Universality in Complex Networks: Random Matrix Analysis

We apply random matrix theory to complex networks. We show that nearest neighbor spacing distribution of the eigenvalues of the adjacency matrices of various model networks, namely scale-free, small-world and random networks follow universal Gaussian orthogonal ensemble statistics of random matrix theory. Secondly we show an analogy between the onset of small-world behavior, quantified by the structural properties of networks, and the transition from Poisson to Gaussian orthogonal ensemble statistics, quantified by Brody parameter characterizing a spectral property. We also present our analysis for a protein-protein interaction network in budding yeast.Comment: 4+ pages, 4 figures, to appear in PRE, major change in the paper including titl

Multifractal analysis of eigenvectors of smallworld networks

Many real-world complex systems have small-world topology characterized by the high clustering of nodes and short path lengths.It is well-known that higher clustering drives localization while shorter path length supports delocalization of the eigenvectors of networks. Using multifractals technique, we investigate localization properties of the eigenvectors of the adjacency matrices of small-world networks constructed using Watts-Strogatz algorithm. We find that the central part of the eigenvalue spectrum is characterized by strong multifractality whereas the tail part of the spectrum have Dq->1. Before the onset of the small-world transition, an increase in the random connections leads to an enhancement in the eigenvectors localization, whereas just after the onset, the eigenvectors show a gradual decrease in the localization. We have verified an existence of sharp change in the correlation dimension at the localization-delocalization transitionComment: 8 pages, 7 figure

Hepatic encephalopathy: a critical current review.

Hepatic encephalopathy (HE) is a serious neuropsychiatric complication of cirrhosis and/or porto-systemic shunting. The clinical symptoms are widely variable, extending from subtle impairment in mental state to coma. The utility of categorizing the severity of HE accurately and efficiently serves not only to provide practical functional information about the current clinical status of the patient but also gives valuable prognostic information. In the past 20-30 years, there has been rapid progress in understanding the pathophysiological basis of HE; however, the lack of direct correlation between pathogenic factors and the severity of HE make it difficult to select appropriate therapy for HE patients. In this review, we will discuss the classification system and its limitations, the neuropsychometric assessments and their challenges, as well as the present knowledge on the pathophysiological mechanisms. Despite the many prevalent hypotheses around the pathogenesis of the disease, most treatments focus on targeting and lowering the accumulation of ammonia as well as inflammation. However, treatment of minimal HE remains a huge unmet need and a big concerted effort is needed to better define this condition to allow the development of new therapies. We review the currently available therapies and future approaches to treat HE as well as the scientific and clinical data that support their effectiveness

Random matrix analysis of network Laplacians

We analyze eigenvalues fluctuations of the Laplacian of various networks under the random matrix theory framework. Analyses of random networks, scale-free networks and small-world networks show that nearest neighbor spacing distribution of the Laplacian of these networks follow Gaussian orthogonal ensemble statistics of random matrix theory. Furthermore, we study nearest neighbor spacing distribution as a function of the random connections and find that transition to the Gaussian orthogonal ensemble statistics occurs at the small-world transition.Comment: 14 pages, 5 figures, replaced with the final versio

Random matrix analysis of complex networks

We study complex networks under random matrix theory (RMT) framework. Using nearest-neighbor and next-nearest-neighbor spacing distributions we analyze the eigenvalues of adjacency matrix of various model networks, namely, random, scale-free and small-world networks. These distributions follow Gaussian orthogonal ensemble statistic of RMT. To probe long-range correlations in the eigenvalues we study spectral rigidity via $\Delta_3$ statistic of RMT as well. It follows RMT prediction of linear behavior in semi-logarithmic scale with slope being $\sim 1/\pi^2$. Random and scale-free networks follow RMT prediction for very large scale. Small-world network follows it for sufficiently large scale, but much less than the random and scale-free networks.Comment: accepted in Phys. Rev. E (replaced with the final version

Modification in CSF specific gravity in acutely decompensated cirrhosis and acute on chronic liver failure independent of encephalopathy, evidences for an early blood-CSF barrier dysfunction in cirrhosis

Although hepatic encephalopathy (HE) on the background of acute on chronic liver failure (ACLF) is associated with high mortality rates, it is unknown whether this is due to increased blood-brain barrier permeability. Specific gravity of cerebrospinal fluid measured by CT is able to estimate blood-cerebrospinal fluid-barrier permeability. This study aimed to assess cerebrospinal fluid specific gravity in acutely decompensated cirrhosis and to compare it in patients with or without ACLF and with or without hepatic encephalopathy. We identified all the patients admitted for acute decompensation of cirrhosis who underwent a brain CT-scan. Those patients could present acute decompensation with or without ACLF. The presence of hepatic encephalopathy was noted. They were compared to a group of stable cirrhotic patients and healthy controls. Quantitative brain CT analysis used the Brainview software that gives the weight, the volume and the specific gravity of each determined brain regions. Results are given as median and interquartile ranges and as relative variation compared to the control/baseline group. 36 patients presented an acute decompensation of cirrhosis. Among them, 25 presented with ACLF and 11 without ACLF; 20 presented with hepatic encephalopathy grade ≥ 2. They were compared to 31 stable cirrhosis patients and 61 healthy controls. Cirrhotic patients had increased cerebrospinal fluid specific gravity (CSF-SG) compared to healthy controls (+0.4 %, p < 0.0001). Cirrhotic patients with ACLF have decreased CSF-SG as compared to cirrhotic patients without ACLF (−0.2 %, p = 0.0030) that remained higher than in healthy controls. The presence of hepatic encephalopathy did not modify CSF-SG (−0.09 %, p = 0.1757). Specific gravity did not differ between different brain regions according to the presence or absence of either ACLF or HE. In patients with acute decompensation of cirrhosis, and those with ACLF, CSF specific gravity is modified compared to both stable cirrhotic patients and healthy controls. This pattern is observed even in the absence of hepatic encephalopathy suggesting that blood-CSF barrier impairment is manifest even in absence of overt hepatic encephalopathy

Effect of the clinical course of acute-on-chronic liver failure prior to liver transplantation on post-transplant survival

BACKGROUND & AIMS: Patients with acute-on-chronic liver failure (ACLF) can be listed for liver transplantation (LT) because LT is the only curative treatment option. We evaluated whether the clinical course of ACLF, particularly ACLF-3, between the time of listing and LT affects 1-year post-transplant survival. METHODS: We identified patients from the United Network for Organ Sharing database who were transplanted within 28 days of listing and categorized them by ACLF grade at waitlist registration and LT, according to the EASL-CLIF definition. RESULTS: A total of 3,636 patients listed with ACLF-3 underwent LT within 28 days. Among those transplanted, 892 (24.5%) recovered to no ACLF or ACLF grade 1 or 2 (ACLF 0–2) and 2,744 (75.5%) had ACLF-3 at transplantation. One-year survival was 82.0% among those transplanted with ACLF-3 vs. 88.2% among those improving to ACLF 0–2 (p 60 years of age, 1-year survival was significantly higher among those who improved from ACLF-3 to ACLF 0–2 than among those who did not. CONCLUSIONS: Improvement from ACLF-3 at listing to ACLF 0–2 at transplantation enhances post-LT survival, particularly in those who recovered from circulatory or brain failure, or were removed from the mechanical ventilator. The beneficial effect of improved ACLF on post-LT survival was also observed among patients >60 years of age. LAY SUMMARY: Liver transplantation (LT) for patients with acute-on-chronic liver failure grade 3 (ACLF-3) significantly improves survival, but 1-year survival probability after LT remains lower than the expected outcomes for transplant centers. Our study reveals that among patients transplanted within 28 days of waitlist registration, improvement of ACLF-3 at listing to a lower grade of ACLF at transplantation significantly enhances post-transplant survival, even among patients aged 60 years or older. Subgroup analysis further demonstrates that improvement in circulatory failure, brain failure, or removal from mechanical ventilation have the strongest impact on post-transplant survival

Patients with severe acute‐on‐chronic liver failure are disadvantaged by model for end‐stage liver disease‐based organ allocation policy

Background: Mortality for patients with acute‐on‐chronic liver failure (ACLF) may be underestimated by the model for end‐stage liver disease‐sodium (MELD‐Na) score. / Aim: To assess waitlist outcomes across varying grades of ACLF among a cohort of patients listed with a MELD‐Na score ≥35, and therefore having similar priority for liver transplantation. / Methods: We analysed the United Network for Organ Sharing (UNOS) database, years 2010‐2017. Waitlist outcomes were evaluated using Fine and Gray's competing risks regression. / Results: We identified 6342 candidates at listing with a MELD‐Na score ≥35, of whom 3122 had ACLF‐3. Extra‐hepatic organ failures were present primarily in patients with four to six organ failures. Competing risks regression revealed that candidates listed with ACLF‐3 had a significantly higher risk for 90‐day waitlist mortality (Sub‐hazard ratio (SHR) = 1.41; 95% confidence interval [CI] 1.12‐1.78) relative to patients with lower ACLF grades. Subgroup analysis of ACLF‐3 revealed that both the presence of three organ failures (SHR = 1.40, 95% CI 1.20‐1.63) or four to six organ failures at listing (SHR = 3.01; 95% CI 2.54‐3.58) was associated with increased waitlist death. Candidates with four to six organ failures also had the lowest likelihood of receiving liver transplantation (SHR = 0.61, 95% CI 0.54‐0.68). The Share 35 rule was associated with reduced 90‐day waitlist mortality among the full cohort of patients listed with ACLF‐3 and MELD‐Na score ≥35 (SHR = 0.59; 95% CI 0.49‐0.70). However, Share 35 rule implementation was not associated with reduced waitlist mortality among patients with four to six organ failures (SHR = 0.76; 95% CI 0.58‐1.02). / Conclusion: The MELD‐Na score disadvantages patients with ACLF‐3, both with and without extra‐hepatic organ failures. Incorporation of organ failures into allocation policy warrants further exploration