Structurally robust biological networks

Background: The molecular circuitry of living organisms performs remarkably robust regulatory tasks, despite the often intrinsic variability of its components. A large body of research has in fact highlighted that robustness is often a structural property of biological systems. However, there are few systematic methods to mathematically model and describe structural robustness. With a few exceptions, numerical studies are often the preferred approach to this type of investigation. Results: In this paper, we propose a framework to analyze robust stability of equilibria in biological networks. We employ Lyapunov and invariant sets theory, focusing on the structure of ordinary differential equation models. Without resorting to extensive numerical simulations, often necessary to explore the behavior of a model in its parameter space, we provide rigorous proofs of robust stability of known bio-molecular networks. Our results are in line with existing literature. Conclusions: The impact of our results is twofold: on the one hand, we highlight that classical and simple control theory methods are extremely useful to characterize the behavior of biological networks analytically. On the other hand, we are able to demonstrate that some biological networks are robust thanks to their structure and some qualitative properties of the interactions, regardless of the specific values of their parameters

How to Increase Earnings by Exploiting the Veblen Effect

— The price/demand curve in a scenario character ized by the so-called Veblen effect is analytically identified as a modification, due to a variable that we call hankering, of the classical monotonic (price/demand) curve. Differentiating this function with respect to price and using a classical time variation of price, we obtain a control dynamical system. We exploit this model to analyse the possible trajectories and the equilibrium points. Based on these results, we design a strategy that maximizes the earnings of the seller

Enhancements on a saturated control for stabilizing a quadcopter: adaptive and robustness analysis in the flat output space

This paper extends our previous study on an explicit saturated control for a quadcopter, which ensures both constraint satisfaction and stability thanks to the linear representation of the system in the flat output space. The novelty here resides in the adaptivity of the controller's gain to enhance the system's performance without exciting its parasitic dynamics and avoid lavishing the input actuation with excessively high gain parameters. Moreover, we provide a thorough robustness analysis of the proposed controller when additive disturbances are affecting the system behavior. Finally, simulation and experimental tests validate the proposed controller

A system-theoretic approach for image-based infectious plant disease severity estimation

The demand for high level of safety and superior quality in agricultural products is of prime concern. The introduction of new technologies for supporting crop management allows the efficiency and quality of production to be improved and, at the same time, reduces the environmental impact. Common strategies to disease control are mainly oriented on spraying pesticides uniformly over cropping areas at different times during the growth cycle. Even though these methodologies can be effective, they present a negative impact in ecological and economic terms, introducing new pests and elevating resistance of the pathogens. Therefore, consideration for new automatic and accurate along with inexpensive and efficient techniques for the detection and severity estimation of pathogenic diseases before proper control measures can be suggested is of great realistic significance and may reduce the likelihood of an infection spreading. In this work, we present a novel system-theoretic approach for leaf image-based automatic quantitative assessment of pathogenic disease severity regardless of disease type. The proposed method is based on a highly efficient and noise-rejecting positive non-linear dynamical system that recursively transforms the leaf image until only the symptomatic disease patterns are left. The proposed system does not require any training to automatically discover the discriminative features. The experimental setup allowed to assess the system ability to generalise symptoms detection beyond any previously seen conditions achieving excellent results. The main advantage of the approach relies in the robustness when dealing with low-resolution and noisy images. Indeed, an essential issue related to digital image processing is to effectively reduce noise from an image whilst keeping its features intact. The impact of noise is effectively reduced and does not affect the final result allowing the proposed system to ensure a high accuracy and reliability

Cascading Failures in the Global Financial System: A Dynamical Model

In this paper, we propose a dynamical model to capture cascading failures among interconnected organizations in the global financial system. Failures can take the form of bankruptcies, defaults, and other insolvencies. The network that underpins the financial interdependencies between different organizations constitutes the backbone of the financial system. A failure in one or more of these organizations can lead the propagation of the financial collapse onto other organizations in a domino effect. Paramount importance is therefore given to the mitigation of these failures. Motivated by the relevance of this problem and recent prominent events connected to it, we develop a framework that allows us to investigate under what conditions organizations remain healthy or are involved in the propagation of the failures in the network. The contribution of this paper is the following: i) we develop a dynamical model that describes the equity values of financial organizations and their evolution over time given an initial condition; ii) we characterize the equilibria for this model by proving the existence and uniqueness of these equilibria, and by providing an explicit expression for them; and iii) we provide a computational method via sign-space iteration to analyze the propagation of failures and the attractive equilibrium point

Robust control strategies for multi-inventory systems with average flow constraints.

In this paper, we consider multi-inventory systems in the presence of uncertain demand. We assume that (i) demand is unknown but bounded in an assigned compact set and (ii) the control inputs (controlled flows) are subject to assigned constraints. Given a long-term average demand, we select a nominal flow that feeds such a demand. In this context, we are interested in a control strategy that meets at each time all possible current demands and achieves the nominal flow in the average. We provide necessary and sufficient conditions for such a strategy to exist and we characterize the set of achievable flows. Such conditions are based on linear programming and thus they are constructive. In the special case of a static flow (i.e. a system with 0-capacity buffers) we show that the strategy must be affine. The dynamic problem can be solved by a linear-saturated control strategy (inspired by the previous one). We provide numerical analysis and illustrative examples

Robust microphase separation through chemical reaction networks

The interaction of phase-separating systems with chemical reactions is of great interest in various contexts, from biology to material science. In biology, phase separation is thought to be the driving force behind the formation of biomolecular condensates, i.e. organelles without a membrane that are associated with cellular metabolism, stress response, and development. RNA, proteins, and small molecules participating in the formation of condensates are also involved in a variety of biochemical reactions: how do the chemical reaction dynamics influence the process of phase separation? Here we are interested in finding chemical reactions that can arrest the growth of condensates, generating stable spatial patterns of finite size (microphase separation), in contrast with the otherwise spontaneous (unstable) growth of condensates. We consider a classical continuum model for phase separation coupled to a chemical reaction network (CRN), and we seek conditions for the emergence of stable oscillations of the solution in space. Given reaction dynamics with uncertain rate constants, but known structure, we derive easily computable conditions to assess whether microphase separation is impossible, possible for some parameter values, or robustly guaranteed for all parameter values within given bounds. Our results establish a framework to evaluate which classes of CRNs favor the emergence of condensates with finite size, a question that is broadly relevant to understanding and engineering life

Model-Free Plant Tuning

Given a static plant described by a differentiable input-output function, which is completely unknown, but whose Jacobian takes values in a known polytope in the matrix space, this paper considers the problem of tuning (i.e., driving to a desired value) the output, by suitably choosing the input. It is shown that, if the polytope is robustly nonsingular (or has full rank, in the nonsquare case), then a suitable tuning scheme drives the output to the desired point. The proof exploits a Lyapunov-like function and applies a well-known game-theoretic result, concerning the existence of a saddle point for a min-max zero-sum game. When the plant output is represented in an implicit form, it is shown that the same result can be obtained, resorting to a different Lyapunov-like function. The case in which proper input or output constraints must be enforced during the transient is considered as well. Some application examples are proposed to show the effectiveness of the approach