Analysis and optimal control of stochastic biological systems

This thesis is concerned with the analysis and control of stochastic biological processes that arise in cells and in the spread of diseases. The modelling methods associated with such processes are typically focused on the average values and based upon ordinary differential equations that are exact only in the limit of large numbers. When a small number of molecules or a low number of individuals are accounted for discrete valued stochastic approaches are suitable. The tools to synthesize control laws and the associated analysis of biological systems in a stochastic setting are however still inadequate when compared to their deterministic counterpart. Despite their practical relevance probabilistic models have indeed received considerably less attention. We try to address this gap in the literature by developing two tools: a) an analytical method to quantify noise for a model of a cellular signalling network, b) highlight the limitations of feedback policies to tame the spread of a disease in a community of individuals. Our first result is associated with analytically quantifying a bound for the second moment of a biochemical species when non linear reaction rates are considered. The existing research in this area has so far focused on introducing approximations that lead to non quantifiable errors. The work here presented introduces a novel method to address this problem without the need of any approximation. In particular, by making use of a discrete expansion we obtain an analytical expression providing a hard bound for the variance. The bound is then shown to be exact when the rates are linear. Our second results considers the problem of taming an epidemic at its early stages by modulating the transmission rate. We formulate an appropriate stochastic optimal control problem in order to select the optimal policy and by exploiting the structure of this problem we show the underlying limitations of using negative feedback in this context. In particular for costs which are linear with the number of infected individuals we show that in an optimal policy there is no decrease in the controlled transmission rate of the disease for increasing infected. From this it follows that negative feedback is not effective in taming the spread of the disease in this setting. The method adopted to derive this limitation is for a simplified epidemic model but accounts for arbitrary feedback policies, a large class of cost functions and for arbitrary system and cost parameters. The results in this thesis thus seek to address the possible pitfalls of adopting models with continuous variables and deterministic dynamics by developing tool for systems that are more adequately described by a stochastic formulations

Sulle epigrafi in lineare A di carattere sacrale

Raccolgo qui le epigrafi cretesi in Lineare A che, per essere scritte su oggetti pertinenti al culto, hanno sicuramente carattere sacrale

Variance bounds for a class of biochemical reactions

We consider the problem of quantifying the variance in molecular numbers in biochemical reactions with nonlinear reaction rates. We address this problem for a specific configuration where a spontaneously formed species determines the rate of formation of another species via a nonlinear reaction rate, with the aim being to quantify the variance of this species. By making use of an appropriate decomposition based on Newton series expansion we derive an analytical expression that provides a hard bound for the variance. The bound becomes an equality when the propensities are linear. Furthermore, numerical investigations demonstrate that this is very close to the actual variance also in regimes where the rate of formation of the species is nonlinear

G. Pugliese Carratelli, Principii della filosofia greca. La nascita della filosofia, Nuova edizione a cura di F. Verde

Tra i massimi storici dell’antichità, Giovanni Pugliese Carratelli è stato un raro esempio di intellettuale capace di avere una visione globale ed essenzialmente onnicomprensiva del mondo antico, racchiudendo in esso non solo la Grecia, l’Etruria e Roma, ma anche la Grecia d’Occidente, il Vicino e l’Estremo Oriente. Il volume che qui si pubblica in una nuova edizione è uno dei pochi lavori che Pugliese dedicò interamente al pensiero antico. Tema centrale è l’origine storica della filosofia greca: essa è affrontata comparativamente nel contesto delle più antiche civiltà dell’Asia Anteriore ed egee (Minoici e Micenei). Pugliese, da storico, non crede nel cosiddetto “miracolo greco” ma valorizza la specificità e la diversità dell’esperienza greca rispetto alle altre culture precedenti e coeve, accentuando la decisiva rilevanza della struttura della polis per la nascita della filosofia

SEA WAVE MEASUREMENT BY RADAR SYSTEMS: BASIC PRINCIPLES FOR MARITIME ENGINEERS

The availability of plentiful and accurate experimental data on the sea state is a prerequisite of real time activities such as civil protection and navigation safety as well as for the construction of the historical data bases which are necessary for the design of coastal and offshore structure. Unfortunately, while a wealth of applied research is available for researchers working in the development of electronic systems and in the analysis of raw data, many practising maritime engineers still lack a clear reference on the principles, the techniques and the objectives of radar-based systems, which nowadays constitute the largest source of such data. The objective of the paper is to introduce engineers and applied oceanographers to the principles of sea wave measurement by radar and to underline their possibilities and their limits

An X-Band Radar System for Bathymetry and Wave Field Analysis in a Harbour Area

Marine X-band radar based systems are well tested to provide information about sea state and bathymetry. It is also well known that complex geometries and non-uniform bathymetries provide a much bigger challenge than offshore scenarios. In order to tackle this issue a retrieval method is proposed, based on spatial partitioning of the data and the application of the Normalized Scalar Product (NSP), which is an innovative procedure for the joint estimation of bathymetry and surface currents. The strategy is then applied to radar data acquired around a harbour entrance, and results show that the reconstructed bathymetry compares well with ground truth data obtained by an echo-sounder campaign, thus proving the reliability of the whole procedure. The spectrum thus retrieved is then analysed to show the evidence of reflected waves from the harbour jetties, as confirmed by chain of hydrodynamic models of the sea wave field. The possibility of using a land based radar to reveal sea wave reflection is entirely new and may open up new operational applications of the system