Modeling of hybrid systems by piecewise decomposition

Piecewise linear models systems arise as mathematical models of systems in many practical applications, often from linearization for nonlinear systems. There are two main approaches of dealing with these systems according to their continuous or discrete-time aspects. We propose an approach which is based on the state transformation, more particularly the partition of the phase portrait in different regions where each subregion is modeled as a two-dimensional linear time invariant system. Then the Takagi-Sugeno model, which is a combination of local model is calculated. The simulation results show that the Alpha partition is well-suited for dealing with such a system

Volatility smile extrapolation with an artificial neural network

I use a multi-layer feedforward perceptron, with backpropagation learning implemented via stochastic gradient descent, to extrapolate the volatility smile of Euribor derivatives over low-strikes by training the network on parametric prices.

Continuum formalism for modeling growing networks with deletion of nodes

We present a continuum formalism for modeling growing random networks under addition and deletion of nodes based on a differential mass balance equation. As examples of its applicability, we obtain new results on the degree distribution for growing networks with a uniform attachment and deletion of nodes, and complete some recent results on growing networks with preferential attachment and uniform removal

Mophological analysis of the human vasculature from medical imaging. Application to cerebral and coranary arteries

In this project, we have investigated new ways of modelling and analysis of human vasculature from Medical images. The research was divided in two main areas: cerebral vasculature analysis and coronary arteries modeling. Regarding cerebral vasculature analysis, we have studed cerebral aneurysms, internal carotid and the Circle of Willis (CoW). Aneurysms are abnormal vessel enlargements that can rupture causing important cerebral damages or death. The understanding of this pathology, together with its virtual treatment, and image diagnosis and prognosis, includes identification and detailed measurement of the aneurysms. In this context, we have proposed two automatic aneurysm isolation method, to separate the abnormal part of the vessel from the healthy part, to homogenize and speed-up the processing pipeline usually employed to study this pathology, [Cardenes2011TMI, arrabide2011MedPhys]. The results obtained from both methods have been also compared and validatied in [Cardenes2012MBEC]. A second important task here the analysis of the internal carotid [Bogunovic2011Media] and the automatic labelling of the CoW, Bogunovic2011MICCAI, Bogunovic2012TMI]. The second area of research covers the study of coronary arteries, specially coronary bifurcations because there is where the formation of atherosclerotic plaque is more common, and where the intervention is more challenging. Therefore, we proposed a novel modelling method from Computed Tomography Angiography (CTA) images, combined with Conventional Coronary Angiography (CCA), to obtain realistic vascular models of coronary bifurcations, presented in [Cardenes2011MICCAI], and fully validated including phantom experiments in [Cardene2013MedPhys]. The realistic models obtained from this method are being used to simulate stenting procedures, and to investigate the hemodynamic variables in coronary bifurcations in the works submitted in [Morlachi2012, Chiastra2012]. Additionally, another preliminary work has been done to reconstruct the coronary tree from rotational angiography, and published in [Cardenes2012ISBI].

Cannabinoid addiction: behavioral models and neural correlates

The use of cannabis sativa preparations as recreational drugs can be traced back to the earliest civilizations. However, animal models of cannabinoid addiction allowing the exploration of neural correlates of cannabinoid abuse have been developed only recently. We review these models and the role of the CB1 cannabinoid receptor, the main target of natural cannabinoids, and its interaction with opioid and dopamine transmission in reward circuits. Extensive reviews on the molecular basis of cannabinoid action are available elsewhere (Piomelli et al., 2000;Schlicker and Kathmann, 2001).

Genetic and genomic analysis modeling of germline c-MYC overexpression and cancer susceptibility

Background: Germline genetic variation is associated with the differential expression of many human genes. The phenotypic effects of this type of variation may be important when considering susceptibility to common genetic diseases. Three regions at 8q24 have recently been identified to independently confer risk of prostate cancer. Variation at 8q24 has also recently been associated with risk of breast and colorectal cancer. However, none of the risk variants map at or relatively close to known genes, with c-MYC mapping a few hundred kilobases distally. Results: This study identifies cis-regulators of germline c-MYC expression in immortalized lymphocytes of HapMap individuals. Quantitative analysis of c-MYC expression in normal prostate tissues suggests an association between overexpression and variants in Region 1 of prostate cancer risk. Somatic c-MYC overexpression correlates with prostate cancer progression and more aggressive tumor forms, which was also a pathological variable associated with Region 1. Expression profiling analysis and modeling of transcriptional regulatory networks predicts a functional association between MYC and the prostate tumor suppressor KLF6. Analysis of MYC/Myc-driven cell transformation and tumorigenesis substantiates a model in which MYC overexpression promotes transformation by down-regulating KLF6. In this model, a feedback loop through E-cadherin down-regulation causes further transactivation of c-MYC.Conclusion: This study proposes that variation at putative 8q24 cis-regulator(s) of transcription can significantly alter germline c-MYC expression levels and, thus, contribute to prostate cancer susceptibility by down-regulating the prostate tumor suppressor KLF6 gene.

What can spike train distances tell us about the neural code?

Time scale parametric spike train distances like the Victor and the van Rossum distancesare often applied to study the neural code based on neural stimuli discrimination.Different neural coding hypotheses, such as rate or coincidence coding,can be assessed by combining a time scale parametric spike train distance with aclassifier in order to obtain the optimal discrimination performance. The time scalefor which the responses to different stimuli are distinguished best is assumed to bethe discriminative precision of the neural code. The relevance of temporal codingis evaluated by comparing the optimal discrimination performance with the oneachieved when assuming a rate code.We here characterize the measures quantifying the discrimination performance,the discriminative precision, and the relevance of temporal coding. Furthermore,we evaluate the information these quantities provide about the neural code. Weshow that the discriminative precision is too unspecific to be interpreted in termsof the time scales relevant for encoding. Accordingly, the time scale parametricnature of the distances is mainly an advantage because it allows maximizing thediscrimination performance across a whole set of measures with different sensitivitiesdetermined by the time scale parameter, but not due to the possibility toexamine the temporal properties of the neural code.

Neuronal adaptation effects in decision making

Recently, there has been an increased interest on the neural mechanisms underlying perceptual decision making. However, the effect of neuronal adaptation in this context has not yet been studied. We begin our study by investigating how adaptation can bias perceptual decisions. We considered behavioral data from an experiment on high-level adaptation-related aftereffects in a perceptual decision task with ambiguous stimuli on humans. To understand the driving force behind the perceptual decision process, a biologically inspired cortical network model was used. Two theoretical scenarios arose for explaining the perceptual switch from the category of the adaptor stimulus to the opposite, nonadapted one. One is noise-driven transition due to the probabilistic spike times of neurons and the other is adaptation-driven transition due to afterhyperpolarization currents. With increasing levels of neural adaptation, the system shifts from a noise-driven to an adaptation-driven modus. The behavioral results show that the underlying model is not just a bistable model, as usual in the decision-making modeling literature, but that neuronal adaptation is high and therefore the working point of the model is in the oscillatory regime. Using the same model parameters, we studied the effect of neural adaptation in a perceptual decision-making task where the same ambiguous stimulus was presented with and without a preceding adaptor stimulus. We find that for different levels of sensory evidence favoring one of the two interpretations of the ambiguous stimulus, higher levels of neural adaptation lead to quicker decisions contributing to a speed–accuracy trade off.

Dynamic estimation of three-dimensional cerebrovascular deformation from rotational angiography

Purpose: The objective of this study is to investigate the feasibility of detecting and quantifying 3D cerebrovascular wall motion from a single 3D rotational x-ray angiography (3DRA) acquisition within a clinically acceptable time and computing from the estimated motion field for the further biomechanical modeling of the cerebrovascular wall. Methods: The whole motion cycle of the cerebral vasculature is modeled using a 4D B-spline transformation, which is estimated from a 4D to 2D + t image registration framework. The registration is performed by optimizing a single similarity metric between the entire 2D + t measured projection sequence and the corresponding forward projections of the deformed volume at their exact time instants. The joint use of two acceleration strategies, together with their implementation on graphics processing units, is also proposed so as to reach computation times close to clinical requirements. For further characterizing vessel wall properties, an approximation of the wall thickness changes is obtained through a strain calculation. Results: Evaluation on in silico and in vitro pulsating phantom aneurysms demonstrated an accurate estimation of wall motion curves. In general, the error was below 10% of the maximum pulsation, even in the situation when substantial inhomogeneous intensity pattern was present. Experiments on in vivo data provided realistic aneurysm and vessel wall motion estimates, whereas in regions where motion was neither visible nor anatomically possible, no motion was detected. The use of the acceleration strategies enabled completing the estimation process for one entire cycle in 5-10 min without degrading the overall performance. The strain map extracted from our motion estimation provided a realistic deformation measure of the vessel wall. Conclusions: The authors' technique has demonstrated that it can provide accurate and robust 4D estimates of cerebrovascular wall motion within a clinically acceptable time, although it has to be applied to a larger patient population prior to possible wide application to routine endovascular procedures. In particular, for the first time, this feasibility study has shown that in vivo cerebrovascular motion can be obtained intraprocedurally from a 3DRA acquisition. Results have also shown the potential of performing strain analysis using this imaging modality, thus making possible for the future modeling of biomechanical properties of the vascular wall.

Student modeling based on fuzzy inference mechanisms

The paper presents a competence-based instructional design system and a way to provide a personalization of navigation in the course content. The navigation aid tool builds on the competence graph and the student model, which includes the elements of uncertainty in the assessment of students. An individualized navigation graph is constructed for each student, suggesting the competences the student is more prepared to study. We use fuzzy set theory for dealing with uncertainty. The marks of the assessment tests are transformed into linguistic terms and used for assigning values to linguistic variables. For each competence, the level of difficulty and the level of knowing its prerequisites are calculated based on the assessment marks. Using these linguistic variables and approximate reasoning (fuzzy IF-THEN rules), a crisp category is assigned to each competence regarding its level of recommendation.

New Trends in Public Facility Location Modeling

The past four decades have witnessed an explosive growth in the field of networkbased facility location modeling. This is not at all surprising since location policy is one of the most profitable areas of applied systems analysis in regional science and ample theoretical and applied challenges are offered. Location-allocation models seek the location of facilities and/or services (e.g., schools, hospitals, and warehouses) so as to optimize one or several objectives generally related to the efficiency of the system or to the allocation of resources. This paper concerns the location of facilities or services in discrete space or networks, that are related to the public sector, such as emergency services (ambulances, fire stations, and police units), school systems and postal facilities. The paper is structured as follows: first, we will focus on public facility location models that use some type of coverage criterion, with special emphasis in emergency services. The second section will examine models based on the P-Median problem and some of the issues faced by planners when implementing this formulation in real world locational decisions. Finally, the last section will examine new trends in public sector facility location modeling.

On the relevance of modeling volatility for pricing purposes

This paper presents a two-factor (Vasicek-CIR) model of the term structure of interest rates and develops its pricing and empirical properties. We assume that default free discount bond prices are determined by the time to maturity and two factors, the long-term interest rate and the spread. Assuming a certain process for both factors, a general bond pricing equation is derived and a closed-form expression for bond prices is obtained. Empirical evidence of the model's performance in comparisson with a double Vasicek model is presented. The main conclusion is that the modeling of the volatility in the long-term rate process can help (in a large amount) to fit the observed data can improve - in a reasonable quantity - the prediction of the future movements in the medium- and long-term interest rates. However, for shorter maturities, it is shown that the pricing errors are, basically, negligible and it is not so clear which is the best model to be used.

Pitfalls in the modeling of forward-looking price setting and investment decisions

The present paper makes progress in explaining the role of capital for inflation and output dynamics. We followWoodford (2003, Ch. 5) in assuming Calvo pricing combined with a convex capital adjustment cost at the firm level. Our main result is that capital accumulation affects inflation dynamics primarily through its impact on the marginal cost. This mechanism is much simpler than the one implied by the analysis in Woodford's text. The reason is that his analysis suffers from a conceptual mistake, as we show. The latter obscures the economic mechanism through which capital affects inflation and output dynamics in the Calvo model, as discussed in Woodford (2004).

Flexible multivariate GARCH modeling with an application to international stock markets

The goal of this paper is to estimate time-varying covariance matrices.Since the covariance matrix of financial returns is known to changethrough time and is an essential ingredient in risk measurement, portfolioselection, and tests of asset pricing models, this is a very importantproblem in practice. Our model of choice is the Diagonal-Vech version ofthe Multivariate GARCH(1,1) model. The problem is that the estimation ofthe general Diagonal-Vech model model is numerically infeasible indimensions higher than 5. The common approach is to estimate more restrictive models which are tractable but may not conform to the data. Our contributionis to propose an alternative estimation method that is numerically feasible,produces positive semi-definite conditional covariance matrices, and doesnot impose unrealistic a priori restrictions. We provide an empiricalapplication in the context of international stock markets, comparing thenew estimator to a number of existing ones.

Macroeconomic modeling for monetary policy evaluation

We describe some of the main features of the recent vintage macroeconomic models used for monetary policy evaluation. We point to some of the key differences with respect to the earlier generation ofmacro models, and highlight the insights for policy that these new frameworks have to offer. Our discussion emphasizes two key aspects of the new models: the significant role of expectations of future policy actions in the monetary transmission mechanism, and the importance for the central bank of tracking of the flexible price equilibrium values of the natural levels of output and the real interest rate. We argue that both features have important implications for the conduct of monetary policy.