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Researcher profile

Bin Jiang

Bin Jiang contributes to research discovery and scholarly infrastructure.

ResearcherAffiliation not importedOpen to collaborate
physics.soc-phComputer Visionphysics.chem-phphysics.comp-pheess.IVnlin.AOcond-mat.mtrl-sciMachine LearningMultimediaQuantitative MethodsArtificial Intelligencecond-mat.mes-hallcond-mat.str-elDatabasesInformation Theorymath.GMmath.HOmath.ITmath.NANumerical Analysisphysics.atom-phphysics.class-phphysics.data-anphysics.opticsSocial and Information Networks

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Published work

32 published item(s)

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.

0 citations0 reviewsNo code linkedOpen access
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.

0 citations0 reviewsNo code linkedOpen access
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.

0 citations0 reviewsNo code linkedOpen access
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.

0 citations0 reviewsNo code linkedOpen access
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.

0 citations0 reviewsNo code linkedOpen access
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.

0 citations0 reviewsNo code linkedOpen access
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.

0 citations0 reviewsNo code linkedOpen access
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.

0 citations0 reviewsNo code linkedOpen access
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.

0 citations0 reviewsNo code linkedOpen access
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

0 citations0 reviewsNo code linkedOpen access
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.

0 citations0 reviewsNo code linkedOpen access
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.

0 citations0 reviewsNo code linkedOpen access
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.

0 citations0 reviewsNo code linkedOpen access
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.

0 citations0 reviewsNo code linkedOpen access
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.

0 citations0 reviewsNo code linkedOpen access
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.

0 citations0 reviewsNo code linkedOpen access
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.

0 citations0 reviewsNo code linkedOpen access
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.

0 citations0 reviewsNo code linkedOpen access
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.

0 citations0 reviewsNo code linkedOpen access
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

0 citations0 reviewsNo code linkedOpen access
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

0 citations0 reviewsNo code linkedOpen access
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

0 citations0 reviewsNo code linkedOpen access
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

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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.

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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.

0 citations0 reviewsNo code linkedOpen access
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

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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

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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

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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

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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

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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

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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

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