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This paper is the last of the series investigating renormalization group aspects of stochastic random matrices, including a Wigner-like disorder. We consider the equilibrium dynamics formalism that can be merged with the Ward identities arising from the large N effective kinetics. We construct a regulator that does not break time-reversal symmetry and show that the resulting flow equations reduce to the equilibrium flow built in our previous works. Finally, we investigate the flow equations beyond the equilibrium dynamics assumption and study the stability of the perturbation around the fluctuation-dissipation theorem.

This paper, as a continuation of our previous investigation [Nucl. Phys. B 1005 (2024) 116582] aims to study the glassy random matrices with quenched Wigner disorder. In this previous work, we have constructed a renormalization group based on the effective deterministic kinetic spectrum emerging from large N limit, and we extended approximate solutions using standard vertex expansion, at the leading order of the derivative expansion. Now in the following work, by introducing the non-trivial Ward identities which come from the (U(N))×2 symmetry broken of the effective kinetic action, we provide in the deep IR the explicit solution of the functional renormalization group for a model with quartic coupling by solving the Hierarchy to all orders in the local sector, which in particular imply the vanishing of the anomalous dimension. The numerical investigations confirm the first-order phase transition discovered in the vertex expansion framework, both in the active and passive schemes. Finally, we extend the discussion to hermitian matrices.

In this paper, we study the equilibrium states of a N×N stochastic complex random matrix M, whose entries evolve in time accordingly with a Langevin equation including both Gaussian white noises and a linear disorder, materialized by the Wigner random matrices. In large N-limit, the disorders behave as effective kinetics, and we examine a coarse-graining over the Wigner spectrum accordingly with two different schemes that we call respectively “active” and “passive”. We then investigate explicit solutions of the nonperturbative renormalization group using vertex and derivative expansion, a simple way to deal with the nonlocal nature of the effective field theory at large N. Our main statement is the existence of well-behaved fixed point solutions and at least some evidence about a discontinuous (first order) phase transition between a condensed and a dilute phase. We finally interpret the resulting phase space regarding the out-of-equilibrium process related to the dynamical phase transitions.

The probability laws associated with random tensors or tensor field theories are traditionally equilibrium distributions. In this paper, we consider a stochastic point of view, and approach the quantization by a Langevin type equation. We especially address the low-temperature behavior of the phase ordering kinetics of a stochastic complex tensor field Ti1⋯id(x,t) of size N and rank d in dimension D. The method we propose use the self averaging property of the tensorial invariants in the large N limit. In this regime, the dynamics is governed by the melonic sector, whose behavior is studied in the quenched limit, where the contractions involving d−1 indices self-average around a diagonal matrix proportional to the identity. The following work especially focuses on the cyclic (i.e. non-branching) melonic sector, and we study the way that the system returns to the equilibrium regime regarding the temperature and the shape of the potential. In particular, we provide a general formula for the transition temperature between these regimes. The manuscript is accompanied by numerical simulations to support the theoretical analysis, and essentially aims to open towards this new field of investigation.

Referring to recent works concerning the functional renormalization group for tensorial group fields theories (Lahoche and Ousmane Samary (2018) [2] and [1]), this paper gives in-depth explanation for, the ambiguity around the search of fixed points in the Wetterich flow equation and the Ward–Takahashi identities. We consider the U(1)-tensors models and discuss the non-existence of phase transition taking into account the Ward-identities as new constraint along the flow. We prove that the quartic melonic tensorial group fields theories without closure constraint are devoid with the fixed points and therefore the phase transitions.

In recent years, interesting investigations of the nonperturbative renormalization group equations for tensorial group field theories have been performed in the truncation method, while completely discarding the Ward identities from their analysis. In this letter, in continuation of our recent series of papers, we present a new framework of the investigation, namely, the effective vertex expansion, allowing us to consider infinite sectors rather than finite-dimensional subspaces of the full theory space. We focus on the ultraviolet behavior and provide a new and complete description of the renormalization group flow constrained with Ward identities.

Introduction: Hepatocyte nuclear factor 1-beta ( HNF1B ) gene variants or the chromosome 17q12 deletion (17q12del) represent the most common monogenic cause of developmental kidney disease. Although neurodevelopmental disorders have been associated with the 17q12del, specific genotype-phenotype associations with respect to kidney function evolution have not yet been fully defined. Here, we aimed to determine whether 17q12del or specific HNF1B variants were associated with kidney survival in a large patient population with HNF1B disease., Methods: This was a retrospective observational study involving 521 patients with HNF1B disease from 14 countries using the European Reference Network for rare kidney diseases with detailed information on the HNF1B genotype ( HNF1B variants or the 17q12del). Median follow-up time was 11 years with 6 visits per patient. The primary end point was progression to chronic kidney disease (CKD) stage 3 (estimated glomerular filtration rate [eGFR] < 60 ml/min per 1.73 m 2 ). Secondary end points were the development of hypomagnesemia or extrarenal disorders, including hyperuricemia and hyperglycemia., Results: Progression toward CKD stage 3 was significantly delayed in patients with the 17q12del compared to patients with HNF1B variants (hazard ratio [HR]: 0.29, 95% confidence interval [CI]: 0.19-0.44, P  < 0.001). Progression toward CKD stage 3 was also significantly delayed when HNF1B variants involved the HNF1B Pit-1, Oct-1, and Unc-86 homeodomain (POU h ) DNA-binding and transactivation domains rather than the POU-specific domain (POU s ) DNA-binding domain (HR: 0.15 [95% CI: 0.06-0.37), P  < 0.001 and HR: 0.25 (95% CI: 0.11-0.57), P  = 0.001, respectively). Finally, the 17q12del was positively associated with hypomagnesemia and negatively associated with hyperuricemia, but not with hyperglycemia., Conclusion: Patients with the 17q12del display a significantly better kidney survival than patients with other HNF1B variants; and for the latter, variants in the POU s DNA-binding domain lead to the poorest kidney survival. These are clinically relevant HNF1B kidney genotype-phenotype correlations that inform genetic counseling., (© 2024 International Society of Nephrology. Published by Elsevier Inc.)

Introduction: Tubulointerstitial nephritis (TIN) and uveitis (TINU) syndrome is a rare disease. The renal prognosis is generally thought to be better in children with TINU syndrome than in adults. However, data are scarce. We aimed to investigate the long-term renal prognosis in a French cohort of children with TINU syndrome., Methods: We performed a national retrospective study including 23 French pediatric nephrology centers enrolling patients with TINU syndrome diagnosed between January 2000 and December 2018., Results: A total of 46 patients were included (52% female, median age 13.8 years). At diagnosis of TIN, the median estimated glomerular filtration rate (eGFR) was 30.6 ml/min per 1.73 m 2 (4.9-62.8). The median time between diagnosis of uveitis and TIN was 0.4 months (-4.1; +17.1). All patients had anterior uveitis, but 12 (29%) were asymptomatic. Nearly all patients (44 of 46) received steroid treatment, and 12 patients (26%) received a second-line therapy. At last follow-up (median 2.8 years), the median eGFR was 87.5 ml/min per 1.73 m 2 (60.3-152.7) and <90 ml/min per 1.73 m 2 in 20 patients., Conclusion: In our study, nearly half of the patients had renal sequelae at last follow-up. Given the possible progression to chronic kidney disease, long-term monitoring of children with TINU syndrome is mandatory. Approximately a quarter of the children had asymptomatic uveitis suggesting all children presenting with TIN should undergo systematic ophthalmologic screening even in the absence of ocular signs., (© 2021 International Society of Nephrology. Published by Elsevier Inc.)

The optimal duration of eculizumab treatment in patients with atypical hemolytic uremic syndrome (aHUS) remains poorly defined. We conducted a prospective national multicenter open-label study to assess eculizumab discontinuation in children and adults with aHUS. Fifty-five patients (including 19 children) discontinued eculizumab (mean treatment duration, 16.5 months). Twenty-eight patients (51%) had rare variants in complement genes, mostly in MCP (n = 12; 22%), CFH (n = 6; 11%), and CFI (n = 6; 10%). At eculizumab discontinuation, 17 (30%) and 4 patients (7%) had stage 3 and 4 chronic kidney disease, respectively. During follow-up, 13 patients (23%; 6 children and 7 adults) experienced aHUS relapse. In multivariable analysis, female sex and presence of a rare variant in a complement gene were associated with an increased risk of aHUS relapse, whereas requirement for dialysis during a previous episode of acute aHUS was not. In addition, increased sC5b-9 plasma level at eculizumab discontinuation was associated with a higher risk of aHUS relapse in all patients and in the subset of carriers with a complement gene rare variant, both by log-rank test and in multivariable analysis. Of the 13 relapsing patients, all of whom restarted eculizumab, 11 regained their baseline renal function and 2 had a worsening of their preexisting chronic kidney disease, including 1 patient who progressed to end-stage renal disease. A strategy of eculizumab discontinuation in aHUS patients based on complement genetics is reasonable and safe. It improves the management and quality of life of a sizeable proportion of aHUS patients while reducing the cost of treatment. This trial was registered at www.clinicaltrials.gov as #NCT02574403., (© 2021 by The American Society of Hematology.)

Socioeconomic status is an important determinant of health. Its impact on kidney transplantation outcome has been studied among adults but data in children are scarce, especially in Europe. Here, we investigate the association between the level of social deprivation (determined by the continuous score European Deprivation Index) and graft failure risk in pediatric kidney transplant recipients. All patients listed under 18 years of age who received a first kidney transplant between 2002 and 2014 in France were included. Of 1050 kidney transplant recipients (males 59%, median age at transplantation 13.2 years, preemptive transplantation 23%), 211 graft failures occurred within a median followup of 5.9 years. Thirty-seven percent of these patients belong to the most deprived quintile, suggesting that deprivation is more frequent in pediatric patients with end-stage kidney disease (ESKD) than in the general population. Five- and ten-year graft survival were 85% and 69%, respectively, in the most deprived quintile vs. 90% and 83%, respectively, in the least deprived quintile. At any time after transplantation, patients in the most deprived quintile had almost a two-fold higher hazard of graft failure compared with the least deprived quintile, after adjustment for age at renal replacement therapy, duration of dialysis, primary kidney disease, and rural/urban living environment (hazard ratio 1.99; 95% confidence interval 1.20-3.28). The hazard of graft failure did not differ significantly between girls and boys. Thus, our findings suggest a lower socioeconomic status is independently associated with poor graft outcome in pediatric kidney transplantation., (Copyright © 2019 International Society of Nephrology. Published by Elsevier Inc. All rights reserved.)

Eculizumab (anti-C5) has been sporadically reported as an efficient therapy for atypical hemolytic uremic syndrome (aHUS). However, the lack of series precludes any firm conclusion about the optimal use of anti-C5 for preventing or treating aHUS posttransplant aHUS recurrence. We thoroughly studied 22 renal transplant recipients with aHUS who received off-label therapy with anti-C5, including 12 cases, which have not been reported yet. Nine patients, all carrying a complement genetic abnormality associated with a high risk of aHUS recurrence, received prophylactic anti-C5 therapy to prevent posttransplant recurrence. Eight of them had a successful recurrence-free posttransplant course and achieved a satisfactory graft function, while the remaining patient experienced early arterial thrombosis of the graft. Thirteen renal transplant recipients were given anti-C5 for posttransplant aHUS recurrence. A complete reversal of aHUS activity was obtained in all of them. Importantly, the delay of anti-C5 initiation after the onset of the aHUS episode inversely correlated with the degree of renal function improvement. Three patients in whom anti-C5 was subsequently stopped experienced a relapse. Altogether these data suggest that long-term eculizumab is highly effective for preventing and treating posttransplant aHUS recurrence. Our study also indicates that anti-C5 should be promptly started if a recurrence occurs., (© Copyright 2012 The American Society of Transplantation and the American Society of Transplant Surgeons.)