the estimation instead of the joint, bi-dimensional, unconditional characteristic function. As result, the preference for one or the other depends on the model to be estimated. Thus, the computational effort can be reduced in some cases without affecting the efficiency of the estimator. The improvement of the estimator s efficiency by increasing its dimensionality faces more difficulties. The third chapter of this thesis, in addition to what was discussed above, compares the performance of the estimators with bi- and three-dimensional unconditional characteristic functions on the simulated data. It shows that the theoretical efficiency of the Continuous ECF estimator based on the three-dimensional unconditional characteristic function is not attainable in practice, at least for the moment, due to the limitations on the computer power and optimization toolboxes available to the general public. Thus, the Continuous ECF estimator based on the joint, bi-dimensional, unconditional characteristic function has all the reasons to exist and to be used for the estimation of parameters of the stochastic volatility jump-diffusion models.

SOIL PHOSPHORUS THRESHOLDS IN EVALUATING RISK OF ENVIRONMENTAL TRANSFER TO SURFACE WATERS IN SANTA CATARINA, BRAZIL

The State of Santa Catarina, Brazil, has agricultural and livestock activities, such as pig farming, that are responsible for adding large amounts of phosphorus (P) to soils. However, a method is required to evaluate the environmental risk of these high soil P levels. One possible method for evaluating the environmental risk of P fertilization, whether organic or mineral, is to establish threshold levels of soil available P, measured by Mehlich-1 extractions, below which there is not a high risk of P transfer from the soil to surface waters. However, the Mehlich-1 extractant is sensitive to soil clay content, and that factor should be considered when establishing such P-thresholds. The objective of this study was to determine P-thresholds using the Mehlich-1 extractant for soils with different clay contents in the State of Santa Catarina, Brazil. Soil from the B-horizon of an Oxisol with 800 g kg-1 clay was mixed with different amounts of sand to prepare artificial soils with 200, 400, 600, and 800 g kg-1 clay. The artificial soils were incubated for 30 days with moisture content at 80 % of field capacity to stabilize their physicochemical properties, followed by additional incubation for 30 days after liming to raise the pH(H2O) to 6.0. Soil P sorption curves were produced, and the maximum sorption (Pmax) was determined using the Langmuir model for each soil texture evaluated. Based on the Pmax values, seven rates of P were added to four replicates of each soil, and incubated for 20 days more. Following incubation, available P contents (P-Mehlich-1) and P dissolved in the soil solution (P-water) were determined. A change-point value (the P-Mehlich-1 value above which P-water starts increasing sharply) was calculated through the use of segmented equations. The maximum level of P that a soil might safely adsorb (P-threshold) was defined as 80 % of the change-point value to maintain a margin for environmental safety. The P-threshold value, in mg dm-3, was dependent on the soil clay content according to the model P-threshold = 40 + Clay, where the soil clay content is expressed as a percentage. The model was tested in 82 diverse soil samples from the State of Santa Catarina and was able to distinguish samples with high and low environmental risk.

Surface Complexation Modeling in Variable Charge Soils: Charge Characterization by Potentiometric Titration

ABSTRACT Intrinsic equilibrium constants of 17 representative Brazilian Oxisols were estimated from potentiometric titration measuring the adsorption of H+ and OH− on amphoteric surfaces in suspensions of varying ionic strength. Equilibrium constants were fitted to two surface complexation models: diffuse layer and constant capacitance. The former was fitted by calculating total site concentration from curve fitting estimates and pH-extrapolation of the intrinsic equilibrium constants to the PZNPC (hand calculation), considering one and two reactive sites, and by the FITEQL software. The latter was fitted only by FITEQL, with one reactive site. Soil chemical and physical properties were correlated to the intrinsic equilibrium constants. Both surface complexation models satisfactorily fit our experimental data, but for results at low ionic strength, optimization did not converge in FITEQL. Data were incorporated in Visual MINTEQ and they provide a modeling system that can predict protonation-dissociation reactions in the soil surface under changing environmental conditions.

Surface Complexation Modeling in Variable Charge Soils: Prediction of Cadmium Adsorption

ABSTRACT Intrinsic equilibrium constants for 22 representative Brazilian Oxisols were estimated from a cadmium adsorption experiment. Equilibrium constants were fitted to two surface complexation models: diffuse layer and constant capacitance. Intrinsic equilibrium constants were optimized by FITEQL and by hand calculation using Visual MINTEQ in sweep mode, and Excel spreadsheets. Data from both models were incorporated into Visual MINTEQ. Constants estimated by FITEQL and incorporated in Visual MINTEQ software failed to predict observed data accurately. However, FITEQL raw output data rendered good results when predicted values were directly compared with observed values, instead of incorporating the estimated constants into Visual MINTEQ. Intrinsic equilibrium constants optimized by hand calculation and incorporated in Visual MINTEQ reliably predicted Cd adsorption reactions on soil surfaces under changing environmental conditions.

Exact temporal evolution for some non-linear diffusion process

Exact solutions to FokkerPlanck equations with nonlinear drift are considered. Applications of these exact solutions for concrete models are studied. We arrive at the conclusion that for certain drifts we obtain divergent moments (and infinite relaxation time) if the diffusion process can be extended without any obstacle to the whole space. But if we introduce a potential barrier that limits the diffusion process, moments converge with a finite relaxation time.

Understanding and modulating the competitive surface-adsorption of proteins through coarse-grained molecular dynamics simulations

It is now well accepted that cellular responses to materials in a biological medium reflect greatly the adsorbed biomolecular layer, rather than the material itself. Here, we study by molecular dynamics simulations the competitive protein adsorption on a surface (Vroman effect), i.e. the non-monotonic behavior of the amount of protein adsorbed on a surface in contact with plasma as functions of contact time and plasma concentration. We find a complex behavior, with regimes during which small and large proteins are not necessarily competing between them, but are both competing with others in solution ("cooperative" adsorption). We show how the Vroman effect can be understood, controlled and inverted.

Counter-ion effect on surfactant-DNA gel particles as controlled DNA delivery systems

The ability to entrap drugs within vehicles and subsequently release them has led to new treatments for a number of diseases. Based on an associative phase separation and interfacial diffusion approach, we developed a way to prepare DNA gel particles without adding any kind of cross-linker or organic solvent. Among the various agents studied, cationic surfactants offered particularly efficient control for encapsulation and DNA release from these DNA gel particles. The driving force for this strong association is the electrostatic interaction between the two components, as induced by the entropic increase due to the release of the respective counter-ions. However, little is known about the influence of the respective counter-ions on this surfactant-DNA interaction. Here we examined the effect of different counter-ions on the formation and properties of the DNA gel particles by mixing DNA (either single- (ssDNA) or double-stranded (dsDNA)) with the single chain surfactant dodecyltrimethylammonium (DTA). In particular, we used as counter-ions of this surfactant the hydrogen sulfate and trifluoromethane sulfonate anions and the two halides, chloride and bromide. Effects on the morphology of the particles obtained, the encapsulation of DNA and its release, as well as the haemocompatibility of these particles, are presented, using the counter-ion structure and the DNA conformation as controlling parameters. Analysis of the data indicates that the degree of counter-ion dissociation from the surfactant micelles and the polar/hydrophobic character of the counter-ion are important parameters in the final properties of the particles. The stronger interaction with amphiphiles for ssDNA than for dsDNA suggests the important role of hydrophobic interactions in DNA.

Pavement Surface on Macadam Base: Adair County Final Report, Iowa Highway Reserach Board Project HR-209

The quality and availability of aggregate for pc concrete stone varies across Iowa. Southwest Iowa is one area of the state that is short of quality aggregates. The concrete stone generally available in the area is limestone from the Argentine or Winterset ledges with an overburden of up to 150 feet. This concrete stone is classified as Class 1 durability and is susceptible to 'ID"-cracking. In addition, the general engineering soil classification rates the soils of southwest Iowa as having the poorest subgrade bearing characteristics in the state. 1 The combination of poor soils and low quality aggregate has contributed to premature deterioration of many miles of portland cement concrete pavement. Research project HR-209 was initiated in 1979 to explore alternative construction methods that may produce better pavements for southwest Iowa.