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Jiang Zhang

Jiang Zhang appears in the imported research catalog. Authorship, coauthor and topic links are available while profile ownership is still unclaimed.

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physics.soc-phMachine LearningSocial and Information NetworksBiological Physicsastro-ph.SRcond-mat.supr-conCryptography and Securityphysics.data-anPopulations and Evolutionq-fin.GNquant-phArtificial IntelligenceComputer Visioncond-mat.mtrl-scicond-mat.stat-mechcond-mat.str-elcs.CYInformation RetrievalInformation Theorymath.ITMolecular Networksnlin.AOnlin.CDphysics.med-phQuantitative Methods

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Published work

37 published item(s)

preprint2026arXiv

Partial Effective Information Decomposition for Synergistic Causality

Causality is a central topic in scientific inquiry, yet for complex systems, the identification and analysis of synergistic causation remain a challenging and fundamental problem. In the context of causal relations among multivariate variables, a decomposition framework grounded in interventionist causation is still lacking. To address this gap, this paper proposes Partial Effective Information Decomposition (PEID), a framework that decomposes the influence of multiple source variables on a target variable under maximum-entropy interventions into unique and synergistic information, thereby providing a unified and computable characterization of synergistic causal relations. Theoretically, in the three-variable case, the proposed framework is compatible with the major axioms of Partial Information Decomposition (PID). Empirically, under maximum-entropy interventions, correlations among input variables are removed, causing redundancy to vanish and thereby enabling PEID to compute synergistic relations. Furthermore, based on this framework, it is possible to define causal graphs containing hyperedges as well as downward causation, thus offering a unified toolkit for analyzing cross-scale and multivariate causal mechanisms in complex systems. Finally, applying the framework to a machine-learning-based air quality forecasting task on KnowAir-V2, we demonstrate that PEID can extract interpretable inter-station causal structures from a learned dynamical model. These results suggest that PEID provides a general interventionist information-theoretic tool for analyzing multivariate and synergistic causal mechanisms in complex systems.

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preprint2025arXiv

Accelerating quantum adiabatic evolution with $π$-pulse sequences

In quantum information processing, the development of fast and robust control schemes remains a central challenge. Although quantum adiabatic evolution is inherently robust against control errors, it typically demands long evolution times. In this work, we propose to achieve rapid adiabatic evolution, in which nonadiabatic transitions induced by fast changes in the system Hamiltonian are mitigated by flipping the nonadiabatic transition matrix using $π$ pulses. This enables a faster realization of adiabatic evolution while preserving its robustness. We demonstrate the effectiveness of our scheme in both two-level and three-level systems. Numerical simulations show that, for the same evolution duration, our scheme achieves higher fidelity and significantly suppresses nonadiabatic transitions compared to the traditional STIRAP protocol.

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preprint2024arXiv

Location Leakage in Federated Signal Maps

We consider the problem of predicting cellular network performance (signal maps) from measurements collected by several mobile devices. We formulate the problem within the online federated learning framework: (i) federated learning (FL) enables users to collaboratively train a model, while keeping their training data on their devices; (ii) measurements are collected as users move around over time and are used for local training in an online fashion. We consider an honest-but-curious server, who observes the updates from target users participating in FL and infers their location using a deep leakage from gradients (DLG) type of attack, originally developed to reconstruct training data of DNN image classifiers. We make the key observation that a DLG attack, applied to our setting, infers the average location of a batch of local data, and can thus be used to reconstruct the target users' trajectory at a coarse granularity. We build on this observation to protect location privacy, in our setting, by revisiting and designing mechanisms within the federated learning framework including: tuning the FL parameters for averaging, curating local batches so as to mislead the DLG attacker, and aggregating across multiple users with different trajectories. We evaluate the performance of our algorithms through both analysis and simulation based on real-world mobile datasets, and we show that they achieve a good privacy-utility tradeoff.

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preprint2022arXiv

A Universal Framework for Reconstructing Complex Networks and Node Dynamics from Discrete or Continuous Dynamics Data

Many dynamical processes of complex systems can be understood as the dynamics of a group of nodes interacting on a given network structure. However, finding such interaction structure and node dynamics from time series of node behaviours is tough. Conventional methods focus on either network structure inference task or dynamics reconstruction problem, very few of them can work well on both. This paper proposes a universal framework for reconstructing network structure and node dynamics at the same time from observed time-series data of nodes. We use a differentiable Bernoulli sampling process to generate a candidate network structure, and use neural networks to simulate the node dynamics based on the candidate network. We then adjust all the parameters with a stochastic gradient descent algorithm to maximize the likelihood function defined on the data. The experiments show that our model can recover various network structures and node dynamics at the same time with high accuracy. It can also work well on binary, discrete and continuous time-series data, and the reconstruction results are robust against noise and missing information.

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preprint2022arXiv

Completing Networks by Learning Local Connection Patterns

Network completion is a harder problem than link prediction because it does not only try to infer missing links but also nodes. Different methods have been proposed to solve this problem, but few of them employed structural information - the similarity of local connection patterns. In this paper, we propose a model named C-GIN to capture the local structural patterns from the observed part of a network based on the Graph Auto-Encoder framework equipped with Graph Isomorphism Network model and generalize these patterns to complete the whole graph. Experiments and analysis on synthetic and real-world networks from different domains show that competitive performance can be achieved by C-GIN with less information being needed, and higher accuracy compared with baseline prediction models in most cases can be obtained. We further proposed a metric "Reachable Clustering Coefficient(CC)" based on network structure. And experiments show that our model perform better on a network with higher Reachable CC.

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preprint2022arXiv

How Much Privacy Does Federated Learning with Secure Aggregation Guarantee?

Federated learning (FL) has attracted growing interest for enabling privacy-preserving machine learning on data stored at multiple users while avoiding moving the data off-device. However, while data never leaves users' devices, privacy still cannot be guaranteed since significant computations on users' training data are shared in the form of trained local models. These local models have recently been shown to pose a substantial privacy threat through different privacy attacks such as model inversion attacks. As a remedy, Secure Aggregation (SA) has been developed as a framework to preserve privacy in FL, by guaranteeing the server can only learn the global aggregated model update but not the individual model updates. While SA ensures no additional information is leaked about the individual model update beyond the aggregated model update, there are no formal guarantees on how much privacy FL with SA can actually offer; as information about the individual dataset can still potentially leak through the aggregated model computed at the server. In this work, we perform a first analysis of the formal privacy guarantees for FL with SA. Specifically, we use Mutual Information (MI) as a quantification metric and derive upper bounds on how much information about each user's dataset can leak through the aggregated model update. When using the FedSGD aggregation algorithm, our theoretical bounds show that the amount of privacy leakage reduces linearly with the number of users participating in FL with SA. To validate our theoretical bounds, we use an MI Neural Estimator to empirically evaluate the privacy leakage under different FL setups on both the MNIST and CIFAR10 datasets. Our experiments verify our theoretical bounds for FedSGD, which show a reduction in privacy leakage as the number of users and local batch size grow, and an increase in privacy leakage with the number of training rounds.

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preprint2022arXiv

NEDMP: Neural Enhanced Dynamic Message Passing

Predicting stochastic spreading processes on complex networks is critical in epidemic control, opinion propagation, and viral marketing. We focus on the problem of inferring the time-dependent marginal probabilities of states for each node which collectively quantifies the spreading results. Dynamic Message Passing (DMP) has been developed as an efficient inference algorithm for several spreading models, and it is asymptotically exact on locally tree-like networks. However, DMP can struggle in diffusion networks with lots of local loops. We address this limitation by using Graph Neural Networks (GNN) to learn the dependency amongst messages implicitly. Specifically, we propose a hybrid model in which the GNN module runs jointly with DMP equations. The GNN module refines the aggregated messages in DMP iterations by learning from simulation data. We demonstrate numerically that after training, our model's inference accuracy substantially outperforms DMP in conditions of various network structure and dynamics parameters. Moreover, compared to pure data-driven models, the proposed hybrid model has a better generalization ability for out-of-training cases, profiting from the explicitly utilized dynamics priors in the hybrid model. A PyTorch implementation of our model is at https://github.com/FeiGSSS/NEDMP.

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preprint2022arXiv

Neural Information Squeezer for Causal Emergence

The classic studies of causal emergence have revealed that in some Markovian dynamical systems, far stronger causal connections can be found on the higher-level descriptions than the lower-level of the same systems if we coarse-grain the system states in an appropriate way. However, identifying this emergent causality from the data is still a hard problem that has not been solved because the correct coarse-graining strategy can not be found easily. This paper proposes a general machine learning framework called Neural Information Squeezer to automatically extract the effective coarse-graining strategy and the macro-state dynamics, as well as identify causal emergence directly from the time series data. By decomposing a coarse-graining operation into two processes: information conversion and information dropping out, we can not only exactly control the width of the information channel, but also can derive some important properties analytically including the exact expression of the effective information of a macro-dynamics. We also show how our framework can extract the dynamics on different levels and identify causal emergence from the data on several exampled systems.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Privacy-Utility Trades in Crowdsourced Signal Map Obfuscation

Cellular providers and data aggregating companies crowdsource celluar signal strength measurements from user devices to generate signal maps, which can be used to improve network performance. Recognizing that this data collection may be at odds with growing awareness of privacy concerns, we consider obfuscating such data before the data leaves the mobile device. The goal is to increase privacy such that it is difficult to recover sensitive features from the obfuscated data (e.g. user ids and user whereabouts), while still allowing network providers to use the data for improving network services (i.e. create accurate signal maps). To examine this privacy-utility tradeoff, we identify privacy and utility metrics and threat models suited to signal strength measurements. We then obfuscate the measurements using several preeminent techniques, spanning differential privacy, generative adversarial privacy, and information-theoretic privacy techniques, in order to benchmark a variety of promising obfuscation approaches and provide guidance to real-world engineers who are tasked to build signal maps that protect privacy without hurting utility. Our evaluation results, based on multiple, diverse, real-world signal map datasets, demonstrate the feasibility of concurrently achieving adequate privacy and utility, with obfuscation strategies which use the structure and intended use of datasets in their design, and target average-case, rather than worst-case, guarantees.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Scaling laws and a general theory for the growth of public companies

Publicly traded companies are fundamental units of contemporary economies and markets and are important mechanisms through which humans interact with their environments. Understanding the general properties that underlie the processes of their growth has long been of interest, yet fundamental debates about the effects of firm size on growth have persisted. Here we develop a scaling framework that focuses on company size as the critical feature determining a variety of tradeoffs, and use this to reveal novel systematic behavior across the diversity of publicly-traded companies. Using a large database of 31,553 US companies over nearly 70 years, and 3,160 Chinese companies over 24 year, we show how the dynamics of companies expressed as scaling relationships leads to a quantitative, analytic theory for their growth. This theory produces several predictions that are in good agreement with data for both the US and China, whose markets have strikingly different histories and underlying structures. In both cases sales scale sublinearly with assets and exhibit nearly identical exponents leading, surprisingly and nontrivially, to assets that grow as a power law in time rather than exponentially, as often assumed. On the other hand, liabilities scale linearly in the US (exponent of $1.0$) but superlinearly in China (exponent of $1.09$). We show that such small differences in scaling exponents can have a significant impact on the character and long-term evolution of growth trajectories. These results illustrate that while companies are part of a larger class of growth phenomena driven by incomes and costs that scale with size, they are unique in that they grow following a temporal power-function which sets them apart from organisms, cities, nations, and markets, whose growth over time is often exponential.

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preprint2020arXiv

An interpretable planning bot for pancreas stereotactic body radiation therapy

Pancreas stereotactic body radiotherapy treatment planning requires planners to make sequential, time consuming interactions with the treatment planning system (TPS) to reach the optimal dose distribution. We seek to develop a reinforcement learning (RL)-based planning bot to systematically address complex tradeoffs and achieve high plan quality consistently and efficiently. The focus of pancreas SBRT planning is finding a balance between organs-at-risk sparing and planning target volume (PTV) coverage. Planners evaluate dose distributions and make planning adjustments to optimize PTV coverage while adhering to OAR dose constraints. We have formulated such interactions between the planner and the TPS into a finite-horizon RL model. First, planning status features are evaluated based on human planner experience and defined as planning states. Second, planning actions are defined to represent steps that planners would commonly implement to address different planning needs. Finally, we have derived a reward system based on an objective function guided by physician-assigned constraints. The planning bot trained itself with 48 plans augmented from 16 previously treated patients and generated plans for 24 cases in a separate validation set. All 24 bot-generated plans achieve similar PTV coverages compared to clinical plans while satisfying all clinical planning constraints. Moreover, the knowledge learned by the bot can be visualized and interpreted as consistent with human planning knowledge, and the knowledge maps learned in separate training sessions are consistent, indicating reproducibility of the learning process.

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preprint2020arXiv

Gumbel-softmax-based Optimization: A Simple General Framework for Optimization Problems on Graphs

In computer science, there exist a large number of optimization problems defined on graphs, that is to find a best node state configuration or a network structure such that the designed objective function is optimized under some constraints. However, these problems are notorious for their hardness to solve because most of them are NP-hard or NP-complete. Although traditional general methods such as simulated annealing (SA), genetic algorithms (GA) and so forth have been devised to these hard problems, their accuracy and time consumption are not satisfying in practice. In this work, we proposed a simple, fast, and general algorithm framework based on advanced automatic differentiation technique empowered by deep learning frameworks. By introducing Gumbel-softmax technique, we can optimize the objective function directly by gradient descent algorithm regardless of the discrete nature of variables. We also introduce evolution strategy to parallel version of our algorithm. We test our algorithm on three representative optimization problems on graph including modularity optimization from network science, Sherrington-Kirkpatrick (SK) model from statistical physics, maximum independent set (MIS) and minimum vertex cover (MVC) problem from combinatorial optimization on graph. High-quality solutions can be obtained with much less time consuming compared to traditional approaches.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Inference for Network Structure and Dynamics from Time Series Data via Graph Neural Network

Network structures in various backgrounds play important roles in social, technological, and biological systems. However, the observable network structures in real cases are often incomplete or unavailable due to measurement errors or private protection issues. Therefore, inferring the complete network structure is useful for understanding complex systems. The existing studies have not fully solved the problem of inferring network structure with partial or no information about connections or nodes. In this paper, we tackle the problem by utilizing time series data generated by network dynamics. We regard the network inference problem based on dynamical time series data as a problem of minimizing errors for predicting future states and proposed a novel data-driven deep learning model called Gumbel Graph Network (GGN) to solve the two kinds of network inference problems: Network Reconstruction and Network Completion. For the network reconstruction problem, the GGN framework includes two modules: the dynamics learner and the network generator. For the network completion problem, GGN adds a new module called the States Learner to infer missing parts of the network. We carried out experiments on discrete and continuous time series data. The experiments show that our method can reconstruct up to 100% network structure on the network reconstruction task. While the model can also infer the unknown parts of the structure with up to 90% accuracy when some nodes are missing. And the accuracy decays with the increase of the fractions of missing nodes. Our framework may have wide application areas where the network structure is hard to obtained and the time series data is rich.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Understanding the mesoscopic scaling patterns within cities

Understanding quantitative relationships between urban elements is crucial for a wide range of applications. The observation at the macroscopic level demonstrates that the aggregated urban quantities (e.g., gross domestic product) scale systematically with population sizes across cities, also known as urban scaling laws. However, at the mesoscopic level, we lack an understanding of whether the simple scaling relationship holds within cities, which is a fundamental question regarding the spatial origin of scaling in urban systems. Here, by analyzing four extensive datasets covering millions of mobile phone users and urban facilities, we investigate the scaling phenomena within cities. We find that the mesoscopic infrastructure volume and socioeconomic activity scale sub- and super-linearly with the active population, respectively. For a same scaling phenomenon, however, the exponents vary in cities of similar population sizes. To explain these empirical observations, we propose a conceptual framework by considering the heterogeneous distributions of population and facilities, and the spatial interactions between them. Analytical and numerical results suggest that, despite the large number of complexities that influence urban activities, the simple interaction rules can effectively explain the observed regularity and heterogeneity in scaling behaviors within cities.

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preprint2018arXiv

Complex Network Classification with Convolutional Neural Network

Classifying large scale networks into several categories and distinguishing them according to their fine structures is of great importance with several applications in real life. However, most studies of complex networks focus on properties of a single network but seldom on classification, clustering, and comparison between different networks, in which the network is treated as a whole. Due to the non-Euclidean properties of the data, conventional methods can hardly be applied on networks directly. In this paper, we propose a novel framework of complex network classifier (CNC) by integrating network embedding and convolutional neural network to tackle the problem of network classification. By training the classifiers on synthetic complex network data and real international trade network data, we show CNC can not only classify networks in a high accuracy and robustness, it can also extract the features of the networks automatically.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

Holonomic quantum computation in the ultrastrong-coupling regime of circuit QED

We present an experimentally feasible scheme to implement holonomic quantum computation in the ultrastrong-coupling regime of light-matter interaction. The large anharmonicity and the Z2 symmetry of the quantum Rabi model allow us to build an effective three-level Λ-structured artificial atom for quantum computation. The proposed physical implementation includes two gradiometric flux qubits and two microwave resonators where single-qubit gates are realized by a two-tone driving on one physical qubit, and a two-qubit gate is achieved with a time-dependent coupling between the field quadratures of both resonators. Our work paves the way for scalable holonomic quantum computation in ultrastrongly coupled systems.

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preprint2015arXiv

Exploring multi-layer flow network of international trade based on flow distances

Based on the approach of flow distances, the international trade flow system is studied from the perspective of multi-layer flow network. A model of multi-layer flow network is proposed for modelling and analyzing multiple types of flows in flow systems. Then, flow distances are introduced, and symmetric minimum flow distance is presented. Subsequently, we discuss the establishment of the multi-layer flow networks of international trade from two coupled viewpoints, i.e., the viewpoint of commodity flow and that of money flow. Thus, the multi-layer flow networks of international trade is explored. First, trading "trophic levels" are adopted to depict positions that economies occupied in the flow network. We find that the distributions of trading "trophic levels" have the similar clustering pattern for different types of commodity, and there are some regularities between money flow network and commodity flow network. Second, we find that active and competitive countries trade a wide spectrum of products, while inactive and underdeveloped countries trade a limited variety of products. Besides, some abnormal countries import many types of goods, which the vast majority of countries do not need to import. It may indicate an abnormal economic status. Third, harmonic node centrality is proposed and we find the phenomenon of centrality stratification. It means that competitive countries tend to occupy the central positions in the trading of a large variety of commodities, while underdeveloped countries likely in the peripheral positions in the trading of their limited varieties of products. Fourth, we find that manufactured products have significant larger mean first-passage flow distances from the source to the sink than that of primary products.

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preprint2015arXiv

Flow Distances on Open Flow Networks

Open flow network is a weighted directed graph with a source and a sink, depicting flux distributions on networks in the steady state of an open flow system. Energetic food webs, economic input-output networks, and international trade networks, are open flow network models of energy flows between species, money or value flows between industrial sectors, and goods flows between countries, respectively. Flow distances (first-passage or total) between any given two nodes $i$ and $j$ are defined as the average number of transition steps of a random walker along the network from $i$ to $j$ under some conditions. They apparently deviate from the conventional random walk distance on a closed directed graph because they consider the openness of the flow network. Flow distances are explicitly expressed by underlying Markov matrix of a flow system in this paper. With this novel theoretical conception, we can visualize open flow networks, calculating centrality of each node, and clustering nodes into groups. We apply flow distances to two kinds of empirical open flow networks, including energetic food webs and economic input-output network. In energetic food webs example, we visualize the trophic level of each species and compare flow distances with other distance metrics on graph. In input-output network, we rank sectors according to their average distances away other sectors, and cluster sectors into different groups. Some other potential applications and mathematical properties are also discussed. To summarize, flow distance is a useful and powerful tool to study open flow systems.

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preprint2015arXiv

The Hidden Geometry of Attention Diffusion

We propose a geometric model to quantify the dynamics of attention in online communities. Using clicks as a proxy of attention, we find that the diffusion of collective attention in Web forums and news sharing sites forms time-invariant "fields" whose density vary solely with distance from the center of the fields that represents the input of attention from the physical world. As time goes by, old information pieces are pushed farther from the center by new pieces, receive fewer and fewer clicks, and eventually become invisible in the virtual world. The discovered "attention fields" not only explain the fast decay of attention to information pieces, but also predict the accelerating growth of clicks against the active user population, which is a universal pattern relevant to the economics of scales of online interactions.

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preprint2013arXiv

Allometry and Dissipation of Ecological Flow Networks

An ecological flow network is a weighted directed graph in which nodes are species, edges are "who eats whom" relationships and weights are rates of energy or nutrients transfer between species. Allometric scaling is a ubiquitous feature for flow systems like river basins, vascular networks and food webs. By "ecological network analysis" method, we can reveal the hidden allometry directly on the original flow networks without cutting edges. On the other hand, dissipation law, which is another significant scaling relationship between the energy dissipation (respiration) and the throughflow of any species is also discovered on the collected flow networks. Interestingly, the exponents of allometric law ($η$) and the dissipation law ($γ$) have a strong connection for both empirical and simulated flow networks. The dissipation law exponent $γ$ rather than the topology of the network is the most important ingredient to the allometric exponent $η$. By reinterpreting $η$ as the inequality of species impacts (direct and indirect influences) to the whole network along all energy flow pathways but not the energy transportation efficiency, we found that as $γ$ increases, the relative energy loss of large nodes (with high throughflow) increases, $η$ decreases, and the inequality of the whole flow network as well as the relative importance of large species decreases. Therefore, flow structure and thermodynamic constraint are connected.

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preprint2013arXiv

Capabilities' Substitutability and the "S" Curve of Export Diversity

Product diversity, which is highly important in economic systems, has been highlighted by recent studies on international trade. We found an empirical pattern, designated as the "S-shaped curve", that models the relationship between economic size (logarithmic GDP) and export diversity (the number of varieties of export products) on the detailed international trade data. As the economic size of a country begins to increase, its export diversity initially increases in an exponential manner, but overtime, this diversity growth slows and eventually reaches an upper limit. The interdependence between size and diversity takes the shape of an S-shaped curve that an be fitted by a logistic equation. To explain this phenomenon, we introduce a new parameter called "substitutability" into the list of capabilities or factors of products in the tri-partite network model (i.e., the country-capability-product model) of Hidalgo et al. As we observe, when the substitutability is zero, the model returns to Hidalgo's original model but failed to reproduce the S-shaped curve. However, in a plot of data, the data increasingly resembles an the S-shaped curve as the substitutability expands. Therefore, the diversity ceiling effect can be explained by the substitutability of different capabilities.

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preprint2013arXiv

Constrain on superconductivity of potassium intercalated phenanthrene

Raman-scattering measurements are performed in K${_x}$phenanthrene with the nominal value ${x}$ ranging from 0 to 6.0 at room temperature. Based on the Raman spectra, two phases (${x}$ = 3.0 and 4.0) are observed among the K${_x}$phenanthrene, and the immediate phase (${x}$ = 3.5) is produced. Only the ${x}$ = 3.0 phase is found to exhibit the superconducting transition at 5 K. The C-C stretching mods are observed to broaden and become disorder in K${_x}$phenanthrene (nominal value ${x}$ =2.0, 2.5, 6.0), indicating some molecular disorder in the metal intercalation process. This disorder is expected to influence the nonmetallic nature of these materials. The absence of metallic characteristics in those nonsuperconducting phases is provided from the calculated electronic structures based on the local density approximation.

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preprint2013arXiv

Structural and vibrational properties of phenanthrene under pressure

The structural and vibrational properties of phenanthrene are measured at high pressures up to 30.2 GPa by Raman spectroscopy and synchrotron x-ray diffraction techniques. Two phase transitions are observed in raman spectra under pressures of 2.3 GPa and 5.4 GPa with significant changes of intermolecular and intramolecular vibrational modes, and all the raman peaks disappeared in the luminesce background above 10.2 GPa. Upon further compression above 20.0 GPa, three broad bands are observed respectively around 1600, 2993 and 3181 cm$^{-1}$ in Raman spectra, strongly indicating that phenanthrene has transformed into amorphous hydrogenated carbon. Based on x-ray diffraction, the structures of corresponding phases observed in Raman spectra are identified with space group of $P_{\rm}2_{1}$ for phase I at 0-2.2 GPa, $P_{\rm}$2/\emph{m} for phase II at 2.2-5.6 GPa and $P_{\rm}$2/\emph{m}+\emph{Pmmm} for phase III at 5.6-11.4 GPa, and the structure above 11.4 GPa is identified with space group of \emph{Pmmm}. Although phenanthrene has amorphized above 20.0 GPa, the amorphous hydrogenated carbon clusters still remain the crystalline characteristic based on x-ray diffraction patterns. Our results suggest that the long-range periodicity and the local disorder state coexist in phenanthrene at high pressures.

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preprint2013arXiv

The Metabolism and Growth of Web Forums

We view web forums as virtual living organisms feeding on user's attention and investigate how these organisms grow at the expense of collective attention. We find that the "body mass" ($PV$) and "energy consumption" ($UV$) of the studied forums exhibits the allometric growth property, i.e., $PV_t \sim UV_t ^ θ$. This implies that within a forum, the network transporting attention flow between threads has a structure invariant of time, despite of the continuously changing of the nodes (threads) and edges (clickstreams). The observed time-invariant topology allows us to explain the dynamics of networks by the behavior of threads. In particular, we describe the clickstream dissipation on threads using the function $D_i \sim T_i ^ γ$, in which $T_i$ is the clickstreams to node $i$ and $D_i$ is the clickstream dissipated from $i$. It turns out that $γ$, an indicator for dissipation efficiency, is negatively correlated with $θ$ and $1/γ$ sets the lower boundary for $θ$. Our findings have practical consequences. For example, $θ$ can be used as a measure of the "stickiness" of forums, because it quantifies the stable ability of forums to convert $UV$ into $PV$, i.e., to remain users "lock-in" the forum. Meanwhile, the correlation between $γ$ and $θ$ provides a convenient method to evaluate the `stickiness" of forums. Finally, we discuss an optimized "body mass" of forums at around $10^5$ that minimizes $γ$ and maximizes $θ$.

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preprint2012arXiv

Common Patterns of Energy Flow and Biomass Distribution on Weighted Food Webs

Weights of edges and nodes on food webs which are available from the empirical data hide much information about energy flows and biomass distributions in ecosystem. We define a set of variables related to weights for each species $i$, including the throughflow $T_i$, the total biomass $X_i$, and the dissipated flow $D_i$ (output to the environment) to uncover the following common patterns in 19 empirical weighted food webs: (1) DGBD distributions (Discrete version of a Generalized Beta Distribution), a kind of deformed Zipf's law, of energy flow and storage biomass; (2) The allometric scaling law $T_i\propto X_i^α$, which can be viewed as the counterpart of the Kleiber's 3/4 law at the population level; (3) The dissipation law $D_i\propto T_i^β$; and (4) The gravity law, including univariate version $f_{ij}\propto (T_iT_j)^γ$ and bivariate approvement $f_{ij}\propto T_i^{γ_1}T_j^{γ_2}$. These patterns are very common and significant in all collected webs, as a result, some remarkable regularities are hidden in weights.

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preprint2012arXiv

Growing Random Geometric Graph Models of Super-linear Scaling Law

Recent researches on complex systems highlighted the so-called super-linear growth phenomenon. As the system size $P$ measured as population in cities or active users in online communities increases, the total activities $X$ measured as GDP or number of new patents, crimes in cities generated by these people also increases but in a faster rate. This accelerating growth phenomenon can be well described by a super-linear power law $X \propto P^γ$($γ>1$). However, the explanation on this phenomenon is still lack. In this paper, we propose a modeling framework called growing random geometric models to explain the super-linear relationship. A growing network is constructed on an abstract geometric space. The new coming node can only survive if it just locates on an appropriate place in the space where other nodes exist, then new edges are connected with the adjacent nodes whose number is determined by the density of existing nodes. Thus the total number of edges can grow with the number of nodes in a faster speed exactly following the super-linear power law. The models cannot only reproduce a lot of observed phenomena in complex networks, e.g., scale-free degree distribution and asymptotically size-invariant clustering coefficient, but also resemble the known patterns of cities, such as fractal growing, area-population and diversity-population scaling relations, etc. Strikingly, only one important parameter, the dimension of the geometric space, can really influence the super-linear growth exponent $γ$.

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preprint2012arXiv

The Decentralized Structure of Collective Attention on the Web

Background: The collective browsing behavior of users gives rise to a flow network transporting attention between websites. By analyzing the structure of this network we uncovered a nontrivial scaling regularity concerning the impact of websites. Methodology: We constructed three clickstreams networks, whose nodes were websites and edges were formed by the users switching between sites. We developed an indicator Ci as a measure of the impact of site i and investigated its correlation with the traffic of the site Ai both on the three networks and across the language communities within the networks. Conclusions: We found that the impact of websites increased slower than their traffic. Specifically, there existed a scaling relationship between Ci and Ai with an exponent gamma smaller than 1. We suggested that this scaling relationship characterized the decentralized structure of the clickstream circulation: the World Wide Web is a system that favors small sites in reassigning the collective attention of users.

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preprint2011arXiv

Accelerating Growth and Size-dependent Distribution of Human Activities Online

Research on human online activities usually assumes that total activity $T$ increases linearly with active population $P$, that is, $T\propto P^γ(γ=1)$. However, we find examples of systems where total activity grows faster than active population. Our study shows that the power law relationship $T\propto P^γ(γ>1)$ is in fact ubiquitous in online activities such as micro-blogging, news voting and photo tagging. We call the pattern "accelerating growth" and find it relates to a type of distribution that changes with system size. We show both analytically and empirically how the growth rate $γ$ associates with a scaling parameter $b$ in the size-dependent distribution. As most previous studies explain accelerating growth by power law distribution, the model of size-dependent distribution is novel and worth further exploration.

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preprint2011arXiv

Exact Solution for Optimal Navigation with Total Cost Restriction

Recently, Li \textit{et al.} have concentrated on Kleinberg's navigation model with a certain total length constraint $Λ= cN$, where $N$ is the number of total nodes and $c$ is a constant. Their simulation results for the 1- and 2-dimensional cases indicate that the optimal choice for adding extra long-range connections between any two sites seems to be $α=d+1$, where $d$ is the dimension of the lattice and $α$ is the power-law exponent. In this paper, we prove analytically that for the 1-dimensional large networks, the optimal power-law exponent is $α=2$ Further, we study the impact of the network size and provide exact solutions for time cost as a function of the power-law exponent $α$. We also show that our analytical results are in excellent agreement with simulations.

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preprint2011arXiv

Size-Dependency of Income Distributions and Its Implications

This paper highlights the size-dependency of income distributions, i.e. the income distribution curves versus the population of a country systematically. By using the generalized Lotka-Volterra model to fit the empirical income data in the United States during 1996-2007, we found an important parameter $λ$ can scale with a $β$ power of the size (population) of U.S. in that year. We pointed out that the size-dependency of the income distributions, which is a very important property but seldom addressed by previous studies, has two non-trivial implications: (1) the allometric growth pattern, i.e. the power law relationship between population and GDP in different years, which can be mathematically derived from the size-dependent income distributions and also supported by the empirical data; (2) the connection with the anomalous scaling for the probability density function in critical phenomena since the re-scaled form of the income distributions has the exactly same mathematical expression for the limit distribution of the sum of many correlated random variables asymptotically.

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preprint2011arXiv

The "S" Curve Relationship between Export Diversity and Economic Size of Countries

The highly detailed international trade data among all countries in the world during 1971-2000 shows that the kinds of export goods and the logarithmic GDP (gross domestic production) of a country has an S-shaped relationship. This indicates all countries can be divided into three stages accordingly. First, the poor countries always export very few kinds of products as we expect. Second, once the economic size (GDP) of a country is beyond a threshold, its export diversity may increase dramatically. However, this is not the case for rich countries because a ceiling on the export diversity is observed when their GDPs are higher than another threshold. This pattern is very stable for different years although the concrete parameters of the fitting sigmoid functions may change with time. In addition, we also discussed other relationships such as import diversity with respect to logarithmic GDP, diversity of exporters with respect to the number of export goods etc., all of these relationships show S-shaped or power law patterns. Although this paper does not explain the origin of the S-shaped curve, it may provide a basic empirical fact and insights for economic diversity.

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preprint2011arXiv

Toward a General Understanding of the Scaling Laws in Human and Animal Mobility

Recent research highlighted the scaling property of human and animal mobility. An interesting issue is that the exponents of scaling law for animals and humans in different situations are quite different. This paper proposes a general optimization model, a random walker following scaling laws (whose traveling distances in each step obey a power law distribution with exponent α) tries to diversify its visiting places under a given total traveling distance with a home-return probability. The results show that different optimal exponents in between 1 and 2 can emerge naturally. Therefore, the scaling property of human and animal mobility can be understood in our framework where the discrepancy of the scaling law exponents is due to the home-return constraint under the maximization of the visiting places diversity.

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preprint2010arXiv

A holistic abundance analysis of r-rich stars

The chemical abundances of metal-poor stars are an excellent test bed by which to set new constraints on models of neutron-capture processes at low metallicity. Some r-process-rich (hereafter r-rich) metal-poor stars, such as HD221170, show an overabundance of the heavier neutron-capture elements and excesses of lighter neutron-capture elements. The study of these r-rich stars could give us a better understanding of weak and main r-process nucleosynthesis at low metallicity. Based on conclusions from the observation of metal-poor stars and neutron-capture element nucleosynthesis theory, we set up a model to determine the relative contributions from weak and main r-processes to the heavy-element abundances in metal-poor stars. Using this model, we find that the abundance patterns of light elements for most sample stars are close to the pattern of weak r-process stars, and those of heavier neutron-capture elements very similar to the pattern of main r-process stars, while the lighter neutron-capture elements can be fitted by the mixing of weak and main r-process material. The production of weak r-process elements appears to be associated with the light elements, while the production of main r-process elements is almost decoupled from that of the light elements. We compare our results with the observed data at low metallicities, showing that the predicted trends are in good agreement with the observed trends, at least for the metallicity range [Fe/H] < -2.1. For most sample stars, the abundance patterns of both neutron-capture elements and light elements could be best explained by a star formed in a molecular cloud that has been polluted by both weak and main r-process material.

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preprint2010arXiv

Allometric Scaling of Countries

As huge complex systems consisting of geographic regions, natural resources, people and economic entities, countries follow the allometric scaling law which is ubiquitous in ecological, urban systems. We systematically investigated the allometric scaling relationships between a large number of macroscopic properties and geographic (area), demographic (population) and economic (GDP, gross domestic production) sizes of countries respectively. We found that most of the economic, trade, energy consumption, communication related properties have significant super-linear (the exponent is larger than 1) or nearly linear allometric scaling relations with GDP. Meanwhile, the geographic (arable area, natural resources, etc.), demographic(labor force, military age population, etc.) and transportation-related properties (road length, airports) have significant and sub-linear (the exponent is smaller than 1) allometric scaling relations with area. Several differences of power law relations with respect to population between countries and cities were pointed out. Firstly, population increases sub-linearly with area in countries. Secondly, GDP increases linearly in countries but not super-linearly as in cities. Finally, electricity or oil consumptions per capita increases with population faster than cities.

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preprint2010arXiv

Investigation for the enrichment pattern of the element abundances in r+s star HE 0338-3945: a special r-II star?

The very metal-poor star HE 0338-3945 shows a double-enhanced pattern of the neutron-capture elements. The study to this sample could make people gain a better understanding of s- and r-process nucleosynthesis at low metallicity. Using a parametric model,we find that the abundance pattern of the neutron-capture elements could be best explained by a binary system formed in a molecular cloud, which had been polluted by r-process material. The observed abundance pattern of C and N can be explained by an AGB model(Karakas & Lattanzio 2007), . Combing with the parameters obtained from Cui & Zhang (2006), we suggest that the initial mass of the AGB companion is most likely to be about 2.5Msun, which excludes the possibility of forming a type-1.5 supernova. By comparing with the observational abundance pattern of CS 22892-052, we find that the dominating production of O should accompany with the production of the heavy r-process elements of r+s stars. Similar to r-II stars, the heavy r-process elements are not produced in conjunction with all the light elements from Na to Fe group. The abundance pattern of the light and r-process elements for HE 0338-3945 is very close to the pattern of the r-II star CS 22892-052. So, we suggest that this star HE 0338-3945 should be a special r-II star.

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preprint2010arXiv

Scaling Behaviors of Weighted Food Webs as Energy Transportation Networks

Food webs can be regarded as energy transporting networks in which the weight of each edge denotes the energy flux between two species. By investigating 21 empirical weighted food webs as energy flow networks, we found several ubiquitous scaling behaviors. Two random variables $A_i$ and $C_i$ defined for each vertex $i$, representing the total flux (also called vertex intensity) and total indirect effect or energy store of $i$, were found to follow power law distributions with the exponents $α\approx 1.32$ and $β\approx 1.33$, respectively. Another scaling behavior is the power law relationship, $C_i\sim A_i^η$, where $η\approx 1.02$. This is known as the allometric scaling power law relationship because $A_i$ can be treated as metabolism and $C_i$ as the body mass of the sub-network rooted from the vertex $i$, according to the algorithm presented in this paper. Finally, a simple relationship among these power law exponents, $η=(α-1)/(β-1)$, was mathematically derived and tested by the empirical food webs.

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preprint2010arXiv

Study of isotopic fractions and abundances of the neutron-capture elements in HD 175305

The chemical abundances of metal-poor stars are excellent sources of information for setting new constraints on models of Galactic chemical evolution at low metallicities. In this paper we present an attempt to fit the elemental abundances observed in the bright, metal-poor giant HD 175305, and derive isotopic fractions using a parametric model. The observed abundances can be wellmatched by the combined contributions froms- and r-processmaterial. The component coefficients of the r- and s-processes are C1 = 3.220 and C3 = 1.134, respectively. The Smisotopic fraction in this star where the observed neutron-capture elements are produced is predicted to be f 152+154 =0.582,which suggests that, even though the r-process is predominantly responsible for the synthesis of the neutron-capture elements in the early Galaxy, the onset of the s-process had already occurred at this metallicity of [Fe/H] = -1.6.

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