Necessary conditions involving Lie brackets for impulsive optimal control problems; the commutative case

In this article we study control problems with systems that are governed by ordinary differential equations whose vector fields depend linearly in the time derivatives of some components of the control. The remaining components are considered as classical controls. This kind of system is called `impulsive system'. We assume that the vector fields multiplying the derivatives of each component of the control are commutative. We derive new necessary conditions in terms of the adjoint state and the Lie brackets of the data functions

Bootstrap based uncertainty bands for prediction in functional kriging

The increasing interest in spatially correlated functional data has led to the development of appropriate geostatistical techniques that allow to predict a curve at an unmonitored location using a functional kriging with external drift model that takes into account the effect of exogenous variables (either scalar or functional). Nevertheless uncertainty evaluation for functional spatial prediction remains an open issue. We propose a semi-parametric bootstrap for spatially correlated functional data that allows to evaluate the uncertainty of a predicted curve, ensuring that the spatial dependence structure is maintained in the bootstrap samples. The performance of the proposed methodology is assessed via a simulation study. Moreover, the approach is illustrated on a well known data set of Canadian temperature and on a real data set of PM$_{10}$ concentration in the Piemonte region, Italy. Based on the results it can be concluded that the method is computationally feasible and suitable for quantifying the uncertainty around a predicted curve. Supplementary material including R code is available upon request

Maximising ophthalmic theatre time : part 1

Part 2 of the article can be found through this link : https://www.um.edu.mt/library/oar//handle/123456789/12822Aim: To establish whether the available ophthalmic theatre time is being used efficiently and to find ways how to improve our surgical output and reduce the waiting list. Methods: All ophthalmic surgeries under the care of Mr Franco Mercieca carried out in Theatre 13 in the sample months of May and October 2009, were retrospectively analyzed. Average times were estimated for all types of ophthalmic procedures. The total number of cataract operations and patients listed for surgery were noted from beginning of 2006 till end of 2009. Results: In 2009, this firm has carried out 572 cataract operations, 81% increase from 2008, of which 52% were performed on weekends and public holidays. The theatre usage time in the sample months under study was 89.25% on weekdays and over 94% on extra sessions. Theatre time wastage was an average of 8%, half of which being due to cancellations on the day. On average over 71% of our theatre time is used for cataract surgery. Conclusions: In order to maximize our theatre time efficiency, we need to set up a Preoperative Assessment clinic and encourage more patients to have their surgery under local anaesthesia. To reduce the waiting list the need for a parallel theatre dedicated solely to cataract surgery under local anaesthesia is of paramount importance.peer-reviewe

Lax orthogonal factorisation systems

This paper introduces lax orthogonal algebraic weak factorisation systems on 2-categories and describes a method of constructing them. This method rests in the notion of simple 2-monad, that is a generalisation of the simple reflections studied by Cassidy, H\'ebert and Kelly. Each simple 2-monad on a finitely complete 2-category gives rise to a lax orthogonal algebraic weak factorisation system, and an example of a simple 2-monad is given by completion under a class of colimits. The notions of KZ lifting operation, lax natural lifting operation and lax orthogonality between morphisms are studied.Comment: 59 page

Maximising ophthalmic theatre time : part 2

Part 1 of the article can be found through this link : https://www.um.edu.mt/library/oar//handle/123456789/12827Part 2 of the article. Aim: To establish whether the available ophthalmic theatre time is being used efficiently and to find ways how to improve our surgical output and reduce the waiting list. Methods: All ophthalmic surgeries under the care of Mr Franco Mercieca carried out in Theatre 13 in the sample months of May and October 2009, were retrospectively analyzed. Average times were estimated for all types of ophthalmic procedures. The total number of cataract operations and patients listed for surgery were noted from beginning of 2006 till end of 2009. Results: In 2009, this firm has carried out 572 cataract operations, 81% increase from 2008, of which 52% were performed on weekends and public holidays. The theatre usage time in the sample months under study was 89.25% on weekdays and over 94% on extra sessions. Theatre time wastage was an average of 8%, half of which being due to cancellations on the day. On average over 71% of our theatre time is used for cataract surgery. Conclusions: In order to maximize our theatre time efficiency, we need to set up a Preoperative Assessment clinic and encourage more patients to have their surgery under local anaesthesia. To reduce the waiting list the need for a parallel theatre dedicated solely to cataract surgery under local anaesthesia is of paramount importance.peer-reviewe

Maximising ophthalmic theatre time : part 2

Part 1 of the article can be found through this link : https://www.um.edu.mt/library/oar//handle/123456789/12827Part 2 of the article. Aim: To establish whether the available ophthalmic theatre time is being used efficiently and to find ways how to improve our surgical output and reduce the waiting list. Methods: All ophthalmic surgeries under the care of Mr Franco Mercieca carried out in Theatre 13 in the sample months of May and October 2009, were retrospectively analyzed. Average times were estimated for all types of ophthalmic procedures. The total number of cataract operations and patients listed for surgery were noted from beginning of 2006 till end of 2009. Results: In 2009, this firm has carried out 572 cataract operations, 81% increase from 2008, of which 52% were performed on weekends and public holidays. The theatre usage time in the sample months under study was 89.25% on weekdays and over 94% on extra sessions. Theatre time wastage was an average of 8%, half of which being due to cancellations on the day. On average over 71% of our theatre time is used for cataract surgery. Conclusions: In order to maximize our theatre time efficiency, we need to set up a Preoperative Assessment clinic and encourage more patients to have their surgery under local anaesthesia. To reduce the waiting list the need for a parallel theatre dedicated solely to cataract surgery under local anaesthesia is of paramount importance.peer-reviewe

Comparison of non-Markovianity criteria in a qubit system under random external fields

We give the map representing the evolution of a qubit under the action of non-dissipative random external fields. From this map we construct the corresponding master equation that in turn allows us to phenomenologically introduce population damping of the qubit system. We then compare, in this system, the time-regions when non-Markovianity is present on the basis of different criteria both for the non-dissipative and dissipative case. We show that the adopted criteria agree both in the non-dissipative case and in the presence of population damping.Comment: 8 pages, 1 figure. Some changes made. In press on Physica Scripta T (special issue

Detecting spatial homogeneity in the world trade web with Detrended Fluctuation Analysis

In a spatially embedded network, that is a network where nodes can be uniquely determined in a system of coordinates, links' weights might be affected by metric distances coupling every pair of nodes (dyads). In order to assess to what extent metric distances affect relationships (link's weights) in a spatially embedded network, we propose a methodology based on DFA (Detrended Fluctuation Analysis). DFA is a well developed methodology to evaluate autocorrelations and estimate long-range behaviour in time series. We argue it can be further extended to spatially ordered series in order to assess autocorrelations in values. A scaling exponent of 0.5 (uncorrelated data) would thereby signal a perfect homogeneous space embedding the network. We apply the proposed methodology to the World Trade Web (WTW) during the years 1949-2000 and we find, in some contrast with predictions of gravity models, a declining influence of distances on trading relationships.Comment: 15 pages, 7 figure