Robustness and structure of complex networks

This dissertation covers the two major parts of my PhD research on statistical physics and complex networks: i) modeling a new type of attack – localized attack, and investigating robustness of complex networks under this type of attack; ii) discovering the clustering structure in complex networks and its influence on the robustness of coupled networks. Complex networks appear in every aspect of our daily life and are widely studied in Physics, Mathematics, Biology, and Computer Science. One important property of complex networks is their robustness under attacks, which depends crucially on the nature of attacks and the structure of the networks themselves. Previous studies have focused on two types of attack: random attack and targeted attack, which, however, are insufficient to describe many real-world damages. Here we propose a new type of attack – localized attack, and study the robustness of complex networks under this type of attack, both analytically and via simulation. On the other hand, we also study the clustering structure in the network, and its influence on the robustness of a complex network system. In the first part, we propose a theoretical framework to study the robustness of complex networks under localized attack based on percolation theory and generating function method. We investigate the percolation properties, including the critical threshold of the phase transition pc and the size of the giant component P∞. We compare localized attack with random attack and find that while random regular (RR) networks are more robust against localized attack, Erd ̋os-R ́enyi (ER) networks are equally robust under both types of attacks. As for scale-free (SF) networks, their robustness depends crucially on the degree exponent λ. The simulation results show perfect agreement with theoretical predictions. We also test our model on two real-world networks: a peer-to-peer computer network and an airline network, and find that the real-world networks are much more vulnerable to localized attack compared with random attack. In the second part, we extend the tree-like generating function method to incorporating clustering structure in complex networks. We study the robustness of a complex network system, especially a network of networks (NON) with clustering structure in each network. We find that the system becomes less robust as we increase the clustering coefficient of each network. For a partially dependent network system, we also find that the influence of the clustering coefficient on network robustness decreases as we decrease the coupling strength, and the critical coupling strength qc, at which the first-order phase transition changes to second-order, increases as we increase the clustering coefficient

Effects of Acid Deposition and Changing Climate on the Hydrochemistry and Critical Loads of Watersheds in the Adirondack Region of New York

Despite decreases in acidic deposition since the 1970s, the recovery of surface waters from acidification has been limited primarily due to the depletion of exchangeable base cations, net mineralization of organic sulfur and nitrogen and release of previously retained SO42- and NO3-, and increases in concentrations of naturally occurring organic acids from soil. The future recovery of stream chemistry from acidic deposition may be altered by projected increases in temperature and precipitation associated with a changing climate. The goals of this study were to conduct a modeling analysis of the response of soils and streams in the Adirondack Park, New York, USA to future changes in acidic deposition and climate. I conducted the research for this dissertation in three phases. In phase one, the integrated biogeochemical model PnET-BGC was applied to 25 forested watersheds that represent a range of acid sensitivity in the Adirondack region to simulate the response of streams to past and future changes in atmospheric S and N deposition, and to calculate the target loads of acidity for protecting and restoring stream water quality and ecosystem health. Using measured data, the model was calibrated and applied to simulate soil and stream chemistry at all study sites. Model hindcasts indicate that historically, stream water chemistry in the Adirondacks was variable, but inherently sensitive to acid deposition. Model projections suggest that simultaneous decreases in sulfate, nitrate and ammonium deposition are more effective in restoring stream ANC than individual decreases in sulfur or nitrogen species in deposition. However, the increases in stream ANC per unit equivalent decrease in S deposition is greater than for equivalent decreases in N deposition. Using empirical algorithms, fish community density and biomass are projected to increase under several deposition-control scenarios that coincide with increases in stream ANC. However, model projections suggest that even under the most aggressive deposition-reduction scenarios, stream chemistry and fisheries will not fully recover to pre-industrial values by 2200 due to legacy effects of historical acidification. In phase two, the PnET-BGC model was applied to two montane forested watersheds in the Adirondack region to evaluate the effects of future climate change on the recovery of surface waters from historical acidification in response to future changes in atmospheric sulfur and nitrogen deposition. Statistically downscaled climate scenarios, on average, projected warmer temperatures and greater precipitation for the Adirondacks by the end of the century. Model simulations suggest under constant climate, acid-sensitive Buck Creek would gain more acid neutralizing capacity (ANC) than acid insensitive Archer Creek by 2100 from large reductions in acidic deposition. However, climate change could limit those improvements in stream acid-base status. Under climate change, acid-insensitive Archer Creek is projected to experience less of an ANC increase than Buck Creek by 2100. Calculated target loads for 2150 for both sites decreased when future climate change was considered in model simulations, which suggests further reductions in acid deposition may be necessary to restore ecosystem structure and function under a changing climate. In phase three, the One-at-A-Time (OAT) first-order sensitivity index method and Monte Carlo method were used to analyze the uncertainty in modeling Adirondack stream ANC. The results of first-order sensitivity analysis indicated that in general the model simulations of stream ANC are most sensitive to variation in precipitation quantity, Ca2+ and Na+ weathering rates, maximum monthly air temperature, SO42- wet deposition, and DOC site density (the moles of organic anions per moles of organic carbon). The results of the first-order sensitivity analysis showed that even if the order of the most sensitive parameters between different research sites were consistent, there were differences in projected uncertainty of stream ANC among sites. Monte Carlo analysis was conducted under the assumption of a 30% interval uncertainty (± 15%) in 16 input factors for 500 simulations that were normally distributed around the original simulated stream ANC for year 2050. The Monte Carlo analysis indicated that the model simulation of ANC is most sensitive to precipitation quantity, Ca2+ weathering rate, Na+ weathering rate, SO42- wet deposition, and maximum monthly air temperature. Future simulations could be improved with further research to improve characterization of these inputs

New Planar P-time Computable Six-Vertex Models and a Complete Complexity Classification

We discover new P-time computable six-vertex models on planar graphs beyond Kasteleyn's algorithm for counting planar perfect matchings. We further prove that there are no more: Together, they exhaust all P-time computable six-vertex models on planar graphs, assuming #P is not P. This leads to the following exact complexity classification: For every parameter setting in ${\mathbb C}$ for the six-vertex model, the partition function is either (1) computable in P-time for every graph, or (2) #P-hard for general graphs but computable in P-time for planar graphs, or (3) #P-hard even for planar graphs. The classification has an explicit criterion. The new P-time cases in (2) provably cannot be subsumed by Kasteleyn's algorithm. They are obtained by a non-local connection to #CSP, defined in terms of a "loop space". This is the first substantive advance toward a planar Holant classification with not necessarily symmetric constraints. We introduce M\"obius transformation on ${\mathbb C}$ as a powerful new tool in hardness proofs for counting problems.Comment: 61 pages, 16 figures. An extended abstract appears in SODA 202

Despicable Me: Shame and Guilt on Self-Avoidance Behaviours – An Eye-Tracking Study

Shame and guilt are often used interchangeably in our daily lives, however, this project aims to differentiate between the two emotions based on people’s self-avoidance behaviours. Existing theories propose that while feelings of shame lead to increased self-avoidance behaviours, feelings of guilt do not. Using a modernised version of the mirror paradigm, this project captured participants’ gaze behaviours around their own face reflections. In this pre-registered study, the gaze behaviour of 30 participants were collected while emotions (either shame or guilt) were induced. Their state shame and guilt as well as trait shame and guilt were also collected through self-reports. It was hypothesised that participants in the shame condition would exhibit less eye-fixation and saccades toward their face reflection and those in the guilt condition would exhibit more. Results in this project showed that also a strong difference on gaze behaviours was detected between shame an guilt experimental conditions, this effect was reduced after adding other regressors, including trait shame and trait guilt. In later regression models, only a marginal negative effect of shame on gaze behaviours was found whereas feelings of guilt has not found to be correlated with gaze behaviours. Keywords: objective self-awareness, shame, guilt, self-avoidanc