The generalized monotonicity property of the Perron root

The paper presents a new monotonicity property of the Perron root of a nonnegative matrix. It is shown that this new property implies known monotonicity properties and also the Chistyakov two-sided bounds for the Perron root of a block-partitioned nonnegative matrix. Moreover, based on the monotonicity property suggested, the equality cases in Chistyakov's theorem are analyzed. Applications to bounding above the spectral radius of a complex matrix are presented. Bibliography: 9 titles. © 2007 Springer Science+Business Media, Inc

Robust Dropping Criteria for F-norm Minimization Based Sparse Approximate Inverse Preconditioning

Dropping tolerance criteria play a central role in Sparse Approximate Inverse preconditioning. Such criteria have received, however, little attention and have been treated heuristically in the following manner: If the size of an entry is below some empirically small positive quantity, then it is set to zero. The meaning of "small" is vague and has not been considered rigorously. It has not been clear how dropping tolerances affect the quality and effectiveness of a preconditioner $M$. In this paper, we focus on the adaptive Power Sparse Approximate Inverse algorithm and establish a mathematical theory on robust selection criteria for dropping tolerances. Using the theory, we derive an adaptive dropping criterion that is used to drop entries of small magnitude dynamically during the setup process of $M$. The proposed criterion enables us to make $M$ both as sparse as possible as well as to be of comparable quality to the potentially denser matrix which is obtained without dropping. As a byproduct, the theory applies to static F-norm minimization based preconditioning procedures, and a similar dropping criterion is given that can be used to sparsify a matrix after it has been computed by a static sparse approximate inverse procedure. In contrast to the adaptive procedure, dropping in the static procedure does not reduce the setup time of the matrix but makes the application of the sparser $M$ for Krylov iterations cheaper. Numerical experiments reported confirm the theory and illustrate the robustness and effectiveness of the dropping criteria.Comment: 27 pages, 2 figure

Allergy education and training for physicians.

The increasing prevalence of allergic diseases has placed a significant burden on global healthcare and society as whole. This has necessitated a rapid development of "allergy" as a specialist area. However, as allergy is so common and, for most, relatively easy to diagnose and control, all clinicians need to have basic knowledge and competence  to manage  mild disease and recognize when referral is required. The allergology specialty has not yet been recognized in many countries and even where allergy is fully recognized as a specialty, the approach to training in allergy differs significantly. In the light of recent developments in allergy diagnosis and management, there is an urgent need to harmonize core competences for physicians, as well as the standardization of core principles for medical education and post-graduate training in allergy. All physicians and allied health professionals must appreciate the multidisciplinary team (MDT) approach to allergy, which is key to achieving the highest standards in holistic care. Due to worldwide variation in resources and personnel, some MDT roles will need to be absorbed by the treating physician or other healthcare professionals. We draw particular attention to the role of psychological input for all allergy patients, dietetic input in the case of food allergy and patient education to support all patients in the supported self-management of their condition on a daily basis. A strong appreciation of these multidisciplinary aspects will help physicians provide quality patient-centered care. We consider that harmonization of allergy components within undergraduate curricula is crucial to ensure all physicians develop the appropriate allergy-related knowledge and skills, particularly in light of inconsistencies seen in the primary care management of allergy. This review from the World Allergy Organization (WAO) Education and Training Committee also outlines allergy-related competences required of physicians working with allergic patients and provides recommendations to promote harmonization of allergy training and practice worldwide

Результаты неинтервенционного наблюдательного многоцентрового исследования тактики ведения пациентов с аксиальным псориатическим артритом в условиях реальной клинической практики (NiSaXPA)

Psoriatic arthritis (PsA) is a chronic immunoinflammatory disease of the joints, spine and entheses from the group of spondyloarthritis, which is usually observed in patients with psoriasis. In recent years, the axial form of PsA (axPsA) has been actively researched. However, there is insufficient data on approaches to the diagnosis and treatment of patients with axPsA in real-life clinical practice. This article presents the results of an interim analysis of data from a non-interventional multicenter observational study on the treatment of patients with axPsA in real-life clinical practice (NiSaXPA) in Russian centers.Objective: to identify patients with axPsA, their characteristics and describe treatment tactics in real-life clinical practice.Material and methods. Patients with PsA who met the inclusion criteria were prospectively followed up during routine visits to a rheumatologist. Participants' axial radiographs were uploaded to a database in order for it to be confirmed the presence or absence of axPsA by two independent experts, a rheumatologist and a radiologist. Patients with a confirmed axPsA diagnosis participated in a further data collection phase (Visit 2, week 24).Results and discussion. Six hundred patients were enrolled into the study. At the time of analysis, 386 (64.3%) of them (209 men and 177 women) were screened for axPsA. The diagnosis of axPsA was confirmed in 241 (62.4%) cases; these patients formed the Per Protocol (PP) population. The mean age of patients with axPsA in the PP population was 46.30±12.6 years and the body mass index (BMI) was 27.4±5.2 kg/m2 . In 14.9% of patients, the duration of psoriasis was less than 1–5 years, in 21.5% – 5–10 years and in 63.6% – more than 10 years. The duration of PsA symptoms was less than 1–5 years in 31.2 % of patients, 5–10 years in 31.6 % and more than 10 years in 37.2 %. Low disease activity (BASDAI ˂ 4) was achieved in 33.3 % of patients with axPsA at visit 1 and in 64.3 % at visit 2; the BASDAI index declined on average from 4.67±1.95 to 3.31±1.89 points.In real-life clinical practice, patients were most frequently prescribed non-steroidal anti-inflammatory drugs (NSAIDs) – 88.7% and 71.7% (visits 1 and 2, respectively), and synthetic disease-modifying antirheumatic drugs (sDMARDs) –79.1% and 70.7%, respectively; therapy with biologic disease-modifying antirheumatic drugs (bDMARDs) was initiated in 40.2% and 60.6% of patients, respectively.Conclusion. The results of the interim analysis of this observational study showed that in 87.2% of patients who met the CASPAR criteria for PsA there was a suspicion of axial manifestations of PsA on the primary care level. However, only 62.4% of them had a confirmed diagnosis of axPsA on centralized expert assessment, which may indicate a possible overdiagnosis of axial lesions in real-life practice and emphasizes the importance of collaboration between a rheumatologist and a radiologist when analyzing the results of imaging studies. 33.3% of patients with axPsA had low disease activity according to BASDAI at baseline and 64.3% after 24 weeks, meaning that the disease was only adequately controlled in one third of cases despite therapy; the number of these patients doubled after a change in therapy. In real-world clinical practice, patients with axPsA are most commonly prescribed drugs from the NSAID and sDMARD groups; the frequency of use of biologic drugs varied between 40.2 and 60.6% by the end of the observation period.Псориатический артрит (ПсА) – хроническое иммуновоспалительное заболевание суставов, позвоночника и энтезисов из группы спондилоартритов, которое обычно наблюдается у больных псориазом. В последние годы активно изучается аксиальная форма ПсА (аксПсА). Вместе с тем данных о подходах к диагностике и ведению пациентов с аксПсА в реальной клинической практике недостаточно. В настоящей публикации представлены результаты промежуточного анализа данных неинтервенционного наблюдательного многоцентрового исследования тактики ведения пациентов с аксПсА в условиях реальной клинической практики (NiSaXPA) в российских центрах.Цель исследования – выявление пациентов с аксПсА, их характеристика и описание тактики ведения в условиях реальной клинической практики.Материал и методы. Во время плановых визитов к ревматологу проводилось проспективное наблюдение пациентов с ПсА, соответствовавших критериям включения. Аксиальные рентгенограммы участников были загружены в базу данных для подтверждения наличия или отсутствия аксПсА двумя независимыми экспертами – ревматологом и рентгенологом. Пациенты с подтвержденным диагнозом аксПсА участвовали в дальнейшей фазе сбора данных (визит 2, неделя 24).Результаты и обсуждение. В исследование включено 600 пациентов. На момент проведения анализа с целью выявления аксПсА обследовано 386 (64,3%) из них (209 мужчин и 177 женщин). Диагноз аксПсА подтвержден в 241 (62,4%) случае; эти больные составили популяцию по протоколу (PP, Per Protocol). У 145 (37,6%) пациентов аксПсА не выявлен. Возраст пациентов с аксПсА в популяции РР составил в среднем 46,30±12,6 года, индекс массы тела (ИМТ) – 27,4±5,2 кг/м2 . У 14,9% пациентов длительность псориаза была менее 1–5 лет, у 21,5% – 5–10 лет и у 63,6% – более 10 лет. Давность симптомов ПсА у 31,2% пациентов составляла менее 1–5 лет, у 31,6% – 5–10 лет и у 37,2% – более 10 лет. Низкой активности заболевания (BASDAI ˂ 4) к визиту 1 достигли 33,3% больных аксПсА, к визиту 2 – 64,3%; было отмечено снижение индекса BASDAI в среднем с 4,67±1,95 до 3,31±1,89 балла. В реальной клинической практике пациентам наиболее часто назначали нестероидные противовоспалительные препараты (НПВП) – 88,7% и 71,7% (визиты 1 и 2 соответственно) и синтетические базисные противовоспалительные препараты (сБПВП) – 79,1% и 70,7% соответственно; терапия генно-инженерными биологическими препаратами (ГИБП) была инициирована 40,2% и 60,6% больных соответственно.Заключение. Результаты промежуточной оценки данного наблюдательного исследования показали, что у 87,2% пациентов, отвечавших критериям CASPAR для ПсА, исходно при обследовании по месту жительства были заподозрены аксиальные проявления ПсА. Однако при центральной экспертной оценке диагноз аксПсА был верифицирован только у 62,4% из них, что может свидетельствовать о возможной гипердиагностике аксиального поражения в реальной практике и подчеркивает важность кооперации ревматолога и рентгенолога при анализе результатов визуализационных методов обследования. 33,3% пациентов с аксПсА имели низкую активность заболевания по BASDAI исходно и 64,3% – через 24 нед. Таким образом, несмотря на проводимую терапию, адекватно контролировать заболевание удавалось только в трети случаев, после смены терапии число таких пациентов увеличилось вдвое. В реальной клинической практике пациентам с аксПсА наиболее часто назначают препараты из группы НПВП и сБПВП, частота использования ГИБП варьировалась от 40,2 до 60,6% к концу наблюдения

The generalized monotonicity property of the Perron root

The paper presents a new monotonicity property of the Perron root of a nonnegative matrix. It is shown that this new property implies known monotonicity properties and also the Chistyakov two-sided bounds for the Perron root of a block-partitioned nonnegative matrix. Moreover, based on the monotonicity property suggested, the equality cases in Chistyakov's theorem are analyzed. Applications to bounding above the spectral radius of a complex matrix are presented. Bibliography: 9 titles. © 2007 Springer Science+Business Media, Inc

Inequalities for the Perron root related to Levinger's theorem

For the Perron roots of square nonnegative matrices A,B, and A + D-1BTD, where D is a diagonal matrix with positive diagonal entries, the inequality ρ(A + D-1BTD) ≥ ρ(A) + ρ(B) is proved under the assumption that A and B have a common unordered pair of nonorthogonal right and left Perron vectors. The case of equality is analyzed. The above inequality generalizes the inequality ρ(αA + (1 - α)BT) ≥ αρ(A) + (1 - α)ρ(B), proved under stronger assumptions by Bapat, and implies a generalization of Levinger's theorem on the monotonicity of the Perron root of a weighted arithmetic mean of a nonnegative matrix and its transpose. Also, for the Perron root ρ(A(α) ○ (D-1ATD)(c-α)), c ≥ 1, 0≤α≤c, of a weighted (entrywise) geometric mean of A and D-1ATD, where A(α) = (aα ij) and "○" denotes the Hadamard product, the monotonicity property dual to that asserted by generalized Levinger's theorem is established. © 1998 Elsevier Science Inc. All rights reserved

The generalized monotonicity property of the Perron root

The paper presents a new monotonicity property of the Perron root of a nonnegative matrix. It is shown that this new property implies known monotonicity properties and also the Chistyakov two-sided bounds for the Perron root of a block-partitioned nonnegative matrix. Moreover, based on the monotonicity property suggested, the equality cases in Chistyakov's theorem are analyzed. Applications to bounding above the spectral radius of a complex matrix are presented. Bibliography: 9 titles. © 2007 Springer Science+Business Media, Inc

La Patrie : journal quotidien, politique, commercial et littéraire

02 juillet 19091909/07/02 (A69)