Positive dynamical systems with delays

In the paper using algebraic methods and method of steps new sufficient conditions for positivity of linear continuous-time dynamical systems with variable coefficients and distributed delay and several constant point delays are established. Neutral linear dynamical systems with several constant point delays are also discussed. As a special case linear dynamical systems without delays are also considered. Finally, illustrative example is given

Late-onset bloodstream infections of Very-Low-Birth-Weight infants: data from the Polish Neonatology Surveillance Network in 2009–2011

BACKGROUND: Late-Onset Bloodstream Infections (LO-BSI) continue to be one of the most important complications associated with hospitalization of infants born with very low birth weight (VLBW). The aims of this study were to assess the epidemiology of LO-BSI together with the risk factors and the distribution of causative pathogens at six Polish neonatal intensive care units that participated in the Polish Neonatology Surveillance Network from January 1, 2009 to December 31, 2011. METHODS: The surveillance covered 1,695 infants whose birth weights were <1501 grams (VLBW) in whom LO-BSI was diagnosed >72 hours after delivery. Case LO-BSI patients were defined according to NeoKISS. RESULTS: Four hundred twenty seven episodes of LO-BSI were diagnosed with a frequency of 25.3% and an incidence density of 6.7/1000 patient-days (pds). Results of our multivariate analysis demonstrated that surgical procedures and lower gestational age were significantly associated with the risk of LO-BSI. Intravascular catheters were used in infants with LO-BSI significantly more frequently and/or for longer duration: Central venous cathters (CVC) (OR 1.29) and Peripheral venous catheters (PVC) (OR 2.8), as well as, the total duration of total parenteral nutrition (13 vs. 29 days; OR 1.81). Occurrence of LO-BSI was significantly associated with increased the length of mechanical ventilation (MV) (OR 2.65) or the continuous positive airway pressure (CPAP) (OR 2.51), as well as, the duration of antibiotic use (OR 2.98). The occurrence of more than one infection was observed frequently (OR 9.2) with VLBW with LO-BSI. Microorganisms isolated in infants with LO-BSI were dominated by Gram-positive cocci, and predominantly by coagulase-negative staphylococci (62.5%). CONCLUSIONS: Independent risk factor for LO-BSI in VLBV infants are: low gestational age and requirement for surgery. The incidence rates of LO-BSI especially CVC-BSI were higher in the Polish NICUs surveillance than those of other national networks, similar to the central- and peripheral utilization ratio

Noise effects in the quantum search algorithm from the computational complexity point of view

We analyse the resilience of the quantum search algorithm in the presence of quantum noise modelled as trace preserving completely positive maps. We study the influence of noise on computational complexity of the quantum search algorithm. We show that only for small amounts of noise the quantum search algorithm is still more efficient than any classical algorithm.Comment: 7 pages, 2 figure

Controllability of dynamical systems

Sterowalność, podobnie jak obserwowalność oraz stabilność, należy do podstawowych pojęć matematycznej teorii układów dynamicznych. Ogólnie mówiąc, sterowalność oznacza, że w rozpatrywanym układzie dynamicznym możliwe jest osiągnięcie zadanego stanu końcowego przy użyciu odpowiednio dobranego sterowania dopuszczalnego, należącego do zadanego zbioru sterowań dopuszczalnych. Zatem sterowalność zależy w istotny sposób zarówno od modelu matematycznego układu dynamicznego reprezentowanego równaniem stanu, jak i od postaci zbioru sterowań dopuszczalnych. Pojęcie sterowalności układu dynamicznego jest wykorzystywane między innymi do analizowania i tworzenia tak zwanych form kanonicznych układów dynamicznych oraz przy formułowaniu twierdzeń z zakresu sterowania optymalnego. Odgrywa ono również istotną rolę w teorii gier oraz w analizie jakościowej układów dynamicznych. Do analizowania problematyki sterowalności układów dynamicznych wykorzystuje się metody zaczerpnięte z różnych, często odległych od siebie dziedzin matematyki, między innymi takich jak: algebra, analiza funkcjonalna, równania różniczkowe, teoria optymalizacji. W artykule, wykorzystując metody algebraiczne, sformułowano kryteria badania sterowalności dla liniowych, skończenie-wymiarowych, ciągłych układów dynamicznych o stałych współczynnikach zarówno dla przypadku braku ograniczeń, jak i dla stożkowo ograniczonych wartości sterowań. Rozpatrzono związki zachodzące pomiędzy sterowalnością a stabilizowalnością układu dynamicznego. Zakładając sterowalność układu, podano także analityczną postać rozwiązania zagadnienia sterowania z minimalną energią. W drugiej części artykułu, w oparciu o spektralną teorię liniowych operatorów różniczkowych oraz twierdzenia z zakresu analizy funkcjonalnej, sformułowano warunki konieczne wystarczające aproksymacyjnej sterowalności dla liniowych układów dynamicznych o parametrach rozłożonych.The paper contains systems descriptions and fundamental results concerning the solution of the most popular linear continuous-time control models with constant coefficients. First, different kinds of stability are discussed. Next fundamental definitions of controllability both for finite-dimensional and infinite-dimensional systems are recalled and necessary and sufficient conditions for different kinds of controllability are formulated. Moreover, fundamental definitions of controllability both for finite-dimensional and infinite-dimensional control systems are presented and necessary and sufficient conditions for different kinds of controllability are given. Finally, concluding remarks and comments concerning possible extensions are presented

Controllability of nonlinear discrete systems

Local constrained controllability problems for nonlinear finite-dimensional discrete 1-D and 2-D control systems with constant coefficients are formulated and discussed. Using some mapping theorems taken from nonlinear functional analysis and linear approximation methods, sufficient conditions for constrained controllability in bounded domains are derived and proved. The paper extends the controllability conditions with unconstrained controls given in the literature to cover both 1-D and 2-D nonlinear discrete systems with constrained controls