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Bin Jiang

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preprint2026arXiv

CFSPMNet: Cross-subject Fourier-guided Spatial-Patch Mamba Network for EEG Motor Imagery Decoding in Stroke Patients

Motor imagery electroencephalography (MI-EEG) decoding offers a non-invasive route for post-stroke rehabilitation, but cross-patient use remains difficult because pathological neural reorganization changes task-related EEG dynamics, aperiodic activity, local excitability, cross-regional coordination, and trial-level brain-state context. This makes source-learned MI representations unreliable for unseen patients. To address this problem, we propose CFSPMNet, a cross-patient adaptation framework that models post-stroke MI-EEG as latent neural-state organization. CFSPMNet combines a Fourier-Reorganized State Mamba Network (FRSM) with Shared-Private Prototype Matching (SPPM). FRSM represents each trial as a latent physiological token sequence, reorganizes token states in the Fourier domain, and uses Fourier-derived trial context to guide Mamba state-space propagation. SPPM improves target pseudo-label updating by combining semantic confidence with shared-private physiological consistency, filtering confident but physiologically inconsistent target predictions. Leave-one-subject-out experiments on two stroke MI-EEG datasets show that CFSPMNet outperforms representative CNN-, Transformer-, Mamba-, and adaptation-based baselines, achieving average accuracies of 68.23% on XW-Stroke and 73.33% on 2019-Stroke, with gains of 5.63 and 8.25 percentage points over the strongest competitors. Ablation, sensitivity, feature-alignment, pseudo-label selection, and neurophysiological visualization analyses further support the roles of Fourier-domain token-state reorganization and calibrated pseudo-label updating. These results suggest that latent neural-state modeling can improve rehabilitation-oriented cross-patient BCI decoding. Code is available at https://github.com/wxk1224/CFSPMNet.

preprint2026arXiv

Multi-proposal Collaboration and Multi-task Training for Weakly-supervised Video Moment Retrieval

This study focuses on weakly-supervised Video Moment Retrieval (VMR), aiming to identify a moment semantically similar to the given query within an untrimmed video using only video-level correspondences, without relying on temporal annotations during training. Previous methods either aggregate predictions for all instances in the video, or indirectly address the task by proposing reconstructions for the query. However, these methods often produce low-quality temporal proposals, struggle with distinguishing misaligned moments in the same video, or lack stability due to a reliance on a single auxiliary task. To address these limitations, we present a novel weakly-supervised method called Multi-proposal Collaboration and Multi-task Training (MCMT). Initially, we generate multiple proposals and derive corresponding learnable Gaussian masks from them. These masks are then combined to create a high-quality positive sample mask, highlighting video clips most relevant to the query. Concurrently, we classify other clips in the same video as the easy negative sample and the entire video as the hard negative sample. During training, we introduce forward and inverse masked query reconstruction tasks to impose more substantial constraints on the network, promoting more robust and stable retrieval performance. Extensive experiments on two standard benchmarks affirm the effectiveness of the proposed method in VMR.

preprint2024arXiv

First-principles Nonadiabatic Dynamics of Molecules at Metal Surfaces with Vibrationally Coupled Electron Transfer

Accurate description of nonadiabatic dynamics of molecules at metal surfaces involving electron transfer has been a longstanding challenge for theory. Here, we tackle this problem by first constructing high-dimensional neural network diabatic potentials including state crossings determined by constrained density functional theory, then applying mixed quantum-classical surface hopping simulations to evolve coupled electron-nuclear motion. Our approach accurately describes the nonadiabatic effects in CO scattering from Au(111) without empirical parameters and yields results agreeing well with experiments under various conditions for this benchmark system. We find that both adiabatic and nonadiabatic energy loss channels have important contributions to the vibrational relaxation of highly vibrationally excited CO(vi = 17), whereas relaxation of low vibrationally excited states of CO(vi = 2) is weak and dominated by nonadiabatic energy loss. The presented approach paves the way for accurate first-principles simulations of electron transfer mediated nonadiabatic dynamics at metal surfaces.

preprint2023arXiv

Living Images: A Recursive Approach to Computing the Structural Beauty of Images or the Livingness of Space

Any image is perceived subconsciously as a coherent structure (or whole) with two contrast substructures: figure and ground. The figure consists of numerous auto-generated substructures with an inherent hierarchy of far more smalls than larges. Through these substructures, the structural beauty of an image (L) can be computed by the multiplication of the number of substructures (S) and their inherent hierarchy (H). This definition implies that the more substructures, the more living or more structurally beautiful, and the higher hierarchy of the substructures, the more living or more structurally beautiful. This is the non-recursive approach to the structural beauty of images or the livingness of space. In this paper we develop a recursive approach, which derives all substructures of an image (instead of its figure) and continues the deriving process for those decomposable substructures until none of them are decomposable. All of the substructures derived at different iterations (or recursive levels) together constitute a living structure; hence the notion of living images. We applied the recursive approach to a set of images and found that (1) the number of substructures of an image is far lower (3 percent on average) than the number of pixels and the centroids of the substructures can effectively capture the skeleton or saliency of the image; (2) all the images have the recursive levels more than three, indicating that they are indeed living images; (3) no more than 2 percent of the substructures are decomposable; (4) structural beauty can be measured by the recursively defined substructures, as well as their decomposable subsets. The recursive approach is proved to be more robust than the non-recursive approach. The recursive approach and the non-recursive approach both provide a powerful means to study the livingness or vitality of space in cities and communities.

preprint2022arXiv

Cerebrovascular morphology in aging and disease -- imaging biomarkers for ischemic stroke and Alzheimers disease

Background and Purpose: Altered brain vasculature is a key phenomenon in several neurologic disorders. This paper presents a quantitative assessment of vascular morphology in healthy and diseased adults including changes during aging and the anatomical variations in the Circle of Willis (CoW). Methods: We used our automatic method to segment and extract novel geometric features of the cerebral vasculature from MRA scans of 175 healthy subjects, 45 AIS, and 50 AD patients after spatial registration. This is followed by quantification and statistical analysis of vascular alterations in acute ischemic stroke (AIS) and Alzheimer's disease (AD), the biggest cerebrovascular and neurodegenerative disorders. Results: We determined that the CoW is fully formed in only 35 percent of healthy adults and found significantly increased tortuosity and fractality, with increasing age and with disease -- both AIS and AD. We also found significantly decreased vessel length, volume and number of branches in AIS patients. Lastly, we found that AD cerebral vessels exhibited significantly smaller diameter and more complex branching patterns, compared to age-matched healthy adults. These changes were significantly heightened with progression of AD from early onset to moderate-severe dementia. Conclusion: Altered vessel geometry in AIS patients shows that there is pathological morphology coupled with stroke. In AD due to pathological alterations in the endothelium or amyloid depositions leading to neuronal damage and hypoperfusion, vessel geometry is significantly altered even in mild or early dementia. The specific geometric features and quantitative comparisons demonstrate potential for using vascular morphology as a non-invasive imaging biomarker for neurologic disorders.

preprint2022arXiv

Mixed-UNet: Refined Class Activation Mapping for Weakly-Supervised Semantic Segmentation with Multi-scale Inference

Deep learning techniques have shown great potential in medical image processing, particularly through accurate and reliable image segmentation on magnetic resonance imaging (MRI) scans or computed tomography (CT) scans, which allow the localization and diagnosis of lesions. However, training these segmentation models requires a large number of manually annotated pixel-level labels, which are time-consuming and labor-intensive, in contrast to image-level labels that are easier to obtain. It is imperative to resolve this problem through weakly-supervised semantic segmentation models using image-level labels as supervision since it can significantly reduce human annotation efforts. Most of the advanced solutions exploit class activation mapping (CAM). However, the original CAMs rarely capture the precise boundaries of lesions. In this study, we propose the strategy of multi-scale inference to refine CAMs by reducing the detail loss in single-scale reasoning. For segmentation, we develop a novel model named Mixed-UNet, which has two parallel branches in the decoding phase. The results can be obtained after fusing the extracted features from two branches. We evaluate the designed Mixed-UNet against several prevalent deep learning-based segmentation approaches on our dataset collected from the local hospital and public datasets. The validation results demonstrate that our model surpasses available methods under the same supervision level in the segmentation of various lesions from brain imaging.

preprint2022arXiv

REANN: A PyTorch-based End-to-End Multi-functional Deep Neural Network Package for Molecular, Reactive and Periodic Systems

In this work, we present a general purpose deep neural network package for representing energies, forces, dipole moments, and polarizabilities of atomistic systems. This so-called recursively embedded atom neural network model takes both advantages of the physically inspired atomic descriptor based neural networks and the message-passing based neural networks. Implemented in the PyTorch framework, the training process is parallelized on both CPU and GPU with high efficiency and low memory, in which all hyperparameters can be optimized automatically. We demonstrate the state-of-the-art accuracy, high efficiency, scalability, and universality of this package by learning not only energies (with or without forces), but also dipole moment vectors and polarizability tensors, in various molecular, reactive, and periodic systems. An interface between a trained model and LAMMPs is provided for large scale molecular dynamics simulations. We hope that this open-source toolbox will allow future method development and applications of machine learned potential energy surfaces and quantum-chemical properties of molecules, reactions, and materials.

preprint2021arXiv

An all-dielectric photonic crystal with unconventional higher-order topology

Photonic crystals have been demonstrated as a versatile platform for the study of topological phenomena. The recent discovery of higher order topological insulators introduces new aspects of topological photonic crystals which are yet to be explored. Here, we propose a dielectric photonic crystal with unconventional higher order band topology. Besides the conventional spectral features of gapped edge states and in gap corner states, topological band theory predicts that the corner boundary of the higher-order topological insulator hosts a 2/3 fractional charge. We demonstrate that in the photonic crystal such a fractional charge can be verified from the local density of states of photons, through the concept of local spectral charge as an analog of the local electric charge due to band filling anomaly in electronic systems. Furthermore, we show that by introducing a disclination in the proposed photonic crystal, localized states and a 2/3 fractional spectral charge emerge around the disclination core, as the manifestation of the bulk disclination correspondence. The predicted effects can be readily observed in the state-of-the-art experiments and may lead to potential applications in integrated and quantum photonics.

preprint2021arXiv

Experimental realization of single-plaquette gauge flux insertion and topological Wannier cycles

Gauge fields are at the heart of the fundamental science of our universe and various materials. For instance, Laughlin's gedanken experiment of gauge flux insertion played a major role in understanding the quantum Hall effects. Gauge flux insertion into a single unit-cell, though crucial for detecting exotic quantum phases and for the ultimate control of quantum dynamics and classical waves, however, has not yet been achieved in laboratory. Here, we report on the experimental realization of gauge flux insertion into a single plaquette in a lattice system with the gauge phase ranging from 0 to 2pi which is realized through a novel approach based on three consecutive procedures: the dimension extension, creating an engineered dislocation and the dimensional reduction. Furthermore, we discover that the single-plaquette gauge flux insertion leads to a new phenomenon termed as the topological Wannier cycles, i.e., the cyclic spectral flows across multiple band gaps which are manifested as the topological boundary states (TBSs) on the plaquette. Such topological Wannier cycles emerge only if the Wannier centers are enclosed by the flux-carrying plaquette. Exploiting acoustic metamaterials and versatile pump-probe measurements, we observe the topological Wannier cycles by detecting the TBSs in various ways and confirm the single-plaquette gauge flux insertion by measuring the gauge phase accumulation on the plaquette. Our work unveils an unprecedented regime for lattice gauge systems and a fundamental topological response which could empower future studies on artificial gauge fields and topological materials.

preprint2021arXiv

Representing Geographic Space as a Hierarchy of Recursively Defined Subspaces for Computing the Degree of Order

As Christopher Alexander discovered, all space or matter - either organic or inorganic - has some degree of order in it according to its structure and arrangement. The order refers to a kind of structural character, called living structure, which is defined as a mathematical structure that consists of numerous substructures with an inherent hierarchy. Across the hierarchy, there are far more small substructures than large ones, while on each level of the hierarchy the substructures are more or less similar in size. In this paper we develop a new approach to representing geographic space as a hierarchy of recursively defined subspaces for computing the degree of order. A geographic space is first represented as a hierarchy of recursively defined subspaces, and all the subspaces are then topologically represented as a network for computing the degree of order of the geographic space, as well as that of its subspaces. Unlike conventional geographic representations, which are mechanical in nature, this new geographic representation is organic, conceived, and developed under the third view of space; that is, space is neither lifeless nor neutral, but a living structure capable of being more living or less living. Thus, the order can also be referred to as life, beauty, coherence, or harmony. We applied the new representation to three urban environments, 253 patterns, and 35 black-white strips to verify it and to demonstrate advantages of the new approach and the new kind of order. We further discuss the implications of the approach and the order on geographic information science and sustainable urban planning. Keywords: Living structure, pattern language, life, wholeness, coherence, structural beauty

preprint2020arXiv

Accelerating Atomistic Simulations with Piecewise Machine Learned Ab Initio Potentials at Classical Force Field-like Cost

Machine learning methods have nowadays become easy-to-use tools for constructing high-dimensional interatomic potentials with ab initio accuracy. Although machine learned interatomic potentials are generally orders of magnitude faster than first-principles calculations, they remain much slower than classical force fields, at the price of using more complex structural descriptors. To bridge this efficiency gap, we propose an embedded atom neural network approach with simple piecewise switching function based descriptors, resulting in a favorable linear scaling with the number of neighbor atoms. Numerical examples validate that this piecewise machine learning model can be over an order of magnitude faster than various popular machine learned potentials with comparable accuracy for both metallic and covalent materials, approaching the speed of the fastest embedded atom method (i.e. several μs/atom per CPU core). The extreme efficiency of this approach promises its potential in first-principles atomistic simulations of very large systems and/or in long timescale.

preprint2020arXiv

Automatic Segmentation, Feature Extraction and Comparison of Healthy and Stroke Cerebral Vasculature

Accurate segmentation of cerebral vasculature and a quantitative assessment of cerebrovascular morphology is critical to various diagnostic and therapeutic purposes and is pertinent to studying brain health and disease. However, this is still a challenging task due to the complexity of the vascular imaging data. We propose an automated method for cerebral vascular segmentation without the need of any manual intervention as well as a method to skeletonize the binary volume to extract vascular geometric features which can characterize vessel structure. We combine a probabilistic vessel-enhancing filtering with an active-contour technique to segment magnetic resonance and computed tomography angiograms (MRA and CTA) and subsequently extract the vessel centerlines and diameters to calculate the geometrical properties of the vasculature. Our method was validated using a 3D phantom of the Circle-of-Willis region with 84% mean Dice Similarity and 85% mean Pearson Correlation with minimal modified Hausdorff distance error. We applied this method to a dataset of healthy subjects and stroke patients and present a quantitative comparison between them. We found significant differences in the geometric features including total length (2.88 +/- 0.38 m for healthy and 2.20 +/- 0.67 m for stroke), volume (40.18 +/- 25.55 ml for healthy and 34.43 +/- 21.83 ml for stroke), tortuosity (3.24 +/- 0.88 rad/cm for healthy and 5.80 +/- 0.92 rad/cm for stroke) and fractality (box dimension 1.36 +/- 0.28 for healthy vs. 1.69 +/- 0.20 for stroke). This technique can be applied on any imaging modality and can be used in the future to automatically obtain the 3D segmented vasculature for diagnosis and treatment planning of Stroke and other cerebrovascular diseases (CVD) in the clinic and also to study the morphological changes caused by various CVD.

preprint2020arXiv

Automatically growing global reactive neural network potential energy surfaces: a trajectory free active learning strategy

An efficient and trajectory-free active learning method is proposed to automatically sample data points for constructing globally accurate reactive potential energy surfaces (PESs) using neural networks (NNs). Although NNs do not provide the predictive variance as the Gaussian process regression does, we can alternatively minimize the negative of the squared difference surface (NSDS) given by two different NN models to actively locate the point where the PES is least confident. A batch of points in the minima of this NSDS can be iteratively added into the training set to improve the PES. The configuration space is gradually and globally covered with no need to run classical trajectory (or equivalently molecular dynamics) simulations. Through refitting the available analytical PESs of H3 and OH3 reactive systems, we demonstrate the efficiency and robustness of this new strategy, which enables fast convergence of the reactive PESs with respect to the number of points in terms of quantum scattering probabilities.

preprint2020arXiv

Constrained R-CNN: A general image manipulation detection model

Recently, deep learning-based models have exhibited remarkable performance for image manipulation detection. However, most of them suffer from poor universality of handcrafted or predetermined features. Meanwhile, they only focus on manipulation localization and overlook manipulation classification. To address these issues, we propose a coarse-to-fine architecture named Constrained R-CNN for complete and accurate image forensics. First, the learnable manipulation feature extractor learns a unified feature representation directly from data. Second, the attention region proposal network effectively discriminates manipulated regions for the next manipulation classification and coarse localization. Then, the skip structure fuses low-level and high-level information to refine the global manipulation features. Finally, the coarse localization information guides the model to further learn the finer local features and segment out the tampered region. Experimental results show that our model achieves state-of-the-art performance. Especially, the F1 score is increased by 28.4%, 73.2%, 13.3% on the NIST16, COVERAGE, and Columbia dataset.

preprint2020arXiv

Context-Integrated and Feature-Refined Network for Lightweight Object Parsing

Semantic segmentation for lightweight object parsing is a very challenging task, because both accuracy and efficiency (e.g., execution speed, memory footprint or computational complexity) should all be taken into account. However, most previous works pay too much attention to one-sided perspective, either accuracy or speed, and ignore others, which poses a great limitation to actual demands of intelligent devices. To tackle this dilemma, we propose a novel lightweight architecture named Context-Integrated and Feature-Refined Network (CIFReNet). The core components of CIFReNet are the Long-skip Refinement Module (LRM) and the Multi-scale Context Integration Module (MCIM). The LRM is designed to ease the propagation of spatial information between low-level and high-level stages. Furthermore, channel attention mechanism is introduced into the process of long-skip learning to boost the quality of low-level feature refinement. Meanwhile, the MCIM consists of three cascaded Dense Semantic Pyramid (DSP) blocks with image-level features, which is presented to encode multiple context information and enlarge the field of view. Specifically, the proposed DSP block exploits a dense feature sampling strategy to enhance the information representations without significantly increasing the computation cost. Comprehensive experiments are conducted on three benchmark datasets for object parsing including Cityscapes, CamVid, and Helen. As indicated, the proposed method reaches a better trade-off between accuracy and efficiency compared with the other state-of-the-art methods.

preprint2020arXiv

Efficient and Accurate Simulations of Vibrational and Electronic Spectra with Symmetry-Preserving Neural Network Models for Tensorial Properties

Machine learning has revolutionized the high-dimensional representations for molecular properties such as potential energy. However, there are scarce machine learning models targeting tensorial properties, which are rotationally covariant. Here, we propose tensorial neural network (NN) models to learn both tensorial response and transition properties, in which atomic coordinate vectors are multiplied with scalar NN outputs or their derivatives to preserve the rotationally covariant symmetry. This strategy keeps structural descriptors symmetry invariant so that the resulting tensorial NN models are as efficient as their scalar counterparts. We validate the performance and universality of this approach by learning response properties of water oligomers and liquid water, and transition dipole moment of a model structural unit of proteins. Machine learned tensorial models have enabled efficient simulations of vibrational spectra of liquid water and ultraviolet spectra of realistic proteins, promising feasible and accurate spectroscopic simulations for biomolecules and materials.

preprint2020arXiv

Joint Beamforming And Power Splitting Design For C-RAN With Multicast Fronthaul

In this paper, we investigate the joint beamforming and power splitting design problem in a base station (BS) cluster-based cloud radio access network (C-RAN) with multicast fronthaul, where users are jointly served by BSs within each cluster. Meanwhile, each user can simultaneously obtain information and energy from received signals. On this basis, under predefined minimum harvested energy of each user and maximum transmit power of each BS and central processor, we formulate a sum rate maximization problem by jointly optimizing multicast fronthaul beamforming, cooperative access beamforming and power split ratios. Due to the difficulty in solving the formulated problem, we first transform it into a convex one by successive convex approximate and semidefinite program (SDP) relaxation techniques, and then propose an effective iterative algorithm. Moreover, we design a randomization method that can always obtain the rank-one solution. Finally, numerical results are conducted to validate the effectiveness of our proposed algorithm.

preprint2020arXiv

Regularized L21-Based Semi-NonNegative Matrix Factorization

We present a general-purpose data compression algorithm, Regularized L21 Semi-NonNegative Matrix Factorization (L21 SNF). L21 SNF provides robust, parts-based compression applicable to mixed-sign data for which high fidelity, individualdata point reconstruction is paramount. We derive a rigorous proof of convergenceof our algorithm. Through experiments, we show the use-case advantages presentedby L21 SNF, including application to the compression of highly overdeterminedsystems encountered broadly across many general machine learning processes.

preprint2020arXiv

Rethinking Image Inpainting via a Mutual Encoder-Decoder with Feature Equalizations

Deep encoder-decoder based CNNs have advanced image inpainting methods for hole filling. While existing methods recover structures and textures step-by-step in the hole regions, they typically use two encoder-decoders for separate recovery. The CNN features of each encoder are learned to capture either missing structures or textures without considering them as a whole. The insufficient utilization of these encoder features limit the performance of recovering both structures and textures. In this paper, we propose a mutual encoder-decoder CNN for joint recovery of both. We use CNN features from the deep and shallow layers of the encoder to represent structures and textures of an input image, respectively. The deep layer features are sent to a structure branch and the shallow layer features are sent to a texture branch. In each branch, we fill holes in multiple scales of the CNN features. The filled CNN features from both branches are concatenated and then equalized. During feature equalization, we reweigh channel attentions first and propose a bilateral propagation activation function to enable spatial equalization. To this end, the filled CNN features of structure and texture mutually benefit each other to represent image content at all feature levels. We use the equalized feature to supplement decoder features for output image generation through skip connections. Experiments on the benchmark datasets show the proposed method is effective to recover structures and textures and performs favorably against state-of-the-art approaches.

preprint2019arXiv

A Recursive Definition of Goodness of Space for Bridging the Concepts of Space and Place for Sustainability

Conceived and developed by Christopher Alexander through his life's work: The Nature of Order, wholeness is defined as a mathematical structure of physical space in our surroundings. Yet, there was no mathematics, as Alexander admitted then, that was powerful enough to capture his notion of wholeness. Recently, a mathematical model of wholeness, together with its topological representation, has been developed that is capable of addressing not only why a space is good, but also how much goodness the space has. This paper develops a structural perspective on goodness of space - both large- and small-scale - in order to bridge two basic concepts of space and place through the very concept of wholeness. The wholeness provides a de facto recursive definition of goodness of space from a holistic and organic point of view. A space is good, genuinely and objectively, if its adjacent spaces are good, the larger space to which it belongs is good, and what is contained in the space is also good. Eventually, goodness of space - sustainability of space - is considered a matter of fact rather than of opinion under the new view of space: space is neither lifeless nor neutral, but a living structure capable of being more living or less living, or more sustainable or less sustainable. Under the new view of space, geography or architecture will become part of complexity science, not only for understanding complexity, but also for making and remaking complex or living structures. Keywords: Scaling law, head/tail breaks, living structure, beauty, streets, cities

preprint2019arXiv

Alexander's Wholeness as the Scientific Foundation of Sustainable Urban Design and Planning

As Christopher Alexander conceived and defined through his life's work - The Nature of Order - wholeness is a recursive structure that recurs in space and matter and is reflected in human minds and cognition. Based on the definition of wholeness, a mathematical model of wholeness, together with its topological representation, has been developed, and it is able to address not only why a structure is beautiful, but also how much beauty the structure has. Given the circumstance, this paper is attempted to argue for the wholeness as the scientific foundation of sustainable urban design and planning, with the help of the mathematical model and topological representation. We start by introducing the wholeness as a mathematical structure of physical space that pervasively exists in our surroundings, along with two fundamental laws - scaling law and Tobler's law - that underlie the 15 properties for characterizing and making living structures. We argue that urban design and planning can be considered to be wholeness-extending processes, guided by two design principles of differentiation and adaptation, to transform a space - in a piecemeal fashion - into a living or more living structure. We further discuss several other urban design theories and how they can be justified by and placed within the theory of wholeness. With the wholeness as the scientific foundation, urban design can turn into a rigorous science with creation of living structures as the primary aim. Keywords: Beauty, life, scaling law, adaptation, differentiation, and organic world view

preprint2018arXiv

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

preprint2018arXiv

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

preprint2018arXiv

Spatial Heterogeneity, Scale, Data Character, and Sustainable Transport in the Big Data Era

In light of the emergence of big data, I have advocated and argued for a paradigm shift from Tobler's law to scaling law, from Euclidean geometry to fractal geometry, from Gaussian statistics to Paretian statistics, and - more importantly - from Descartes' mechanistic thinking to Alexander's organic thinking. Fractal geometry falls under the third definition of fractal - that is, a set or pattern is fractal if the scaling of far more small things than large ones recurs multiple times (Jiang and Yin 2014) - rather than under the second definition of fractal, which requires a power law between scales and details (Mandelbrot 1982). The new fractal geometry is more towards living geometry that "follows the rules, constraints, and contingent conditions that are, inevitably, encountered in the real world" (Alexander et al. 2012, p. 395), not only for understanding complexity, but also for creating complex or living structure (Alexander 2002-2005). This editorial attempts to clarify why the paradigm shift is essential and to elaborate on several concepts, including spatial heterogeneity (scaling law), scale (or the fourth meaning of scale), data character (in contrast to data quality), and sustainable transport in the big data era.

preprint2018arXiv

Why Topology Matters in Predicting Human Activities

Geographic space is better understood through the topological relationship of the underlying streets (note: entire streets rather than street segments), which enables us to see scaling or fractal or living structure of far more less-connected streets than well-connected ones. It is this underlying scaling structure that makes human activities predictable, albeit in the sense of collective rather than individual human moving behavior. This topological analysis has not yet received its deserved attention in the literature, as many researchers continue to rely on segment analysis for predicting human activities. The segment-analysis-based methods are essentially geometric, with a focus on geometric details of locations, lengths, and directions, and are unable to reveal the scaling property, which means they cannot be used for human activities prediction. We conducted a series of case studies using London streets and tweet location data, based on related concepts such as natural streets, and natural street segments (or street segments for short), axial lines, and axial line segments (or line segments for short). We found that natural streets are the best representation in terms of human activities or traffic prediction, followed by axial lines, and that neither street segments nor line segments bear a good correlation between network parameters and tweet locations. These findings point to the fact that the reason why axial lines-based space syntax, or the kind of topological analysis in general, works has little to do with individual human travel behavior or ways that human conceptualize distances or spaces. Instead, it is the underlying scaling hierarchy of streets - numerous least-connected, a very few most-connected, and some in between the least- and most-connected - that makes human activities predictable.

preprint2017arXiv

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

preprint2017arXiv

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

preprint2016arXiv

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

preprint2016arXiv

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

preprint2016arXiv

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

preprint2016arXiv

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

preprint2016arXiv

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

preprint2015arXiv

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

preprint2015arXiv

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

preprint2015arXiv

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

preprint2015arXiv

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.

preprint2014arXiv

Different Ways of Thinking about Street Networks and Spatial Analysis

Street networks, as one of the oldest infrastructures of transport in the world, play a significant role in modernization, sustainable development, and human daily activities in both ancient and modern times. Although street networks have been well studied in a variety of engineering and scientific disciplines, including for instance transport, geography, urban planning, economics, and even physics, our understanding of street networks in terms of their structure and dynamics remains limited, especially when dealing with such real-world problems as traffic jams, pollution, and human evacuations for disaster management. One goal of this special issue is to promote different ways of thinking about understanding street networks, and of conducting spatial analysis.

preprint2014arXiv

Geospatial Analysis Requires a Different Way of Thinking: The Problem of Spatial Heterogeneity

Geospatial analysis is very much dominated by a Gaussian way of thinking, which assumes that things in the world can be characterized by a well-defined mean, i.e., things are more or less similar in size. However, this assumption is not always valid. In fact, many things in the world lack a well-defined mean, and therefore there are far more small things than large ones. This paper attempts to argue that geospatial analysis requires a different way of thinking - a Paretian way of thinking that underlies skewed distribution such as power laws, Pareto and lognormal distributions. I review two properties of spatial dependence and spatial heterogeneity, and point out that the notion of spatial heterogeneity in current spatial statistics is only used to characterize local variance of spatial dependence. I subsequently argue for a broad perspective on spatial heterogeneity, and suggest it be formulated as a scaling law. I further discuss the implications of Paretian thinking and the scaling law for better understanding of geographic forms and processes, in particular while facing massive amounts of social media data. In the spirit of Paretian thinking, geospatial analysis should seek to simulate geographic events and phenomena from the bottom up rather than correlations as guided by Gaussian thinking.

preprint2014arXiv

The Evolution of Natural Cities from the Perspective of Location-Based Social Media

This paper examines the former location-based social medium Brightkite, over its three-year life span, based on the concept of natural cities. The term 'natural cities' refers to spatially clustered geographic events, such as the agglomerated patches aggregated from individual social media users' locations. We applied the head/tail division rule to derive natural cities, based on the fact that there are far more low-density locations than high-density locations on the earth surface. More specifically, we generated a triangulated irregular network, made up of individual unique user locations, and then categorized small triangles (smaller than an average) as natural cities for the United States (mainland) on a monthly basis. The concept of natural cities provides a powerful means to develop new insights into the evolution of real cities, because there are virtually no data available to track the history of cities across their entire life spans and at very fine spatial and temporal scales. Therefore, natural cities can act as a good proxy of real cities, in the sense of understanding underlying interactions, at a global level, rather than of predicting cities, at an individual level. Apart from the data produced and the contributed methods, we established new insights into the structure and dynamics of natural cities, e.g., the idea that natural cities evolve in nonlinear manners at both spatial and temporal dimensions. Keywords: Big data, head/tail breaks, ht-index, power laws, fractal, and nonlinearity

preprint2014arXiv

The Fractal Nature of Maps and Mapping

A fractal can be simply understood as a set or pattern in which there are far more small things than large ones, e.g., far more small geographic features than large ones on the earth surface, or far more large-scale maps than small-scale maps for a geographic region. This paper attempts to argue and provide evidence for the fractal nature of maps and mapping. It is the underlying fractal structure of geographic features, either natural or human-made, that make reality mappable, large-scale maps generalizable, and cities imageable. The fractal nature is also what underlies the beauty of maps. After introducing some key fractal concepts such as recursion, self-similarity, scaling ratio, and scaling exponent, this paper demonstrates that fractal thought is rooted in long-standing map-making practices such as series maps subdivision, visual hierarchy, and Töpfer's radical law. Drawing on previous studies on head/tail breaks, mapping can be considered a head/tail breaks process; that is to divide things around an average, according to their geometric, topological and/or semantic properties, into the head (for those above the average) and the tail (for those below the average), and recursively continue the dividing process for the head for map generalization, statistical mapping, and cognitive mapping. Given the fractal nature of maps and mapping, cartography should be considered a perfect combination of science and art, and scaling must be formulated as a law of cartography or that of geography in general. Keywords: Scaling of geographic features, map generalization, statistical mapping, cognitive mapping, head/tail breaks

preprint2013arXiv

A New Kind of Beauty Out of the Underlying Scaling of Geographic Space

Geographic space demonstrates scaling or hierarchy, implying that there are far more small things than large ones. The scaling pattern of geographic space, if visualized properly (i.e., based on head/tail breaks), can evoke a sense of beauty. This is our central argument. This beauty is a new type of aesthetic at a deeper structural level, and differs in essence from an intuitive sense of harmony, perceived in terms of color, shape, texture, and ratio. This new kind of beauty was initially defined and discovered by Christopher Alexander, and promoted in his master work The Nature of Order. To paraphrase Mandelbrot, this is the beauty for the sake of science rather than for art's sake or for the sake of commerce. Throughout the paper, we attempt to argue and illustrate that the scaling of geographic space possesses this new kind of beauty, which has a positive impact on human well-being. The paper further draws upon the previous work of Nikos Salingaros and Richard Taylor on the beauty in architecture and arts to support our argument. Keywords: Aesthetics, heavy-tailed distributions, head/tail breaks, Zipf's law, and fractals

preprint2013arXiv

Editorial: Making GIScience Research More Open Access

This is the editorial for the special issue on "data-intensive geospatial computing", which I guest edited with the International Journal of Geographical Information Science (Taylor & Francis). As remarked in the editorial, the special issue is particularly special in the sense that all source and data are published together with the published papers. This editorial elaborates on scholarly communication, with particular attention to publishing data alongside papers and the emergence of open access journals, in order to make our research more open access.

preprint2013arXiv

Ht-Index for Quantifying the Fractal or Scaling Structure of Geographic Features

Although geographic features, such as mountains and coastlines, are fractal, some studies have claimed that the fractal property is not universal. This claim, which is false, is mainly attributed to the strict definition of fractal dimension as a measure or index for characterizing the complexity of fractals. In this paper, we propose an alternative, the ht-index, to quantify the fractal or scaling structure of geographic features. A geographic feature has ht-index h if the pattern of far more small things than large ones recurs (h-1) times at different scales. The higher the ht-index, the more complex the geographic feature. We conduct three case studies to illustrate how the computed ht-indices capture the complexity of different geographic features. We further discuss how the ht-index is complementary to fractal dimension, and elaborate on a dynamic view behind the ht-index that enables better understanding of geographic forms and processes. Keywords: Scaling of geographic space, fractal dimension, Richardson plot, nested rank-size plots, and head/tail breaks

preprint2013arXiv

Scaling of Geographic Space as a Universal Rule for Map Generalization

Map generalization is a process of producing maps at different levels of detail by retaining essential properties of the underlying geographic space. In this paper, we explore how the map generalization process can be guided by the underlying scaling of geographic space. The scaling of geographic space refers to the fact that in a geographic space small things are far more common than large ones. In the corresponding rank-size distribution, this scaling property is characterized by a heavy tailed distribution such as a power law, lognormal, or exponential function. In essence, any heavy tailed distribution consists of the head of the distribution (with a low percentage of vital or large things) and the tail of the distribution (with a high percentage of trivial or small things). Importantly, the low and high percentages constitute an imbalanced contrast, e.g., 20 versus 80. We suggest that map generalization is to retain the objects in the head and to eliminate or aggregate those in the tail. We applied this selection rule or principle to three generalization experiments, and found that the scaling of geographic space indeed underlies map generalization. We further relate the universal rule to Töpfer's radical law (or trained cartographers' decision making in general), and illustrate several advantages of the universal rule. Keywords: Head/tail division rule, head/tail breaks, heavy tailed distributions, power law, and principles of selection

preprint2013arXiv

Scaling of Geographic Space from the Perspective of City and Field Blocks and Using Volunteered Geographic Information

Scaling of geographic space refers to the fact that for a large geographic area its small constituents or units are much more common than the large ones. This paper develops a novel perspective to the scaling of geographic space using large street networks involving both cities and countryside. Given a street network of an entire country, we decompose the street network into individual blocks, each of which forms a minimum ring or cycle such as city blocks and field blocks. The block sizes demonstrate the scaling property, i.e., far more small blocks than large ones. Interestingly, we find that the mean of all the block sizes can easily separate between small and large blocks- a high percentage (e.g., 90%) of smaller ones and a low percentage (e.g., 10%) of larger ones. Based on this regularity, termed as the head/tail division rule, we propose an approach to delineating city boundaries by grouping the smaller blocks. The extracted city sizes for the three largest European countries (France, Germany and UK) exhibit power law distributions. We further define the concept of border number as a topological distance of a block far from the outmost border to map the center(s) of the country and the city. We draw an analogy between a country and a city (or geographic space in general) with a complex organism like the human body or the human brain to further elaborate on the power of this block perspective in reflecting the structure or patterns of geographic space. Keywords: Power law distribution, scaling of geographic space, data-intensive geospatial computing, street networks

preprint2013arXiv

Topological Structure of Urban Street Networks from the Perspective of Degree Correlations

Many complex networks demonstrate a phenomenon of striking degree correlations, i.e., a node tends to link to other nodes with similar (or dissimilar) degrees. From the perspective of degree correlations, this paper attempts to characterize topological structures of urban street networks. We adopted six urban street networks (three European and three North American), and converted them into network topologies in which nodes and edges respectively represent individual streets and street intersections, and compared the network topologies to three reference network topologies (biological, technological, and social). The urban street network topologies (with the exception of Manhattan) showed a consistent pattern that distinctly differs from the three reference networks. The topologies of urban street networks lack striking degree correlations in general. Through reshuffling the network topologies towards for example maximum or minimum degree correlations while retaining the initial degree distributions, we found that all the surrogate topologies of the urban street networks, as well as the reference ones, tended to deviate from small world properties. This implies that the initial degree correlations do not have any positive or negative effect on the networks' performance or functions. Keywords: Scale free, small world, rewiring, rich club effect, reshuffle, and complex networks

preprint2012arXiv

Computing the Image of the City

Kevin Lynch proposed a theory of the image of the city identifying five elements that make the city legible or imageable. The resulting mental map of the city was conventionally derived through some qualitative processes, relying on interactions with city residents to ask them to recall city elements from their minds. This paper proposes a process by which the image of the city can be quantitatively derived automatically using computer technology and geospatial databases of the city. This method is substantially based on and inspired by Christopher Alexander's living structure and Nikos Salingaros' structural order, as a city with the living structure or structural order tends to be legible and imageable. With the increasing availability of geographic information of urban environments at very fine scales or resolutions (for example, trajectories data about human activities), the proposal or solution described in this paper is particularly timely and relevant for urban studies and architectural design. Keywords: Mental maps, head/tail division rule, legibility, imageability, power law, scaling, and hierarchy.

preprint2012arXiv

Head/tail Breaks: A New Classification Scheme for Data with a Heavy-tailed Distribution

This paper introduces a new classification scheme - head/tail breaks - in order to find groupings or hierarchy for data with a heavy-tailed distribution. The heavy-tailed distributions are heavily right skewed, with a minority of large values in the head and a majority of small values in the tail, commonly characterized by a power law, a lognormal or an exponential function. For example, a country's population is often distributed in such a heavy-tailed manner, with a minority of people (e.g., 20 percent) in the countryside and the vast majority (e.g., 80 percent) in urban areas. This heavy-tailed distribution is also called scaling, hierarchy or scaling hierarchy. This new classification scheme partitions all of the data values around the mean into two parts and continues the process iteratively for the values (above the mean) in the head until the head part values are no longer heavy-tailed distributed. Thus, the number of classes and the class intervals are both naturally determined. We therefore claim that the new classification scheme is more natural than the natural breaks in finding the groupings or hierarchy for data with a heavy-tailed distribution. We demonstrate the advantages of the head/tail breaks method over Jenks' natural breaks in capturing the underlying hierarchy of the data. Keywords: data classification, head/tail division rule, natural breaks, scaling, and hierarchy

preprint2012arXiv

On joint ruin probabilities of a two-dimensional risk model with constant interest rate

In this note we consider the two-dimensional risk model introduced in Avram et al. \cite{APP08} with constant interest rate. We derive the integral-differential equations of the Laplace transforms, and asymptotic expressions for the finite time ruin probabilities with respect to the joint ruin times $T_{\rm max}(u_1,u_2)$ and $T_{\rm min}(u_1,u_2)$ respectively.

preprint2012arXiv

Temperature-dependent steady and transient emission properties of InGaN/GaN multiple quantum well nanorods

We observed different temperature-dependent behaviors of steady and transient emission properties in dry-etched InGaN/GaN multiple-quantum-well (MQW) nanorods and the parent MQWs. To clarify the impacts of nanofabrication on the emission properties, time-resolved photoluminescence spectra were recorded at various temperatures with carrier density in different regimes. The confinement of carrier transport was observed to play an important role to the emission properties in nanorods, inducing different temperature-dependent photoluminescence decay rates between the nanorods and MQWs. Moreover, together with other effects, such as surface damages and partial relaxation of the strain, the confinement effect causes faster recombination of carriers in nanorods.

preprint2012arXiv

The Image of the City Out of the Underlying Scaling of City Artifacts or Locations

Two fundamental issues surrounding research on the image of the city respectively focus on the city's external and internal representations. The external representation in the context of this paper refers to the city itself, external to human minds, while the internal representation concerns how the city is represented in human minds internally. This paper deals with the first issue, i.e., what trait the city has that make it imageable? We develop an argument that the image of the city arises from the underlying scaling of city artifacts or locations. This scaling refers to the fact that, in an imageable city (a city that can easily be imaged in human minds), small city artifacts are far more common than large ones; or alternatively low dense locations are far more common than high dense locations. The sizes of city artifacts in a rank-size plot exhibit a heavy tailed distribution consisting of the head, which is composed of a minority of unique artifacts (vital and very important), and the tail, which is composed of redundant other artifacts (trivial and less important). Eventually, those extremely unique and vital artifacts in the top head, i.e., what Lynch called city elements, make up the image of the city. We argue that the ever-increasing amount of geographic information on cities, in particular obtained from social media such as Flickr and Twitter, can turn research on the image of the city, or cognitive mapping in general, into a quantitative manner. The scaling property might be formulated as a law of geography. Keywords: Scaling of geographic space, face of the city, cognitive maps, power law, and heavy tailed distributions.

preprint2012arXiv

Why Can the Image of the City be Formed?

The aim of this short paper is to summarize my recent preprint (arXiv:1209.1112), in which I proposed a novel and probably controversial view about cognitive mapping; that is, the image of the city out of the underlying scaling of city artifacts or locations. The scaling refers to a recurring structure of far more small things than large ones. In this paper, I attempt to further clarify the central argument, and identify some possible areas of misunderstanding for readers.

preprint2011arXiv

AxialGen: A Research Prototype for Automatically Generating the Axial Map

AxialGen is a research prototype for automatically generating the axial map, which consists of the least number of the longest visibility lines (or axial lines) for representing individual linearly stretched parts of open space of an urban environment. Open space is the space between closed spaces such as buildings and street blocks. This paper aims to provide an accessible guide to software AxialGen, and the underlying concepts and ideas. We concentrate on the explanation and illustration of the key concept of bucket: its definition, formation and how it is used in generating the axial map. Keywords: Bucket, visibility, medial axes, axial lines, isovists, axial map

preprint2011arXiv

Defining and Generating Axial Lines from Street Center Lines for better Understanding of Urban Morphologies

Axial lines are defined as the longest visibility lines for representing individual linear spaces in urban environments. The least number of axial lines that cover the free space of an urban environment or the space between buildings constitute what is often called an axial map. This is a fundamental tool in space syntax, a theory developed by Bill Hillier and his colleagues for characterizing the underlying urban morphologies. For a long time, generating axial lines with help of some graphic software has been a tedious manual process that is criticized for being time consuming, subjective, or even arbitrary. In this paper, we redefine axial lines as the least number of individual straight line segments mutually intersected along natural streets that are generated from street center lines using the Gestalt principle of good continuity. Based on this new definition, we develop an automatic solution to generating the newly defined axial lines from street center lines. We apply this solution to six typical street networks (three from North America and three from Europe), and generate a new set of axial lines for analyzing the urban morphologies. Through a comparison study between the new axial lines and the conventional or old axial lines, and between the new axial lines and natural streets, we demonstrate with empirical evidence that the newly defined axial lines are a better alternative in capturing the underlying urban structure. Keywords: Space syntax, street networks, topological analysis, traffic, head/tail division rule

preprint2011arXiv

Exploring Human Mobility Patterns Based on Location Information of US Flights

A range of early studies have been conducted to illustrate human mobility patterns using different tracking data, such as dollar notes, cell phones and taxicabs. Here, we explore human mobility patterns based on massive tracking data of US flights. Both topological and geometric properties are examined in detail. We found that topological properties, such as traffic volume (between airports) and degree of connectivity (of individual airports), including both in- and outdegrees, follow a power law distribution but not a geometric property like travel lengths. The travel lengths exhibit an exponential distribution rather than a power law with an exponential cutoff as previous studies illustrated. We further simulated human mobility on the established topologies of airports with various moving behaviors and found that the mobility patterns are mainly attributed to the underlying binary topology of airports and have little to do with other factors, such as moving behaviors and geometric distances. Apart from the above findings, this study adopts the head/tail division rule, which is regularity behind any heavy-tailed distribution for extracting individual airports. The adoption of this rule for data processing constitutes another major contribution of this paper. Keywords: scaling of geographic space, head/tail division rule, power law, geographic information, agent-based simulations

preprint2010arXiv

Agent-based Simulation of Human Movement Shaped by the Underlying Street Structure

Relying on random and purposive moving agents, we simulated human movement in large street networks. We found that aggregate flow, assigned to individual streets, is mainly shaped by the underlying street structure, and that human moving behavior (either random or purposive) has little effect on the aggregate flow. This finding implies that given a street network, the movement patterns generated by purposive walkers (mostly human beings) and by random walkers are the same. Based on the simulation and correlation analysis, we further found that the closeness centrality is not a good indicator for human movement, in contrast to a long standing view held by space syntax researchers. Instead we suggest that Google's PageRank, and its modified version - weighted PageRank, betweenness and degree centralities are all better indicators for predicting aggregate flow.

preprint2010arXiv

Computing the Fewest-turn Map Directions based on the Connectivity of Natural Roads

In this paper, we introduced a novel approach to computing the fewest-turn map directions or routes based on the concept of natural roads. Natural roads are joined road segments that perceptually constitute good continuity. This approach relies on the connectivity of natural roads rather than that of road segments for computing routes or map directions. Because of this, the derived routes posses the fewest turns. However, what we intend to achieve are the routes that not only possess the fewest turns, but are also as short as possible. This kind of map direction is more effective and favorable by people, because they bear less cognitive burden. Furthermore, the computation of the routes is more efficient, since it is based on the graph encoding the connectivity of roads, which is significantly smaller than the graph of road segments. We made experiments applied to eight urban street networks from North America and Europe in order to illustrate the above stated advantages. The experimental results indicate that the fewest-turn routes posses fewer turns and shorter distances than the simplest paths and the routes provided by Google Maps. For example, the fewest-turn-and-shortest routes are on average 15% shorter than the routes suggested by Google Maps, while the number of turns is just half as much. This approach is a key technology behind FromToMap.org - a web mapping service using openstreetmap data.

preprint2010arXiv

Measuring Urban Sprawl Based on Massive Street Nodes and the Novel Concept of Natural Cities

In this paper, we develop a novel approach to measuring urban sprawl based on street nodes and naturally defined urban boundaries, both extracted from massive volunteered geographic information OpenStreetMap databases through some data-intensive computing processes. The street nodes are defined as street intersections and ends, while the naturally defined urban boundaries constitute what we call natural cities. We find that the street nodes are significantly correlated with population of cities. Based on this finding, we set street nodes as a proxy of population to measure urban sprawl. We further find that street nodes bear a significant linear relationship with city areal extents. In the plot with the x axis representing city areal extents, and the y axis street nodes, sprawling cities are located below the regression line. We verified the approach using urban areas and population from the US census, and then applied the approach to three European countries: France, Germany, and the United Kingdom for the categorization of natural cities into three classes: sprawling, compact, and normal. This categorization sets a uniform standard for cross comparing sprawling levels across an entire country. Keywords: Street networks, openstreetmap, volunteered geographic information, GIS

preprint2010arXiv

Zipf's Law for All the Natural Cities in the United States: A Geospatial Perspective

This paper provides a new geospatial perspective on whether or not Zipf's law holds for all cities or for the largest cities in the United States using a massive dataset and its computing. A major problem around this issue is how to define cities or city boundaries. Most of the investigations of Zipf's law rely on the demarcations of cities imposed by census data, e.g., metropolitan areas and census-designated places. These demarcations or definitions (of cities) are criticized for being subjective or even arbitrary. Alternative solutions to defining cities are suggested, but they still rely on census data for their definitions. In this paper we demarcate urban agglomerations by clustering street nodes (including intersections and ends), forming what we call natural cities. Based on the demarcation, we found that Zipf's law holds remarkably well for all the natural cities (over 2-4 million in total) across the United States. There is little sensitivity for the holding with respect to the clustering resolution used for demarcating the natural cities. This is a big contrast to urban areas, as defined in the census data, which do not hold stable for Zipf's law. Keywords: Natural cities, power law, data-intensive geospatial computing, scaling of geographic space

preprint2009arXiv

Automatic Generation of the Axial Lines of Urban Environments to Capture What We Perceive

Based on the concepts of isovists and medial axes, we developed a set of algorithms that can automatically generate axial lines for representing individual linearly stretched parts of open space of an urban environment. Open space is the space between buildings, where people can freely move around. The generation of the axial lines has been a key aspect of space syntax research, conventionally relying on hand-drawn axial lines of an urban environment, often called axial map, for urban morphological analysis. Although various attempts have been made towards an automatic solution, few of them can produce the axial map that consists of the least number of longest visibility lines, and none of them really works for different urban environments. Our algorithms provide a better solution than existing ones. Throughout this paper, we have also argued and demonstrated that the axial lines constitute a true skeleton, superior to medial axes, in capturing what we perceive about the urban environment. Keywords: Visibility, space syntax, topological analysis, medial axes, axial lines, isovists

preprint2009arXiv

Statistical Eigenmode Transmission over Jointly-Correlated MIMO Channels

We investigate MIMO eigenmode transmission using statistical channel state information at the transmitter. We consider a general jointly-correlated MIMO channel model, which does not require separable spatial correlations at the transmitter and receiver. For this model, we first derive a closed-form tight upper bound for the ergodic capacity, which reveals a simple and interesting relationship in terms of the matrix permanent of the eigenmode channel coupling matrix and embraces many existing results in the literature as special cases. Based on this closed-form and tractable upper bound expression, we then employ convex optimization techniques to develop low-complexity power allocation solutions involving only the channel statistics. Necessary and sufficient optimality conditions are derived, from which we develop an iterative water-filling algorithm with guaranteed convergence. Simulations demonstrate the tightness of the capacity upper bound and the near-optimal performance of the proposed low-complexity transmitter optimization approach.

preprint2007arXiv

A Topological Pattern of Urban Street Networks: Universality and Peculiarity

In this paper, we derive a topological pattern of urban street networks using a large sample (the largest so far to the best of our knowledge) of 40 U.S. cities and a few more from elsewhere of different sizes. It is found that all the topologies of urban street networks based on street-street intersection demonstrate a small world structure, and a scale-free property for both street length and connectivity degree. More specifically, for any street network, about 80% of its streets have length or degrees less than its average value, while 20% of streets have length or degrees greater than the average. Out of the 20%, there are less than 1% of streets which can form a backbone of the street network. Based on the finding, we conjecture that the 20% streets account for 80% of traffic flow, and the 1% streets constitute a cognitive map of the urban street network. We illustrate further a peculiarity about the scale-free property.

Bin Jiang

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62 published item(s)

CFSPMNet: Cross-subject Fourier-guided Spatial-Patch Mamba Network for EEG Motor Imagery Decoding in Stroke Patients

Multi-proposal Collaboration and Multi-task Training for Weakly-supervised Video Moment Retrieval

First-principles Nonadiabatic Dynamics of Molecules at Metal Surfaces with Vibrationally Coupled Electron Transfer

Living Images: A Recursive Approach to Computing the Structural Beauty of Images or the Livingness of Space

Cerebrovascular morphology in aging and disease -- imaging biomarkers for ischemic stroke and Alzheimers disease

Mixed-UNet: Refined Class Activation Mapping for Weakly-Supervised Semantic Segmentation with Multi-scale Inference

REANN: A PyTorch-based End-to-End Multi-functional Deep Neural Network Package for Molecular, Reactive and Periodic Systems

An all-dielectric photonic crystal with unconventional higher-order topology

Experimental realization of single-plaquette gauge flux insertion and topological Wannier cycles

Representing Geographic Space as a Hierarchy of Recursively Defined Subspaces for Computing the Degree of Order

Accelerating Atomistic Simulations with Piecewise Machine Learned Ab Initio Potentials at Classical Force Field-like Cost

Automatic Segmentation, Feature Extraction and Comparison of Healthy and Stroke Cerebral Vasculature

Automatically growing global reactive neural network potential energy surfaces: a trajectory free active learning strategy

Constrained R-CNN: A general image manipulation detection model

Context-Integrated and Feature-Refined Network for Lightweight Object Parsing

Efficient and Accurate Simulations of Vibrational and Electronic Spectra with Symmetry-Preserving Neural Network Models for Tensorial Properties

Joint Beamforming And Power Splitting Design For C-RAN With Multicast Fronthaul

Regularized L21-Based Semi-NonNegative Matrix Factorization

Rethinking Image Inpainting via a Mutual Encoder-Decoder with Feature Equalizations

A Recursive Definition of Goodness of Space for Bridging the Concepts of Space and Place for Sustainability

Alexander's Wholeness as the Scientific Foundation of Sustainable Urban Design and Planning

A Smooth Curve as a Fractal Under the Third Definition

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

Spatial Heterogeneity, Scale, Data Character, and Sustainable Transport in the Big Data Era

Why Topology Matters in Predicting Human Activities

A Topological Representation for Taking Cities as a Coherent Whole

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

A City Is a Complex Network

A Complex-Network Perspective on Alexander's Wholeness

A Fractal Perspective on Scale in Geography

A Socio-geographic Perspective on Human Activities in Social Media

Spatial Distribution of City Tweets and Their Densities

Characterizing the Heterogeneity of the OpenStreetMap Data and Community

Defining Least Community as a Homogeneous Group in Complex Networks

Head/tail Breaks for Visualization of City Structure and Dynamics

Wholeness as a Hierarchical Graph to Capture the Nature of Space

Different Ways of Thinking about Street Networks and Spatial Analysis

Geospatial Analysis Requires a Different Way of Thinking: The Problem of Spatial Heterogeneity

The Evolution of Natural Cities from the Perspective of Location-Based Social Media

The Fractal Nature of Maps and Mapping

A New Kind of Beauty Out of the Underlying Scaling of Geographic Space

Editorial: Making GIScience Research More Open Access

Ht-Index for Quantifying the Fractal or Scaling Structure of Geographic Features

Scaling of Geographic Space as a Universal Rule for Map Generalization

Scaling of Geographic Space from the Perspective of City and Field Blocks and Using Volunteered Geographic Information

Topological Structure of Urban Street Networks from the Perspective of Degree Correlations

Computing the Image of the City

Head/tail Breaks: A New Classification Scheme for Data with a Heavy-tailed Distribution

On joint ruin probabilities of a two-dimensional risk model with constant interest rate

Temperature-dependent steady and transient emission properties of InGaN/GaN multiple quantum well nanorods

The Image of the City Out of the Underlying Scaling of City Artifacts or Locations

Why Can the Image of the City be Formed?

AxialGen: A Research Prototype for Automatically Generating the Axial Map

Defining and Generating Axial Lines from Street Center Lines for better Understanding of Urban Morphologies

Exploring Human Mobility Patterns Based on Location Information of US Flights

Agent-based Simulation of Human Movement Shaped by the Underlying Street Structure

Computing the Fewest-turn Map Directions based on the Connectivity of Natural Roads

Measuring Urban Sprawl Based on Massive Street Nodes and the Novel Concept of Natural Cities

Zipf's Law for All the Natural Cities in the United States: A Geospatial Perspective

Automatic Generation of the Axial Lines of Urban Environments to Capture What We Perceive

Statistical Eigenmode Transmission over Jointly-Correlated MIMO Channels

A Topological Pattern of Urban Street Networks: Universality and Peculiarity