Valerio Cusimano

Stochastic modeling of expression kinetics identifies messenger half-lives and reveals sequential waves of co-ordinated transcription and decay.

The transcriptome in a cell is finely regulated by a large number of molecular mechanisms able to control the balance between mRNA production and degradation. Recent experimental findings have evidenced that fine and specific regulation of degradation is needed for proper orchestration of a global cell response to environmental conditions. We developed a computational technique based on stochastic modeling, to infer condition-specific individual mRNA half-lives directly from gene expression time-courses. Predictions from our method were validated by experimentally measured mRNA decay rates during the intraerythrocytic developmental cycle of Plasmodium falciparum. We then applied our methodology to publicly available data on the reproductive and metabolic cycle of budding yeast. Strikingly, our analysis revealed, in all cases, the presence of periodic changes in decay rates of sequentially induced genes and co-ordination strategies between transcription and degradation, thus suggesting a general principle for the proper coordination of transcription and degradation machinery in response to internal and/or external stimuli.

An efficient approach to the design of observers for continuous-time systems with discrete-time measurements

This paper describes an efficient discretization approach for nonlinear continuous-time systems. A Carleman linearization approach is used to evaluate the exact coefficients of the Taylor-Lie expansion of the dynamics of the system. The resulting discretization scheme is used to build a discrete-time observer that displays good performance. The paper shows the advantages of using an integrated discretization - observation approach for large discretization intervals.

Observer-based techniques for the identification and analysis of avascular tumor growth

Cancer represents one of the most challenging issues for the biomedical research, due its large impact on the public health state. For this reason, many mathematical methods have been proposed to forecast the time evolution of cancer size and invasion. In this paper, we study how to apply the Gompertzs model to describe the growth of an avascular tumor in a realistic setting. To this aim, we introduce mathematical techniques to discretize the model, an important requirement when discrete-time measurements are available. Additionally, we describe observed-based techniques, borrowed from the field of automation theory, as a tool to estimate the model unknown parameters. This identification approach is a promising alternative to traditional statistical methods, and it can be easily extended to other models of cancer growth as well as to the evaluation of not measurable variables, on the basis of the available measurements. We show an application of this method to the analysis of solid tumor growth and parameters estimation in presence of a chemotherapy agent.

Optimal Polynomial Filtering for Planar Tracking via Virtual Measurement Process

Abstract In this paper it is studied the classical problem of target tracking by a new approach consisting in the treatment of the classical nonlinear measurement process in a form amenable for polynomial filtering without the need of the measure map linearization, as required by other standard sub-optimal algorithms. The main idea is to transfer the nonlinearity of the measure map into a modification of the noise sequence distribution in a nongaussian white sequence. This is indeed the property required for Kalman filtering which, although non more optimal, remains to be the optimal linear filtering algorithm. Conditions for polynomial filtering are also satisfied, allowing to face the nongaussian nature of the modified noise sequence. Simulations show high performances of the proposed algorithm.

Robust planar tracking via a virtual measurement approach

Abstract In this paper the classical problem of planar tracking is studied. The approach here proposed is based on the idea of considering, as system output, a vector of “virtual” measurements directly obtained from the actual ones. In this way, the measurement map is split into the sum of a linear time-varying transformation of the state and an uncorrelated white noise process, which is generally nongaussian. The resulting model is amenable for applying standard linear and polynomial Kalman like algorithms avoiding any linearization procedure of the measurement map, which is required by other standard suboptimal solutions (e.g. EKF). Finally, the proposed algorithms are checked through numerical simulations.

Closed-loop control of tumor growth by means of anti-angiogenic administration

A tumor growth model accounting for angiogenic stimulation and inhibition is here considered, and a closed-loop control law is presented with the aim of tumor volume reduction by means of anti-angiogenic administration. To this end the output-feedback linearization theory is exploited, with the feedback designed on the basis of a state observer for nonlinear systems. The control scheme allows to set independently the control and the observer parameters thanks to the special structural properties of the tumor growth model that guarantee the separability of estimation and feedback control algorithms. Preliminary results seem extremely promising, showing a noticeable level of robustness against a wide range of the initial state estimate.

A Carleman discretization approach to filter nonlinear stochastic systems with sampled measurements

Abstract The state estimation problem, here investigated, regards a class of nonlinear stochastic systems, characterized by having the state model described through stochastic differential equations meanwhile the measurements are sampled in discrete times. This kind of model (continuous-discrete system) is widely used in different frameworks (i.e. tracking, finance and systems biology). The proposed methodology is based on a proper discretization of the stochastic nonlinear system, achieved by means of a Carleman linearization approach. The result is a bilinear discrete-time system (i.e. linear drift and multiplicative noise), to which the Kalman Filter equations (or the Extended Kalman Filter equations in case of nonlinear measurements) can be applied. Because the approximation scheme is parameterized by a couple of indexes, related to the degree of approximation with respect to the deterministic and the stochastic terms, in the numerical simulations, different approximation orders have been used in comparison with standard methodologies. The obtained results encourage the use of the proposed approach.

The Observer Follower Filter for stochastic differential systems with sampled measurements

This note deals with stochastic continuous-discrete state-space models, that is stochastic differential systems with sampled discrete measurements. The filtering problem is investigated, with the purpose to provide the state estimate at the samples times. The general setting of a nonlinear drift and of a nonlinear multiplicative noise is considered, as well as of a nonlinear state-to-output function. According to the spirit of the Extended Kalman Filter, the original nonlinear differential system is linearized and discretized; then a bilinear system in the discrete-time framework is obtained, and the minimum variance filter equations are written. The novelty of the paper consists in the use of a state observer for nonlinear differential systems that provides the prediction to the filter equations and also the point around which the linear approximation is achieved. The observer equations make use of a modified version of a class of observers for nonlinear differential systems, coping with the problem of the discrete feature of the measurements, by modeling them as continuous measurements affected by a time-varying delay. Such an Observer Follower Filter approach has been recently applied to stochastic (purely) continuous-time framework. Numerical results show the good performances of the proposed approach with respect to the standard methodologies.

Video-rhino-hygrometer: a new method for evaluation of nasal breathing after nasal surgery.

Background Nasal obstruction is one of the most frequent symptoms in the ear, nose, and throat (ENT) setting. It can be evaluated either subjectively or objectively. In a subjective way, a visual analog scale (VAS) and the Sino-Nasal Outcome Test 20 (SNOT 20) can rapidly quantify the degree of obstruction, whereas the most commonly used objective methods are nasal endoscopy and active anterior rhinomanometry (AAR). It is still a matter of controversy to what extent the sense of nasal obstruction is associated with objective measures for nasal space and airflow. The aim of the study was to evaluate nasal breathing before and after functional nasal surgery by video-rhino-hygrometer (VRH) comparing the results with widely accepted methods. Methods Twenty patient candidates for septoplasty and inferior turbinate reduction were included in the study. SNOT-20, VAS, nasal endoscopy, and AAR were analyzed and compared with VRH values. Results Before surgery VRH showed variability of nasal respiratory flow between individuals and between nostrils. After surgery we had an increase (p < 0.05) of airflow in both nostrils. VRH data were found to be correlated with VAS and SNOT-20 values (p < 0.05) both pre- and postoperatively. Despite the statistically significant correlation of AAR with SNOT-20 and VAS, no statistically significant correlation between AAR and VRH was found. Conclusion VRH provides an immediate, easy, and noninvasive assessment of nasal respiration. For these reasons it can be used, in association with rhinoscopic data and other instrumental tests, to evaluate nasal breathing in daily ENT practice.

Carleman discretization of impulsive systems: application to the optimal control problem of anti-angiogenic tumor therapies

Impulsive systems model continuous-time frameworks with control actions occurring at discrete time instants. Among the others, such models assume relevance in medical situations, where the physical system under control evolves continuously in time, whilst the control therapy is instantaneously administered, e.g. by means of intra-venous injections. This note proposes a discretization algorithm for an impulsive system, whose methods relies on the Carleman embedding techinique. The discretization times are given by the impulsive control action and do not require to have a fixed discretization period. On the ground of the resulting discrete-time system (which can be computed with arbitrary level of accuracy) we propose an optimal control algorithm on a finite horizon. Simulations are carried out on a model exploited for anti-angiogenic tumor therapies and show the effectiveness of the theoretical results.