On the Geometry of Message Passing Algorithms for Gaussian Reciprocal Processes

Reciprocal processes are acausal generalizations of Markov processes introduced by Bernstein in 1932. In the literature, a significant amount of attention has been focused on developing dynamical models for reciprocal processes. Recently, probabilistic graphical models for reciprocal processes have been provided. This opens the way to the application of efficient inference algorithms in the machine learning literature to solve the smoothing problem for reciprocal processes. Such algorithms are known to converge if the underlying graph is a tree. This is not the case for a reciprocal process, whose associated graphical model is a single loop network. The contribution of this paper is twofold. First, we introduce belief propagation for Gaussian reciprocal processes. Second, we establish a link between convergence analysis of belief propagation for Gaussian reciprocal processes and stability theory for differentially positive systems.Comment: 15 pages; Typos corrected; This paper introduces belief propagation for Gaussian reciprocal processes and extends the convergence analysis in arXiv:1603.04419 to the Gaussian cas

Mathematical modeling of local perfusion in large distensible microvascular networks

Microvessels -blood vessels with diameter less than 200 microns- form large, intricate networks organized into arterioles, capillaries and venules. In these networks, the distribution of flow and pressure drop is a highly interlaced function of single vessel resistances and mutual vessel interactions. In this paper we propose a mathematical and computational model to study the behavior of microcirculatory networks subjected to different conditions. The network geometry is composed of a graph of connected straight cylinders, each one representing a vessel. The blood flow and pressure drop across the single vessel, further split into smaller elements, are related through a generalized Ohm's law featuring a conductivity parameter, function of the vessel cross section area and geometry, which undergo deformations under pressure loads. The membrane theory is used to describe the deformation of vessel lumina, tailored to the structure of thick-walled arterioles and thin-walled venules. In addition, since venules can possibly experience negative transmural pressures, a buckling model is also included to represent vessel collapse. The complete model including arterioles, capillaries and venules represents a nonlinear system of PDEs, which is approached numerically by finite element discretization and linearization techniques. We use the model to simulate flow in the microcirculation of the human eye retina, a terminal system with a single inlet and outlet. After a phase of validation against experimental measurements, we simulate the network response to different interstitial pressure values. Such a study is carried out both for global and localized variations of the interstitial pressure. In both cases, significant redistributions of the blood flow in the network arise, highlighting the importance of considering the single vessel behavior along with its position and connectivity in the network

On the Projective Geometry of Kalman Filter

Convergence of the Kalman filter is best analyzed by studying the contraction of the Riccati map in the space of positive definite (covariance) matrices. In this paper, we explore how this contraction property relates to a more fundamental non-expansiveness property of filtering maps in the space of probability distributions endowed with the Hilbert metric. This is viewed as a preliminary step towards improving the convergence analysis of filtering algorithms over general graphical models.Comment: 6 page

RISK AVERSION AND MAJOR CHOICE: EVIDENCE FROM ITALIAN STUDENTS

Does the choice of the field of study depend on individual risk aversion? The direction of the relationship between individual risk attitudes and type of college major chosen is potentially ambiguous. On the one hand, risk adverse individuals may prefer majors allowing high returns on the labour market; on the other hand, if these majors expose students to a higher probability of dropping out, those who are more risk adverse may be induced to choose less challenging fields. Using data from a sample of students enrolled in 2009 at a middle-sized Italian public University, we find that, controlling for a large number of individual characteristics, including cognitive abilities, personality traits and family background, more risk adverse students are more likely to choose any other field (Humanities, Engineering and Sciences) compared to Social Sciences. We interpret this result considering that some of these fields, such as Humanities, allow to reduce the risk of dropping out, while others (such as Engineering and Sciences)involve a lower risk on the labour market. It also emerges that the effect of risk aversion on major choice is related to student ability. Risk adverse students characterized by high abilities tend to prefer Engineering, while the propensity of risk adverse students to enrol in Humanities decreases when ability increases, suggesting that the attention paid to labour market risks and drop out risks varies according to student skills.Risk aversion, College choice, Education

Maximum Entropy Kernels for System Identification

A new nonparametric approach for system identification has been recently proposed where the impulse response is modeled as the realization of a zero-mean Gaussian process whose covariance (kernel) has to be estimated from data. In this scheme, quality of the estimates crucially depends on the parametrization of the covariance of the Gaussian process. A family of kernels that have been shown to be particularly effective in the system identification framework is the family of Diagonal/Correlated (DC) kernels. Maximum entropy properties of a related family of kernels, the Tuned/Correlated (TC) kernels, have been recently pointed out in the literature. In this paper we show that maximum entropy properties indeed extend to the whole family of DC kernels. The maximum entropy interpretation can be exploited in conjunction with results on matrix completion problems in the graphical models literature to shed light on the structure of the DC kernel. In particular, we prove that the DC kernel admits a closed-form factorization, inverse and determinant. These results can be exploited both to improve the numerical stability and to reduce the computational complexity associated with the computation of the DC estimator.Comment: Extends results of 2014 IEEE MSC Conference Proceedings (arXiv:1406.5706

Challenges for the Evaluation of the P.I.P.P.I. - Programme of Intervention for Prevention of Institutionalisation: between Partecipative and Experimental Pathways

Evaluation is constantly requested by governments and decision-makers, to prove that social policies and actions undertaken are effective in responding to problems. Also programmes contrasting child neglect are involved in such request to guarantee that children enjoy their childhood and ensure access to quality service. This paper focuses on an Italian evaluation experience of one such programme named the P.I.P.P.I. (Programme of Intervention for Prevention of Institutionalisation), the outcome of a collaboration between the University of Padua and the Italian Ministry of Welfare. The paper questions and challenges the experimental designs normally used for these evaluation purposes, highlighting how knowledge of effective treatments is far from the practices delivered. The study proposes an innovative evaluation path in which the participative evaluation, where the professionals build their own knowledge through an evaluation in the field, coexists with the choice of matching as a (quasi) experimental evaluation, responding to the Government\u2019s request for effective investments

P.I.P.P.I.: What has changed? How and why? The empirical evidence

This paper provides a summary of the results of the P.I.P.P.I. Program in achieving the prefixed goals on the final, intermediate and proximal outcome variables, regarding children\u2019s development, the positive exercise of parental competences and the effective action of services respectively. Therefore, the main purpose is to describe the impact of the program on the overall well-being of children and families in relation to the processes implemented. This is possible thanks to the wealth of information gathered by professionals through the tools provided for the analysis, design and monitoring activities in the work with families

The PEP Survey: evidence for intense star-forming activity in the majority of radio-selected AGN at z>~1

In order to investigate the FIR properties of radio-active AGN, we have considered three different fields where both radio and FIR observations are the deepest to-date: GOODS-South, GOODS-North and the Lockman Hole. Out of a total of 92 radio-selected AGN, ~64% are found to have a counterpart in Herschel maps. The percentage is maximum in the GOODS-North (72%) and minimum (~50%) in the Lockman Hole, where FIR observations are shallower. Our study shows that in all cases FIR emission is associated to star-forming activity within the host galaxy. Such an activity can even be extremely intense, with star-forming rates as high as ~10^3-10^4 Msun/yr. AGN activity does not inhibit star formation in the host galaxy, just as on-site star-formation does not seem to affect AGN properties, at least those detected at radio wavelengths and for z>~1. Furthermore, physical properties such as the mass and age distributions of the galaxies hosting a radio-active AGN do not seem to be affected by the presence of an ongoing star-forming event. Given the very high rate of FIR detections, we stress that this refers to the majority of the sample: most radio-active AGN are associated with intense episodes of star-formation. However, the two processes proceed independently within the same galaxy, at all redshifts but in the local universe, where powerful enough radio activity reaches the necessary strength to switch off the on-site star formation. Our data also show that for z>~1 the hosts of radio-selected star-forming galaxies and AGN are indistinguishable from each other both in terms of mass and IR luminosity distributions. The two populations only differentiate in the very local universe, whereby the few AGN which are still FIR-active are found in galaxies with much higher masses and luminosities.Comment: 20 pages, 22 figures, to appear in MNRA