Lyapunov functions and strict stability of Caputo fractional differential equations

One of the main properties studied in the qualitative theory of differential equations is the stability of solutions. The stability of fractional order systems is quite recent. There are several approaches in the literature to study stability, one of which is the Lyapunov approach. However, the Lyapunov approach to fractional differential equations causes many difficulties. In this paper a new definition (based on the Caputo fractional Dini derivative) for the derivative of Lyapunov functions to study a nonlinear Caputo fractional differential equation is introduced. Comparison results using this definition and scalar fractional differential equations are presented, and sufficient conditions for strict stability and uniform strict stability are given. Examples are presented to illustrate the theory

Cosmology of the selfaccelerating third order Galileon

In this paper we start from the original formulation of the galileon model with the original choice for couplings to gravity. Within this framework we find that there is still a subset of possible Lagrangians that give selfaccelerating solutions with stable spherically symmetric solutions. This is a certain constrained subset of the third order galileon which has not been explored before. We develop and explore the background cosmological evolution of this model drawing intuition from other even more restricted galileon models. The numerical results confirm the presence of selfacceleration, but also reveals a possible instability with respect to galileon perturbations.Comment: 30 pages, 24 figure

Insights from CREDENCE trial indicate an acute drop in estimated glomerular filtration rate during treatment with canagliflozin with implications for clinical practice

Canagliflozin slows the progression of chronic kidney disease in patients with type 2 diabetes and induces a reversible acute drop in estimated glomerular filtration rate (eGFR), believed to be a hemodynamic effect. Predictors of the initial drop and its association with long-term eGFR trajectories and safety outcomes are unknown. To assess this, we performed a post-hoc analysis of 4289 participants in the CREDENCE trial with type 2 diabetes and chronic kidney disease equally split into treatment and placebo groups who had eGFR measured at both baseline and week three. The eGFR was categorized at week three as greater than a 10% decline; between 0 and 10% decline; and no decline. Long-term eGFR trajectories and safety outcomes were estimated in each category of acute eGFR change by linear mixed effects models and Cox regression after adjustment for baseline characteristics and medications use. Significantly more participants in the canagliflozin (45%) compared to the placebo (21%) group experienced an acute drop in eGFR over 10%. An over 30% drop occurred infrequently (4% of participants with canagliflozin and 2% with placebo). The odds ratio for a drop in eGFR over 10% with canagliflozin compared to placebo was significant at 3.03 (95% confidence interval 2.65, 3.47). Following the initial drop in eGFR, multivariable adjusted long-term eGFR trajectories, as well as overall and kidney safety profiles, in those treated with canagliflozin were similar across eGFR decline categories. Thus, although acute drops in eGFR over 10% occurred in nearly half of all participants following initiation of canagliflozin, the clinical benefit of canagliflozin was observed regardless. Additionally, safety outcomes were similar among subgroups of acute eGFR drop

Evaluating the Effects of Canagliflozin on Cardiovascular and Renal Events in Patients with Type 2 Diabetes and Chronic Kidney Disease According to Baseline HbA1c, Including Those with HbA1c <7%: Results From the CREDENCE Trial

Traditional management of diabetes mellitus has focused on glycemic control, beginning with lifestyle changes, followed by metformin, and then other classes of antiglycemic agents.1 Sodium glucose co-transporter 2 (SGLT2) inhibitors reduce cardiovascular (CV) events, including CV death, myocardial infarction (MI) and heart failure, and slow progression of renal dysfunction, including prevention of end-stage kidney disease (ESKD).2-3 Because initial clinical trials included mostly patients with baseline HbA1c >7%, current guidelines have recommended this class as add-on therapy for patients whose HbA1c is not at goal, typically ≥7%.1 We hypothesized that there would be similar benefits on CV and renal endpoints regardless of baseline HbA1c, including those with HbA1c <7%

Effects of Canagliflozin on Cardiovascular, Renal, and Safety Outcomes in Participants With Type 2 Diabetes and Chronic Kidney Disease According to History of Heart Failure: Results From the CREDENCE Trial

We aimed to assess the efficacy and safety of canagliflozin in patients with type 2 diabetes and nephropathy according to prior history of heart failure in the Canagliflozin and Renal Events in Diabetes With Established Nephropathy Clinical Evaluation (CREDENCE) trial. We found that participants with a prior history of heart failure at baseline (15%) were more likely to be older, female, white, have a history of atherosclerotic cardiovascular disease, and use diuretics and beta blockers (all P0.150). These results support the efficacy and safety of canagliflozin in patients with type 2 diabetes and nephropathy regardless of prior history of heart failure

Cardiorenal protective effects of canagliflozin in CREDENCE according to glucose lowering

Introduction Relationships between glycemic-lowering effects of sodium glucose co-transporter 2 inhibitors and impact on kidney and cardiovascular outcomes are uncertain. Research design and methods We analyzed 4395 individuals with prebaseline and postbaseline hemoglobin A1c (HbA1c) randomized to canagliflozin (n=2193) or placebo (n=2202) in The Canagliflozin and Renal Events in Diabetes with Established Nephropathy Clinical Evaluation trial. Effects on HbA1c were assessed using mixed models. Mediation of treatment effects by achieved glycemic control was analyzed using proportional hazards regression with and without adjustment for achieved HbA1c. End points included combined kidney or cardiovascular death, end-stage kidney disease or doubling of serum creatinine (primary trial outcome), and individual end point components. Results HbA1c lowering was modified by baseline estimated glomerular filtration rate (eGFR). For baseline eGFR 60-90, 45-59, and 30-44 mL/min/1.73 m 2, overall HbA1c (canagliflozin vs placebo) decreased by -0.24%, -0.14%, and -0.08% respectively and likelihood of >0.5% decrease in HbA1c decreased with ORs of 1.47 (95% CI 1.27 to 1.67), 1.12 (0.94 to 1.33) and 0.99 (0.83 to 1.18), respectively. Adjustment for postbaseline HbA1c marginally attenuated canagliflozin effects on primary and kidney composite outcomes: unadjusted HR 0.67 (95% CI 0.57 to 0.80) and 0.66 (95% CI 0.53 to 0.81); adjusted for week 13 HbA1c, HR 0.71 (95% CI 0.060 to 0.84) and 0.68 (95% CI 0.55 to 0.83). Results adjusted for time-varying HbA1c or HbA1c as a cubic spline were similar and consistent with preserved clinical benefits across a range of excellent and poor glycemic control. Conclusions The glycemic effects of canagliflozin are attenuated at lower eGFR but effects on kidney and cardiac end points are preserved. Non-glycemic effects may be primarily responsible for the kidney and cardioprotective benefits of canagliflozin.2

Refined Checks and Exact Dualities in Three Dimensions

We discuss and provide nontrivial evidence for a large class of dualities in three-dimensional field theories with different gauge groups. We match the full partition functions of the dual phases for any value of the couplings to underpin our proposals. We focus on two classes of models. The first class, motivated by the AdS/CFT conjecture, consists of necklace U(N) quiver gauge theories with non chiral matter fields. We also consider orientifold projections and establish dualities among necklace quivers with alternating orthogonal and symplectic groups. The second class consists of theories with tensor matter fields with free theory duals. In most of these cases the R-symmetry mixes with IR accidental symmetries and we develop the prescription to include their contribution into the partition function and the extremization problem accordingly.Comment: 38 pages, 3 figure, using jheppu

Blood pressure effects of canagliflozin and clinical outcomes in type 2 diabetes and chronic kidney disease: Insights from the CREDENCE trial

Background: People with type 2 diabetes mellitus (T2DM) and chronic kidney disease (CKD) experience a high burden of hypertension but the magnitude and consistency of blood pressure (BP) lowering with canagliflozin in this population is uncertain. Whether the effects of canagliflozin on kidney and cardiovascular outcomes vary by baseline BP or BP lowering therapy is also unknown. Methods: The CREDENCE trial randomized people with T2DM and CKD to canagliflozin or placebo. Post-hoc, we investigated the effect of canagliflozin on systolic BP across subgroups defined by baseline systolic BP, number of BP lowering drug classes, and history of apparent treatment-resistant hypertension (BP ≥130/80 mmHg while receiving ≥3 classes of BP lowering drugs, including a diuretic). We also assessed whether effects on clinical outcomes differed across these subgroups. Results: The trial included 4,401 participants of whom 3,361 (76.4%) had baseline systolic BP ≥130 mmHg, and 1371 (31.2%) had resistant hypertension. By week 3, canagliflozin reduced systolic BP by 3.50mmHg (95% CI, -4.27 to -2.72), an effect maintained over the duration of the trial, with similar reductions across BP and BP lowering therapy subgroups (all P-interaction ≥0.05). Canagliflozin also reduced the need for initiation of additional BP lowering agents during the trial (HR 0.68, 95% CI 0.61-0.75). The effect of canagliflozin on kidney failure, doubling of serum creatinine, or death due to kidney or cardiovascular disease (HR 0.70, 95% CI 0.59-0.82) was consistent across BP and BP lowering therapy subgroups (all P-interaction ≥0.35), as were effects on other key kidney, cardiovascular and safety outcomes. Conclusions: In people with T2DM and CKD, canagliflozin lowers systolic BP across all BP defined subgroups and reduces the need for additional BP lowering agents. These findings support use of canagliflozin for end-organ protection and as an adjunct BP lowering therapy in people with CKD. Clinical Trial Registration: URL: https://clinicaltrials.gov. Unique Identifier: NCT02065791