Unusual percolation in simple small-world networks

We present an exact solution of percolation in a generalized class of Watts-Strogatz graphs defined on a 1-dimensional underlying lattice. We find a non-classical critical point in the limit of the number of long-range bonds in the system going to zero, with a discontinuity in the percolation probability and a divergence in the mean finite-cluster size. We show that the critical behavior falls into one of three regimes depending on the proportion of occupied long-range to unoccupied nearest-neighbor bonds, with each regime being characterized by different critical exponents. The three regimes can be united by a single scaling function around the critical point. These results can be used to identify the number of long-range links necessary to secure connectivity in a communication or transportation chain. As an example, we can resolve the communication problem in a game of "telephone".Comment: 10 pages, 4 figures, revtex

Spatial networks with wireless applications

Many networks have nodes located in physical space, with links more common between closely spaced pairs of nodes. For example, the nodes could be wireless devices and links communication channels in a wireless mesh network. We describe recent work involving such networks, considering effects due to the geometry (convex,non-convex, and fractal), node distribution, distance-dependent link probability, mobility, directivity and interference.Comment: Review article- an amended version with a new title from the origina

Decay of localized states in the SIS model

Nella tesi si prende in esame la transizione di localizzazione nella matrice delle adiacenze di network random regolari con un HUB ad alta connettività aggiunto. L'indagine ha la forma di simulazioni numeriche che studiano le conseguenze nella dinamica del modello SIS attraverso misure di suscettività epidemica e di tempo di vita del processo di contagio

Beyond COVID-19: Network science and sustainable exit strategies

On May $28^{th}$ and $29^{th}$, a two day workshop was held virtually, facilitated by the Beyond Center at ASU and Moogsoft Inc. The aim was to bring together leading scientists with an interest in Network Science and Epidemiology to attempt to inform public policy in response to the COVID-19 pandemic. Epidemics are at their core a process that progresses dynamically upon a network, and are a key area of study in Network Science. In the course of the workshop a wide survey of the state of the subject was conducted. We summarize in this paper a series of perspectives of the subject, and where the authors believe fruitful areas for future research are to be found

Optimal water allocation for joint sustainability of irrigated agriculture and urban growth

2017 Fall.Includes bibliographical references.Historically, agriculture was the main water consumer in Colorado. But the state's demand for water has increased because of rapid urban growth and development of oil and gas industry. Urban communities started buying agricultural water rights to satisfy their growing demands. However, alternative land uses for farms without water right are limited and often they are left fallow. Colorado's newly finalized water plan recognizes agriculture dry-up as one of the primary water challenges of the state and supports projects that explore alternatives to the permanent transfer of agricultural water rights to municipal and industrial users. This research has investigated deficit irrigation and limited irrigation strategies as methods of reducing farm water consumption as well as methods of temporary transfer of water, viable under Colorado's Water Law. These two sets of information formed a conceptual framework for defining an effective transfer method. An economic model was developed to determine optimal water partitioning between on-farm water uses and off-farm water renting. The model proves partitioning water is only optimal when crop water production function is concave; for linear functions the optimal option is to allocate all farm water to the most profitable. Field experimentation has determined the effect of water scarcity on agricultural production and revenue. In particular, crop yield response to water stress was quantified in experimental farms for three common crops in Colorado: corn, sunflower, and sorghum-sudangrass. The filed observations support a linear crop water production function for sorghum-sudangrass and a concave function for corn and sunflower with corn function being more concave than sunflower function. The economic model was used for South Platte River Basin to determine the minimum renting price of water for water partitioning to be optimal. The results show current renting prices of water in South Platte River Basin are too low and need to increase to more than six times before partitioning of water becomes a worthwhile practice. It was also concluded that two set of engineering tools are required for implementation of deficit irrigation; 1) tools to accurately apply desired amount of water, and 2) tools to measure farm consumptive use on a daily basis. At institutional level, Colorado Water Law's no-injury and anti-speculation rules need to be simplified for deficit irrigation to be a worthwhile alternative method to buy-and-dry

Synchronization of spatiotemporal patterns and modeling disease spreading using excitable media

Studies of the photosensitive Belousov-Zhabotinsky (BZ) reaction are reviewed and the essential features of excitable media are described. The synchronization of two distributed Belousov-Zhabotinsky systems is experimentally and theoretically investigated. Symmetric local coupling of the systems is made possible with the use of a video camera-projector scheme. The spatial disorder of the coupled systems, with random initial configurations of spirals, gradually decreases until a final state is attained, which corresponds to a synchronized state with a single spiral in each system. The experimental observations are compared with numerical simulations of two identical Oregonator models with symmetric local coupling, and a systematic study reveals generalized synchronization of spiral waves. Modeling studies on disease spreading have been reviewed. The excitable medium of the photosensitive BZ reaction is used to model disease spreading, with static networks, dynamic networks, and a domain model. The spatiotemporal dynamics of disease spreading in these complex networks with diffusive and non-diffusive connections is characterized. The experimental and numerical studies reveal that disease spreading in these model systems is highly dependent on the non-diffusive connections