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

An Unusual Case of Hematochezia

Lower gastrointestinal bleeding (LGIB) is a serious and potentially life-threatening condition warranting hospital admission. The most frequent causes include diverticular disease, colitis, hemorrhoids, neoplasm, inflammatory bowel disease, and varices. Varices usually occur secondary to liver cirrhosis and are frequently located in the gastroesophageal region. Those occurring elsewhere are known as ectopic varices. The diagnosis and management of ectopic varices is challenging, and guidelines are not currently available. We report the case of recurrent large-volume hematochezia secondary to a cecal varix in a 60-year-old female with alcoholic liver cirrhosis. Initial investigation with CT angiography and endoscopy failed to identify the source of bleeding. A second CT angiogram identified a large varix in the cecum, and the patient was successfully managed with radiological embolization and transjugular intra-hepatic porto-systemic shunt (TIPSS)

Giant lipoma: an unusual cause of carpal tunnel syndrome

Carpal tunnel syndrome, in its idiopathic form, is an extremely common entrapment neuropathy in the clinical practice however secondary compressive causes are rare. Among secondary causes, tumors are even rarer. Although lipomas are the most common soft tissue tumor in the body, <5% of the benign tumors of the hand are lipomas. A 48-year old manual laborer man presented to us with a two-year history of numbness, tingling and burning pain in the palmar surface of the left hand and fingers along with a progressively increasing swelling in the hand and wrist. His medical history was unremarkable and no trauma episode was reported. According to the clinical examination and the result of median nerve conduction study (NCS) the diagnosis of carpal tunnel syndrome was established. Operative release of the transverse carpal ligament was subsequently performed along with excision of the lipoma using extensile open approach. Intraoperatively, median nerve and its digital branches were found to be stretched over the giant lipoma causing substantial compression to median nerve. Histopathological findings of the resected mass were consistent with lipoma. After two years the patient was pain-free without any sign of tumor recurrence. Lipomas are infrequently seen in hand and wrist, however giant lipoma as a cause of secondary carpal tunnel syndrome is even more rare, which makes this case interesting.Key words: Lipoma, carpal tunnel syndrome, median nerve, nerve compressio

Spectral analysis of deformed random networks

We study spectral behavior of sparsely connected random networks under the random matrix framework. Sub-networks without any connection among them form a network having perfect community structure. As connections among the sub-networks are introduced, the spacing distribution shows a transition from the Poisson statistics to the Gaussian orthogonal ensemble statistics of random matrix theory. The eigenvalue density distribution shows a transition to the Wigner's semicircular behavior for a completely deformed network. The range for which spectral rigidity, measured by the Dyson-Mehta $\Delta_3$ statistics, follows the Gaussian orthogonal ensemble statistics depends upon the deformation of the network from the perfect community structure. The spacing distribution is particularly useful to track very slight deformations of the network from a perfect community structure, whereas the density distribution and the $\Delta_3$ statistics remain identical to the undeformed network. On the other hand the $\Delta_3$ statistics is useful for the larger deformation strengths. Finally, we analyze the spectrum of a protein-protein interaction network for Helicobacter, and compare the spectral behavior with those of the model networks.Comment: accepted for publication in Phys. Rev. E (replaced with the final version

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

Spectral statistics of random geometric graphs

We use random matrix theory to study the spectrum of random geometric graphs, a fundamental model of spatial networks. Considering ensembles of random geometric graphs we look at short range correlations in the level spacings of the spectrum via the nearest neighbour and next nearest neighbour spacing distribution and long range correlations via the spectral rigidity Delta_3 statistic. These correlations in the level spacings give information about localisation of eigenvectors, level of community structure and the level of randomness within the networks. We find a parameter dependent transition between Poisson and Gaussian orthogonal ensemble statistics. That is the spectral statistics of spatial random geometric graphs fits the universality of random matrix theory found in other models such as Erdos-Renyi, Barabasi-Albert and Watts-Strogatz random graph.Comment: 19 pages, 6 figures. Substantially updated from previous versio

Long-Term Outcomes of Everolimus Therapy in De Novo Liver Transplantation: A Systematic Review and Meta-Analysis of Randomized Controlled Trials

BACKGROUND: Risk of nephrotoxicity in liver transplant patients on calcineurin inhibitors (CnIs) is a concern. Several controlled trials reported benefit of everolimus (EVR) in minimizing this risk when combined with a reduced CnI dose. BACKGROUND: To systematically review the efficacy and safety of EVR, alone or with reduced CnI dose, as compared to CnI alone post-liver transplantation. METHODS: We searched MEDLINE, Scopus, and the Cochrane Library for randomized controlled trials comparing EVR- and CnI-based regimens post-liver transplantation. Assessment of studies and data extraction were undertaken independently. RESULTS: Eight studies were selected, describing 769 patients. Cockcroft-Gault GFR was higher at one (P = .05), 3, and 5 years (P = .030) in patients on EVR compared to those receiving CnI therapy. The composite endpoint of efficacy failure was similar between the 2 arms after 1, 3, and 5 years of study. More patients discontinued EVR due to adverse effects in 1 year; however, no difference was noted after 3 or 5 years. A higher rates of proteinuria, peripheral edema, and incisional hernia occurred in patients on EVR. CONCLUSIONS: The analysis confirms noninferiority of EVR and reduced CnI combination. Combination regimen resulted in better renal function compared to standard CnI therapy