Manuela Loi, Francesca Valenti, Giorgio Medici
et al.
CDKL5 deficiency disorder (CDD), a developmental encephalopathy caused by mutations in the cyclin-dependent kinase-like 5 (CDKL5) gene, is characterized by a complex and severe clinical picture, including early-onset epilepsy and cognitive, motor, visual, and gastrointestinal disturbances. This disease still lacks a medical treatment to mitigate, or reverse, its course and improve the patient’s quality of life. Although CDD is primarily a genetic brain disorder, some evidence indicates systemic abnormalities, such as the presence of a redox imbalance in the plasma and skin fibroblasts from CDD patients and in the cardiac myocytes of a mouse model of CDD. In order to shed light on the role of oxidative stress in the CDD pathophysiology, in this study, we aimed to investigate the therapeutic potential of Coenzyme Q10 (CoQ10), which is known to be a powerful antioxidant, using in vitro and in vivo models of CDD. We found that CoQ10 supplementation not only reduces levels of reactive oxygen species (ROS) and normalizes glutathione balance but also restores the levels of markers of DNA damage (γ-H2AX) and senescence (lamin B1), restoring cellular proliferation and improving cellular survival in a human neuronal model of CDD. Importantly, oral supplementation with CoQ10 exerts a protective role toward lipid peroxidation and DNA damage in the heart of a murine model of CDD, the Cdkl5 (+/−) female mouse. Our results highlight the therapeutic potential of the antioxidant supplement CoQ10 in counteracting the detrimental oxidative stress induced by CDKL5 deficiency.
Abstract Funding Acknowledgements Type of funding sources: None. Background Atrial and ventricular functional tricuspid regurgitation (A-FTR and V-FTR) have recently emerged as different phenotypes of FTR. Given the difference in mechanisms that are postulated to be underlying these 2 entities, a different remodeling of tricuspid valve (TV) apparatus can occur and therefore also a specific quantitative approach could be deemed. Aim Aim of this study was to investigate the TV apparatus remodeling in the two different phenotypes of FTR: ventricular (V-FTR) and atrial (A-FTR) and the role of echocardiographic parameters of TV remodeling and TR severity to predict clinical outcomes. Material and methods The present retrospective study included consecutive patients with moderate to severe functional tricuspid regurgitation (FTR) referred for echocardiography in two Italian centers. The composite endpoint of death for any cause and heart failure (HF) hospitalization was used as primary outcome of this analysis. According to more recent guidelines, patients were considered having A-FTR if having history of long- standing atrial fibrillation, without history of pulmonary hypertension and left side heart disease. Results. A total of 180 patients were included. Despite the right atrial volume (RAV) was not different in the 2 groups, in A-FTR tethering height was significantly lower (11.7 ±4.8 mm vs 15.0 ± 5.5 in V-FTR. p <0.01) and the 3D-derived tricuspid annulus (TA) diameters were larger both in end-diastolic and mid-systolic phase (3D-TA-End diastolic- major axis: 45.2 ± 6.2 mm in A-FTR vs 42.8 ± 5.4 in V-FTR. p= 0.04; 3D-TA mid systolic major axis: 41,7 ± 6,4mm in A-FTR vs 37,9 ± 5,1 in V-FTR, P <0,01). 3D-TA-End diastolic- minor axis: 39.7 ± 6.8 vs 37.1 ± 5.2. p= 0.03). Regarding the parameters of severity of FTR. patients with V-FTR had larger vena contracta (VC). either when 2D estimated or 3D (2D-VC-average: 5.3 ± 2.8 mm in A-FTR vs 6.6 ± 3.7 in V-FTR. P= 0.02; 3D-VCA: 0.9 ± 0.4 cm2 vs 1.3 ± 1.1 cm2 p= 0.02); conversely the value of 2D-ERO and regurgitant volume estimated with 2D-PISA method did not show significant difference between the 2 groups (table 1). After a median follow-up of 24 months (IQR: 2-48) 72 patients (40%) reached the primary end-point and 64 (36%) hospitalized for HF. Different predictors of combined end point were found in the 2 groups: tenting height. 2D-VC. 3D-VCA and regurgitant fraction were prognostic correlates in V-FTR; TA dimensions as well as all the parameters of severe TR. including EROA with PISA method were related to the prognosis in A-FTR (table 2). Conclusions Prognostic role of quantitative parameters of FTR in A-FTR and V-FTR is different, thus reaffirming the difference in underlying pathogenic mechanisms and the needing for a more specific diagnostic approach and prognostic stratification in these two FTR phenotypes
We explore the classical pattern avoidance question in the case of irreducible permutations, <i>i.e.</i>, those in which there is no index $i$ such that $\sigma (i+1) - \sigma (i)=1$. The problem is addressed completely in the case of avoiding one or two patterns of length three, and several well known sequences are encountered in the process, such as Catalan, Motzkin, Fibonacci, Tribonacci, Padovan and Binary numbers. Also, we present constructive bijections between the set of Motzkin paths of length $n-1$ and the sets of irreducible permutations of length $n$ (respectively fixed point free irreducible involutions of length $2n$) avoiding a pattern $\alpha$ for $\alpha \in \{132,213,321\}$. This induces two new bijections between the set of Dyck paths and some restricted sets of permutations.
We investigate a family of algorithms minimizing energetic effort in random networks computing aggregative functions. In contrast to previously considered models, our results minimize maximal energetic effort over all stations instead of the average usage of energy. Such approach seems to be much more suitable for some kinds of networks, in particular ad hoc radio networks, wherein we need all stations functioning and replacing batteries after the deployment is not feasible. We analyze also the latency of proposed energy-optimal algorithms. We model a network by placing randomly and independently $n$ points in a $d$-dimensional cube of side-length $n^{1/d}$. We place an edge between vertices that interact with each other. We analyze properties of the resulting graphs in order to obtain estimates on energetic effort and latency of proposed algorithms.
In 1968 and 1969, Andrews proved two partition theorems of the Rogers-Ramanujan type which generalise Schur’s celebrated partition identity (1926). Andrews’ two generalisations of Schur’s theorem went on to become two of the most influential results in the theory of partitions, finding applications in combinatorics, representation theory and quantum algebra. In this paper we generalise both of Andrews’ theorems to overpartitions. The proofs use a new technique which consists in going back and forth from $q$-difference equations on generating functions to recurrence equations on their coefficients.
We give a recursive definition of generalized parking functions that allows them to be viewed as a species. From there we compute a non-commutative characteristic of the generalized parking function module and deduce some enumeration formulas of structures and isomorphism types. We give as well an interpretation in several bases of non commutative symmetric functions. Finally, we investigate an inclusion-exclusion formula given by Kung and Yan.
We expose a rule for multiplying a general Schubert polynomial with a power sum polynomial in $k$ variables. A signed sum over cyclic permutations replaces the signed sum over rim hooks in the classical Murgnahan-Nakayama rule. In the intersection theory of flag manifolds this computes all intersections of Schubert cycles with tautological classes coming from the Chern character. We also discuss extensions of this rule to small quantum cohomology.
In a recent paper with Bousquet-Mélou, de Gier, Duminil-Copin and Guttmann (2012), we proved that a model of self-avoiding walks on the honeycomb lattice, interacting with an impenetrable surface, undergoes an adsorption phase transition when the surface fugacity is 1+√2. Our proof used a generalisation of an identity obtained by Duminil-Copin and Smirnov (2012), and confirmed a conjecture of Batchelor and Yung (1995). Here we consider a similar model of self-avoiding walk adsorption on the honeycomb lattice, but with the impenetrable surface placed at a right angle to the previous orientation. For this model there also exists a conjecture for the critical surface fugacity, made by Batchelor, Bennett-Wood and Owczarek (1998). We adapt the methods of the earlier paper to this setting in order to prove the critical surface fugacity, but have to deal with several subtle complications which arise. This article is an abbreviated version of a paper of the same title, currently being prepared for submission.
Olivier Bodini, Antoine Genitrini, Frédéric Peschanski
In this paper, we study the shuffle operator on concurrent processes (represented as trees) using analytic combinatorics tools. As a first result, we show that the mean width of shuffle trees is exponentially smaller than the worst case upper-bound. We also study the expected size (in total number of nodes) of shuffle trees. We notice, rather unexpectedly, that only a small ratio of all nodes do not belong to the last two levels. We also provide a precise characterization of what ``exponential growth'' means in the case of the shuffle on trees. Two practical outcomes of our quantitative study are presented: (1) a linear-time algorithm to compute the probability of a concurrent run prefix, and (2) an efficient algorithm for uniform random generation of concurrent runs.
We use the polynomial ring $\mathbb{C}[x_{1,1},\ldots,x_{n,n}]$ to modify the Kazhdan-Lusztig construction of irreducible $S_n$-modules. This modified construction produces exactly the same matrices as the original construction in [$\textit{Invent. Math}$ $\mathbf{53}$ (1979)], but does not employ the Kazhdan-Lusztig preorders. We also show that our modules are related by unitriangular transition matrices to those constructed by Clausen in [$\textit{J. Symbolic Comput.}$ $\textbf{11}$ (1991)]. This provides a $\mathbb{C}[x_{1,1},\ldots,x_{n,n}]$-analog of results of Garsia-McLarnan in [$\textit{Adv. Math.}$ $\textbf{69}$ (1988)].
The median problem seeks a permutation whose total distance to a given set of permutations (the base set) is minimal. This is an important problem in comparative genomics and has been studied for several distance measures such as reversals. The transposition distance is less relevant biologically, but it has been shown that it behaves similarly to the most important biological distances, and can thus give important information on their properties. We have derived an algorithm which solves the transposition median problem, giving all transposition medians (the median cloud). We show that our algorithm can be modified to accept median clouds as elements in the base set and briefly discuss the new concept of median iterates (medians of medians) and limit medians, that is the limit of this iterate.
We prove that for each $k \geq 0$, the probability that a root vertex in a random planar graph has degree $k$ tends to a computable constant $d_k$, and moreover that $\sum_k d_k =1$. The proof uses the tools developed by Gimènez and Noy in their solution to the problem of the asymptotic enumeration of planar graphs, and is based on a detailed analysis of the generating functions involved in counting planar graphs. However, in order to keep track of the degree of the root, new technical difficulties arise. We obtain explicit, although quite involved expressions, for the coefficients in the singular expansions of interest, which allow us to use transfer theorems in order to get an explicit expression for the probability generating function $p(w)=\sum_k d_k w^k$. From the explicit expression for $p(w)$ we can compute the $d_k$ to any degree of accuracy, and derive asymptotic estimates for large values of $k$.