Dynamics over Signed Networks

A signed network is a network with each link associated with a positive or negative sign. Models for nodes interacting over such signed networks, where two different types of interactions take place along the positive and negative links, respectively, arise from various biological, social, political, and economic systems. As modifications to the conventional DeGroot dynamics for positive links, two basic types of negative interactions along negative links, namely the opposing rule and the repelling rule, have been proposed and studied in the literature. This paper reviews a few fundamental convergence results for such dynamics over deterministic or random signed networks under a unified algebraic-graphical method. We show that a systematic tool of studying node state evolution over signed networks can be obtained utilizing generalized Perron-Frobenius theory, graph theory, and elementary algebraic recursions.Comment: In press, SIAM Revie

Emergent Behaviors over Signed Random Networks in Dynamical Environments

We study asymptotic dynamical patterns that emerge among a set of nodes that interact in a dynamically evolving signed random network. Node interactions take place at random on a sequence of deterministic signed graphs. Each node receives positive or negative recommendations from its neighbors depending on the sign of the interaction arcs, and updates its state accordingly. Positive recommendations follow the standard consensus update while two types of negative recommendations, each modeling a different type of antagonistic or malicious interaction, are considered. Nodes may weigh positive and negative recommendations differently, and random processes are introduced to model the time-varying attention that nodes pay to the positive and negative recommendations. Various conditions for almost sure convergence, divergence, and clustering of the node states are established. Some fundamental similarities and differences are established for the two notions of negative recommendations

The Evolution of Beliefs over Signed Social Networks

We study the evolution of opinions (or beliefs) over a social network modeled as a signed graph. The sign attached to an edge in this graph characterizes whether the corresponding individuals or end nodes are friends (positive links) or enemies (negative links). Pairs of nodes are randomly selected to interact over time, and when two nodes interact, each of them updates its opinion based on the opinion of the other node and the sign of the corresponding link. This model generalizes DeGroot model to account for negative links: when two enemies interact, their opinions go in opposite directions. We provide conditions for convergence and divergence in expectation, in mean-square, and in almost sure sense, and exhibit phase transition phenomena for these notions of convergence depending on the parameters of the opinion update model and on the structure of the underlying graph. We establish a {\it no-survivor} theorem, stating that the difference in opinions of any two nodes diverges whenever opinions in the network diverge as a whole. We also prove a {\it live-or-die} lemma, indicating that almost surely, the opinions either converge to an agreement or diverge. Finally, we extend our analysis to cases where opinions have hard lower and upper limits. In these cases, we study when and how opinions may become asymptotically clustered to the belief boundaries, and highlight the crucial influence of (strong or weak) structural balance of the underlying network on this clustering phenomenon

Diabetic Aldehyde Dehydrogenase 2 Mutant (ALDH2*2) Mice Are More Susceptible to Cardiac Ischemic-Reperfusion Injury Due to 4-Hydroxy-2-Nonenal Induced Coronary Endothelial Cell Damage

Background: Aldehyde dehydrogenase-2 (ALDH2), a mitochondrial enzyme, detoxifies reactive aldehydes such as 4-hydroxy-2-nonenal (4HNE). A highly prevalent E487K mutation in ALDH2 (ALDH2*2) in East Asian people with intrinsic low ALDH2 activity is implicated in diabetic complications. 4HNE-induced cardiomyocyte dysfunction was studied in diabetic cardiac damage; however, coronary endothelial cell (CEC) injury in myocardial ischemia-reperfusion injury (IRI) in diabetic mice has not been studied. Therefore, we hypothesize that the lack of ALDH2 activity exacerbates 4HNE-induced CEC dysfunction which leads to cardiac damage in ALDH2*2 mutant diabetic mice subjected to myocardial IRI. Methods and Results: Three weeks after diabetes mellitus (DM) induction, hearts were subjected to IRI either in vivo via left anterior descending artery occlusion and release or ex vivo IRI by using the Langendorff system. The cardiac performance was assessed by conscious echocardiography in mice or by inserting a balloon catheter in the left ventricle in the ex vivo model. Just 3 weeks of DM led to an increase in cardiac 4HNE protein adducts and, cardiac dysfunction, and a decrease in the number of CECs along with reduced myocardial ALDH2 activity in ALDH2*2 mutant diabetic mice compared with their wild-type counterparts. Systemic pretreatment with Alda-1 (10 mg/kg per day), an activator of both ALDH2 and ALDH2*2, led to a reduction in myocardial infarct size and dysfunction, and coronary perfusion pressure upon cardiac IRI by increasing CEC population and coronary arteriole opening. Conclusions: Low ALDH2 activity exacerbates 4HNE-mediated CEC injury and thereby cardiac dysfunction in diabetic mouse hearts subjected to IRI, which can be reversed by ALDH2 activation

Comparison of Indocyanine Green Angiography and Swept-Source Wide-Field Optical Coherence Tomography Angiography in Posterior Uveitis

Purpose: To compare indocyanine green angiography (ICGA) and swept-source wide-field optical coherence tomography angiography (SS-OCTA) for the assessment of patients with posterior uveitis. Method: SS-OCTA montage images of 5 x 12 x 12 mm or 2 x 15 x 9 mm, covering ~70–90 degree of the retina of consecutive patients with posterior uveitis were acquired. The choriocapillaries and choroidal slabs were compared to findings on ICGA. Results: Sixty-eight eyes of 41 patients were included (mean age 47.2 ± 20.4 years; 58.5% female). In 23 (34%) lesions were visible on OCTA, but not discernable on ICGA. In turn, out of the 45 eyes with clearly discernable lesions on ICGA, 22 (49%) and 21 (47%) eyes showed no corresponding areas of flow deficit on OCTA in the CC and choroidal slab, respectively. Lesion size strongly correlated among ICGA and OCTA choriocapillaries- (CC) (r = 0.99, p ≤ 0.0001) and choroidal slabs (r = 0.99, p ≤ 0.0001), respectively. The mean lesion size on the late frames of ICGA (8.45 ± 5.47 mm2) was larger compared to the lesion size on OCTA CC scan (7.98 ± 5.47 mm2, p ≤ 0.0001) and choroidal scan (7.69 ± 5.10 mm2, p = 0.002), respectively. The lesion size on OCTA CC scan was significantly larger than on the OCTA choroidal scan (p ≤ 0.0001). Conclusion: SS-wide field OCTA may be a promising tool to assess posterior uveitis patients and may replace ICGA to a certain extent in the future

Emergent Behaviors over Signed Random Dynamical Networks: State-Flipping Model

Recent studies from social, biological, and engineering network systems have drawn attention to the dynamics over signed networks, where each link is associated with a positive/negative sign indicating trustful/mistrustful, activator/inhibitor, or secure/malicious interactions. We study asymptotic dynamical patterns that emerge among a set of nodes that interact in a dynamically evolving signed random network. Node interactions take place at random on a sequence of deterministic signed graphs. Each node receives positive or negative recommendations from its neighbors depending on the sign of the interaction arcs, and updates its state accordingly. Recommendations along a positive arc follow the standard consensus update. As in the work by Altafini, negative recommendations use an update where the sign of the neighbor state is flipped. Nodes may weight positive and negative recommendations differently, and random processes are introduced to model the time-varying attention that nodes pay to these recommendations. Conditions for almost sure convergence and divergence of the node states are established. We show that under this so-called state-flipping model, all links contribute to a consensus of the absolute values of the nodes, even under switching sign patterns and dynamically changing environment. A no-survivor property is established, indicating that every node state diverges almost surely if the maximum network state diverges.Comment: IEEE Transactions on Control of Network Systems, in press. arXiv admin note: substantial text overlap with arXiv:1309.548