Linearly scaling direct method for accurately inverting sparse banded matrices

In many problems in Computational Physics and Chemistry, one finds a special kind of sparse matrices, termed "banded matrices". These matrices, which are defined as having non-zero entries only within a given distance from the main diagonal, need often to be inverted in order to solve the associated linear system of equations. In this work, we introduce a new O(n) algorithm for solving such a system, being n X n the size of the matrix. We produce the analytical recursive expressions that allow to directly obtain the solution, as well as the pseudocode for its computer implementation. Moreover, we review the different options for possibly parallelizing the method, we describe the extension to deal with matrices that are banded plus a small number of non-zero entries outside the band, and we use the same ideas to produce a method for obtaining the full inverse matrix. Finally, we show that the New Algorithm is competitive, both in accuracy and in numerical efficiency, when compared to a standard method based in Gaussian elimination. We do this using sets of large random banded matrices, as well as the ones that appear when one tries to solve the 1D Poisson equation by finite differences.Comment: 24 pages, 5 figures, submitted to J. Comp. Phy

A discrete MMAP for analysing the behaviour of a multi-state complex dynamic system subject to multiple events.

A complex multi-state system subject to different types of failures, repairable and/or nonrepairable, external shocks and preventive maintenance is modelled by considering a discrete Markovian arrival process with marked arrivals (D-MMAP). The internal performance of the system is composed of several degradation states partitioned into minor and major damage states according to the risk of failure. Random external events can produce failures throughout the system. If an external shock occurs, there may be an aggravation of the internal degradation, cumulative external damage or extreme external failure. The internal performance and the cumulative external damage are observed by random inspection. If major degradation is observed, the unit goes to the repair facility for preventive maintenance. If a repairable failure occurs then the system goes to corrective repair with different time distributions depending on the failure state. Time distributions for corrective repair and preventive maintenance depend on the failure state. Rewards and costs depending on the state at which the device failed or was inspected are introduced. The system is modelled and several measures of interest are built into transient and stationary regimes. A preventive maintenance policy is shown to determine the effectiveness of preventive maintenance and the optimum state of internal and cumulative external damage at which preventive maintenance should be taken into account. A numerical example is presented, revealing the efficacy of the model. Correlations between the numbers of different events over time and in non-overlapping intervals are calculated. The results are expressed in algorithmic-matrix form and are implemented computationally with Matlab.Junta de Andalucía, Spain, under the grant FQM307Ministerio de Economía y Competitividad, España, MTM2017-88708-PEuropean Regional Development Fund (ERDF

Pomiar niezawodności eksploatacyjnej oprogramowania komercyjnego: interdyscyplinarne podejście do modelowania

In the software reliability engineering (SRE) literature, few attempts have been made to model the failure phenomenon of commercial software during its operational use. One of the reasons can be attributed to the inability of software engineers to measure the growth in usage of commercial software while it is in the market. It is unlike the testing phase where resources follow a definite pattern. In this paper, an attempt has been made to model the software reliability growth linking it to the number of users. Since the number of instructions executed depends on the number of users. The number of users is estimated through an innovation diffusion model of marketing. Once the estimated value is known, the rate at which instructions are executed can be found. The intensity with which failures would be reported depends upon this value. To model the failure observation or defect removal phenomena, a non-homogenous Poisson process (NHPP) based software reliability models developed in the literature have been employed. Software reliability models are most often used for reliability projection when development work is complete and before the software is shipped to customers. They can also be used to model the failure pattern or the defect arrival pattern in the field and thereby provide valuable input to maintenance planning. Numerical example with real software field reliability data is presented to illustrate descriptive and predictive performance as well as to show practical applications of the proposed models.Literatura dotycząca inżynierii niezawodności oprogramowania, podejmuje zaledwie nieliczne próby modelowania zjawiska uszkodzenia oprogramowania komercyjnego w trakcie jego eksploatacji. Jednym z powodów może być to, iż programiści nie są w stanie zmierzyć wzrostu użytkowania oprogramowania komercyjnego w trakcie obrotu handlowego tego typu oprogramowaniem. Etap ten różni się bowiem od fazy testowania, gdzie zasoby funkcjonują według określonego wzorca. W niniejszej pracy podjęto próbę stworzenia modelu wzrostu niezawodności oprogramowania łącząc to pojęcie z pojęciem liczby użytkowników, jako że liczba wykonywanych poleceń zależy właśnie od liczby użytkowników. Liczbę użytkowników szacuje się na podstawie modelu marketingu opartego na dyfuzji innowacji. Gdy szacowana wartość jest już znana, można określić częstość wykonywania poleceń. Intensywność zgłaszania uszkodzeń zależy od tej wartości. Do modelowania zjawisk zaobserwowania uszkodzenia lub usunięcia usterki zastosowano opracowane wcześniej w literaturze modele niezawodności oprogramowania oparte na niejednorodnym procesie Poissona (NHPP). Modele niezawodności oprogramowania są najczęściej wykorzystywane do projektowania niezawodności już po zakończeniu prac rozwojowych, ale zanim jeszcze oprogramowanie dotrze do klientów. Mogą być również stosowane do modelowania wzorców uszkodzeń lub wzorców występowania usterek w trakcie eksploatacji, stanowiąc tym samym cenny wkład do planowania czynności konserwacyjnych. Przykład liczbowy uwzględniający dane z eksploatacji rzeczywistego oprogramowania ilustruje opisowe i predykcyjne możliwości proponowanych modeli, jak również pokazuje, jak można je stosować w praktyce

Effects of intramammary infusion of sage (Salvia officinalis) essential oil on milk somatic cell count, milk composition parameters and selected hematology and serum biochemical parameters in Awassi sheep with subclinical mastitis

Aim: The aims of this study were to evaluate the effects of intramammary infusion of sage (Salvia officinalis) essential oil (EO) on milk somatic cell count (SCC), milk composition parameters and selected hematology and serum biochemical parameters in 20 Awassi ewes affected with subclinical mastitis. Materials and Methods: The dried leaves of sage were used to extract the EO by hydrodistillation. The minimum inhibitory concentration (MIC) and minimum bactericidal concentration (MBC) of sage EO against Staphylococcus aureus were determined by the broth dilution method. Ewes were divided randomly into three main groups and received one of the following treatments; Group 1 (n=5): Dimethyl sulfoxide (DMSO) alone (5 ml; 0.2 ml of DMSO in 4.8 ml of saline), Group 2 (n=5): Amoxicillin alone (3 ml), and Group 3 (n=10): Sage EO (5 ml of sage EO solution [0.2 ml DMSO+1 ml EO+3.8 ml sterile saline]). All treatments were administered by intramammary infusion into each teat twice per day for 3 consecutive days. Milk samples for SCC and milk components determination and whole blood samples for hematology and serum biochemical analyses were collected before treatment (T0) and at 24 (T24) and 48 (T48) h after the last treatment. Results: The MIC and MBC of sage EO against S. aureus were 12.5% and 6.1%, respectively. SCC was decreased significantly (p<0.05) at T24 and T48 h in sage EO and amoxicillin treated groups. Milk fat and lactose were increased significantly (p<0.05) in sage EO and amoxicillin treated ewes while no significant changes were observed in the percentages of solids-not-fat, protein and total solids. No significant effects of sage EO treatment on any of the hematology or serum biochemical parameters were observed. There were no local or systemic side effects observed in any of the treated ewes. However, further clinical trials are warranted to determine safety and possible withdrawal times in milk before its recommendation for use in organic operations. Conclusion: In this study, the intramammary infusion of sage EO to ewes affected with subclinical mastitis resulted in a significant decrease in SCC 24 h and 48 h posttreatment. In addition, milk fat and lactose were increased in animals that received the EO as well as in those treated with the antibiotic

COVID-19 presenting as intussusception in infants: A case report with literature review

From Elsevier via Jisc Publications RouterHistory: accepted 2020-12-31, issue date 2021-01-07Article version: AMPublication status: AcceptedThe novel Corona virus disease 2019 (COVID-19) first presented in Wuhan, China. The virus was able to spread throughout the world, causing a global health crisis. The virus spread widely in Jordan after a wedding party held in northern Jordan. In most cases of COVID-19 infection, respiratory symptoms are predominant. However, in rare cases the disease may present with non-respiratory symptoms. The presentation of COVID-19 as a case of intussusception in children is a strange and rare phenomenon. We present here a case of a two-and-a-half month old male baby who was brought to hospital due to fever, frequent vomiting, dehydration and blood in stool. He was diagnosed as intussusception. The child was tested for corona due to the large societal spread of the virus and because he was near his mother, who was suffering from symptoms similar to corona or seasonal flu (she did not conduct a corona test). Patient was treated without surgery and recovered quickly. The COVID-19 infection was without respiratory symptoms, and there was no need for the child to remain in hospital after treatment of intussusception. The relationship between viruses, mesenteric lymphoid hyperplasia, and intussusception is a confirmed relation. ACE2 is the key receptor required for SARA-COV-2 to enter the host cells. ACE2 has been also found in the brush border of the intestinal mucosa, as well as it is a key inflammatory regulator in the intestine. This may suggest that SARSA-COV-2 could invade the respiratory tract as well as gastrointestinal tract or both. Few case reports documented the presentation of COVID-19 as intussusception in children. In the light of the wide-spread of corona virus, performing COVID-19 tests for children with intussusception can help linking the two entities. Development of gastrointestinal symptoms in COVID-19 positive children should raise concern about the development of intussusception