arXiv subjects

Bin Jiang

Publications and source records attributed to Bin Jiang.

At least 127 records · Page 7Linked to original sources

arXiv2018

Hierarchical Scaling in Systems of Natural Cities

Hierarchies can be modeled by a set of exponential functions, from which we can derive a set of power laws indicative of scaling. The solution to a scaling relation equation is always a power law. The scaling laws are followed by many natural and social phenomena such as cities, earthquakes, and rivers. This paper is devoted to revealing the power law behaviors in systems of natural cities by reconstructing the hierarchy with cascade structure. The cities of America, Britain, France, and Germany are taken as examples to make empirical analyses. The hierarchical scaling relations can be well fitted to the data points within the scaling ranges of the size and area of the natural cities. The size-number and area-number scaling exponents are close to 1, and the allometric scaling exponent is slightly less than 1. The results show that natural cities follow hierarchical scaling laws and hierarchical conservation law very well. The hierarchical scaling law proved to be derived from entropy maximization principle, and this suggests that the evolution of natural cities is dominated by entropy maximization laws. This study is helpful for scientists to understand the power law behavior in the development of cities and systems of cities.

physics.soc-ph↗

arXiv2018

A Smooth Curve as a Fractal Under the Third Definition

It is commonly believed in the literature that smooth curves, such as circles, are not fractal, and only non-smooth curves, such as coastlines, are fractal. However, this paper demonstrates that a smooth curve can be fractal, under the new, relaxed, third definition of fractal - a set or pattern is fractal if the scaling of far more small things than large ones recurs at least twice. The scaling can be rephrased as a hierarchy, consisting of numerous smallest, a very few largest, and some in between the smallest and the largest. The logarithmic spiral, as a smooth curve, is apparently fractal because it bears the self-similar property, or the scaling of far more small squares than large ones recurs multiple times, or the scaling of far more small bends than large ones recurs multiple times. A half-circle or half-ellipse and the UK coastline (before or after smooth processing) are fractal, if the scaling of far more small bends than large ones recurs at least twice. Keywords: Third definition of fractal, head/tail breaks, bends, ht-index, scaling hierarchy

math.GM↗

arXiv2018

Geographic Space as a Living Structure for Predicting Human Activities Using Big Data

Inspired by Christopher Alexanders conception of the world - space is not lifeless or neutral but a living structure involving far more small things than large ones a topological representation has been previously developed to characterize the living structure or the wholeness of geographic space. This paper further develops the topological representation and living structure for predicting human activities in geographic space. Based on millions of street nodes of the United Kingdom extracted from OpenStreetMap, we established living structures at different levels of scale in a nested manner. We found that tweet locations at different levels of scale, such as country and city, can be well predicted by the underlying living structure. The high predictability demonstrates that the living structure and the topological representation are efficient and effective for better understanding geographic forms. Based on this major finding, we argue that the topological representation is a truly multi-scale representation, and point out that existing geographic representations are essentially single scale, so they bear many scale problems such as modifiable areal unit problem, the conundrum of length, and the ecological fallacy. We further discuss on why the living structure is an efficient and effective instrument for structuring geospatial big data, and why Alexanders organic worldview constitutes the third view of space. Keywords: Organic worldview, topological representation, tweet locations, natural cities, scaling of geographic space

physics.soc-ph↗

arXiv2017

How Complex Is a Fractal? Head/tail Breaks and Fractional Hierarchy

A fractal bears a complex structure that is reflected in a scaling hierarchy, indicating that there are far more small things than large ones. This scaling hierarchy can be effectively derived using head/tail breaks - a clustering and visualization tool for data with a heavy-tailed distribution - and quantified by an ht-index, indicating the number of clusters or hierarchical levels, a head/tail breaks-induced integer. However, this integral ht-index has been found to be less precise for many fractals at their different phrases of development. This paper refines the ht-index as a fraction to measure the scaling hierarchy of a fractal more precisely within a coherent whole, and further assigns a fractional ht-index - the fht-index - to an individual data value of a data series that represents the fractal. We developed two case studies to demonstrate the advantages of the fht-index, in comparison with the ht-index. We found that the fractional ht-index or fractional hierarchy in general can help characterize a fractal set or pattern in a much more precise manner. The index may help create intermediate map scales between two consecutive map scales. Keywords: Ht-index, fractal, scaling, complexity, fht-index

physics.data-an↗

arXiv2017

Final State Resolved Quantum Predissociation Dynamics of SO2(C1B2) and Its Isotopomers via a Crossing with a Singlet Repulsive State

The fragmentation dynamics of predissociative SO2(C1B2) is investigated on an accurate adiabatic potential energy surface (PES) determined from high level ab initio data. This singlet PES features non-C2v equilibrium geometries for SO2, which are separated from the SO + O dissociation limit by a barrier resulting from a conical intersection with a repulsive singlet state. The ro-vibrational state distribution of the SO fragment is determined quantum mechanically for many predissociative states of several sulfur isotopomers of SO2. Significant rotational and vibrational excitations are found in the SO fragment. It is shown that these fragment internal state distributions are strongly dependent on the predissociative vibronic states, and the excitation typically increases with the photon energy.

physics.chem-ph↗

arXiv2017

A Topological Representation for Taking Cities as a Coherent Whole

A city is a whole, as are all cities in a country. Within a whole, individual cities possess different degrees of wholeness, defined by Christopher Alexander as a life-giving order or simply a living structure. To characterize the wholeness and in particular to advocate for wholeness as an effective design principle, this paper develops a geographic representation that views cities as a whole. This geographic representation is topology-oriented, so fundamentally differs from existing geometry-based geographic representations. With the topological representation, all cities are abstracted as individual points and put into different hierarchical levels, according to their sizes and based on head/tail breaks - a classification scheme and visualization tool for data with a heavy tailed distribution. These points of different hierarchical levels are respectively used to create Thiessen polygons. Based on polygon-polygon relationships, we set up a complex network. In this network, small polygons point to adjacent large polygons at the same hierarchical level and contained polygons point to containing polygons across two consecutive hierarchical levels. We computed the degrees of wholeness for individual cities, and subsequently found that the degrees of wholeness possess both properties of differentiation and adaptation. To demonstrate, we developed four case studies of all China and UK natural cities, as well as Beijing and London natural cities, using massive amounts of street nodes and Tweet locations. The topological representation and the kind of topological analysis in general can be applied to any design or pattern, such as carpets, Baroque architecture and artifacts, and fractals in order to assess their beauty, echoing the introductory quote from Christopher Alexander. Keywords: Wholeness, natural cities, head/tail breaks, complex networks, scaling hierarchy, urban design

nlin.AO↗

arXiv2017

Mode specific electronic friction in dissociative chemisorption on metal surfaces: H$_2$ on Ag(111)

Electronic friction and the ensuing nonadiabatic energy loss play an important role in chemical reaction dynamics at metal surfaces. Using molecular dynamics with electronic friction evaluated on-the-fly from Density Functional Theory, we find strong mode dependence and a dominance of nonadiabatic energy loss along the bond stretch coordinate for scattering and dissociative chemisorption of H$_2$ on the Ag(111) surface. Exemplary trajectories with varying initial conditions indicate that this mode-specificity translates into modulated energy loss during a dissociative chemisorption event. Despite minor nonadiabatic energy loss of about 5\%, the directionality of friction forces induces dynamical steering that affects individual reaction outcomes, specifically for low-incidence energies and vibrationally excited molecules. Mode-specific friction induces enhanced loss of rovibrational rather than translational energy and will be most visible in its effect on final energy distributions in molecular scattering experiments.

cond-mat.mtrl-sci↗

arXiv2016

A Socio-geographic Perspective on Human Activities in Social Media

Location-based social media make it possible to understand social and geographic aspects of human activities. However, previous studies have mostly examined these two aspects separately without looking at how they are linked. The study aims to connect two aspects by investigating whether there is any correlation between social connections and users' check-in locations from a socio-geographic perspective. We constructed three types of networks: a people-people network, a location-location network, and a city-city network from former location-based social media Brightkite and Gowalla in the U.S., based on users' check-in locations and their friendships. We adopted some complexity science methods such as power-law detection and head/tail breaks classification method for analysis and visualization. Head/tail breaks recursively partitions data into a few large things in the head and many small things in the tail. By analyzing check-in locations, we found that users' check-in patterns are heterogeneous at both the individual and collective levels. We also discovered that users' first or most frequent chec-in locations can be the representatives of users' spatial information. The constructed networks based on these locations are very heterogeneous, as indicated by the high ht-index. Most importantly, the node degree of the networks correlates highly with the population at locations (mostly with R-square being 0.7) or cities (above 0.9). This correlation indicates that the geographic distributions of the social media users relate highly to their online social connections. Keywords: social networks, check-in locations, natural cities, power law, head/tail breaks, ht-index

nlin.AO↗

arXiv2016

A Complex-Network Perspective on Alexander's Wholeness

The wholeness, conceived and developed by Christopher Alexander, is what exists to some degree or other in space and matter, and can be described by precise mathematical language. However, it remains somehow mysterious and elusive, and therefore hard to grasp. This paper develops a complex network perspective on the wholeness to better understand the nature of order or beauty for sustainable design. I bring together a set of complexity-science subjects such as complex networks, fractal geometry, and in particular underlying scaling hierarchy derived by head/tail breaks - a classification scheme and a visualization tool for data with a heavy-tailed distribution, in order to make Alexander's profound thoughts more accessible to design practitioners and complexity-science researchers. Through several case studies (some of which Alexander studied), I demonstrate that the complex-network perspective helps reduce the mystery of wholeness and brings new insights to Alexander's thoughts on the concept of wholeness or objective beauty that exists in fine and deep structure. The complex-network perspective enables us to see things in their wholeness, and to better understand how the kind of structural beauty emerges from local actions guided by the 15 fundamental properties, and by differentiation and adaptation processes. The wholeness goes beyond current complex network theory towards design or creation of living structures. Keywords: Theory of centers, living geometry, Christopher Alexander, head/tail breaks, and beauty

nlin.AO↗

arXiv2016

A Fractal Perspective on Scale in Geography

Scale is a fundamental concept that has attracted persistent attention in geography literature over the past several decades. However, it creates enormous confusion and frustration, particularly in the context of geographic information science, because of scale-related issues such as image resolution, and the modifiable areal unit problem (MAUP). This paper argues that the confusion and frustration mainly arise from Euclidean geometric thinking, with which locations, directions, and sizes are considered absolute, and it is time to reverse this conventional thinking. Hence, we review fractal geometry, together with its underlying way of thinking, and compare it to Euclidean geometry. Under the paradigm of Euclidean geometry, everything is measurable, no matter how big or small. However, geographic features, due to their fractal nature, are essentially unmeasurable or their sizes depend on scale. For example, the length of a coastline, the area of a lake, and the slope of a topographic surface are all scale-dependent. Seen from the perspective of fractal geometry, many scale issues, such as the MAUP, are inevitable. They appear unsolvable, but can be dealt with. To effectively deal with scale-related issues, we introduce topological and scaling analyses based on street-related concepts such as natural streets, street blocks, and natural cities. We further contend that spatial heterogeneity, or the fractal nature of geographic features, is the first and foremost effect of two spatial properties, because it is general and universal across all scales. Keywords: Scaling, spatial heterogeneity, conundrum of length, MAUP, topological analysis

math.HO↗

arXiv2016

Spatial Distribution of City Tweets and Their Densities

Social media outlets such as Twitter constitute valuable data sources for understanding human activities in the virtual world from a geographic perspective. This paper examines spatial distribution of tweets and densities within cities. The cities refer to natural cities that are automatically aggregated from a country's small street blocks, so called city blocks. We adopted street blocks (rather than census tracts) as the basic geographic units and topological center (rather than geometric center) in order to assess how tweets and densities vary from the center to the peripheral border. We found that, within a city from the center to the periphery, the tweets first increase and then decrease, while the densities decrease in general. These increases and decreases fluctuate dramatically, and differ significantly from those if census tracts are used as the basic geographic units. We also found that the decrease of densities from the center to the periphery is less significant, and even disappears, if an arbitrarily defined city border is adopted. These findings prove that natural cities and their topological centers are better than their counterparts (conventionally defined cities and city centers) for geographic research. Based on this study, we believe that tweet densities can be a good surrogate of population densities. If this belief is proved to be true, social media data could help solve the dispute surrounding exponential or power function of urban population density. Keywords: Big data, natural cities, street blocks, urban density, topological distance

physics.soc-ph↗

arXiv2016

A City Is a Complex Network

A city is not a tree but a semi-lattice. To use a perhaps more familiar term, a city is a complex network. The complex network constitutes a unique topological perspective on cities and enables us to better understand the kind of problem a city is. The topological perspective differentiates it from the perspectives of Euclidean geometry and Gaussian statistics that deal with essentially regular shapes and more or less similar things. Many urban theories, such as the Central Place Theory, Zipf's Law, the Image of the City, and the Theory of Centers can be interpreted from the point of view of complex networks. A livable city consists of far more small things than large ones, and their shapes tend to be irregular and rough. This chapter illustrates the complex network view and argues that we must abandon the kind of thinking (mis-)guided by Euclidean geometry and Gaussian statistics, and instead adopt fractal geometry, power-law statistics, and Alexander's living geometry to develop sustainable cities. Keywords: Scaling, living structure, theory of centers, objective beauty, head/tail breaks

physics.soc-ph↗

arXiv2015

Big Data Is not just a New Type, but a New Paradigm

This paper is a first draft of the introduction to the special issue on volunteered geographic information published in Computers, Environment and Urban Systems (2015, 53, 1-122). In this short paper, I put georeferenced big data (hereafter, big data) such as tweets locations in comparison with small data such as census data in terms of data characteristics, and further argued that big data differs fundamentally from small data in terms of data analytics, both geometrially and statistically. I would like to thank my colleague Dr. Jean-Claude Thill, who expanded the draft towards a broader scope.

physics.data-an↗

arXiv2015

Line Simplification

As an important practice of map generalization, the aim of line simplification is to reduce the number of points without destroying the essential shape or the salient character of a cartographic curve. This subject has been well-studied in the literature. This entry attempts to introduce how line simplification can be guided by fractal geometry, or the recurring scaling pattern of far more small things than large ones. The line simplification process involves nothing more than removing small things while retaining large ones based on head/tail breaks.

math.HO↗

arXiv2015

Characterizing the Heterogeneity of the OpenStreetMap Data and Community

OpenStreetMap (OSM) constitutes an unprecedented, free, geographic information source contributed by millions of individuals, resulting in a database of great volume and heterogeneity. In this study, we characterize the heterogeneity of the entire OSM database and historical archive in the context of big data. We consider all users, geographic elements, and user contributions from an eight-year data archive, at a size of 692 GB. We rely on some nonlinear methods such as power-law statistics and head/tail breaks to uncover and illustrate the underlying scaling properties. All three aspects (users, elements, and contributions) demonstrate striking power laws or heavy-tailed distributions. The heavy-tailed distributions imply that there are far more small elements than large ones, far more inactive users than active ones, and far more lightly edited elements than heavily edited ones. Furthermore, about 500 users in the core group of the OSM are highly networked in terms of collaboration. Keywords: OpenStreetMap, big data, power laws, head/tail breaks, ht-index

cs.SI↗

arXiv2015

Wholeness as a Hierarchical Graph to Capture the Nature of Space

According to Christopher Alexander's theory of centers, a whole comprises numerous, recursively defined centers for things or spaces surrounding us. Wholeness is a type of global structure or life-giving order emerging from the whole as a field of the centers. The wholeness is an essential part of any complex system and exists, to some degree or other, in spaces. This paper defines wholeness as a hierarchical graph, in which individual centers are represented as the nodes and their relationships as the directed links. The hierarchical graph gets its name from the inherent scaling hierarchy revealed by the head/tail breaks, which is a classification scheme and visualization tool for data with a heavy-tailed distribution. We suggest that (1) the degrees of wholeness for individual centers should be measured by PageRank (PR) scores based on the notion that high-degree-of-life centers are those to which many high-degree-of-life centers point, and (2) that the hierarchical levels, or the ht-index of the PR scores induced by the head/tail breaks can characterize the degree of wholeness for the whole: the higher the ht-index, the more life or wholeness in the whole. Three case studies applied to the Alhambra building complex and the street networks of Manhattan and Sweden illustrate that the defined wholeness captures fairly well human intuitions on the degree of life for the geographic spaces. We further suggest that the mathematical model of wholeness be an important model of geographic representation, because it is topological oriented that enables us to see the underlying scaling structure. The model can guide geodesign, which should be considered as the wholeness-extending transformations that are essentially like the unfolding processes of seeds or embryos, for creating beautiful built and natural environments or with a high degree of wholeness.

physics.soc-ph↗

arXiv2015

Defining Least Community as a Homogeneous Group in Complex Networks

This paper introduces a new concept of least community that is as homogeneous as a random graph, and develops a new community detection algorithm from the perspective of homogeneity or heterogeneity. Based on this concept, we adopt head/tail breaks - a newly developed classification scheme for data with a heavy-tailed distribution - and rely on edge betweenness given its heavy-tailed distribution to iteratively partition a network into many heterogeneous and homogeneous communities. Surprisingly, the derived communities for any self-organized and/or self-evolved large networks demonstrate very striking power laws, implying that there are far more small communities than large ones. This notion of far more small things than large ones constitutes a new fundamental way of thinking for community detection. Keywords: head/tail breaks, ht-index, scaling, k-means, natural breaks, and classification

physics.soc-ph↗

arXiv2015

Head/tail Breaks for Visualization of City Structure and Dynamics

The things surrounding us vary dramatically, which implies that there are far more small things than large ones, e.g., far more small cities than large ones in the world. This dramatic variation is often referred to as fractal or scaling. To better reveal the fractal or scaling structure, a new classification scheme, namely head/tail breaks, has been developed to recursively derive different classes or hierarchical levels. The head/tail breaks works as such: divide things into a few large ones in the head (those above the average) and many small ones (those below the average) in the tail, and recursively continue the dividing process for the large ones (or the head) until the notion of far more small things than large ones has been violated. This paper attempts to argue that head/tail breaks can be a powerful visualization tool for illustrating structure and dynamics of natural cities. Natural cities refer to naturally or objectively defined human settlements based on a meaningful cutoff averaged from a massive amount of units extracted from geographic information. To illustrate the effectiveness of head/tail breaks in visualization, I have developed several case studies applied to natural cities derived from the points of interest, social media location data, and time series nighttime images. I further elaborate on head/tail breaks related to fractals, beauty, and big data. Keywords: Big data, social media, nighttime images, natural cities, fractals, head/tail breaks, ht-index

physics.soc-ph↗