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Diffusion Models (diffusion + models)
Selected AbstractsSpecification Analysis of Diffusion Models for the Italian Short RateECONOMIC NOTES, Issue 1 2005Monica Gentile In recent years, diffusion models for interest rates became very popular. In this paper, we perform a selection of a suitable diffusion model for the Italian short rate. Our data set is given by the yields on 3-month BOT (Buoni Ordinari del Tesoro), from 1981 to 2001, for a total of 470 observations. We investigate among stochastic volatility models, paying more attention to affine models. Estimating diffusion models via maximum likelihood, which would lead to efficiency, is usually unfeasible because the transition density is not available. Recently, Gallant and Tauchen (1996) proposed a method of moments which gains full efficiency, hence its name of Efficient Method of Moments (EMM); it selects the moments as the scores of an auxiliary model, to be computed via simulation; thus, EMM is suitable to diffusions whose transition density is unknown, but which are convenient to simulate. The auxiliary model is selected among a family of densities which spans the density space. As a by-product, EMM provides diagnostics that are easy to compute and interpret. We find evidence that one-factor models and multi-factor affine models are rejected, while a logarithmic specification of the volatility provides the best fit to the data. [source] Diffusion models for animals in complex landscapes: incorporating heterogeneity among substrates, individuals and edge behavioursJOURNAL OF ANIMAL ECOLOGY, Issue 5 2008John D. Reeve Summary 1Animals move commonly through a variety of landscape elements and edges in search of food, mates and other resources. We developed a diffusion model for the movement of an insect herbivore, the planthopper Prokelisia crocea, that inhabits a landscape composed of patches of its host plant, prairie cordgrass Spartina pectinata, embedded in a matrix of mudflat or smooth brome Bromus inermis. 2We used mark,release,resight experiments to quantify planthopper movements within cordgrass,brome and cordgrass,mudflat arenas. A diffusion model was then fitted that included varying diffusion rates for cordgrass and matrix, edge behaviour in the form of a biased random walk and heterogeneity among planthoppers (sessile vs. mobile). The model parameters were estimated by maximum likelihood using the numerical solution of the diffusion model as a probability density. Akaike's information criterion (AIC) values were used to compare models with different subsets of features. 3There was clear support for models incorporating edge behaviour and both sessile and mobile insects. The most striking difference between the cordgrass,brome and cordgrass,mudflat experiments involved edge behaviour. Planthoppers crossed the cordgrass,brome edge readily in either direction, but traversed the cordgrass,mudflat edge primarily in one direction (mudflat to cordgrass). Diffusion rates were also significantly higher on mudflat than for cordgrass and brome. 4The differences in behaviour for cordgrass,brome vs. cordgrass,mudflat edges have implications for the connectivity of cordgrass patches as well as their persistence. Higher dispersal rates are expected between cordgrass patches separated by brome relative to mudflat, but patches surrounded by mudflat appear more likely to persist through time. 5The experimental design and diffusion models used here could potentially be extended to any organism where mass mark,recapture experiments are feasible, as well as complex natural landscapes. [source] Influence of crop edges on movement of generalist predators: a diffusion approachAGRICULTURAL AND FOREST ENTOMOLOGY, Issue 1 2002Riccardo Bommarco Abstract 1,Diffusion models were applied to recapture data for the generalist predator Pterostichus cupreus (Coleoptera: Carabidae) moving between two adjacent crop habitats (perennial ley and annual barley) first excluding, and then including, terms in the model quantifying the influences of edges on beetle movements. 2,Adult beetles were released at the centre of experimental 3 × 3 m plots that overlapped the edge separating perennial ley (mixed perennial crop of grass and clover) and annual barley crops, both early and later in the growing season. 3,Mathematical description of the data improved when the attractive or repulsive effects of habitat edges on dispersal were considered in the model. 4,Early in the season, when a sharp habitat edge was present, P. cupreus beetles appeared ,attracted' to ley. 5,Diffusion rates were consistently higher in barley than in ley early in the season, and vice versa late in the season. These patterns were probably linked to variation in prey availability. 6,Despite the risk of experiencing food limitation in the annual crop, our analyses suggest that these beetles regularly move from ley into the early barley habitat and then continue to disperse within the barley, providing opportunities for enhanced biological control of pest species. [source] Specification Analysis of Diffusion Models for the Italian Short RateECONOMIC NOTES, Issue 1 2005Monica Gentile In recent years, diffusion models for interest rates became very popular. In this paper, we perform a selection of a suitable diffusion model for the Italian short rate. Our data set is given by the yields on 3-month BOT (Buoni Ordinari del Tesoro), from 1981 to 2001, for a total of 470 observations. We investigate among stochastic volatility models, paying more attention to affine models. Estimating diffusion models via maximum likelihood, which would lead to efficiency, is usually unfeasible because the transition density is not available. Recently, Gallant and Tauchen (1996) proposed a method of moments which gains full efficiency, hence its name of Efficient Method of Moments (EMM); it selects the moments as the scores of an auxiliary model, to be computed via simulation; thus, EMM is suitable to diffusions whose transition density is unknown, but which are convenient to simulate. The auxiliary model is selected among a family of densities which spans the density space. As a by-product, EMM provides diagnostics that are easy to compute and interpret. We find evidence that one-factor models and multi-factor affine models are rejected, while a logarithmic specification of the volatility provides the best fit to the data. [source] A multiple-theory analysis of a diffusion of information technology caseINFORMATION SYSTEMS JOURNAL, Issue 3 2001Richard Baskerville Abstract. This paper describes a multiple-theory analysis of a diffusion of information technology case. Three innovation diffusion models, the interactive model, the linked-chain model and the emergent model, are used to develop an analysis that describes the essential knowledge that each model produces. Rather than develop conflicting stories, each model leads to distinctly different, but complementary, knowledge about the case setting. More generally, the analysis enables us to circumscribe the distinct conceptual domain of each model. These domains define the scope of research questions that can be addressed by each of the innovation diffusion models. In addition to the theoretical implications, the paper also describes the practical indications and actions of the case subjects. [source] Linking movement behaviour, dispersal and population processes: is individual variation a key?JOURNAL OF ANIMAL ECOLOGY, Issue 5 2009Colin Hawkes Summary 1Movement behaviour has become increasingly important in dispersal ecology and dispersal is central to the development of spatially explicit population ecology. The ways in which the elements have been brought together are reviewed with particular emphasis on dispersal distance distributions and the value of mechanistic models. 2There is a continuous range of movement behaviours and in some species, dispersal is a clearly delineated event but not in others. The biological complexities restrict conclusions to high-level generalizations but there may be principles that are common to dispersal and other movements. 3Random walk and diffusion models when appropriately elaborated can provide an understanding of dispersal distance relationships on spatial and temporal scales relevant to dispersal. Leptokurtosis in the relationships may be the result of a combination of factors including population heterogeneity, correlation, landscape features, time integration and density dependence. The inclusion in diffusion models of individual variation appears to be a useful elaboration. The limitations of the negative exponential and other phenomenological models are discussed. 4The dynamics of metapopulation models are sensitive to what appears to be small differences in the assumptions about dispersal. In order to represent dispersal realistically in population models, it is suggested that phenomenological models should be replaced by those based on movement behaviour incorporating individual variation. 5The conclusions are presented as a set of candidate principles for evaluation. The main features of the principles are that uncorrelated or correlated random walk, not linear movement, is expected where the directions of habitat patches are unpredictable and more complex behaviour when organisms have the ability to orientate or navigate. Individuals within populations vary in their movement behaviour and dispersal; part of this variation is a product of random elements in movement behaviour and some of it is heritable. Local and metapopulation dynamics are influenced by population heterogeneity in dispersal characteristics and heritable changes in dispersal propensity occur on time-scales short enough to impact population dynamics. [source] Continuous-time models, realized volatilities, and testable distributional implications for daily stock returnsJOURNAL OF APPLIED ECONOMETRICS, Issue 2 2010Torben G. Andersen We provide an empirical framework for assessing the distributional properties of daily speculative returns within the context of the continuous-time jump diffusion models traditionally used in asset pricing finance. Our approach builds directly on recently developed realized variation measures and non-parametric jump detection statistics constructed from high-frequency intra-day data. A sequence of simple-to-implement moment-based tests involving various transformations of the daily returns speak directly to the importance of different distributional features, and may serve as useful diagnostic tools in the specification of empirically more realistic continuous-time asset pricing models. On applying the tests to the 30 individual stocks in the Dow Jones Industrial Average index, we find that it is important to allow for both time-varying diffusive volatility, jumps, and leverage effects to satisfactorily describe the daily stock price dynamics. Copyright © 2009 John Wiley & Sons, Ltd. [source] ADSORPTION CHARACTERISTICS OF CROCIN IN THE EXTRACT OF GARDENIA FRUITS (GARDENIA JASMINOIDES ELLIS) ON MACROPOROUS RESINSJOURNAL OF FOOD PROCESS ENGINEERING, Issue 1 2009BIN YANG ABSTRACT To study resin adsorptions and investigate the differences between processes in crude extracts and microfiltrates, the adsorption characteristics of crocin in the extract of Gardenia jasminoides Ellis on 10 macroporous styrene-divinylbenzene (SDVB) resins were investigated. Ground gardenia fruit was extracted with water and the crude extract was partially purified by microfiltration. The crude extract and microfiltrate were mixed with the 10 resins until the adsorption of crocin reached equilibrium on resins. The adsorption followed the pseudo-second-order kinetics closely, but the data also fitted the first-order and intraparticle diffusion models. Furthermore, the Freundlich isotherm was found suitable for describing the equilibrate adsorption data. XAD-1180, HP20, HPD-100A and AB-8 stood out as the best performing resins in terms of their adsorptive capacities and selectivities for crocin. The thermodynamics of the adsorption process was shown to be spontaneous and exothermal in nature, and controlled by physical rather than chemical mechanisms. Adsorption with SDVB resins in conjunction with microfiltration was found to be an efficient process for the purification of crocin in gardenia extract. PRACTICAL APPLICATIONS Macroporous resins have been industrially applied in the recovery and purification of some products from plant extracts. However, there is a lack of understanding of the adsorption process and many of the applications are based on empirical data rather than on predicable models. Therefore, the development of reliable mathematical models that can accurately describe and predicate experimental data of adsorption would be extremely helpful in understanding the adsorption process as well as optimizing the design of adsorption systems. [source] A fractal forecasting model for financial time seriesJOURNAL OF FORECASTING, Issue 8 2004Gordon R. Richards Abstract Financial market time series exhibit high degrees of non-linear variability, and frequently have fractal properties. When the fractal dimension of a time series is non-integer, this is associated with two features: (1) inhomogeneity,extreme fluctuations at irregular intervals, and (2) scaling symmetries,proportionality relationships between fluctuations over different separation distances. In multivariate systems such as financial markets, fractality is stochastic rather than deterministic, and generally originates as a result of multiplicative interactions. Volatility diffusion models with multiple stochastic factors can generate fractal structures. In some cases, such as exchange rates, the underlying structural equation also gives rise to fractality. Fractal principles can be used to develop forecasting algorithms. The forecasting method that yields the best results here is the state transition-fitted residual scale ratio (ST-FRSR) model. A state transition model is used to predict the conditional probability of extreme events. Ratios of rates of change at proximate separation distances are used to parameterize the scaling symmetries. Forecasting experiments are run using intraday exchange rate futures contracts measured at 15-minute intervals. The overall forecast error is reduced on average by up to 7% and in one instance by nearly a quarter. However, the forecast error during the outlying events is reduced by 39% to 57%. The ST-FRSR reduces the predictive error primarily by capturing extreme fluctuations more accurately. Copyright © 2004 John Wiley & Sons, Ltd. [source] Ground truth hardware phantoms for validation of diffusion-weighted MRI applicationsJOURNAL OF MAGNETIC RESONANCE IMAGING, Issue 2 2010Pim Pullens MSc Abstract Purpose: To quantitatively validate diffusion-weighted MRI (DW-MRI) applications, a hardware phantom containing crossing fibers at a sub-voxel level is presented. It is suitable for validation of a large spectrum of DW-MRI applications from acquisition to fiber tracking, which is an important recurrent issue in the field. Materials and Methods: Phantom properties were optimized to resemble properties of human white matter in terms of anisotropy, fractional anisotropy, and T2. Sub-voxel crossings were constructed at angles of 30, 50, and 65 degrees, by wrapping polyester fibers, with a diameter close to axon diameter, into heat shrink tubes. We show our phantoms are suitable for the acquisition of DW-MRI data using a clinical protocol. Results: The phantoms can be used to succesfully estimate both the diffusion tensor and non-Gaussian diffusion models, and perform streamline fiber tracking. DOT (Diffusion Orientation Transform) and q-ball reconstruction of the diffusion profiles acquired at b = 3000 s/mm2 and 132 diffusion directions reveal multimodal diffusion profiles in voxels containing crossing yarn strands. Conclusion: The highly purpose adaptable phantoms provide a DW-MRI validation platform: applications include optimisation of acquisition schemes, validation of non-Gaussian diffusion models, comparison and validation of fiber tracking algorithms, and quality control in multi-center DWI studies. J. Magn. Reson. Imaging 2010;32:482,488. © 2010 Wiley-Liss, Inc. [source] Mathematical modeling of water uptake through diffusion in 3D inhomogeneous swelling substratesAICHE JOURNAL, Issue 7 2009L. R. van den Doel Abstract Diffusion-driven water uptake in a substrate (imbibition) is a subject of great interest in the field of food technology. This is a particular challenge for rice grains that are preprocessed to accelerate the water uptake, i.e., to reduce the cooking time. Rice preprocessing disrupts the mesostructural order of starch and induces a microporous structure in the grains. The meso- and microstructural length scales have not been considered in joint approach until now. The (re)hydration of rice grains can be modeled by free (concentration-driven) diffusion or by water demand-driven diffusion. The latter is driven by the ceiling moisture content related to the extent of gelatinization of the rice substrate network. This network can be regarded as a fractal structure. As the spatial resolution of our models is limited, we choose to model the apparent water transport by a set of coupled partial differential equations (PDEs). Current models of water uptake are often limited to a single dimension, and the swelling of the substrate is not taken into account. In this article, we derive a set of PDEs to model water uptake in a three-dimensional (3D) inhomogeneous substrate for different types of water diffusion as well as the swelling of the substrate during water uptake. We will present simulation results for different 3D (macroscopic) structures and diffusion models and compare these results, qualitatively, with the experimental results acquired from magnetic resonance imaging. © 2009 American Institute of Chemical Engineers AIChE J, 2009 [source] Carbon-13 chemical shift anisotropy in DNA bases from field dependence of solution NMR relaxation rates,MAGNETIC RESONANCE IN CHEMISTRY, Issue 3 2006Jinfa Ying Abstract Knowledge of 13C chemical shift anisotropy (CSA) in nucleotide bases is important for the interpretation of solution-state NMR relaxation data in terms of local dynamic properties of DNA and RNA. Accurate knowledge of the CSA becomes particularly important at high magnetic fields, prerequisite for adequate spectral resolution in larger oligonucleotides. Measurement of 13C relaxation rates of protonated carbons in the bases of the so-called Dickerson dodecamer, d(CGCGAATTCGCG)2, at 500 and 800 MHz 1H frequency, together with the previously characterized structure and diffusion tensor yields CSA values for C5 in C, C6 in C and T, C8 in A and G, and C2 in A that are closest to values previously reported on the basis of solid-state FIREMAT NMR measurements, and mostly larger than values obtained by in vacuo DFT calculations. Owing to the noncollinearity of dipolar and CSA interactions, interpretation of the NMR relaxation rates is particularly sensitive to anisotropy of rotational diffusion, and use of isotropic diffusion models can result in considerable errors. Copyright © 2006 John Wiley & Sons, Ltd. [source] A simple method for rectified noise floor suppression: Phase-corrected real data reconstruction with application to diffusion-weighted imagingMAGNETIC RESONANCE IN MEDICINE, Issue 2 2010Douglas E. Prah Abstract Diffusion-weighted MRI is an intrinsically low signal-to-noise ratio application due to the application of diffusion-weighting gradients and the consequent longer echo times. The signal-to-noise ratio worsens with increasing image resolution and diffusion imaging methods that use multiple and higher b-values. At low signal-to-noise ratios, standard magnitude reconstructed diffusion-weighted images are confounded by the existence of a rectified noise floor, producing poor estimates of diffusion metrics. Herein, we present a simple method of rectified noise floor suppression that involves phase correction of the real data. This approach was evaluated for diffusion-weighted imaging data, obtained from ethanol and water phantoms and the brain of a healthy volunteer. The parameter fits from monoexponential, biexponential, and stretched-exponential diffusion models were computed using phase-corrected real data and magnitude data. The results demonstrate that this newly developed simple approach of using phase-corrected real images acts to reduce or even suppress the confounding effects of a rectified noise floor, thereby producing more accurate estimates of diffusion parameters. Magn Reson Med, 2010. © 2010 Wiley-Liss, Inc. [source] CONSTANT PROPORTION PORTFOLIO INSURANCE IN THE PRESENCE OF JUMPS IN ASSET PRICESMATHEMATICAL FINANCE, Issue 3 2009Rama Cont Constant proportion portfolio insurance (CPPI) allows an investor to limit downside risk while retaining some upside potential by maintaining an exposure to risky assets equal to a constant multiple of the cushion, the difference between the current portfolio value and the guaranteed amount. Whereas in diffusion models with continuous trading, this strategy has no downside risk, in real markets this risk is nonnegligible and grows with the multiplier value. We study the behavior of CPPI strategies in models where the price of the underlying portfolio may experience downward jumps. Our framework leads to analytically tractable expressions for the probability of hitting the floor, the expected loss, and the distribution of losses. This allows to measure the gap risk but also leads to a criterion for adjusting the multiplier based on the investor's risk aversion. Finally, we study the problem of hedging the downside risk of a CPPI strategy using options. The results are applied to a jump-diffusion model with parameters estimated from returns series of various assets and indices. [source] SEPARABLE TERM STRUCTURES AND THE MAXIMAL DEGREE PROBLEMMATHEMATICAL FINANCE, Issue 4 2002Damir Filipovi This paper discusses separablc term structure diffusion models in an arbitrage-free environment. Using general consistency results we exploit the interplay between the diffusion coefficients and the functions determining the forward curve. We introduce the particular class of polynomial term structure models. We formulate the appropriate conditions under which the diffusion for a quadratic term structure model is necessarily an Ornstein-Uhlenbeck type process. Finally, we explore the maximal degree problem and show that basically any consistent polynomial term structure model is of degree two or less. [source] Patterning by genetic networksMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 2 2006S. Genieys Abstract We consider here the morphogenesis (pattern formation) problem for some genetic network models. First, we show that any given spatio-temporal pattern can be generated by a genetic network involving a sufficiently large number of genes. Moreover, patterning process can be performed by an effective algorithm. We also show that Turing's or Meinhardt's type reaction,diffusion models can be approximated by genetic networks. These results exploit the fundamental fact that the genes form functional units and are organized in blocks. Due to this modular organization, the genes always are capable to construct any new patterns and even any time sequences of new patterns from old patterns. Computer simulations illustrate some analytical results. Copyright © 2005 John Wiley & Sons, Ltd. [source] Single dopant diffusion in semiconductor technologyMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 2 2004A. Glitzky Abstract The paper deals with the analysis of pair diffusion models in semiconductor technology. The underlying model contains reaction-drift-diffusion equations for the mobile point defects and dopant-defect pairs as well as reaction equations for immobile dopants which are coupled with a non-linear Poisson equation for the chemical potential of the electrons. For homogeneous structures we present an existence and uniqueness result for strong solutions. Starting with energy estimates we derive further a priori estimates such that fixed point arguments due to Leray,Schauder guarantee the solvability of the model equations. Copyright © 2004 John Wiley & Sons, Ltd. [source] Statistical models of shape for the analysis of protein spots in two-dimensional electrophoresis gel imagesPROTEINS: STRUCTURE, FUNCTION AND BIOINFORMATICS, Issue 6 2003Mike Rogers Abstract In image analysis of two-dimensional electrophoresis gels, individual spots need to be identified and quantified. Two classes of algorithms are commonly applied to this task. Parametric methods rely on a model, making strong assumptions about spot appearance, but are often insufficiently flexible to adequately represent all spots that may be present in a gel. Nonparametric methods make no assumptions about spot appearance and consequently impose few constraints on spot detection, allowing more flexibility but reducing robustness when image data is complex. We describe a parametric representation of spot shape that is both general enough to represent unusual spots, and specific enough to introduce constraints on the interpretation of complex images. Our method uses a model of shape based on the statistics of an annotated training set. The model allows new spot shapes, belonging to the same statistical distribution as the training set, to be generated. To represent spot appearance we use the statistically derived shape convolved with a Gaussian kernel, simulating the diffusion process in spot formation. We show that the statistical model of spot appearance and shape is able to fit to image data more closely than the commonly used spot parameterizations based solely on Gaussian and diffusion models. We show that improvements in model fitting are gained without degrading the specificity of the representation. [source] Do Stock Prices and Volatility Jump?THE JOURNAL OF FINANCE, Issue 3 2004Option Prices, Reconciling Evidence from Spot This paper examines the empirical performance of jump diffusion models of stock price dynamics from joint options and stock markets data. The paper introduces a model with discontinuous correlated jumps in stock prices and stock price volatility, and with state-dependent arrival intensity. We discuss how to perform likelihood-based inference based upon joint options/returns data and present estimates of risk premiums for jump and volatility risks. The paper finds that while complex jump specifications add little explanatory power in fitting options data, these models fare better in fitting options and returns data simultaneously. [source] Modelling and forecasting vehicle stocks using the trends of stochastic Gompertz diffusion models: The case of SpainAPPLIED STOCHASTIC MODELS IN BUSINESS AND INDUSTRY, Issue 3 2009R. Gutiérrez Abstract In the present study, we treat the stochastic homogeneous Gompertz diffusion process (SHGDP) by the approach of the Kolmogorov equation. Firstly, using a transformation in diffusion processes, we show that the probability transition density function of this process has a lognormal time-dependent distribution, from which the trend and conditional trend functions and the stationary distribution are obtained. Second, the maximum likelihood approach is adapted to the problem of parameters estimation in the drift and the diffusion coefficient using discrete sampling of the process, then the approximated asymptotic confidence intervals of the parameter are obtained. Later, we obtain the corresponding inference of the stochastic homogeneous lognormal diffusion process as limit from the inference of SHGDP when the deceleration factor tends to zero. A statistical methodology, based on the above results, is proposed for trend analysis. Such a methodology is applied to modelling and forecasting vehicle stocks. Finally, an application is given to illustrate the methodology presented using real data, concretely the total vehicle stocks in Spain. Copyright © 2008 John Wiley & Sons, Ltd. [source] | |||||||||||||||||||