91 results on '"Patrick Fitzpatrick"'
Search Results
2. Staff competence in caring for LGBTQ+ patients in the paediatric emergency department
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Sean T Kelleher, Michael J Barrett, Sheena Durnin, Patrick Fitzpatrick, Agnes Higgins, and Dani Hall
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Pediatrics, Perinatology and Child Health - Abstract
ObjectiveThis study aimed to assess the competency of paediatric emergency department (PED) multidisciplinary staff in caring for LGBTQ+ (lesbian, gay, bisexual, transgender, queer/questioning, + inclusive of all identities) adolescents.DesignThis was an observational study within which participants were required to complete the LGBT-Development of Clinical Skills Scale self-assessment tool of clinical competence.SettingIt was conducted across three PEDs and one urgent care centre pertaining to the Children’s Health Ireland healthcare group.ParticipantsDoctors, nurses and healthcare workers were eligible to participate. Exclusion criteria: non-front facing staff; prior completion of an eLearning module intended to serve as a future educational intervention.Main outcome measuresParticipants were assessed on: (1) attitudinal awareness towards LGBTQ+ individuals; (2) knowledge of LGBTQ+ health issues and (3) clinical preparedness in caring for LGBTQ+ patients. Each domain is scored out of a maximum of 7 points.Results71 eligible participants completed the study. 40/71 (56%) were doctors, and 31/71 (44%) were nurses. The mean score for attitudinal awareness was 6.54/7 (SD 0.59), indicating overall positive attitudes. The mean score for knowledge was lower (5.34/7, SD 1.03) and lowest for clinical preparedness (3.39/7, SD 0.94). Participants were less confident in caring for transgender than LGB patients and scored very low when asked if they had received adequate training in caring for transgender young people (2.11/7).ConclusionsThis study demonstrates positive attitudes towards LGBTQ+ patients among PED staff. However, there was a gap in knowledge and clinical preparedness. Increased training in caring for LGBTQ+ young people is necessary.
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- 2023
3. Fully Parameterizable Elliptic Curve Cryptography Processor over GF(2).
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Tim Kerins, Emanuel M. Popovici, William P. Marnane, and Patrick Fitzpatrick
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- 2002
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4. FPGA Design Trade-Offs for Solving the Key Equation in Reed-Solomon Decoding.
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Emanuel M. Popovici, Patrick Fitzpatrick, and Colin C. Murphy
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- 1999
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5. Respective roles of non-pharmaceutical interventions in bronchiolitis outbreaks: an interrupted time-series analysis based on a multinational surveillance system
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Lea, Lenglart, Naim, Ouldali, Kate, Honeyford, Zsolt, Bognar, Silvia, Bressan, Danilo, Buonsenso, Liviana, Da Dalt, Tisham, De, Ruth, Farrugia, Ian K, Maconochie, Henriette A, Moll, Rianne, Oostenbrink, Niccolo, Parri, Damian, Roland, Katy, Rose, Esra, Akyüz Özkan, François, Angoulvant, Camille, Aupiais, Clarissa, Barber, Michael, Barrett, Romain, Basmaci, Susana, Castanhinha, Antonio, Chiaretti, Sheena, Durnin, Patrick, Fitzpatrick, Laszlo, Fodor, Borja, Gomez, Susanne, Greber-Platzer, Romain, Guedj, Florian, Hey, Lina, Jankauskaite, Daniela, Kohlfuerst, Ines, Mascarenhas, Anna Maria, Musolino, Zanda, Pučuka, Sofia, Reis, Alexis, Rybak, Petra, Salamon, Matthias, Schaffert, Keren, Shahar-Nissan, Maria Chiara, Supino, Ozlem, Teksam, Caner, Turan, Roberto, Velasco, Ruud G, Nijman, Luigi, Titomanlio, Vanda, Anacleto, Orkun, Aydin, Elena, Bellelli, Ron, Berant, Thibault, De Groc, Sara, Geitoeira, Florian, Hoffmann, Franziska, Leeb, Fiona, Leonard, Mark, Lyttle, Lia, Mano, Vytenis, Masillonis, Rosa, Morello, Francisa, Saraiva, Gabor, Simon, Ines Silva, Costa, Joao Sous, Marques, Jonas, Thüminger, Corinne, Vasilico, Anna Chiara, Vittucci, Christoph, Zurl, Pediatrics, Business Economics, Hôpital Robert Debré, Hôpital Robert Debré-Centre Hospitalier Universitaire de Reims (CHU Reims), CHU Sainte Justine [Montréal], Epidémiologie Clinique et Evaluation Economique Appliquées aux Populations Vulnérables (ECEVE (U1123 / UMR_S_1123)), Institut National de la Santé et de la Recherche Médicale (INSERM)-AP-HP Hôpital universitaire Robert-Debré [Paris], Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-Université Paris Cité (UPCité), Association Clinique et Thérapeutique Infantile du Val de Marne (ACTIV), The institute of cancer research [London], Pál Heim Children's Hospital = Heim Pál Gyermekkórház [Budapest], Azienda Ospedale Università di Padova = Hospital-University of Padua (AOUP), Fondazione Policlinico Universitario Agostino Gemelli IRCCS, Imperial College London, Mater Dei Hospital [Malta], St Mary's Hospital [London], Hammersmith Hospital NHS Imperial College Healthcare, Erasmus University Medical Center [Rotterdam] (Erasmus MC), Azienda Ospedaliero Universitaria A. Meyer [Firenze, Italy], University of Leicester, University Hospitals Leicester, Ondokuz Mayis University (OMU), Université Paris Cité (UPCité), AP-HP Hôpital universitaire Robert-Debré [Paris], Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP), Hôpital Jean Verdier [AP-HP], North Bristol NHS Trust [Bristol, UK], Children's Health Ireland [Crumlin, Dublin, Ireland] (CHI), University College Dublin [Dublin] (UCD), Hôpital Louis Mourier - AP-HP [Colombes], Centro Hospitalar de Lisboa Central E.P.E, CHI at Tallaght Children's Outpatient and Emergency Care Unit [Tallaght, Ireland] (COECU), CHI at Temple Street [Temple Street, Ireland] (TS), Fejér County Szent György University Teaching Hospital [Szekesfehervar, Hungary] (FCSGUTH), Hospital Universitario Cruces = Cruces University Hospital, Medizinische Universität Wien = Medical University of Vienna, Equipe 1 : EPOPé - Épidémiologie Obstétricale, Périnatale et Pédiatrique (CRESS - U1153), Centre de Recherche Épidémiologie et Statistique Sorbonne Paris Cité (CRESS (U1153 / UMR_A_1125 / UMR_S_1153)), Conservatoire National des Arts et Métiers [CNAM] (CNAM), HESAM Université - Communauté d'universités et d'établissements Hautes écoles Sorbonne Arts et métiers université (HESAM)-HESAM Université - Communauté d'universités et d'établissements Hautes écoles Sorbonne Arts et métiers université (HESAM)-Université Sorbonne Paris Cité (USPC)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Université Paris Cité (UPCité)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE)-Conservatoire National des Arts et Métiers [CNAM] (CNAM), HESAM Université - Communauté d'universités et d'établissements Hautes écoles Sorbonne Arts et métiers université (HESAM)-HESAM Université - Communauté d'universités et d'établissements Hautes écoles Sorbonne Arts et métiers université (HESAM)-Université Sorbonne Paris Cité (USPC)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Université Paris Cité (UPCité)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), Dr von Hauner Children's Hospital [Munich, Germany], Ludwig-Maximilians-Universität München (LMU), Ludwig-Maximilians University [Munich] (LMU), Hospital of Lithuanian University of Health Sciences Kauno Klinikos [Kaunas, Lithuania], Medical University of Graz, Hospital Prof Doutor Fernando Fonseca [Amadora, Portugal], Bambino Gesù Children’s Hospital [Rome, Italy], Children's Clinical University Hospital [Riga, Latvia] (CCUH), Centro Hospitalar Tondela-Viseu [Viseu, Portugal] (CHTV), Paracelsus Medizinische Privatuniversität = Paracelsus Medical University (PMU), Schneider Children’s Medical Center [Petah Tikva, Israel] (SCMC), Hacettepe University = Hacettepe Üniversitesi, Mersin University, Rio Hortega University Hospital (Hospital Universitario Río Hortega) [Valladolid, Spain] (RHUH), Maladies neurodéveloppementales et neurovasculaires (NeuroDiderot (UMR_S_1141 / U1141)), Institut National de la Santé et de la Recherche Médicale (INSERM)-Université Paris Cité (UPCité), EPISODES Study Group., and Angoulvant, François
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[SDV] Life Sciences [q-bio] ,Pulmonary and Respiratory Medicine ,SDG 3 - Good Health and Well-being ,[SDV]Life Sciences [q-bio] - Abstract
BackgroundBronchiolitis is a major source of morbimortality among young children worldwide. Non-pharmaceutical interventions (NPIs) implemented to reduce the spread of severe acute respiratory syndrome coronavirus 2 may have had an important impact on bronchiolitis outbreaks, as well as major societal consequences. Discriminating between their respective impacts would help define optimal public health strategies against bronchiolitis. We aimed to assess the respective impact of each NPI on bronchiolitis outbreaks in 14 European countries.MethodsWe conducted a quasi-experimental interrupted time-series analysis based on a multicentre international study. All children diagnosed with bronchiolitis presenting to the paediatric emergency department of one of 27 centres from January 2018 to March 2021 were included. We assessed the association between each NPI and change in the bronchiolitis trend over time by seasonally adjusted multivariable quasi-Poisson regression modelling.ResultsIn total, 42 916 children were included. We observed an overall cumulative 78% (95% CI −100– −54%; pConclusionsSeveral NPIs were associated with a reduction of bronchiolitis outbreaks, including full lockdown, school closure, teleworking and facial masking. Some of these public health interventions may be considered to further reduce the global burden of bronchiolitis.
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- 2022
6. Fault tolerant matrix triangularization and solution of linear systems of equations.
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Patrick Fitzpatrick and Colin C. Murphy
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- 1992
- Full Text
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7. An improved systolic extended Euclidean algorithm for Reed-Solomon decoding: design and implementation.
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Rory Doyle, Patrick Fitzpatrick, and John Nelson
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- 1990
- Full Text
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8. Introduction of the low risk ankle rule to a paediatric emergency department
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I Okafor, Nandini Kandamany, R McNamara, O. Callender, P. Tormey, and Patrick Fitzpatrick
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Male ,Risk ,medicine.medical_specialty ,Adolescent ,Health Personnel ,Radiography ,Clinical prediction rule ,Audit ,Fractures, Bone ,03 medical and health sciences ,0302 clinical medicine ,Ankle injury ,Clinical Decision Rules ,Humans ,Medicine ,Ankle Injuries ,Practice Patterns, Physicians' ,Child ,General Environmental Science ,030222 orthopedics ,business.industry ,030208 emergency & critical care medicine ,Knowledge ,medicine.anatomical_structure ,Child, Preschool ,Physical therapy ,General Earth and Planetary Sciences ,Female ,Ankle ,Emergency Service, Hospital ,business ,Paediatric emergency - Abstract
Introduction Ankle injuries are a common presentation to the paediatric emergency department (PED), accounting for approximately 2% of presentations.1 X-rays are ordered for 85–95% of patients but only 12% of x-rays reveal a fracture. Clinical prediction rules, such as The Low Risk Ankle Rule (LRAR) exist to help clinicians safely reduce the frequency of radiography in these injuries. The LRAR has been shown to reduce imaging by up to 60% without missing any clinically significant fractures. We sought to introduce The LRAR into our department and study its outcomes on our practice. Aims To introduce the LRAR into our department and study its effects on our radiography rate and length of stay (LOS). Methods An audit of x-ray rates in ankle injuries in 2016 was performed to determine our department's baseline rate of radiography and LOS. We then conducted education sessions and created x-ray ordering prompts to encourage clinicians to use the LRAR. We introduced the LRAR, with a pilot period initially, and gathered data prospectively. Results 969 patients presented in with an ankle injury in 2016, 90.7% of these patients had an x-ray. The median LOS was 109 min. 92 patients presented during the LRAR implementation period with an ankle injury. Nine patients had exclusion criteria from using the LRAR and the attending physician did not use the LRAR in four patients. Of the remaining 79 patients, 49 had a LRAR positive exam. Only one of these patients went on to have an x-ray, which was normal. The 30 patients with a LRAR negative exam all had an x-ray. Overall, our x-ray rate during the study period was 40/92 (43.4%), a reduction of 47.3%. The average LOS during the study was 101 min. No clinically significant fractures were missed. Conclusion The LRAR can safely and effectively reduce the rate of radiography in ankle injuries, without missing any clinically significant fractures.
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- 2020
9. National rotavirus vaccination programme implementation and gastroenteritis presentations: the paediatric emergency medicine perspective
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Stanley Koe, R McNamara, Patrick Fitzpatrick, Ikechukwu Okafor, John Coveney, Nandini Kandamany, and Michael Barrett
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Male ,Rotavirus ,medicine.medical_specialty ,Adolescent ,030204 cardiovascular system & hematology ,Rotavirus vaccination ,medicine.disease_cause ,Rotavirus Infections ,03 medical and health sciences ,0302 clinical medicine ,Paediatric emergency medicine ,Interquartile range ,Humans ,Medicine ,030212 general & internal medicine ,Child ,Retrospective Studies ,Pediatric Emergency Medicine ,business.industry ,Incidence (epidemiology) ,Infant, Newborn ,Rotavirus Vaccines ,Infant ,General Medicine ,Emergency department ,Gastroenteritis ,Child, Preschool ,Emergency medicine ,Female ,Observational study ,business ,Developed country - Abstract
Throughout the developed world, the introduction of rotavirus vaccination has led to reductions in the incidence and severity of acute gastroenteritis (AGE) in young children and consequently to reductions in paediatric emergency department (PED) attendances with AGE. Rotavirus vaccination was added to the Irish National Immunisation Schedule in November 2016. To assess the impact of vaccine introduction on citywide PED attendances and hospital admissions with all-cause AGE during rotavirus season. In an observational study, a retrospective search was performed of electronic records in three independent PEDs in Dublin. Weekly presentations and admissions with AGE in the first 30 weeks (gastroenteritis season) of the years 2012–2018 were counted and stratified by age. Median weekly presentations in 2017–2018, 126 (interquartile range (IQR) 103–165) were significantly lower than in 2012–2016, 160 (IQR 128–214) (p
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- 2019
10. Use of anti-reflux medications in infants under 1 year of age: a retrospective drug utilization study using national prescription reimbursement data
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Robert Conway, Lois O'Connor, Patrick Fitzpatrick, and Daniel O'Reilly
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Drug Utilization ,Pediatrics ,medicine.medical_specialty ,Population ,General medical services ,Irritability ,03 medical and health sciences ,0302 clinical medicine ,030225 pediatrics ,medicine ,Humans ,030212 general & internal medicine ,Medical prescription ,education ,Child ,Reimbursement ,Retrospective Studies ,education.field_of_study ,business.industry ,Infant ,Proton Pump Inhibitors ,Prescriptions ,Histamine H2 Antagonists ,Pediatrics, Perinatology and Child Health ,Cohort ,Vomiting ,Gastroesophageal Reflux ,medicine.symptom ,business - Abstract
Non-specific symptoms such as irritability, vomiting, and back arching during the infant period are often attributed to gastroesophageal reflux. While numerous studies have shown no significant benefit to the use of acid suppressant medications in this population, these medications are frequently prescribed in response to these symptoms. Our goals were to understand how often children were being prescribed this medication. To do this, data was extracted from a national database for reimbursement of prescribed medications through the General Medical Services scheme (GMS). Infants aged less than 1 year and eligible for reimbursement under GMS were included for analysis. A total of 450 infants per 10,000 eligible population received an anti-reflux preparation from the following drug classes (H2 antagonists, proton pump inhibitors, or alginate preparations) in 2018. This is compared with that in 2009 where only 137 per 10,000 eligible infants received these medications. This increase was predominantly attributable to an increase in ranitidine prescriptions.Conclusion: Despite a change in clinical guidelines, anti-reflux preparations are increasingly being prescribed to infants aged less than 1 year. The reasons behind the increase in prescriptions containing these medications cannot be ascertained from this data. This may suggest a proportion of these prescriptions may be unwarranted in this population. What is Known: • The prescription of PPIs in infants has increased in a number of countries. • Use of anti-reflux medications has a very poor evidence base in infancy. What is New: • This data focuses only on an infant age group in a "well" cohort. • Ranitidine may contribute to increased acid-suppressant use in infancy.
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- 2020
11. Clean catch urine collection: Time taken and diagnostic implication. A prospective observational study
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Sandy M Hopper, Shidan Tosif, Susan Donath, Monsurul Hoq, Franz E Babl, Patrick Fitzpatrick, and Jonathan Kaufman
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Reflux nephropathy ,Pediatrics ,medicine.medical_specialty ,Urine Specimen Collection ,business.industry ,Collection Time ,Emergency department ,Urine ,medicine.disease ,Confidence interval ,03 medical and health sciences ,0302 clinical medicine ,Interquartile range ,030225 pediatrics ,Pediatrics, Perinatology and Child Health ,medicine ,030212 general & internal medicine ,business ,Prospective cohort study - Abstract
Aim Clean catch urine (CCU) collection is commonly used in pre-continent children. CCU can be time-consuming and specimens may be contaminated. Our aim was to determine the time taken for CCU attempts and to describe the success of this method in diagnosing or excluding urinary tract infection. Methods Prospective observational study of CCU in pre-continent children aged 2–48 months in the emergency department. Time taken until urine collection, ‘successful’ (voided and caught), ‘missed’ (voided not caught) or the procedure ‘stopped’, were recorded and urine culture results analysed. Results Two hundred and seventeen children (131 (60%) male) were enrolled. There were a total of 247 attempts at CCU. For the first attempt, the median collecting time was 30.5 min (interquartile range (IQR) 11–66). Outcome was ‘successful’ in 64% (95% confidence intervals (CI) 58–70%), ‘missed’ in 16% (95% CI 11–20%) and ‘stopped’ in 20% (95% CI 15–26%). Median time if ‘successful’ was 25 min (IQR 7–46.5), ‘missed’ 27 min (IQR 11.6–59) and 71 min (IQR 42.5–93) when ‘stopped’. One hundred and sixty children had successful CCU collection, 129 were sent for culture. Fifty of 129 (39%) cultures were contaminated. If all urine specimens caught were sent for culture, the estimated yield of an uncontaminated urine specimen was 45%. Contamination was not related to time taken for CCU. Conclusions CCU is time-consuming, frequently unsuccessful and contaminated, resulting in a low overall diagnostic yield. Clinicians could expect a 45% chance of obtaining a definitive urine sample from this method overall.
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- 2017
12. GP163 Improving patient experience through the use of a short stay observation unit in a pediatric hospital, a pilot study
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R McNamara, Sharon Ryan, Claire Fagan, Nandini Kandamany, Joan Broderick, Helen Flynn, Elaine Fitzgerald, Patrick Fitzpatrick, and I Okafor
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Patient safety ,Patient satisfaction ,Short stay ,business.industry ,Patient experience ,Staffing ,medicine ,Workload ,Emergency department ,Medical emergency ,Overcrowding ,medicine.disease ,business - Abstract
The Emergency Department (ED) at Children’s University Hospital, Temple Street is constantly running at maximum capacity due to limited space and in-patient beds, as well as inadequate staffing. This leads to a number of issues including: reduced patient flow, department overcrowding, unacceptable patient experience times and possible adverse events. A short stay observation unit (SSOU) was introduced to improve flow and patient experience. The RCPCH (2017) have defined a short stay unit as a ‘dedicated facility providing assessment, observation and treatment of an illness, without the need for inpatient admission and can be a safe and efficient way of managing their care.’ Our aim was to utilize beds in a different way to improve patient safety and patient flow in the ED, therefore improving PET times and patient satisfaction. We developed a local implementation group that met weekly to progress and change as necessary. We developed set admission criteria and standard operating procedures for the department. Weekly audits for patient length of stay in the SSOU, ED trolley wait times monitored weekly, parent and staff satisfaction surveys, PET times monitored weekly. Over the duration of the 8 week pilot study; Average length of stay in the SSOU was 11.7 hours 164 patients through the SSOU in 8 weeks, at 1.2 patients per available bed/day Trolley wait times have dropped to the previous 2 years Satisfaction surveys showed that the SSOU positively affected patients hospital experience and the ED staffs workload The utilisation of beds and resources in a different way can have a positive impact on patient care. Parent satisfaction and patient flow can be greatly improved from implementing a permanent SSOU. The ED can be used more efficiently and patient safety improved through effective use of resources. Welcomed changes can have a big impact on staff morale. We recommend that for future use, the SSOU be run as a standalone unit by the ED staff on a daily basis for the entirety of its opening hours. The SSOU should be in operation for at minimum the busy winter period, that being from late September to early May.
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- 2019
13. P592 Paediatric ECG interpretation by non-consultant hospital doctors (NCHDs) working in an irish tertiary paediatric centre
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Catherine Crowe, Adam James, Michael Pio Fitzgerald, and Patrick Fitzpatrick
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medicine.medical_specialty ,business.industry ,Interpretation (philosophy) ,Teaching method ,education ,language.human_language ,Likert scale ,Irish ,Wolf parkinson white ,Hospital doctor ,Physical therapy ,language ,Medicine ,cardiovascular diseases ,Medical diagnosis ,Clinical competence ,business - Abstract
Introduction Paediatric ECG interpretation is a core clinical competence in postgraduate paediatric specialist training. Doctors treating paediatric patients with potential cardiac conditions should be familiar with the principles of ECG interpretation and the diagnoses requiring emergency treatment. Research has shown that paediatric ECG interpretation amongst doctors may be suboptimal and that the most effective method of teaching ECG interpretation is unclear.1 Aims This study aims to establish the accuracy of paediatric ECG interpretation by NCHDs working in an Irish Tertiary Paediatric Hospital and to measure the impact of a teaching intervention. Methodology NCHDs working in acute clinical areas in an Irish tertiary paediatric hospital were invited to participate (n=45). Participants were asked to report three ECGs (long QT, Wolf Parkinson White and normal). This was followed by a 40 minutes lecture. Participants were then asked to re-report the same 3 ECGs. Participants also completed questionnaires pre and post the study, including self-rating their ability to report paediatric ECGs on a Likert Scale from 1(poor) to 6 (expert). Results 25 NCHDs completed the study. The pre-teaching accuracy for ECG1 (long QT), ECG 2 (Wolf Parkinson White) and ECG 3 (normal) was 37%, 32% and 24% respectively. Following the teaching intervention these figures rose to 76%, 40% and 44%. There was a statistically significant improvement in the combined before and after accuracy of ECG interpretation (31% v 53%) (p=0.02). There was also an improvement in participant self-rated ability to report paediatric ECG following the study. The mean pre-lecture score on the 1 (Poor)-6(Expert) Likert Scale was 2.84, the mean post lecture score on was 3.8 with the same scale. All participants found the teaching intervention helpful and reported that they would like further teaching on the topic. Discussion The initial accuracy of paediatric ECG interpretation amongst participants was lower than reported in the literature.2 Lectures were shown to be an effective teaching method to improve short-term ECG accuracy rates among participants. Conclusion There is currently no structured post-graduate teaching for paediatric ECG interpretation resulting in a varied knowledge base. This study shows that further education on ECG’s is required. References Jheeta J, et al. Accuracy in interpreting the paediatric ECG: a UK-wide study and the need for improvement. Arch Dis Child 2014;99:646–. Auseon AJ, et al. Methods of teaching and evaluating electrocardiogram interpretation skills among cardiology fellowship programs in the United States. J Electrocardiol 2009;42(4):339–44.
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- 2019
14. P272 Management of fingertip injuries in the paediatric emergency department clinic- more than local anaesthesia
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Deborah Cullen, Aileen Egan, and Patrick Fitzpatrick
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medicine.medical_specialty ,business.industry ,Sedation ,Resource planning ,Staffing ,Emergency department ,Finger injury ,Plastic surgery ,Anesthesia ,medicine ,General anaesthesia ,medicine.symptom ,business ,Paediatric emergency - Abstract
Trauma and injuries represent a significant portion of presentations to the Paediatric Emergency Department, with a major subset comprising hand and fingertip injuries. These require input from specialist hand surgeons. In co-ordinating this care pathway, the aim is to provide effective and definitive treatment in a manner that is straightforward for parents and least stressful for the injured child. Frequently, these injuries are suitable for repair under local anaesthesia. In the presence of a well-stocked treatment room, repair of simple fingertip injuries can be facilitated, avoiding the need for full hospital admission and prolonged fasting for repair under general anaesthesia. Our study evaluated all fingertip and nailbed injuries presenting to our Emergency Department in an 8 month period from January to August 2018. Out of 964 presentations for Plastic Surgery review, 226 concerned hand or finger injuries. Of these, 140 represented fingertip or nailbed injuries. Almost 40% of these underwent repair in the Emergency Department under local anaesthesia with or without nitrous oxide sedation. 25% required repair in the operating theatre under general anaesthesia and 35% were managed conservatively. August was the busiest month for such injuries. Children undergoing nitrous sedation with local anaesthesia for these injuries ranged from 15months to 14 years, with a median of 4 years. In general, younger babies and more anxious or upset children were less suitable for sedation and local anaesthesia. All cases were followed up routinely in the Plastic Surgery clinic. Side effects of nitrous sedation were uncommon. There were almost no complications following these procedures. This audit provides a snapshot of the usefulness of nitrous sedation in combination with local anaesthesia as a safe and reproducible method of managing simple fingertip injuries in the paediatric setting. It highlights issues around provision for these services in the Emergency Department- staffing, equipment and training to name but some- but will surely assist in future resource planning.
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- 2019
15. GP196 The use of a rapid antigen detection test for beta haemolytic group a streptococcus to aid the management of pharyngitis and tonsillitis in an irish tertiary paediatric emergency department
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Caroline Fox and Patrick Fitzpatrick
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medicine.medical_specialty ,medicine.diagnostic_test ,business.industry ,Incidence (epidemiology) ,Tonsillitis ,Primary care physician ,Guideline ,Emergency department ,medicine.disease ,Pharyngitis ,Throat culture ,Internal medicine ,medicine ,Rheumatic fever ,medicine.symptom ,business - Abstract
Background Acute sore throat is a common presentation to the Emergency Department (ED). Rapid-antigen detection testing (RADT) is used in our department to aid diagnosis of Group A streptococcus (GAS) as the cause of pharyngitis/tonsillitis as an adjunct to clinical assessment. Our aims were to assess use of RADT in management and treatment of pharyngitis/tonsillitis in the ED and compare our practice with current NICE guidelines. Methods This was a prospective study which took place at the Children’s University Hospital Dublin in 2018. A proforma was created and doctors were asked to complete this for children who had a RADT for GAS. Data collected included patient age, history, examination findings, rapid-antigen swab result, use of throat swab culture, use of antibiotics.The modified Centor score (MCS) was then calculated. Results Data collected on 102 patients. 1 patient excluded as data form incomplete. 16 (15.8%) patients had low MCS of 0,1 or 2. Of these, 1 patient was RADT positive and treated with antibiotics. 85 (84.2%) patients had high MCS of 3, 4 or 5. 26 (30.6%) were RADT positive and were treated with antibiotics. 59 (69.4%) were RADT negative –6 were treated with antibiotics. Of the 74 patients with a negative RADT, 20 of these had a throat culture sent. 25% had GAS positive culture. 42/101 patients were treated with antibiotics. 27 of these were RADT positive. Of the RADT negative patients, 8 were treated with antibiotics by the ED physician for pharyngitis/tonsillitis, 3 were treated for other diagnoses, 4 had antibiotics continued that were started by a primary care physician. Of the 27 children with a positive RADT swab, 92.5% had a MCS of 4 or 5. Conclusions NICE guidelines suggest no benefit of RADT testing over clinical scores alone. The low incidence of RADT positivity in the low risk MCS group (MCS 0,1 or 2) suggests we can safely not test and not offer antibiotics to these children. In the high MCS group (MCS 3, 4 or 5), only 37.6% of patients had antibiotics started by the ED physician suggesting that RADT may have a role in reducing the number of patients treated with antibiotics. A formal guideline will be created for use in our ED. In communities where the incidence of rheumatic fever is low, a balance must be made between reducing symptoms by a modest amount and the emerging issue of antimicrobial resistance.
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- 2019
16. P268 Introduction of the low risk ankle rule to a paediatric emergency department: a quality improvement initiative
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I Okafor, Nandini Kandamany, Orla Callender, Tracey McCrudden, Patrick Fitzpatrick, Peter Tormey, and R McNamara
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medicine.medical_specialty ,Quality management ,medicine.diagnostic_test ,business.industry ,Radiography ,Physical examination ,Audit ,Baseline data ,medicine.anatomical_structure ,medicine ,Physical therapy ,Ankle ,business ,Prospective cohort study ,Paediatric emergency - Abstract
Introduction Ankle injuries are common in children (∼ 2% of presentations to PEDs) 1 X-rays are ordered for 85–95% of patients but only 12% of x-rays reveal a fracture.1 Clinical prediction rules such as The Low Risk Ankle Rule (LRAR) exist to help clinicians safely reduce the frequency of radiography in these injuries. The LRAR has been shown to reduce imaging by up to 60% without missing any clinically signficant fractures.1 Aim To introduce the LRAR to our department and study its effect on our rate of radiography and length of stay (LOS). We also sought to identify complications related to its use, such as missed fractures and representations. Methods A baseline audit was performed to determine our baseline rate of radiography. The implementation strategy involved: staff education sessions, distribution of study information and visual reminders throughout the department, introduction of mandatory prompts into the x-ray ordering system and a 3 week pilot period. Results The baseline ankle x-ray rate was 879/969 (90.7%). This reduced to 40/92 (43.4%) using the LRAR, a reduction of 47.3%. The average LOS decreased from 132 minutes before the implementation to 123 minutes after. There were no re-presentations with missed fractures. Further 12 month follow up data after the initial implementation period showed a persistent 46% reduction in the frequency of ankle x-rays performed, compared with the baseline data. Conclusions The LRAR has been shown to safely reduce the frequency of radiography in ankle injuries.1,2, Other studies have demonstrated a reduction in x-ray frequency of 22–60%. 1,2, Our study was in keeping with these previous studies, while also not missing any fractures, further supporting the use of The LRAR in paediatric emergency departments. The LRAR continues to be used effectively in our department. Follow on data showed an annual saving of €28, 247. References Boutis, K., Von Keyserlingk, C., Willan, A., Narayanan, U. G., Brison, R., Grootendorst, P., … Goeree, R. (2015). Cost Consequence Analysis of Implementing the Low Risk Ankle Rule in Emergency Departments. Annals of Emergency Medicine, 66, 455–463.e4. Boutis, K., Komar, L., Jaramillo, D., Babyn, P., Alman, B., Snyder, B., … Schuh, S. (2001). Sensitivity of a clinical examination to predict need for radiography in children with ankle injuries: a prospective study. The Lancet, 358(9299), 2118–2121
- Published
- 2019
17. GP158 The use of nitrous oxide in temple street emergency department
- Author
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Danielle McCollum, Patrick Fitzpatrick, Niamh Whyte, and Jim Hickson
- Subjects
medicine.medical_specialty ,business.industry ,Sedation ,Psychological intervention ,Emergency department ,Distress ,Patient safety ,Emergency medicine ,medicine ,Vomiting ,Anxiety ,medicine.symptom ,business ,Adverse effect - Abstract
Background A visit to the Emergency Department (ED) can be stressful and frightening for children and their parents.1 Children perceive many of the interventions performed in ED as threatening, and a negative experience can have an impact on any future visits to hospital. 2; 3 Through our procedural sedation programme, we aim to minimise this distress, reduce pain and improve the success rate of a procedure whilst ensuring patient safety at all times. Aims The aim of this study is to review the use of Nitrous Oxide for procedural sedation within the Emergency Department between March and October 2018, and to evaluate the adverse events and outcomes. Methods When performing procedural sedation in ED, a standardised sedation record is completed by the trained staff member and uploaded to a computer database. These forms were reviewed and data was input into Microsoft Excel for interpretation and analysis. Results Over the study period, procedural sedation was performed on 142 occasions. The mean age of the patients was 6.9 years old (11 months – 15 year), and 68% were male. The overall mean duration of sedation was 9.3minutes (3minutes – 40minutes). The most common indication for use of Nitrous Oxide was in the management of a fracture or laceration (93/142). Other indications included removal of foreign bodies, lumbar punctures and IV cannulation. No serious adverse events occurred in the study period. Less significant side effects occurred in 22% of cases. Vomiting was the most common (27/142) side effect and was more likely to occur in children under 10 years of age. Conclusion Nitrous oxide is used for a wide variety of reasons in our department and is generally well tolerated. Procedural sedation can be beneficial to patients in reducing distress and avoiding a general anaesthetic with prolonged hospital stays. The implantation of a database allows for continuous audit of our practices within the department and comparison with national and international standards. References Merritt C. Fear and loathing in the ER: managing procedural pain and anxiety in the Pediatric Emergency Department. R I Med J 2013; 97(1):31–34. Krauss B. S.; GREEN, S. M. Procedural sedation and its place in paediatric emergency medicine. Emergency Medicine Journal; 33(8):525. Krieser D, Kochar A. Paediatric procedural sedation within the emergency department. J Paediatr Child Health 2016; 52(2):197–203.
- Published
- 2019
18. Bounds on codes derived by counting components in Varshamov graphs.
- Author
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Katie O'Brien and Patrick Fitzpatrick
- Published
- 2004
- Full Text
- View/download PDF
19. Quasicyclic irreducible Goppa codes.
- Author
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John A. Ryan and Patrick Fitzpatrick
- Published
- 2004
- Full Text
- View/download PDF
20. Clean catch urine collection: Time taken and diagnostic implication. A prospective observational study
- Author
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Shidan, Tosif, Jonathan, Kaufman, Patrick, Fitzpatrick, Sandy M, Hopper, Monsurul, Hoq, Susan, Donath, and Franz E, Babl
- Subjects
Male ,Time Factors ,Child, Preschool ,Urinary Tract Infections ,Humans ,Infant ,Female ,Prospective Studies ,Specimen Handling ,Urine Specimen Collection - Abstract
Clean catch urine (CCU) collection is commonly used in pre-continent children. CCU can be time-consuming and specimens may be contaminated. Our aim was to determine the time taken for CCU attempts and to describe the success of this method in diagnosing or excluding urinary tract infection.Prospective observational study of CCU in pre-continent children aged 2-48 months in the emergency department. Time taken until urine collection, 'successful' (voided and caught), 'missed' (voided not caught) or the procedure 'stopped', were recorded and urine culture results analysed.Two hundred and seventeen children (131 (60%) male) were enrolled. There were a total of 247 attempts at CCU. For the first attempt, the median collecting time was 30.5 min (interquartile range (IQR) 11-66). Outcome was 'successful' in 64% (95% confidence intervals (CI) 58-70%), 'missed' in 16% (95% CI 11-20%) and 'stopped' in 20% (95% CI 15-26%). Median time if 'successful' was 25 min (IQR 7-46.5), 'missed' 27 min (IQR 11.6-59) and 71 min (IQR 42.5-93) when 'stopped'. One hundred and sixty children had successful CCU collection, 129 were sent for culture. Fifty of 129 (39%) cultures were contaminated. If all urine specimens caught were sent for culture, the estimated yield of an uncontaminated urine specimen was 45%. Contamination was not related to time taken for CCU.CCU is time-consuming, frequently unsuccessful and contaminated, resulting in a low overall diagnostic yield. Clinicians could expect a 45% chance of obtaining a definitive urine sample from this method overall.
- Published
- 2016
21. Linear recurrence relations and an extended subresultant algorithm.
- Author
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Patrick Fitzpatrick and Graham H. Norton
- Published
- 1988
- Full Text
- View/download PDF
22. Quick-Wee: a novel non-invasive urine collection method
- Author
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Jonathan Kaufman, Susan Donath, Patrick Fitzpatrick, Shidan Tosif, Sandy M Hopper, Penelope A Bryant, and Franz E Babl
- Subjects
Male ,medicine.medical_specialty ,Sodium Chloride ,Critical Care and Intensive Care Medicine ,03 medical and health sciences ,Clean catch urine ,0302 clinical medicine ,030225 pediatrics ,Physical Stimulation ,Medicine ,Humans ,030212 general & internal medicine ,Prospective Studies ,Prospective cohort study ,Urine Specimen Collection ,business.industry ,Non invasive ,Infant, Newborn ,Infant ,General Medicine ,Bandages ,Surgery ,Urine collection method ,Emergency medicine ,Emergency Medicine ,Feasibility Studies ,Female ,business ,Cutaneous stimulation - Abstract
Background Clean catch urine (CCU) collection in precontinent children is often time-consuming, with associated collection failure. We hypothesise that stimulating cutaneous reflexes hastens voiding for CCU. Methods 40 children aged 1–24 months in the ED. Standard CCU was augmented with gentle suprapubic cutaneous stimulation using saline-soaked gauze (Quick-Wee method). Results 12/40 (30%) children voided within 5 min for successful CCU. Parental and clinician satisfaction was high. Conclusions Quick-Wee appears to be a simple method to speed CCU in young children.
- Published
- 2016
23. A randomised controlled trial of cognitive aids for emergency airway equipment preparation in a Paediatric Emergency Department
- Author
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Patrick Fitzpatrick, Elliot Long, Michael Barrett, Joanne Grindlay, and Domenic R Cincotta
- Subjects
Male ,medicine.medical_specialty ,Victoria ,medicine.medical_treatment ,education ,Airway management ,Decision support systems ,Critical Care and Intensive Care Medicine ,law.invention ,03 medical and health sciences ,Patient safety ,0302 clinical medicine ,Randomized controlled trial ,law ,Intensive care ,Medicine ,Intubation ,Humans ,030212 general & internal medicine ,Original Research ,business.industry ,030208 emergency & critical care medicine ,Emergency department ,Checklist ,Quality assurance ,3. Good health ,Equipment and Supplies ,Emergency medicine ,Emergency Medicine ,Decision Support Systems, Management ,Female ,Patient Safety ,Airway ,business ,Emergency Service, Hospital - Abstract
Background: Safety of emergency intubation may be improved by standardising equipment preparation; the efficacy of cognitive aids is unknown. Methods: This randomised controlled trial compared no cognitive aid (control) with the use of a checklist or picture template for emergency airway equipment preparation in the Emergency Department of The Royal Children's Hospital, Melbourne. Results: Sixty-three participants were recruited, 21 randomised to each group. Equal numbers of nursing, junior medical, and senior medical staff were included in each group. Compared to controls, the checklist or template group had significantly lower equipment omission rates (median 30 % IQR 20-40 % control, median 10 % IQR 5-10 % checklist, median 10 % IQR 5-20 % template; p < 0.05). The combined omission rate and sizing error rate was lower using a checklist or template (median 35 % IQR 30-45 % control, median 15 % IQR 10-20 % checklist, median 15 % IQR 10-30 % template; p < 0.05). The template group had less variation in equipment location compared to checklist or controls. There was no significant difference in preparation time in controls (mean 3 min 14 s sd 56 s) compared to checklist (mean 3 min 46 s sd 1 min 15 s) or template (mean 3 min 6 s sd 49 s; p = 0.06). Discussion: Template use reduces variation in airway equipment location during preparation foremergency intubation, with an equivalent reduction in equipment omission rate to the use of a checklist. The use of a template for equipment preparation and a checklist for team, patient, and monitoring preparation may provide the best combination of both cognitive aids. Conclusions: The use of a cognitive aid for emergency airway equipment preparation reduces errors of omission. Template utilisation reduces variation in equipment location. Trial registration: Australian and New Zealand Trials Registry ( ACTRN12615000541505 ). Emergency Department of The Royal Children’s Hospital, Melbourne, Australia National Health and Medical Research Council Centre of Research Excellence Grant for Paediatric Emergency Medicine, Canberra, ACT, Australia Victorian Governments Infrastructure Support Program, Melbourne, Australia
- Published
- 2016
24. Gröbner bases and combinatorics for binary codes
- Author
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M. Borges-Quintana, Edgar Martínez-Moro, Patrick Fitzpatrick, and M. A. Borges-Trenard
- Subjects
Discrete mathematics ,Code (set theory) ,Algebra and Number Theory ,Ideal (set theory) ,Mathematics::Commutative Algebra ,Applied Mathematics ,Linear code ,Combinatorics ,Gröbner basis ,Graph (abstract data type) ,Cycle basis ,Binary code ,Decoding methods ,Mathematics - Abstract
In this paper we introduce a binomial ideal derived from a binary linear code. We present some applications of a Grobner basis of this ideal with respect to a total degree ordering. In the first application we give a decoding method for the code. In the second one, by associating the code with the set of cycles in a graph, we can solve the problem of finding all codewords of minimal length (minimal cycles in a graph), and show how to find a minimal cycle basis. Finally we discuss some results on the computation of the Grobner basis.
- Published
- 2008
25. Gröbner basis approach to list decoding of algebraic geometry codes
- Author
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Patrick Fitzpatrick and Henry O’keeffe
- Subjects
Block code ,Algebra and Number Theory ,Berlekamp–Welch algorithm ,Applied Mathematics ,Concatenated error correction code ,List decoding ,Reed–Muller code ,Data_CODINGANDINFORMATIONTHEORY ,Sequential decoding ,Linear code ,Algebra ,Reed–Solomon error correction ,ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION ,Computer Science::Information Theory ,Mathematics - Abstract
We show how our Grobner basis algorithm, which was previously applied to list decoding of Reed Solomon codes, can be used in the hard and soft decision list decoding of Algebraic Geometry codes. In addition, we present a linear functional version of our Grobner basis algorithm in order to facilitate comparisons with methods based on duality.
- Published
- 2007
26. Severe combined immunodeficiency syndrome presenting with disseminated BCG infection
- Author
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Andrea Malone, Patrick J. Gavin, Eilis Twomey, Timothy Ronan Leahy, Michael Jackson, Patrick Fitzpatrick, Mario Abinun, Zohreh Nademi, and Jane Leonard
- Subjects
Male ,medicine.medical_specialty ,Resuscitation ,Bone disease ,Disseminated BCG Infection ,Opportunistic Infections ,Irritability ,Lethargy ,Internal medicine ,medicine ,Humans ,Tuberculosis ,Respiratory distress ,business.industry ,Infant ,medicine.disease ,Dermatology ,Mycobacterium bovis ,Rheumatology ,Severe Combined Immunodeficiency Syndrome ,Pediatrics, Perinatology and Child Health ,Immunology ,BCG Vaccine ,Severe Combined Immunodeficiency ,medicine.symptom ,business - Abstract
A 4-month-old boy presented with fever, lethargy and irritability on a background of faltering growth. He was pale, febrile, in respiratory distress. He had red papular skin lesions on torso and a large discharging ulcer at BCG inoculation site (administered shortly after birth) (figure 1). Figure 1 BCG inoculation site on left upper arm. He was anaemic (haemoglobin 4.8 g/dL) and lymphopenic (1.16×109/L) …
- Published
- 2015
27. Enumeration of inequivalent irreducible Goppa codes
- Author
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John A. Ryan and Patrick Fitzpatrick
- Subjects
Discrete mathematics ,Degree (graph theory) ,Enumeration ,Applied Mathematics ,Cauchy–Frobenius theorem ,Upper and lower bounds ,Combinatorics ,Integer ,Classical Goppa codes ,Goppa code ,Discrete Mathematics and Combinatorics ,Prime power ,Mathematics - Abstract
We consider irreducible Goppa codes over Fq of length qn defined by polynomials of degree r, where q is a prime power and n,r are arbitrary positive integers. We obtain an upper bound on the number of such codes.
- Published
- 2006
- Full Text
- View/download PDF
28. Algorithm and architecture for a Galois field multiplicative arithmetic processor
- Author
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Patrick Fitzpatrick and Emanuel Popovici
- Subjects
Multiplication algorithm ,Computational complexity theory ,business.industry ,Polynomial ring ,Multiplicative function ,Galois theory ,Cryptography ,Library and Information Sciences ,Computer Science Applications ,Finite field ,Arithmetic ,Error detection and correction ,business ,Algorithm ,Information Systems ,Mathematics - Abstract
We present a new algorithm for generic multiplicative computations of the form ab/c in GF(p/sup m/), including multiplication, inversion, squaring, and division. The algorithm is based on solving a sequence of congruences that are derived from the theory of Grobner bases in modules over the polynomial ring GF(p)[x]. Its corresponding hardware and software architectures can be successfully used in applications such as error control coding and cryptography. We describe a versatile circuit associated with the algorithm for the most important case p=2. The same hardware can be used for a range of field sizes thus permitting applications in which different levels of error control or of security are required by different classes of user. The operations listed are all performed by the hardware in the same number of clock cycles, which prevents certain side-channel attacks. The loss in performance by having 2m iterations for multiplication is compensated by the full parameterization of the Galois field and the ability to perform division and multiplication in parallel.
- Published
- 2003
29. Hamming metric decoding of alternant codes over Galois rings
- Author
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Eimear Byrne and Patrick Fitzpatrick
- Subjects
Discrete mathematics ,Polynomial ,Modulo ,List decoding ,Hamming distance ,Sequential decoding ,Library and Information Sciences ,Linear code ,Computer Science Applications ,Combinatorics ,Gröbner basis ,ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION ,Decoding methods ,Information Systems ,Mathematics - Abstract
The standard decoding procedure for alternant codes over fields centers on solving a key equation which relates an error locator polynomial and an error evaluator polynomial by a syndrome sequence. We extend this technique to decode alternant codes over Galois rings. We consider the module M={(a, b): as/spl equiv/b mod x/sup r/} of all solutions to the key equation where s is the syndrome polynomial and r, is the number of rows in a parity-check matrix for the code. In decoding we seek a particular solution (/spl Sigma/, /spl Omega/)/spl isin/M which we prove can be found in a Grobner basis for M. We present an iterative algorithm which generates a Grobner basis modulo x/sup k+1/ from a given basis modulo x/sup k/. At the rth step, a Grobner basis for M is found, and the required solution recovered.
- Published
- 2002
30. Faster clean catch urine collection (Quick-Wee method) from infants: randomised controlled trial
- Author
-
Susan Donath, Penelope A Bryant, Shidan Tosif, Sandy M Hopper, Patrick Fitzpatrick, Jonathan Kaufman, and Franz E Babl
- Subjects
Male ,medicine.medical_specialty ,Time Factors ,media_common.quotation_subject ,Urination ,Urine ,PURLs® ,law.invention ,03 medical and health sciences ,Clean catch urine ,0302 clinical medicine ,Randomized controlled trial ,law ,Physical Stimulation ,030225 pediatrics ,medicine ,Humans ,030212 general & internal medicine ,Urine Specimen Collection ,media_common ,business.industry ,Research ,Australia ,Infant, Newborn ,Infant ,General Medicine ,Hospitals, Pediatric ,Confidence interval ,3. Good health ,Surgery ,Clinical trial ,Number needed to treat ,Female ,Emergency Service, Hospital ,business - Abstract
Objective To determine if a simple stimulation method increases the rate of infant voiding for clean catch urine within five minutes. Design Randomised controlled trial. Setting Emergency department of a tertiary paediatric hospital, Australia. Participants 354 infants (aged 1-12 months) requiring urine sample collection as determined by the treating clinician. 10 infants were subsequently excluded. Interventions Infants were randomised to either gentle suprapubic cutaneous stimulation (n=174) using gauze soaked in cold fluid (the Quick-Wee method) or standard clean catch urine with no additional stimulation (n=170), for five minutes. Main outcome measures The primary outcome was voiding of urine within five minutes. Secondary outcomes were successful collection of a urine sample, contamination rate, and parental and clinician satisfaction with the method. Results The Quick-Wee method resulted in a significantly higher rate of voiding within five minutes compared with standard clean catch urine (31% v 12%, P
- Published
- 2017
31. Counting irreducible Goppa codes
- Author
-
Patrick Fitzpatrick and John A. Ryan
- Subjects
Combinatorics ,Discrete mathematics ,Degree (graph theory) ,General Mathematics ,Goppa code ,Field (mathematics) ,Automorphism ,Mathematics - Abstract
We consider ineducible Goppa codes of length qm over Fq defined by polynomials of degree r, where q = pt and p, m, r are distinct primes. The number of such codes, inequivalent under coordinate permutations and field automorphisms, is determined.
- Published
- 2001
32. Gröbner Bases over Galois Rings with an Application to Decoding Alternant Codes
- Author
-
Eimear Byrne and Patrick Fitzpatrick
- Subjects
Discrete mathematics ,Polynomial ,Algebra and Number Theory ,Mathematics::Commutative Algebra ,Division algorithm ,Extension (predicate logic) ,Characterization (mathematics) ,Method of undetermined coefficients ,Combinatorics ,Computational Mathematics ,Gröbner basis ,Finite field ,ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION ,Computer Science::Symbolic Computation ,Decoding methods ,Mathematics - Abstract
We develop a theory of Gröbner bases over Galois rings, following the usual formulation for Gröbner bases over finite fields. Our treatment includes a division algorithm, a characterization of Gröbner bases, and an extension of Buchberger’s algorithm. One application is towards the problem of decoding alternant codes over Galois rings. To this end we consider the module M= {(a, b) :aS≡b modxr} of all solutions to the so-called key equation for alternant codes, where S is a syndrome polynomial. In decoding, a particular solution (Σ, Ω) ∈M is sought satisfying certain conditions, and such a solution can be found in a Gröbner basis of M. Applying techniques introduced in the first part of this paper, we give an algorithm which returns the required solution.
- Published
- 2001
33. The number of inequivalent irreducible Goppa codes
- Author
-
Patrick Fitzpatrick and John A. Ryan
- Subjects
Discrete mathematics ,Combinatorics ,Degree (graph theory) ,Applied Mathematics ,Goppa code ,Discrete Mathematics and Combinatorics ,Field (mathematics) ,Automorphism ,Mathematics - Abstract
We consider irreducible Goppa codes of length qm over Fq defined by polynomials of degree r, where q = pt and p, m, r are distinct primes. The number of such codes, inequivalent under coordinate permutations and field automorphisms, is determined.
- Published
- 2001
34. Comparison of Two Algorithms for Decoding Alternant Codes
- Author
-
Patrick Fitzpatrick and Sylvia M. Jennings
- Subjects
Algebra and Number Theory ,Computational complexity theory ,Berlekamp–Welch algorithm ,Applied Mathematics ,ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION ,Theory of computation ,Key (cryptography) ,Berlekamp–Massey algorithm ,Algorithm ,Berlekamp's algorithm ,Decoding methods ,Mathematics ,Equation solving - Abstract
We compare the key equation solving algorithm introduced by Fitzpatrick to the Berlekamp-Massey algorithm. Our main result is that the two algorithms have the same computational complexity. It follows that in practice Fitzpatricks algorithm improves on Berlekamp-Massey since it uses less storage and has a simpler control structure. We also give an improved version of Fitzpatricks algorithm and a new simplified proof of the central inductive step in the argument.
- Published
- 1998
35. Fault Tolerant Faddeeva Algorithm
- Author
-
Maura P. Connolly and Patrick Fitzpatrick
- Subjects
Computer Networks and Communications ,Computer science ,Parallel algorithm ,Fault tolerance ,Parallel computing ,Fault (power engineering) ,Column (database) ,Theoretical Computer Science ,Computer Science::Hardware Architecture ,Matrix (mathematics) ,Artificial Intelligence ,Hardware and Architecture ,Schur complement ,Overhead (computing) ,Computer Science::Operating Systems ,Algorithm ,Time complexity ,Software ,Matrix calculus - Abstract
We present an algorithm based fault tolerant scheme suitable for array implementations of the Faddeeva algorithm. Our technique corrects errors due to multiple transient, intermittent, or permanent faults provided these are restricted to a single column of the array. We show how to find the location of the faulty column and to determine the correct Schur complement from the erroneous one. The fault recovery algorithm is of quadratic complexity in the number of rows of the input matrix while the hardware overhead is approximately four times the number of rows.
- Published
- 1998
36. Solving a Multivariable Congruence by Change of Term Order
- Author
-
Patrick Fitzpatrick
- Subjects
Algebra ,Discrete mathematics ,Gröbner basis ,Euclidean algorithm ,Computational Mathematics ,Algebra and Number Theory ,Congruence (geometry) ,Generalization ,Modulo ,Time complexity ,Maximal element ,Mathematics ,Term (time) - Abstract
We consider the congruencea≡∑i=1sbihimodIwhereh1,…,hsare given modulo a zero dimensional idealI. We give two polynomial time algorithms for determining a Gröbner basis, relative to an arbitrary term order, of the moduleMof solutions of the congruence, and, in particular, for finding its minimal element. These are based on a generalization of an algorithm of Faugéreet al. and extend the 1-variable solution techniques that use the Euclidean algorithm and the Berlekamp–Massey algorithm.
- Published
- 1997
- Full Text
- View/download PDF
37. Extending backward error assertions to tolerance of large errors in floating point computations
- Author
-
Patrick Fitzpatrick
- Subjects
Floating point ,Computer science ,Computation ,Reliability (computer networking) ,Linear system ,Fault (power engineering) ,Theoretical Computer Science ,Vector processor ,Computer Science::Hardware Architecture ,Computational Theory and Mathematics ,Hardware and Architecture ,Iterative refinement ,Computer Science::Operating Systems ,Algorithm ,Software - Abstract
The use of backward error assertions combined with iterative refinement has been suggested for the correction of small fault induced errors in the floating point solution of linear systems. We extend this to the correction of large errors, typically caused by the failure of a single processor (or column of processors) in an array.
- Published
- 1997
38. Improved precision of newborn screening for congenital adrenal hyperplasia using weight-adjusted criteria for 17-hydroxyprogesterone levels
- Author
-
David B. Allen, Gary Hoffman, Ronald H. Laessig, Arnold Slyper, Sharon L. Maby, and Patrick Fitzpatrick
- Subjects
Newborn screening ,Pediatrics ,medicine.medical_specialty ,Adrenal Hyperplasia, Congenital ,business.industry ,17-alpha-Hydroxyprogesterone ,Birth weight ,Incidence (epidemiology) ,Body Weight ,Infant, Newborn ,Infant, Low Birth Weight ,Hyperplasia ,medicine.disease ,Low birth weight ,Neonatal Screening ,Pediatrics, Perinatology and Child Health ,Cohort ,medicine ,Humans ,Hydroxyprogesterone ,False Positive Reactions ,Congenital adrenal hyperplasia ,medicine.symptom ,business - Abstract
Objective: To evaluate the efficacy and efficiency of weight-adjusted threshold levels for 17-hydroxyprogesterone (17-OHP) in screening newborn infants for 21-hydroxylase deficiency–congenital adrenal hyperplasia (21-OH-D–CAH). Design: Analysis of the number of false-positive reports and diagnoses in infants, of 21-OH-D–CAH with the use of two strategies. Before October 1993, separate criteria for definite abnormal 17-OHP levels were established and implemented for 41,846 infants on the basis of birth weight: either less than 2200 gm (17-OHP level, 90 ng/ml) or 2200 gm or more (40 ng/ml). To reduce the burden of follow-up testing in low birth weight infants, criteria for definite abnormal 17-OHP results were statistically determined for four, rather than two, birth weight divisions: 1299 gm or less (17-OHP level ≥165 ng/ml), 1300 to 1600 gm (≥135 ng/ml), 1700 to 2200 gm (≥90 ng/ml), and more than 2200 gm (≥40 ng/ml). These criteria were applied to the next 149,684 infants screened, and rates of false-positive test results and of false-positive diagnoses of 21-OH-D–CAH were compared. Results: Before implementation of four-tiered weight-adjusted 17-OHP criteria, 205 definite abnormal reports yielded four confirmed cases of 21-OH-D–CAH (positive predictive value = 2%; incidence of 21-OH-D–CAH = 1 in 10,461). With the revised criteria, 61 of 149,684 infants had definite abnormal results and 14 cases of 21-OH-D–CAH were confirmed (positive predictive value, 20%; incidence of 21-OH-D–CAH, 1 in 10,692). No undetected severe cases of 21-OH-D–CAH have been subsequently reported. Conclusions: Weight-adjusted criteria for 17-OHP levels in screening for 21-OH-D–CAH markedly reduced the number of false-positive results requiring immediate follow-up testing, particularly among low birth weight infants. Increased specificity afforded by these criteria was not accompanied by diminished sensitivity in detecting severe cases. Long-term follow-up of this screened cohort will determine whether the goals of newborn screening for 21-OH-D–CAH are adequately and efficiently fulfilled by this approach. (J Pediatr 1997;130:128-33)
- Published
- 1997
39. Assessment of a glutathione S-transferase and related proteins in the gill and digestive gland of Mytilus edulis (L.), as potential organic pollution biomarkers
- Author
-
John O'Halloran, David Sheehan, Patrick Fitzpatrick, and Andrew R. Walsh
- Subjects
geography ,geography.geographical_feature_category ,biology ,Health, Toxicology and Mutagenesis ,Clinical Biochemistry ,Environmental pollution ,Estuary ,Glutathione ,biology.organism_classification ,medicine.disease_cause ,Biochemistry ,Molecular biology ,Mytilus ,Toxicology ,Cytosol ,chemistry.chemical_compound ,Glutathione S-transferase ,chemistry ,biology.protein ,medicine ,Specific activity ,Oxidative stress - Abstract
The response of the glutathione S-transferase (GST, EC 2.5.1.18) and related proteins of Mytilus edulis to environmental pollution load was assessed. Mussels were reciprocally transplanted between an industrial estuary (Douglas), a rural estuary (Youghal) and a m arine site (Bantry). In addition, m ussels were sam pled along a pollution gradient in an estuary receiving leather tannery effluent (Colligan). These latter m ussels were previously shown to be subject to oxidative stress resulting from the discharges. GST specific activity of cytosolic extracts from the gill and digestive gland tissues was determ ined for all anim als. Specific activity was shown to vary significantly in anim als from different sites, with highest specific activity always observed in sam ples (local and transplanted) taken from the industrial site. By com parison, the m ussels exposed to tannery discharges displayed no significant alteration in GST specific activity. Total intracellular glutathione (GSH) was also determ ined for sam ples taken from the Douglas and Youghal estuaries but no correlation with pollution load was observed. Using FPLC analysis, we observed no specific effect on the relative levels of the GST and the individual GST related proteins in gill or digestive gland sam ples from local or reciprocally transplanted anim als from Douglas or Youghal. The increase in GST specific activity observed in samples from the industrial estuary are indicative of a possible, specific inductive agent at this site. The results from the tannery site, by com parison, indicate that general oxidative stress does not result in elevated G ST specific activity in M. edulis.
- Published
- 2013
40. On the scalar rational interpolation problem
- Author
-
Patrick Fitzpatrick
- Subjects
Discrete mathematics ,Control and Optimization ,Applied Mathematics ,Polynomial ring ,Scalar (mathematics) ,Free module ,Rational function ,Error control coding ,Gröbner basis ,Control and Systems Engineering ,Signal Processing ,Parametrization ,Interpolation ,Mathematics - Abstract
A new technique is derived for determining a parametrization of all minimal complexity rational functionsa(x)/b(x) interpolating an arbitrary sequence of points. Complexity is measured in terms of max{deg(a), deg(b) +r } wherer is an arbitrary integer (so thatr=0 corresponds to the McMillan degree). Our construction uses Grobner bases of submodules of the free module of rank 2 over the polynomial ring in one variable and extends previous work on the key equation of error control coding theory.
- Published
- 1996
41. Assessment of a Parametric Hurricane Surface Wind Model for Tropical Cyclones in the Gulf of Mexico
- Author
-
Kelin Hu, Qin Chen, and Patrick Fitzpatrick
- Subjects
Atlantic hurricane ,010504 meteorology & atmospheric sciences ,Meteorology ,Subtropical cyclone ,Tropical cyclone scales ,010502 geochemistry & geophysics ,01 natural sciences ,Climatology ,Tropical cyclone basins ,Extratropical cyclone ,Cyclone ,Pacific hurricane ,Tropical cyclone ,Geology ,0105 earth and related environmental sciences - Published
- 2012
42. The Berlekamp-Massey algorithm and linear recurring sequences over a factorial domain
- Author
-
Graham H. Norton and Patrick Fitzpatrick
- Subjects
Combinatorics ,Discrete mathematics ,Reciprocal polynomial ,Algebra and Number Theory ,Alternating polynomial ,Stable polynomial ,Minimal polynomial (linear algebra) ,Applied Mathematics ,Degree of a polynomial ,Matrix polynomial ,Characteristic polynomial ,Mathematics ,Square-free polynomial - Abstract
We present an extended polynomial remainder sequence algorithm XPRS for R[X] whereR is a domain. From this we derive a Berlekamp-Massey algorithm BM/R overR. We show that if (α) is a linear recurring sequence in a factorial domainU, then the characteristic polynomials for (α) form aprincipal ideal which is generated by a primitive minimal polynomial. Moreover, this generator ismonic when U[[X]] is factorial (for example, whenU is Z orK[X1,X2,...,Xn] whereK is a field). From XPRS we derive an algorithm MINPOL for determining the minimal polynomial of (α) when an upper bound on the degree of some characteristic polynomial and sufficiently many initial terms of (α) are known. We also show how to obtain a Berlekamp-Massey type minimal polynomial algorithm from BM/U and state BM_MINPOL/K explicitly with a further refinement. Examples are given forU=Z, GF(2)[Y].
- Published
- 1995
43. The QuickWee trial: protocol for a randomised controlled trial of gentle suprapubic cutaneous stimulation to hasten non-invasive urine collection from infants
- Author
-
Patrick Fitzpatrick, Sandy M Hopper, Shidan Tosif, Susan Donath, Franz E Babl, Jonathan Kaufman, and Penelope A Bryant
- Subjects
Male ,Pediatrics ,medicine.medical_specialty ,Urinary system ,law.invention ,Tertiary Care Centers ,03 medical and health sciences ,0302 clinical medicine ,Randomized controlled trial ,law ,Physical Stimulation ,030225 pediatrics ,Protocol ,medicine ,Humans ,030212 general & internal medicine ,Urine Specimen Collection ,business.industry ,Genitourinary system ,Australia ,Infant ,Paediatrics ,General Medicine ,Emergency department ,Hospitals, Pediatric ,GENITOURINARY MEDICINE ,3. Good health ,Cold Temperature ,Clinical trial ,Urinary Tract Infections ,Female ,Emergency Service, Hospital ,business ,Urine collection ,Cutaneous stimulation - Abstract
Introduction Urinary tract infections (UTIs) are common in young children. Urine sample collection is required to diagnose or exclude UTI; however, current collection methods for pre-continent children all have limitations and guidelines vary. Clean catch urine (CCU) collection is a common and favoured non-invasive collection method, despite its high contamination rates and time-consuming nature. This study aims to establish whether gentle suprapubic cutaneous stimulation with cold fluid-soaked gauze can improve the rate of voiding for CCU within 5 min in young pre-continent children. Methods and analysis This study is a randomised controlled trial of 354 infants (aged 1–12 months) who require urine sample collection, conducted in a single emergency department in a tertiary paediatric hospital in Melbourne, Australia. After standard urogenital cleaning, patients will be randomised to either a novel technique of suprapubic cutaneous stimulation using cold saline-soaked gauze in circular motions or no stimulation. The study period is 5 min, after which care is determined by the treating clinician if a urine sample has not been collected. Primary outcome: whether the child voids within 5 min (yes/no). Secondary outcomes: parental and clinician satisfaction with the method, success in catching a urine sample if the child voids, and sample contamination rates. This trial will allow the definitive assessment of this novel technique, gentle suprapubic cutaneous stimulation with cold saline-soaked gauze, and its utility to hasten non-invasive urine collection in infants. Ethics and dissemination The study has hospital ethics approval and is registered with the Australian New Zealand Clinical Trials Registry—ACTRN12615000754549. The results of the study will be published in a peer-reviewed journal. Trial registration number ACTRN12615000754549; Pre-results.
- Published
- 2016
44. Assessment of the impact of organic pollutants on goby (Zosterisessor ophiocephalus) and mussel (Mytilus galloprovincialis) from the Venice Lagoon, Italy: Biochemical studies
- Author
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Cristina Nasci, L.D. Peters, Nicola Wootton, Patrick Fitzpatrick, Philippe Lemaire, Valentino U. Fossato, David R. Livingstone, Cinta Porte, Lars Förlin, Peter S. Goldfarb, and Anne Matthews
- Subjects
Pollution ,Pollutant ,animal structures ,Antioxidant ,media_common.quotation_subject ,medicine.medical_treatment ,Goby ,General Medicine ,Mussel ,Aquatic Science ,Biology ,Oceanography ,biology.organism_classification ,Mytilus ,Superoxide dismutase ,Catalase ,Environmental chemistry ,biology.protein ,medicine ,media_common - Abstract
The use of cytochrome P4501A (CYP1A) and other measurements as biomarkers was investigated in liver of goby (Z. ophiocephalus) and digestive gland of mussel (M. galloprovincialis) from several sites in the Venice lagoon as part of the UNESCO-MURST Venice Lagoon Ecosystem Project. Most tissue contaminants (PAHs, PCBs, DDTs) and biochemical measurements varied seasonally. Elevated 7-ethoxyresorufin O-deethylase activity and CYP1A-protein levels in goby were correlated with high tissue contaminant levels at the industrial Porto Marghera site. On occasions, activities of the antioxidant enzymes catalase and putative DT-diaphorase (resorufin reductase activity) in male but not female goby were also higher at Porto Marghera than other sites, but no differences were seen in Superoxide dismutase (SOD) activity. A range of measurements (SOD, catalase, NADPH-cytochrome c reductase and glutathione S-transferase activities, P450 and ‘418-peak’ contents) in mussel showed little difference between sites. However, indications were obtained of elevated levels of CYP1A1-like mRNA, CYP1A-like protein and metabolism of benzo[a]pyrene to free metabolites in mussels from the Venice lagoon compared to a site in the Adriatic Sea. The studies demonstrate the usefulness of CYP1A as a biomarker for organic pollution in fish and indicate some potential for its application in molluscs.
- Published
- 1995
45. Studies on isoenzymes of glutathione S-transferase in the digestive gland of Mytilus galloprovincialis with exposure to pollution
- Author
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David R. Livingstone, Patrick Fitzpatrick, and David Sheehan
- Subjects
Pollution ,Chromatography ,biology ,media_common.quotation_subject ,Fast protein liquid chromatography ,General Medicine ,Glutathione ,Aquatic Science ,Oceanography ,biology.organism_classification ,Isozyme ,Mytilus ,Cytosol ,chemistry.chemical_compound ,Glutathione S-transferase ,Biochemistry ,chemistry ,biology.protein ,Specific activity ,media_common - Abstract
The possible utility of glutathione S-transferase isoenzymes in affinity purified extracts of digestive gland from Mytilus galloprovincialis as indicators of exposure to organic pollution has been assessed by fast protein liquid chromatography (FPLC) using a Mono-Q ion exchange column. Four main peaks of protein (isoenzymes 1–4) were detected in these chromatographic studies all of which displayed detectable catalytic activity with 1-chloro-2,4-dinitrobenzene and glutathione as substrates. The bulk of the activity with these substrates was associated with isoenzyme 1. The specific activity of cytosolic extracts from six sites in Venice Lagoon and the Adriatic Sea (UNESCO-MURST Venice Lagoon Ecosystem Project) decreased slightly with increasing tissue levels of chemical contaminants (hydrocarbons, PCBs and organochlorines). FPLC of affinity purified extracts from three of these sites was used to assess the possible variation in the levels of individual isoenzymes relative to pollution status. No difference was observed in the levels of these isoenzymes.
- Published
- 1995
46. Characterization of a glutathione S-transferase and a related glutathione-binding protein from gill of the blue mussel, Mytilus edulis
- Author
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P Højrup, T O B Krag, Patrick Fitzpatrick, and David Sheehan
- Subjects
Gills ,Macromolecular Substances ,Protein subunit ,Immunoblotting ,Molecular Sequence Data ,Biochemistry ,Substrate Specificity ,chemistry.chemical_compound ,Affinity chromatography ,Animals ,Amino Acid Sequence ,Amino Acids ,Molecular Biology ,Chromatography, High Pressure Liquid ,Glutathione Transferase ,chemistry.chemical_classification ,Sequence Homology, Amino Acid ,biology ,Sepharose ,Cell Biology ,Glutathione ,Molecular biology ,Bivalvia ,Amino acid ,Isoenzymes ,Kinetics ,Enzyme ,Glutathione S-transferase ,chemistry ,biology.protein ,Protein A ,Glutathione binding ,Protein Binding ,Research Article - Abstract
The major isoenzyme of glutathione S-transferase (GST 1) was purified to homogeneity from cytosolic extracts of Mytilus edulis gill tissue by GSH-agarose affinity chromatography followed by Mono Q ion-exchange f.p.l.c. This enzyme was particularly active with 1-chloro-2,4-dinitrobenzene, ethacrynic acid and cumene hydroperoxide as substrates. Immunoblotting and amino acid sequencing studies indicate that the enzyme belongs to the Pi class of GSTs. A related protein which binds to GSH-agarose was also purified. This GSH-binding protein did not immunoblot with GST antisera and showed no detectable catalytic activity with GST substrates although its N-terminal sequence was similar to Mu-class GSTs. Gel-filtration chromatography indicated that GST 1 is a dimer and the GSH-binding protein a monomer. Mass spectrometry and SDS/PAGE indicate subunit molecular masses of 24 kDa (GST 1) and 25 kDa (GSH-binding protein), respectively. Both proteins have amino acid compositions typical of GSTs.
- Published
- 1995
47. On fault tolerant matrix decomposition
- Author
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Patrick Fitzpatrick
- Subjects
Discrete mathematics ,Computer science ,Systolic array ,Matrix decomposition ,Parity-check matrix ,Factorization ,Signal Processing ,Electrical and Electronic Engineering ,Extended Euclidean algorithm ,Algorithm ,BCH code ,Decoding methods ,Information Systems ,Pivot element - Abstract
We present a fault tolerant algorithm for matrix factorization in the presence of multiple hardware faults which can be used for solving the linear systemAx=b without determining the correctZU decomposition ofA. HereZ is eitherL for ordinary Gaussian decomposition with partial pivoting,X for pairwise or neighbor pivoting (motivated by the Gentleman-Kung systolic array structure), orQ for the usualQR decomposition. Our algorithm generalizes that of Luk and Park whose method allows for the correction of a single error in a single iterate of the matrixU. Using ideas from the theory of error correcting codes we prove that the algorithm of Luk and Park can in fact tolerate multiple errors in multiple iterates ofU provided these are all confined to a single column. We then generalize the algorithm to one that tolerates multiple errors in multiple iterates ofU provided they are confined to two columns. Our procedure for identifying the erroneous columns is based on the extended Euclidean algorithm and it analogous to the decoding algorithms for BCH codes. We indicate how our methods may be adapted to apply to any number of columns and finally we show how to compute a correct factorization ofA.
- Published
- 1994
48. Solution of linear systems of equations in the presence of two transient hardware faults
- Author
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Colin C. Murphy and Patrick Fitzpatrick
- Subjects
business.industry ,Linear system ,System of linear equations ,LU decomposition ,law.invention ,Matrix decomposition ,Computer Science::Hardware Architecture ,law ,Coefficient matrix ,business ,Extended Euclidean algorithm ,Computer Science::Operating Systems ,Algorithm ,Linear equation ,Computer hardware ,BCH code ,Mathematics - Abstract
An algorithmic fault tolerant scheme in presented for the solution via LU decomposition of a linear system of equations in the presence of up to two transient hardware faults. In the general case, where the faults affect arbitrary entries in the coefficient matrix array, the methods are based on an application of the extended Euclidean algorithm scheme for decoding BCH and RS codes. In the special case, where the faults are assumed not to affect (distinct) entries in the same row of the array, a simplified algorithm is given with a corresponding reduction in the hardware overhead. After detection, location and correction of the fault-induced errors, the Sherman—Morrison—Woodbury formula is used to determine the correct solution vector of the linear system, without requiring a valid triangular decomposition of the coefficient matrix.
- Published
- 1993
49. A Gröbner basis technique for Padé approximation
- Author
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Patrick Fitzpatrick and John Flynn
- Subjects
Algebra ,Computational Mathematics ,Gröbner basis ,Euclidean algorithm ,Polynomial ,Algebra and Number Theory ,Mathematics::Commutative Algebra ,Congruence (geometry) ,Generalization ,Padé approximant ,Ideal (ring theory) ,Special case ,Mathematics - Abstract
We consider solving for a and b the congruence a≡bh mod I, where a, b and h are (multivariable) polynomials and I is a polynomial ideal. This is a generalization of the well-known problem of Padé approximation of which decoding Hensel codes is a special case. We show how Gröbner bases of modules may be used to generalize the Euclidean algorithm method of solution of the 1-variable problem.
- Published
- 1992
50. Finding a basis for the characteristic ideal of an n-dimensional linear recurring sequence
- Author
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Patrick Fitzpatrick and Graham H. Norton
- Subjects
Base (group theory) ,Combinatorics ,Sequence ,Polynomial ,Ideal (set theory) ,Basis (linear algebra) ,Sigma ,Field (mathematics) ,Library and Information Sciences ,Information theory ,Computer Science Applications ,Information Systems ,Mathematics - Abstract
An n-dimensional linear recurring sequence ( sigma ) of elements from a field F, for n>or=1 is considered. An algorithm chi -BASE which determines a basis for the ideal characteristic polynomials of ( sigma ) under certain reasonable conditions is presented. This analysis applied to doubly periodic arrays in particular. >
- Published
- 1990
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