On Functions of quasi Toeplitz matrices

Let $a(z)=\sum_{i\in\mathbb Z}a_iz^i$ be a complex valued continuous function, defined for $|z|=1$, such that $\sum_{i=-\infty}^{+\infty}|ia_i|<\infty$. Consider the semi-infinite Toeplitz matrix $T(a)=(t_{i,j})_{i,j\in\mathbb Z^+}$ associated with the symbol $a(z)$ such that $t_{i,j}=a_{j-i}$. A quasi-Toeplitz matrix associated with the continuous symbol $a(z)$ is a matrix of the form $A=T(a)+E$ where $E=(e_{i,j})$, $\sum_{i,j\in\mathbb Z^+}|e_{i,j}|<\infty$, and is called a CQT-matrix. Given a function $f(x)$ and a CQT matrix $M$, we provide conditions under which $f(M)$ is well defined and is a CQT matrix. Moreover, we introduce a parametrization of CQT matrices and algorithms for the computation of $f(M)$. We treat the case where $f(x)$ is assigned in terms of power series and the case where $f(x)$ is defined in terms of a Cauchy integral. This analysis is applied also to finite matrices which can be written as the sum of a Toeplitz matrix and of a low rank correction

Efficient cyclic reduction for QBDs with rank structured blocks

We provide effective algorithms for solving block tridiagonal block Toeplitz systems with $m\times m$ quasiseparable blocks, as well as quadratic matrix equations with $m\times m$ quasiseparable coefficients, based on cyclic reduction and on the technology of rank-structured matrices. The algorithms rely on the exponential decay of the singular values of the off-diagonal submatrices generated by cyclic reduction. We provide a formal proof of this decay in the Markovian framework. The results of the numerical experiments that we report confirm a significant speed up over the general algorithms, already starting with the moderately small size $m\approx 10^2$

Fertility control in Europe: applications for an overcrowded continent

Massei, G., Cowan, D., Miller, L.A

Field evaluation of the immunocontraceptive vaccine GonaConTM in free-living mammal populations

Cowan, D., Massei, G., Ward, A., Miller, L.A

Efficacy Of The Boar-Operated-System To Deliver Baits To Feral Swine.

Feral swine (Sus scrofa) pose a significant disease threat to livestock and humans. Emerging technologies to reduce feral swine disease transmission risks include fertility control, vaccination, and toxicants. However, for these technologies to be appropriate for field application, a feral swine-specific oral delivery system is needed. We used two field trials to generate information related to appropriate field application of the Boar-Operated-System (BOSTM), an oral delivery system designed to provide bait access only to feral swine. Our objectives were to determine whether pre-baiting BOSTM units increased bait removal and to evaluate the proportion of feral swine and non-target animals that ingest baits designed to deliver pharmaceuticals through the BOSTM. During both trials we used baits housed within 10 BOSTM units.Wemonitored wildlife visitation, bait removal, and ingestion using motion sensing digital photography and baits containing the bait marker tetracycline hydrochloride (TH). During trial 1 we found three of five pre-baited BOSTM units were used by feral swine only. Additionally, we found the five BOSTM units that were not pre-baited were not used by feral swine or non-target wildlife. During trial 2 we determined bait removal from the BOSTM to be reduced by only 10% for feral swine when activated, whereas bait removal from the BOSTM by all other wildlife was reduced by 100% when activated. We captured 81 feral swine and 23 raccoons and found 90% and 13% to have TH-marked teeth, respectively. With minor modifications, the BOSTM should be considered a valuable tool to be used in feral swine disease management in conjunction with existing technologies

A decision support system for disaster prevention in Urban Areas

This paper presents the use of Human Behavior Modeling for Disaster Relief and Emergency Management. The authors propose an innovative MS2G (Modeling, Interoperable Simulation and Serious Game) using Intelligent Agents to reproduce a complex scenario used for Verification, Validation and Accreditation of the approach. The case study is inspired to South Sudan situation and to the necessity to provide accommodations, food, health care services, security and administrative support to a large number of IDPs (Internally Displaced Persons) over a wide area. The simulator includes camp preparation and installation, air dr ops, logistics network creation while the model includes populations, entities and units as well as different equipment (e.g. cargo planes, helicopters, ground units, etc.

A computational framework for two-dimensional random walks with restarts

The treatment of two-dimensional random walks in the quarter plane leads to Markov processes which involve semi-infinite matrices having Toeplitz or block Toeplitz structure plus a low-rank correction. Finding the steady state probability distribution of the process requires to perform operations involving these structured matrices. We propose an extension of the framework of [5] which allows to deal with more general situations such as processes involving restart events. This is motivated by the need for modeling processes that can incur in unexpected failures like computer system reboots. Algebraically, this gives rise to corrections with infinite support that cannot be treated using the tools currently available in the literature. We present a theoretical analysis of an enriched Banach algebra that, combined with appropriate algorithms, enables the numerical treatment of these problems. The results are applied to the solution of bidimensional Quasi-Birth-Death processes with infinitely many phases which model random walks in the quarter plane, relying on the matrix analytic approach. This methodology reduces the problem to solving a quadratic matrix equation with coefficients of infinite size. We provide conditions on the transition probabilities which ensure that the solution of interest of the matrix equation belongs to the enriched algebra. The reliability of our approach is confirmed by extensive numerical experimentation on some case studies

A computational framework for two-dimensional random walks with restarts

The treatment of two-dimensional random walks in the quarter plane leads to Markov processes which involve semi-infinite matrices having Toeplitz or block Toeplitz structure plus a low-rank correction. We propose an extension of the framework introduced in [D. A. Bini, S. Massei, and B. Meini, Math. Comp., 87 (2018), pp. 2811-2830] which allows us to deal with more general situations such as processes involving restart events. This is motivated by the need for modeling processes that can incur in unexpected failures like computer system reboots. We present a theoretical analysis of an enriched Banach algebra that, combined with appropriate algorithms, enables the numerical treatment of these problems. The results are applied to the solution of bidimensional quasi-birth-death processes with infinitely many phases which model random walks in the quarter plane, relying on the matrix analytic approach. The reliability of our approach is confirmed by extensive numerical experimentation on several case studies

Introducing Intelligence and Autonomy into Industrial Robots to Address Operations into Dangerous Area

The paper addresses the issue to use new generation robotic systems inside industrial facilities in order to complete operations in dangerous area. The new robotic systems are currently adopting the autonomous approach already in use in military sector; however, in this context the intensity of operations and the necessity to interact with high productivity systems introduce different challenges. Despite the problems, it is evident that this approach could provide very interesting improvements in terms of safety for humans especially in relations to dangerous area. For instance, in confined spaces, Oil &amp; Gas or Hot Metal Industry these new autonomous systems could reduce the number of injures and casualties. In addition, these systems could increase the operation efficiency in this complex frameworks as well as the possibility to carry out inspections systematically; in this sense, this could result in improving the overall reliability, productivity and safety of the whole Industrial Plant. Therefore, it is important to consider that these systems could be used to address also security aspects such as access control, however they could result vulnerable to new threats such as the cyber ones and need to be properly designed in terms of single entities, algorithms, infrastructure and architecture. From this point of view, it is evident that Modeling and Simulation represent the main approach to design properly these new systems. In this paper, the authors present the use of autonomous systems introducing advanced capabilities supported by Artificial Intelligence to deal with complex operations in dangerous industrial frameworks. The proposed examples in oil and gas and hot metal industry confirm the potential of these systems and demonstrate as simulation supports their introduction in terms of engineering, testing, installation, ramp up and training