Search results for: Yilun Xu

Authors: Yilun Shang

Abstract:

In this paper, we deal with the fundamental concepts and properties of ergodicity coefficients in a hierarchical sense by making use of partition. Moreover, we establish a hierarchial Hajnal’s inequality improving some previous results.

Keywords: Stochastic matrix, ergodicity coefficient, partition.

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Authors: Yilun Shang

Abstract:

We consider a heterogeneously mixing SIR stochastic epidemic process in populations described by a general graph. Likelihood theory is developed to facilitate statistic inference for the parameters of the model under complete observation. We show that these estimators are asymptotically Gaussian unbiased estimates by using a martingale central limit theorem.

Keywords: statistic inference, maximum likelihood, epidemicmodel, heterogeneous mixing.

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Authors: Yilun Shang

Abstract:

Let {Xi}i≥1 be a martingale difference sequence with Xi = Si - Si-1. Under some regularity conditions, we show that (X2 1+· · ·+X2N n)-1/2SNn is asymptotically normal, where {Ni}i≥1 is a sequence of positive integer-valued random variables tending to infinity. In a similar manner, a backward (or reverse) martingale central limit theorem with random indices is provided.

Keywords: central limit theorem, martingale difference sequence, backward martingale.

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Authors: Yilun Shang

Abstract:

We study a long-range percolation model in the hierarchical lattice ΩN of order N where probability of connection between two nodes separated by distance k is of the form min{αβ−k, 1}, α ≥ 0 and β > 0. The parameter α is the percolation parameter, while β describes the long-range nature of the model. The ΩN is an example of so called ultrametric space, which has remarkable qualitative difference between Euclidean-type lattices. In this paper, we characterize the sizes of large clusters for this model along the line of some prior work. The proof involves a stationary embedding of ΩN into Z. The phase diagram of this long-range percolation is well understood.

Keywords: percolation, component, hierarchical lattice, phase transition.

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Authors: Yilun Shang

Abstract:

In this paper, we investigate the appearance of the giant component in random subgraphs G(p) of a given large finite graph family Gn = (Vn, En) in which each edge is present independently with probability p. We show that if the graph Gn satisfies a weak isoperimetric inequality and has bounded degree, then the probability p under which G(p) has a giant component of linear order with some constant probability is bounded away from zero and one. In addition, we prove the probability of abnormally large order of the giant component decays exponentially. When a contact graph is modeled as Gn, our result is of special interest in the study of the spread of infectious diseases or the identification of community in various social networks.

Keywords: subgraph, expander, random graph, giant component, percolation.

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Authors: Yilun Shang

Abstract:

In this paper we consider a one-dimensional random geometric graph process with the inter-nodal gaps evolving according to an exponential AR(1) process. The transition probability matrix and stationary distribution are derived for the Markov chains concerning connectivity and the number of components. We analyze the algorithm for hitting time regarding disconnectivity. In addition to dynamical properties, we also study topological properties for static snapshots. We obtain the degree distributions as well as asymptotic precise bounds and strong law of large numbers for connectivity threshold distance and the largest nearest neighbor distance amongst others. Both exact results and limit theorems are provided in this paper.

Keywords: random geometric graph, autoregressive process, degree, connectivity, Markovian, wireless network.

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Authors: Xu Tao, Yilun Xu, Dingwei Xiang, Yaofei Sun

Abstract:

The practice of urban planning and construction based on the concept of the “low carbon eco-city” has been universally accepted by the academic community in response to urban issues such as population, resources, environment, and social development. Based on this, the current article first analyzes the concepts of low carbon eco-city, then builds a complex adaptive system (CAS) theory based on Chinese traditional philosophical thinking, and analyzes the adaptive relationship between material and non-material elements. A three-dimensional evaluation model of natural ecology, economic low carbon, and social harmony was constructed. Finally, the construction of a low carbon eco-city index system in Hexi Newtown of Nanjing was used as an example to verify the effectiveness of the research results; this paradigm provides a new way to achieve a low carbon eco-city system.

Keywords: Complex adaptive system, low carbon ecology, index system, model.

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Authors: Rushi Tan, Yilun Xu, Xiaohui Wang

Abstract:

The restrained construction zoning, an important part in the urban master plan, is a necessary planning tool to control the city sprawl, to guarantee the reservation implementation of the various types of protective elements, and to realize the storage of the essential urban spatial resources. Simultaneously, owing to the diverse constitutes of restrained construction area and the various stakeholders involved in, its planning requires an overall consideration of all elements from the perspective of coordination+, balance and practicability to deal with the problems and conflicts in this process. Taking Yangzijin Ecological Restrained Construction Area in Yangzhou as an example, this study analyzes all the potential actors, agencies and stakeholders in this restrained construction area, as well as the relevant conflicts between each other. Besides, this study tries to build up a planning procedure based on the framework of governance theory, and proposes a possible planning method that combines "rigidity" and "flexibility" to protect the ecological limitation boundary, to take every interest into account, and to promote economic development in a harmonious society.

Keywords: Restrained construction area, governance, stakeholder, flexible stratagem, China.

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Authors: Yang Wenjuan, Xu Yilun

Abstract:

Based on the comparative analysis of the relevant evaluation methods of walking environment, this paper selects the combined evaluation method of macro urban morphology analysis and micro urban design quality survey, then investigates and analyzes the walking environment of three rail transit station area in Nanjing to explore the influence factor and internal relation of walkability of rail transit station area. Analysis shows that micro urban design factors have greater impact on the walkability of rail transit station area compared with macro urban morphology factors, the convenience is the key factor in the four aspects of convenience, security, identity and comfortability of the urban design factors, the convenience is not only affected by the block network form, but also related to the quality of the street space. The overall evaluation of walkability comes from the overlapping and regrouping of the walking environment at different levels, but some environmental factors play a leading role. The social attributes of pedestrians also partly influence their walking perception and evaluation.

Keywords: Rail transit station area, walkability, evaluation, influence factors.

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