Hypercycles are information integration systems which are thought to overcome the information crisis of prebiotic evolution by ensuring the coexistence of several short templates. For imperfect template replication, we derive a simple expression for the maximum number of distinct templates nm that can coexist in a hypercycle and show that it is a decreasing function of the length L of the templates. In the case of high replication accuracy we find that the product nmL tends to a constant value, limiting thus the information content of the hypercycle. Template coexistence is achieved either as a stationary equilibrium (stable fixed point) or a stable periodic orbit in which the total concentration of functional templates is nonzero. For the hypercycle system studied here we find numerical evidence that the existence of an unstable fixed point is a necessary condition for the presence of periodic orbits.

This paper addresses the problem of detecting faults in linear randomized gossip algorithms, where the selection of the dynamics matrix is stochastic. A fault is a disturbance signal injected by an attacker to corrupt the states of the nodes. We propose the use of Set-Valued Observers (SVOs) to detect if the state observations are compatible with the system dynamics for the worst case in a deterministic setting. The concept of Stochastic Set-Valued Observers (SSVOs) is also introduced to construct a set that is guaranteed to contain all possible states with, at least, a pre-specified desired probability. The proposed algorithm is stable in the sense that it requires a finite number of vertices to represent polytopic sets and it allows for the computation of the largest magnitude of the disturbance that an attacker can inject in the network without being detected. Results are presented to reduce the computational cost of this approach and, in particular, by considering only local information and representing the remainder of the network as a disturbance. The case of a consensus algorithm is discussed leading to the conclusion that, by using the proposed SVOs, finite-time consensus is achieved in non-faulty environments. A novel algorithm is proposed that produces less conservative set-valued state estimates by having nodes exchanging local estimates. The algorithm inherits all the previous properties and also enables finite-time consensus computation regardless of the value of the horizon.

Ultrasonographic measurements contribute to demonstrate tumor regression and IH response to propranolol. Thus, ultrasonography is an important instrument to guide therapeutic strategies.

Abstract-We address the problem of a consensus system in the presence of Byzantine faults seen as an attacker injecting a perturbation in the state of the nodes. We propose the use of Set-Valued Observers to detect if the state observations are compatible with the system dynamics. The method is extended to the stochastic case by introducing a strategy to construct a set that is guaranteed to contain all possible states with, at least, a pre-specified desired probability. The proposed algorithm is stable in the sense that it requires a finite number of vertices to represent polytopic sets while also enabling the a priori computation of the largest magnitude of a disturbance that an attacker can inject without being detected.

Abstract-We address the PageRank problem of associating a relative importance value to all web pages in the Internet so that a search engine can use them to sort which pages to show to the user. This precludes finding the eigenvector associated with a particular eigenvalue of the link matrix constructed from the topology graph of the web. In this paper, we investigate the potential benefits of addressing the problem as a solution of a set of linear equations. Initial results suggest that using an asynchronous version of the Gauss-Seidel method can yield a faster convergence than using the traditional power method while maintaining the communications according to the sparse link matrix of the web and avoiding the strict sequential update of the Gauss-Seidel method. Such an alternative poses an interesting path for future research given the benefits of using other more advanced methods to solve systems of linear equations. Additionally, it is investigated the benefits of having a projection after all page ranks have been updated as to maintain all its entries summing to one and positive. In simulations, it is provided evidence to support future research on approximation rules that can be used to avoid the need for the projection to the n-simplex (the projection represents in some cases a threefold increase in the convergence rate over the power method) and on the loss in performance by using an asynchronous algorithm.

This paper addresses the problem of fault detection for linear parameter-varying systems in the presence of measurement noise and exogenous disturbances using Set-Valued Observers (SVOs). The applicability of current methods is limited in the sense that, to increase accuracy, the detection requires a large number of past measurements and the boundedness of the set-valued estimates is only guaranteed for stable systems. In order to widen the class of systems to be modeled and also to reduce the associated computational cost, the aforementioned issues must be addressed. A solution involving left-coprime factorization and deadbeat observers is proposed that reduces the required number of past measurements without compromising accuracy and allowing the design of SVOs for fault detection of unstable systems by using the resulting coprime factorization stable subsystems. The algorithm is shown to produce bounded set-valued estimates and an example is provided. Performance is assessed through simulations, illustrating, in particular that small-magnitude faults (compared to exogenous disturbances) can be detected under mild assumptions.

The coexistence between different informational molecules has been the preferred mode to circumvent the limitation posed by imperfect replication on the amount of information stored by each of these molecules. Here we reexamine a classic package model in which distinct information carriers or templates are forced to coexist within vesicles, which in turn can proliferate freely through binary division. The combined dynamics of vesicles and templates is described by a multitype branching process which allows us to write equations for the average number of the different types of vesicles as well as for their extinction probabilities. The threshold phenomenon associated with the extinction of the vesicle population is studied quantitatively using finite-size scaling techniques. We conclude that the resultant coexistence is too frail in the presence of parasites and so confinement of templates in vesicles without an explicit mechanism of cooperation does not resolve the information crisis of prebiotic evolution.

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