Weak Local Linear Discretizations for Stochastic Differential Equations with Jumps

Weak local linear approximations have played a prominent role in the construction of effective inference methods and numerical integrators for stochastic differential equations. In this note two weak local linear approximations for stochastic differential equations with jumps are introduced as a generalization of previous ones. Their respective order of convergence is obtained as well.

Local Linear Approximations of Jump Diffusion Processes

Local linear approximations have been the main component in the construction of a class of effective numerical integrators and inference methods for diffusion processes. In this note, two local linear approximations of jump diffusion processes are introduced as a generalization of the usual ones. Their rate of uniform strong convergence is also studied.

Antibody and cytokine responses in BALB/c mice immunized with the excreted/secreted proteins of Giardia intestinalis: the role of cysteine proteases

The mechanisms involved in the induction of the immune response in humans or experimental hosts infected with Giardia intestinalis are not well understood. The results of previous studies indicate that the parasite induces a mixed Th1/Th2 response and that, in experimentally infected mice, the parasite's excreted/secreted (E/S) proteins contain cysteine proteases that are recognised by the murine immune system. In the present study, the possible effects of the E/S proteases of G. intestinalis on the host's humoral and cellular immune responses were investigated in BALB/c mice immunized with the parasite's E/S proteins. High titres of specific IgG(1), IgG(2a) and IgE antibodies were detected after immunization with native E/S proteins. Spleen cells stimulated with such proteins in vitro showed a significant antigen-specific proliferative response accompanied by the production of high concentrations of interleukin-4 (IL-4), interleukin-5 (IL-5) and interleukin-10 (IL-10) but little secretion of interferon-gamma (IFN-gamma). When, before use, the proteases in the E/S proteins were inhibited, by heat treatment or the addition of E-64, they elicited much lower titres of specific IgG(1) and IgE in mice while, in splenocytes in vitro, they triggered much lower production of IL-4, IL-5 and IL-10 and reduced antigen-specific proliferation. Since E-64 only inhibits cysteine proteases, these results indicate that the excreted/secreted cysteine proteases of G. intestinalis may be involved in the induction and regulation of a specific immune response in the infected host.

Nonlinear local electrovascular coupling. II: From data to neuronal masses

In the companion article a local electrovascular coupling (LEVC) model was proposed to explain the continuous dynamics of electrical and vascular states within a cortical unit. These states produce certain mesoscopic reflections whose discrete time series can be reconstructed from electroencephalography (EEG) and functional magnetic resonance imaging (fMRI). In this article we develop a recursive optimization algorithm based on the local linearization (LL) filter and an innovation method to make statistical inferences about the LEVC model from both EEG and fMRI data, i.e., to estimate the unobserved states and the unknown parameters of the model. For a better understanding, the LL filter is described from a Bayesian point of view, providing the particulars for the case of hybrid data (e.g., EEG and fMRI), which could be sampled at different rates. The dynamics of the exogenous synaptic inputs going into the cortical unit are also estimated by introducing a set of Gaussian radial basis functions. In order to study the dynamics of the electrical and vascular states in the striate cortex of humans as well as their local interrelationships, we applied this algorithm to EEG and fMRI recordings obtained concurrently from two subjects while passively observing a radial checkerboard with a white/black pattern reversal. The EEG and fMRI data from the first subject was used to estimate the electrical/vascular states and parameters of the LEVC model in V1 for a 4.0 Hz reversion frequency. We used the EEG data from the second subject to investigate the changes in the dynamics of the electrical states when the frequency of reversion is varied from 0.5-4.0 Hz. Then we made use of the estimated electrical states to predict the effects on the vasculature that such variations produce.

Minimally invasive distal limb bypasses. Techniques and results

As endovascular procedures increasingly become the procedures of choice for limb salvage, a subset of patients remains that requires open arterial reconstruction due to anatomic or pathologic reasons. Traditional greater saphenous vein harvest performed during open bypass for peripheral occlusive arterial disease is associated with long surgical incisions, increased operative times devoted to wound closure, and wound complications such as infection and dehiscence. Endoscopic conduit harvest, used with excellent results in coronary artery bypass surgery, can also be used in minimally invasive arterial bypass for limb salvage with certain technical modifications. These approaches to complex limb salvage procedures may result in shortened operating room time, shorter length of stay, reduced readmissions for wound complications, and ultimately, decreased costs to the health care system. The treating surgeon must continue to stay up to date with these approaches and be aware of pertinent issues regarding open and minimally invasive arterial interventions, as well as endovascular approaches.

Minimal deviation melanoma

Minimal deviation melanomas (MDM) are poorly characterized, uncommon naevomelanocytic tumours that are thought to represent part of the continuum from benign atypical naevi to frank malignant melanomas. Exactly where on that continuum they stand and who is most affected remains controversial. The few studies classifying MDM pointed to a less aggressive nature. Furthermore, it is thought that MDM affects patients in the fourth and fifth decades of life. In a recent review conducted at our institution, medical records of all patients with melanoma diagnosed at a tertiary care university medical center between January 1997 and May 2000 were reviewed to identify those with MDM. Those with MDM were examined to determine subtype, age and sex distributions, and location of tumour and findings were compared to those in the published literature. Unlike previous studies, the mean age of patients with MDM was 27 years with 20/31 being under 30 years old. Our results support prior findings that MDM is less aggressive than typical malignant melanomas in that only 1/5 undergoing lymphatic mapping had a positive node. Despite its description more than 30 years ago, MDM remains a poorly understood pathologic entity. Further study in such techniques as sentinel lymph node mapping and determination of angiogenesis factors is warranted to give insight as to what features predict an aggressive nature and to identify prognostic factors.

Iodine-131 treatment of thyroid papillary carcinoma in patients undergoing dialysis for chronic renal failure: a dosimetric method

Until recently, the therapeutic protocol widely accepted for ablation of the thyroid remnant and for metastases of thyroid papillary carcinoma was the administration of 131I after surgery. However, at present, some data question the usefulness of such treatment in patients considered low risk. The treatment with radioiodine in patients suffering from end-stage renal disease (ESRD) undergoing hemodialysis requires controlled dosages and individualized administration guidelines. The need to include these patients on the waiting list for a renal transplantation, once they have overcome the disease, and the higher prevalence of thyroid carcinoma in ESRD patients makes this an increasingly significant problem. The cases reported in the literature are few and the therapeutic models followed are very difficult. In this paper we propose a therapeutic model that provides the highest thyroid ablative dosage, minimizing radiation exposure to the rest of the organs. The main difference between our protocol and that already described is the performance of daily hemodialysis during the first 5 days of treatment, as well as the administration of a dose of 131I equivalent to that administered to patients who show normal renal function.

Testing non-linearity and directedness of interactions between neural groups in the macaque inferotemporal cortex

Information processing in the visual cortex depends on complex and context sensitive patterns of interactions between neuronal groups in many different cortical areas. Methods used to date for disentangling this functional connectivity presuppose either linearity or instantaneous interactions, assumptions that are not necessarily valid. In this paper a general framework that encompasses both linear and non-linear modelling of neurophysiological time series data by means of Local Linear Non-linear Autoregressive models (LLNAR) is described. Within this framework a new test for non-linearity of time series and for non-linearity of directedness of neural interactions based on LLNAR is presented. These tests assess the relative goodness of fit of linear versus non-linear models via the bootstrap technique. Additionally, a generalised definition of Granger causality is presented based on LLNAR that is valid for both linear and non-linear systems. Finally, the use of LLNAR for measuring non-linearity and directional influences is illustrated using artificial data, reference data as well as local field potentials (LFPs) from macaque area TE. LFP data is well described by the linear variant of LLNAR. Models of this sort, including lagged values of the preceding 25 to 60 ms, revealed the existence of both uni- and bi-directional influences between recording sites.

Nonlinear EEG analysis based on a neural mass model

The well-known neural mass model described by Lopes da Silva et al. (1976) and Zetterberg et al. (1978) is fitted to actual EEG data. This is achieved by reformulating the original set of integral equations as a continuous-discrete state space model. The local linearization approach is then used to discretize the state equation and to construct a nonlinear Kalman filter. On this basis, a maximum likelihood procedure is used for estimating the model parameters for several EEG recordings. The analysis of the noise-free differential equations of the estimated models suggests that there are two different types of alpha rhythms: those with a point attractor and others with a limit cycle attractor. These attractors are also found by means of a nonlinear time series analysis of the EEG recordings. We conclude that the Hopf bifurcation described by Zetterberg et al. (1978) is present in actual brain dynamics.

Measuring the dissimilarity between EEG recordings through a non-linear dynamical system approach

A new measure of dissimilarity between two EEG segments is proposed. It is derived from the application of the mathematical concept of distance between series of one-step predictions according to the estimated non-linear autoregressive functions. The non-linear autoregressive estimation is performed by non-parametric regression using kernel estimators. The possibility of applying this measure for automatic classification of EEG segments is explored. For this purpose multidimensional scaling and cluster analyses are applied on the basis of the calculated dissimilarity measures. In particular, its application to different EEG segments with delta activity and also with alpha waves reveals high agreement with visual classification by EEG specialists.

Modeling the electroencephalogram by means of spatial spline smoothing and temporal autoregression

A spatial-temporal model for the description of electroencephalographic (EEG) data is introduced that combines smooth reconstruction in the spatial domain and autoregressive representation in the time domain. Its spatial aspect is formulated in a general framework that covers interpolation, smoothing, and regression. Contrary to the multivariate time series models used for EEG analysis up to date, the introduced model provides a smooth spatial reconstruction of the EEG cross-spectrum, keeping the condition of nonnegative definiteness. As an instance of practical importance, the case in which the spatial reconstruction is based on spherical splines is developed in detail. Illustrative examples are presented that show the flexibility of the model to describe both normal and abnormal EEG data.

High resolution quantitative EEG analysis

High resolution spectral methods are explored as an alternative to broad band spectral parameters (BBSP) in quantitative EEG analysis. In a previous paper (Valdes et al. 1990b) regression equations ("Developmental surfaces") were introduced to characterize the age-frequency distribution of the mean and standard deviation of the log spectral EEG power in a normative sample. These normative surfaces allow the calculation of z transformed spectra for all derivations of the 10/20 system and z maps for each frequency. Clinical material is presented that illustrates how these procedures may pinpoint frequencies of abnormal brain activity and their topographic distribution, avoiding the frequency and spatial "smearing" that may occur using BBSP. The increased diagnostic accuracy of high resolution spectral methods is demonstrated by means of receiver operator characteristic (ROC) curve analysis. Procedures are introduced to avoid type I error inflation due to the use of more variables in this type of procedure.