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

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

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.

Bilinear models for spatio-temporal point distribution analysis: application to extrapolation of left ventricular, biventricular and whole heart cardiac dynamics

In this work we describe the usage of bilinear statistical models as a means of factoring the shape variability into two components attributed to inter-subject variation and to the intrinsic dynamics of the human heart. We show that it is feasible to reconstruct the shape of the heart at discrete points in the cardiac cycle. Provided we are given a small number of shape instances representing the same heart atdifferent points in the same cycle, we can use the bilinearmodel to establish this. Using a temporal and a spatial alignment step in the preprocessing of the shapes, around half of the reconstruction errors were on the order of the axial image resolution of 2 mm, and over 90% was within 3.5 mm. From this, weconclude that the dynamics were indeed separated from theinter-subject variability in our dataset.

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.

Life-Cycle Effects on Household Expenditures: A Latent-Variable Approach

Using data from the Spanish household budget survey, we investigate life- cycle effects on several product expenditures. A latent-variable model approach is adopted to evaluate the impact of income on expenditures, controlling for the number of members in the family. Two latent factors underlying repeated measures of monetary and non-monetary income are used as explanatory variables in the expenditure regression equations, thus avoiding possible bias associated to the measurement error in income. The proposed methodology also takes care of the case in which product expenditures exhibit a pattern of infrequent purchases. Multiple-group analysis is used to assess the variation of key parameters of the model across various household life-cycle typologies. The analysis discloses significant life-cycle effects on the mean levels of expenditures; it also detects significant life-cycle effects on the way expenditures are affected by income and family size. Asymptotic robust methods are used to account for possible non-normality of the data.

Measurement with Some Theory: a New Approach to Evaluate Business Cycle Models

We propose a method to evaluate cyclical models which does not require knowledge of the DGP and the exact empirical specification of the aggregate decision rules. We derive robust restrictions in a class of models; use some to identify structural shocks and others to evaluate the model or contrast sub-models. The approach has good size and excellent power properties, even in small samples. We show how to examine the validity of a class of models, sort out the relevance of certain frictions, evaluate the importance of an added feature, and indirectly estimate structural parameters.

Predictable Life-Cycle Shocks, Income Risk and Consumption Inequality

Was the increase in income inequality in the US due to permanent shocks or merely to an increase in the variance of transitory shocks? The implications for consumption and welfare depend crucially on the answer to this question. We use CEX repeated cross-section data on consumption and income to decompose idiosyncratic changes in income into predictable life-cycle changes, transitory and permanent shocks and estimate the contribution of each to total inequality. Our model fits the joint evolution of consumption and income inequality well and delivers two main results. First, we find that permanent changes in income explain all of the increase in inequality in the 1980s and 90s. Second, we reconcile this finding with the fact that consumption inequality did not increase much over this period. Our results support the view that many permanent changes in income are predictable for consumers, even if they look unpredictable to the econometrician, consistent with models of heterogeneous income profiles.

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.

Credit Constraints, Firms' Precautionary Investment, and the Business Cycle

This paper studies the macroeconomic implications of firms' precautionary investment behavior in response to the anticipation of future financing constraints. Firms increase their demand for liquid and safe investments in order to alleviate future borrowing constraints and decrease the probability of having to forego future profitable investment opportunities. This results in an increase in the share of short-term projects that produces a temporary increase in output, at the expense of lower long-run investment and future output. I show in a calibrated model that this behavior is at the source of a novel and powerful channel of shock transmission of productivity shocks that produces short-run dampening and long-run propagation. Furthermore, it can account for the observed business cycle patterns of the aggregate and firm-level composition of investment.

Lyfe-cycle effects on household expenditures: A latent-variable approach

Using data from the Spanish household budget survey, we investigate life-cycle effects on several product expenditures. A latent-variable model approach is adopted to evaluate the impact of income on expenditures, controlling for the number of members in the family. Two latent factors underlying repeated measures of monetary and non-monetary income are used as explanatory variables in the expenditure regression equations, thus avoiding possible bias associated to the measurement error in income. The proposed methodology also takes care of the case in which product expenditures exhibit a pattern of infrequent purchases. Multiple-group analysis is used to assess the variation of key parameters of the model across various household life-cycle typologies. The analysis discloses significant life-cycle effects on the mean levels of expenditures; it also detects significant life-cycle effects on the way expenditures are affected by income and family size. Asymptotic robust methods are used to account for possible non-normality of the data.

Business cycle measurement with some theory

A method to evaluate cyclical models not requiring knowledge of the DGP and the exact specificationof the aggregate decision rules is proposed. We derive robust restrictions in a class of models; use someto identify structural shocks in the data and others to evaluate the class or contrast sub-models. Theapproach has good properties, even in small samples, and when the class of models is misspecified. Themethod is used to sort out the relevance of a certain friction (the presence of rule-of-thumb consumers)in a standard class of models.

Relative price riddles in international business cycle theory: Are transport costs the explanation?

We study relative price behavior in an international business cyclemodel with specialization in production, in which a goods marketfriction is introduced through transport costs. The transporttechnology allows for flexible transport costs. We analyze whetherthis extension can account for the striking differences betweentheory and data as far as the moments of terms of trade and realexchange rates are concerned. We find that transport costs increaseboth the volatility of the terms of trade and the volatility of thereal exchange rate. However, unless the transport technology isspecified by a Leontief technology, transport costs do not resolvethe quantitative discrepancies between theory and data. Asurprising result is that transport costs may actually lower thepersistence of the real exchange rate, a finding that is in contrastto much of the emphasis of the empirical literature.