For a pair of random Gaussian integers chosen uniformly and independently from the set of Gaussian integers of norm x or less as x goes to infinity, we find asymptotics for the average norm of their greatest common divisor, with explicit error terms. We also present results for higher moments along with computational data which support the results for the second, third, fourth, and fifth moments. The analogous question for integers is studied by Diaconis and Erdös.

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Involve : a Journal of Mathematics

Volume overload represents a hallmark clinical feature linked to the development and progression of heart failure (HF). Alleviating signs and symptoms of volume overload represents a foundational HF treatment target that is achieved using loop diuretics in the acute and chronic setting. Recent work has provided evidence to support guideline-directed medical therapies, such as sodium glucose cotransporter 2 (SGLT2) inhibitors and mineralocorticoid receptor (MR) antagonists, as important adjunct diuretics that may act synergistically when used with background loop diuretics in people with chronic HF. Furthermore, there is growing interest in understanding the role of SGLT2 inhibitors, carbonic anhydrase inhibitors, thiazide diuretics, and MR antagonists in treating volume overload in patients hospitalized for acute HF, particularly in the setting of loop diuretic resistance. Thus, the current review demonstrates that: 1) SGLT2 inhibitors and MR antagonists confer long-term cardioprotection in chronic HF patients but it is unclear if natriuresis or diuresis represents the primary mechanisms for this benefit, 2) SGLT2 inhibitors, carbonic anhydrase inhibitors, and thiazide diuretics increase natriuresis in the acute HF setting, but implications on long-term outcomes remain unclear and warrants further investigation, and 3) a multi-nephron segment approach, using agents that act on distinct segments of the nephron, potentiate diuresis to alleviate signs and symptoms of volume overload in acute HF.

Proximal versus distal diuretics in congestive heart failure.

Nephrology, Dialysis, Transplantation

Cardiogenic shock (CS) is characterized by low cardiac output and sustained tissue hypoperfusion that may result in end-organ dysfunction and death. CS is associated with high short-term mortality, and its management remains challenging despite recent advances in therapeutic options. Timely diagnosis and multidisciplinary team-based management have demonstrated favourable effects on outcomes. We aimed to review evidence-based practices for managing patients with ischemic and non-ischemic CS, detailing the multi-organ supports needed in this critically ill patient population.

Management of cardiogenic shock: a narrative review.

Annals of Intensive Care

The eosinophilias encompass a broad range of non-hematologic (secondary or reactive) and hematologic (primary or clonal) disorders with the potential for end-organ damage.

Hypereosinophilia (HE) has generally been defined as a peripheral blood eosinophil count greater than 1.5&#x2009;&#xd7;&#x2009;109 /L, and may be associated with tissue damage. After the exclusion of secondary causes of eosinophilia, diagnostic evaluation of primary eosinophilias relies on a combination of various tests. They include morphologic review of the blood and marrow, standard cytogenetics, fluorescence in situ hybridization, molecular testing and flow immunophenotyping to detect histopathologic or clonal evidence for an acute or chronic hematolymphoid neoplasm.

Disease prognosis relies on identifying the subtype of eosinophilia. After evaluation of secondary causes of eosinophilia, the 2022 World Health Organization and International Consensus Classification endorse a semi-molecular classification scheme of disease subtypes. This includes the major category "myeloid/lymphoid neoplasms with eosinophilia and tyrosine kinase gene fusions" (MLN-eo-TK), and the MPN subtype, "chronic eosinophilic leukemia" (CEL). Lymphocyte-variant HE is an aberrant T-cell clone-driven reactive eosinophila, and idiopathic hypereosinophilic syndrome (HES) is a diagnosis of exclusion.

The goal of therapy is to mitigate eosinophil-mediated organ damage. For patients with milder forms of eosinophilia (e.g., &lt;1.5&#x2009;&#xd7;&#x2009;109 /L) without symptoms or signs of organ involvement, a watch and wait approach with close follow-up may be undertaken. Identification of rearranged PDGFRA or PDGFRB is critical because of the exquisite responsiveness of these diseases to imatinib. Pemigatinib was recently approved for patients with relapsed or refractory FGFR1-rearranged neoplasms. Corticosteroids are first-line therapy for patients with lymphocyte-variant HE and HES. Hydroxyurea and interferon-&#x3b1; have demonstrated efficacy as initial treatment and in steroid-refractory cases of HES. Mepolizumab, an interleukin-5 (IL-5) antagonist monoclonal antibody, is approved by the U.S Food and Drug Administration for patients with idiopathic HES. Cytotoxic chemotherapy agents, and hematopoietic stem cell transplantation have been used for aggressive forms of HES and CEL, with outcomes reported for limited numbers of patients. Targeted therapies such as the IL-5 receptor antibody benralizumab, IL-5 monoclonal antibody depemokimab, and various tyrosine kinase inhibitors for MLN-eo-TK, are under active investigation.

World Health Organization and International Consensus Classification of eosinophilic disorders: 2024 update on diagnosis, risk stratification, and management.

American Journal of Hematology

The aetiology of heart failure with preserved ejection fraction (HFpEF) is heterogenous and overlaps with that of several comorbidities like atrial fibrillation, diabetes mellitus, chronic kidney disease, valvular heart disease, iron deficiency, or sarcopenia. The diagnosis of HFpEF involves evaluating cardiac dysfunction through imaging techniques and assessing increased left ventricular filling pressure, which can be measured directly or estimated through various proxies including natriuretic peptides. To better narrow down the differential diagnosis of HFpEF, European and American heart failure guidelines advocate the use of different algorithms including comorbidities that require diagnosis and rigorous treatment during the evaluation process. Therapeutic recommendations differ between guidelines. Whilst sodium glucose transporter 2 inhibitors have a solid evidence base, the recommendations differ with regard to the use of inhibitors of the renin-angiotensin-aldosterone axis. Unless indicated for specific comorbidities, the use of beta-blockers should be discouraged in HFpEF. The aim of this article is to provide an overview of the current state of the art in HFpEF diagnosis, clinical evaluation, and treatment.

Heart failure with preserved ejection fraction: diagnosis, risk assessment, and treatment.

Clinical Research in Cardiology : Official Journal of the German Cardiac Society

Chronic insomnia affects 5% to 10% of the US population, increasing the demand for treatment options and the corresponding research to prove their validity.1 This review compares recommendations from 3 clinical guidelines and summarizes hypnotic medications, including their newly reported side effects not mentioned in the guidelines. In addition, we aim to provide an overview of what pharmacotherapies are available for prescribers and patients.

A literature search was conducted for articles published prior to January 10, 2022, and case reports and clinical studies were retrieved from PubMed and Google Scholar.

Definitive conclusions cannot be drawn regarding the safety and efficacy of medications reviewed; however, trends are apparent. All 3 guidelines included in this review remarked most treatment recommendations as weak except for cognitive behavioral therapy for insomnia, which is effective but not readily available. Furthermore, based on the 15 case reports and 13 clinical studies presented in this review, many of the medications used for treatment of insomnia present safety concerns.

Benzodiazepines and benzodiazepine receptor agonists are commonly used hypnotic agents with the "Z-drugs" having robust data establishing their efficacy for the short-term treatment of chronic insomnia. However, significant adverse effects related to the central nervous system (CNS), including developing tolerance, addiction, CNS depression, and amnesia, remain barriers to their long-term use. In comparison, newer agents present more favorable side-effect profiles although with less established efficacy. Additionally, off-label agents, including antidepressants, antihistamines, and natural supplements, are discussed due to their prominent use.

Efficacy and safety of pharmacotherapy in chronic insomnia: A review of clinical guidelines and case reports.

Mental Health Clinician

Fluid volumes in adults with sepsis.

Academic Emergency Medicine

The three pathophysiologic contributors to septic shock include varying combinations of hypovolemia (relative &gt; absolute), decreased vascular tone or vasoplegia, and myocardial dysfunction. The three pillars of hemodynamic support include fluid boluses, vasopressors with or without inotrope infusions. The three end-points of hemodynamic resuscitation include an adequate cardiac output (CO), adequate mean arterial pressure (MAP) and diastolic blood pressure (DBP) for organ perfusion, and avoiding congestion (worse filling) parameters. Only 33-50% of septic patients show post-fluid bolus CO improvements; this may be sustained in &#x2265;10% on account of sepsis-mediated glycocalyx injury. A pragmatic approach is to administer a small bolus (10 mL/kg over 20-30 min) and judge the response based on clinical perfusion markers, pressure elements, and congestive features. Vasoplegia marked by low DBP is a major contributor to hypotension in septic shock. Hence, a strategy of restricted fluid bolus with early low-dose norepinephrine (NE) (0.05-0.1 &#xb5;g/kg/min) can be helpful. NE may also be useful in septic myocardial dysfunction (SMD) as an initial agent to maintain adequate coronary perfusion and DBP while minimizing tachycardia and providing inotropy. Severe SMD may benefit from additional inotropy (epinephrine/dobutamine). Except vasopressin, most vasoactive drugs may safely be administered via a peripheral route. The lowest MAP (5th centile for age) may be an acceptable target, provided end-organ perfusion is satisfactory. A clinical individualized approach combining the history, serial physical examination, laboratory analyses, available monitoring tools, and repeated assessment to individualize circulatory support may to lead to better outcomes than one-size-fits-all algorithms.

Hemodynamic Management Strategies in Pediatric Septic Shock: Ten Concepts for the Bedside Practitioner.

Indian Pediatrics

Sudden cardiac death (SCD) accounts for a substantial proportion of mortality in heart failure with reduced ejection fraction (HFrEF), frequently triggered by ventricular arrhythmias (VA). This review aims to analyze the pathophysiological mechanisms underlying VA and SCD in HFrEF and evaluate the effectiveness of guideline-directed medical therapy (GDMT) in reducing SCD. Beta-blockers, angiotensin receptor-neprilysin inhibitors, and mineralocorticoid receptor antagonists have shown significant efficacy in reducing SCD risk. While angiotensin-converting enzyme inhibitors and angiotensin receptor blockers exert beneficial impacts on the renin-angiotensin-aldosterone system, their direct role in SCD prevention remains less clear. Emerging treatments like sodium-glucose cotransporter 2 inhibitors show promise but necessitate further research for conclusive evidence. The favorable outcomes of those molecules on VA are notably attributable to sympathetic nervous system modulation, structural remodeling attenuation, and ion channel stabilization. A multidimensional pharmacological approach targeting those pathophysiological mechanisms offers a complete and synergy approach to reducing SCD risk, thereby highlighting the importance of optimizing GDMT for HFrEF. The current landscape of HFrEF pharmacotherapy is evolving, with ongoing research needed to clarify the full extent of the anti-arrhythmic benefits offered by both existing and new treatments.

Anti-Arrhythmic Effects of Heart Failure Guideline-Directed Medical Therapy and Their Role in the Prevention of Sudden Cardiac Death: From Beta-Blockers to Sodium-Glucose Cotransporter 2 Inhibitors and Beyond.

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