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Long Wang

Publications and source records attributed to Long Wang.

At least 145 records · Page 8Linked to original sources
arXiv2023

Long-term Visual Localization with Mobile Sensors

Despite the remarkable advances in image matching and pose estimation, image-based localization of a camera in a temporally-varying outdoor environment is still a challenging problem due to huge appearance disparity between query and reference images caused by illumination, seasonal and structural changes. In this work, we propose to leverage additional sensors on a mobile phone, mainly GPS, compass, and gravity sensor, to solve this challenging problem. We show that these mobile sensors provide decent initial poses and effective constraints to reduce the searching space in image matching and final pose estimation. With the initial pose, we are also able to devise a direct 2D-3D matching network to efficiently establish 2D-3D correspondences instead of tedious 2D-2D matching in existing systems. As no public dataset exists for the studied problem, we collect a new dataset that provides a variety of mobile sensor data and significant scene appearance variations, and develop a system to acquire ground-truth poses for query images. We benchmark our method as well as several state-of-the-art baselines and demonstrate the effectiveness of the proposed approach. The code and dataset will be released publicly.

cs.CV↗
arXiv2023

The emergence of burstiness in temporal networks

Human social interactions tend to vary in intensity over time, whether they are in person or online. Variable rates of interaction in structured populations can be described by networks with the time-varying activity of links and nodes. One of the key statistics to summarize temporal patterns is the inter-event time (IET), namely the duration between successive pairwise interactions. Empirical studies have found IET distributions that are heavy-tailed (or "bursty"), for temporally varying interaction, both physical and digital. But it is difficult to construct theoretical models of time-varying activity on a network that reproduces the burstiness seen in empirical data. Here we develop a spanning-tree method to construct temporal networks and activity patterns with bursty behavior. Our method ensures a desired target IET distribution of single nodes/links, provided the distribution fulfills a consistency condition, regardless of whether the underlying topology is static or time-varying. We show that this model can reproduce burstiness found in empirical datasets, and so it may serve as a basis for studying dynamic processes in real-world bursty interactions.

physics.soc-ph↗
arXiv2023

On the origin of the split main sequences of the young massive cluster NGC 1856

The detection of split main sequences (MSs) associated with young clusters ($\lesssim$600 Myr) has caught lots of attention. A prevailing scenario is that a bimodality of stellar rotation distribution drives the MS bifurcation. Nevertheless, the origin of the stellar rotation dichotomy remains unclear. Hypotheses involving tidally-locked binaries or blue straggler stars (BSSs) are proposed to explain the observed split MSs. This work examines if the long-term dynamical evolution of star clusters can produce the observed split MSs, through high-performance $N$-body simulation. As a prototype example, the young massive cluster NGC 1856 exhibits an apparent MS bifurcation. Our simulation reports that at the age of NGC 1856, tidally-locked binaries are fully mixed with single stars. This is consistent with the observation that there is no significant spatial difference between blue MS and red MS stars. However, we find that only high mass-ratio binaries can evolve to the tidally-locked phase at the age of the NGC 1856. These tidally-locked binaries will populate a much redder sequence than the MS of single stars rather than a blue MS, which is inconsistent with the hypothesis. The number of tidally-locked binaries cannot account for the observation. Our simulation shows that BSSs produced by binary interactions do populate the blue periphery in the color-magnitude diagram, and their spatial distribution shows a similar pattern of single stars. However, the number of BSSs does not fit the observation.

astro-ph.SR↗
arXiv2023

Design Project of an Open-Source, Low-Cost, and Lightweight Robotic Manipulator for High School Students

In recent years, there is an increasing interest in high school robotics extracurriculars such as robotics clubs and robotics competitions. The growing demand is a result of more ubiquitous open-source software and affordable off-the-shelf hardware kits, which significantly help lower the barrier for entry-level robotics hobbyists. In this project, we present an open-source, low-cost, and lightweight robotic manipulator designed and developed by a high school researcher under the guidance of a university faculty and a Ph.D. student. We believe the presented project is suitable for high school robotics research and educational activities. Our open-source package consists of mechanical design models, mechatronics specifications, and software program source codes. The mechanical design models include CAD (Computer Aided Design) files that are ready for prototyping (3D printing technology) and serve as an assembly guide accommodated with a complete bill of materials. Electrical wiring diagrams and low-level controllers are documented in detail as part of the open-source software package. The educational objective of this project is to enable high school student teams to replicate and build a robotic manipulator. The engineering experience that high school students acquire in the proposed project is full-stack, including mechanical design, mechatronics, and programming. The project significantly enriches their hands-on engineering experience in a project-based environment. Throughout this project, we discovered that the high school researcher was able to apply multidisciplinary knowledge from K-12 STEM courses to build the robotic manipulator. The researcher was able to go through a system engineering design and development process and obtain skills to use professional engineering tools including SolidWorks and Arduino microcontrollers.

cs.RO↗
arXiv2023

How social influence affects the wisdom of crowds in influence networks

A long-standing debate is whether social influence improves the collective wisdom of a crowd or undermines it. This paper addresses this question based on a naive learning setting in influence systems theory: in our models individuals evolve their estimates of an unknown truth according to the weighted-average opinion dynamics. A formal mathematization is provided with rigorous theoretical analysis. We obtain various conditions for improving, optimizing and undermining the crowd accuracy, respectively. We prove that if the wisdom of finite-size group is improved, then the collective estimate converges to the truth as group size increases, provided individuals' variances are finite. We show that whether social influence improves or undermines the wisdom is determined by the social power allocation of the influence system: if the influence system allocates relatively larger social power to relatively more accurate individuals, it improves the wisdom; on the contrary, if the influence system assigns less social power to more accurate individuals, it undermines the wisdom. At a population level, individuals' susceptibilities to interpersonal influence and network centralities are both crucial. To improve the wisdom, more accurate individuals should be less susceptible and have larger network centralities. Particularly, in democratic influence networks, if relatively more accurate individuals are relatively less susceptible, the wisdom is improved; if more accurate individuals are more susceptible, the wisdom is undermined, which is consistent with the reported empirical evidence. Our investigation provides a theoretical framework for understanding the role social influence plays in the emergence of collective wisdom.

cs.SI↗
arXiv2023

Exponential Consensus of Multiple Agents over Dynamic Network Topology: Controllability, Connectivity, and Compactness

This paper investigates the problem of securing exponentially fast consensus (exponential consensus for short) for identical agents with finite-dimensional linear system dynamics over dynamic network topology. Our aim is to find the weakest possible conditions that guarantee exponentially fast consensus using a Lyapunov function consisting of a sum of terms of the same functional form. We first investigate necessary conditions, starting by examining the system (both agent and network) parameters. It is found that controllability of the linear agents is necessary for reaching consensus. Then, to work out necessary conditions incorporating the network topology, we construct a set of Laplacian matrix-valued functions. The precompactness of this set of functions is shown to be a significant generalization of existing assumptions on network topology, including the common assumption that the edge weights are bounded piecewise constant functions or continuous functions. With the aid of such a precompactness assumption and restricting the Lyapunov function to one consisting of a sum of terms of the same functional form, we prove that a joint $(δ, T)$-connectivity condition on the network topology is necessary for exponential consensus. Finally, we investigate how the above two ``necessities'' work together to guarantee exponential consensus. To partially address this problem, we define a synchronization index to characterize the interplay between agent parameters and network topology. Based on this notion, it is shown that by designing a proper feedback matrix and under the precompactness assumption, exponential consensus can be reached globally and uniformly if the joint $(δ,T)$-connectivity and controllability conditions are satisfied, and the synchronization index is not less than one.

eess.SY↗
arXiv2023

On the Reachability and Controllability of Temporal Continuous-Time Linear Networks: A Generic Analysis

Temporal networks are a class of time-varying networks, which change their topology according to a given time-ordered sequence of static networks (known as subsystems). This paper investigates the reachability and controllability of temporal continuous-time linear networks from a generic viewpoint, where only the zero-nonzero patterns of subsystem matrices are known. We demonstrate that the reachability and controllability on a single temporal sequence are generic properties with respect to the parameters of subsystem matrices and the time durations of subsystems. We then give explicit expressions for the minimal subspace that contains the reachable set across all possible temporal sequences (called overall reachable set). It is found that verifying the structural reachability/controllability and structural overall reachability are at least as hard as the structural target controllability verification problem of a single system, implying that finding verifiable conditions for them is hard. Graph-theoretic lower and upper bounds are provided for the generic dimensions of the reachable subspace on a single temporal sequence and of the minimal subspace that contains the overall reachable set. These bounds extend classical concepts in structured system theory, including the dynamic graph and the cactus, to temporal networks, and can be efficiently calculated using graph-theoretic algorithms. Finally, applications of the results to the structural controllability of switched linear systems are discussed.

eess.SY↗
arXiv2023

Multiple stellar populations at less evolved stages-III: a possible helium spread in NGC 2210

Helium variations are common features of globular clusters (GCs) with multiple stellar populations. All the formation scenarios predict that secondary population stars are enhanced in helium but the exact helium content depends on the polluters. Therefore, searching for helium variations in a star cluster is a straightforward method to understand if it hosts multiple populations or not, and constrain the formation scenario. Although this topic has been well explored for Galactic GCs, GCs beyond the Milky Way are challenging to study because of their large distances. This work studies the helium distribution of GK-type main sequence dwarfs in an old ($\sim$12.5 Gyr) GC in the Large Magellanic Cloud, NGC 2210, using the deep photometry observed by the {\sl Hubble Space Telescope}. We compare the observed morphology of the MS with that of synthetic populations with different helium distributions. We confirm that NGC 2210 dwarfs have a helium spread, with an internal dispersion of $δ{Y}\sim$0.06--0.07. The fraction of helium enriched stars depends on the $δ{Y}$ distribution. A continuous $δ{Y}$ distribution would indicate that more than half of MS stars are helium enriched ($\sim$55\%). If the $δ{Y}$ distribution is discrete (bimodal), a fraction of $\sim$30\% enriched stars is able to explain the observed morphology of the MS. We also find that the He-enriched population stars are more centrally concentrated than He-normal stars.

astro-ph.SR↗
arXiv2023

Smooth projective surfaces with infinitely many real forms

The aim of this paper is twofold. First of all, we confirm a few basic criteria of the finiteness of real forms of a given smooth complex projective variety, in terms of the Galois cohomology set of the discrete part of the automorphism group, the cone conjecture and the topological entropy. We then apply them to show that a smooth complex projective surface has at most finitely many non-isomorphic real forms unless it is either rational or a non-minimal surface birational to either a K3 surface or an Enriques surface. In the second part of the paper, we construct an Enriques surface whose blow-up at one point admits infinitely many non-isomorphic real forms. This answers a question of Kondo to us and also shows the three exceptional cases really occur.

math.AG↗
arXiv2023

High-Accuracy Approximation of Evolutionary Pairwise Games on Complex Networks

Previous studies have shown that the topological properties of a complex network, such as heterogeneity and average degree, affect the evolutionary game dynamics on it. However, traditional numerical simulations are usually time-consuming and demand a lot of computational resources. In this paper, we propose the method of dynamical approximate master equations (DAMEs) to accurately approximate the evolutionary outcomes on complex networks. We demonstrate that the accuracy of DAMEs supersedes previous standard pairwise approximation methods, and DAMEs require far fewer computational resources than traditional numerical simulations. We use prisoner's dilemma and snowdrift game on regular and scale-free networks to demonstrate the applicability of DAMEs. Overall, our method facilitates the investigation of evolutionary dynamics on a broad range of complex networks, and provides new insights into the puzzle of cooperation.

q-bio.PE↗
arXiv2022

Tidal disruption of stellar clusters and their remnants' spatial distribution near the galactic center

The accretion of massive star clusters via dynamical friction has previously been established to be a likely scenario for the build up of nuclear stellar clusters (NSCs). A remaining issue is whether strong external tidal perturbation may lead to the severe disruption of loosely-bound clusters well before they sink deeply into the center of their host galaxies. We carry out a series of $N$-body simulations and verify our early idealized analytic models. We show if the density profile of the host galaxies can be described by a power-law distribution with an index, $α<1$, the cluster would be compressed in the radial direction by the external galactic tidal field. In contrast, the galactic tidal perturbation is disruptive in regions with a steep, $α>1$, density fall-off or in the very center where gravity is dominated by the point-mass potential of super-massive black holes (SMBHs). This sufficient criterion supplements the conventional necessary Roche-lobe-filling condition in determining the preservation versus disintegration of satellite stellar systems. We simulate the disruption of stellar clusters which venture on nearly-circular, modestly- or highly-eccentric orbits into the center of galaxies with a range of background density profiles and SMBHs. We obtain the spatial distribution of the stellar-cluster remnants. We apply these results to the NSC within a few parsecs from SMBH Sgr A$^\ast$ at the Galactic Center. Recent observations indicate the coexistence of two populations of stars with distinctively separate ages and metallicities. We verify that the subsolar-metalicity population can be the debris of disrupted stellar clusters.

astro-ph.GA↗
arXiv2022

A Lightweight Modular Continuum Manipulator with IMU-based Force Estimation

Most aerial manipulators use serial rigid-link designs, which results in large forces when initiating contacts during manipulation and could cause flight stability difficulty. This limitation could potentially be improved by the compliance of continuum manipulators. To achieve this goal, we present the novel design of a compact, lightweight, and modular cable-driven continuum manipulator for aerial drones. We then derive a complete modeling framework for its kinematics, statics, and stiffness (compliance). The modeling framework can guide the control and design problems to integrate the manipulator to aerial drones. In addition, thanks to the derived stiffness (compliance) matrix, and using a low-cost IMU sensor to capture deformation angles, we present a simple method to estimate manipulation force at the tip of the manipulator. We report preliminary experimental validations of the hardware prototype, providing insights on its manipulation feasibility. We also report preliminary results of the IMU-based force estimation method.

cs.RO↗
arXiv2022

Evolutionary games and spatial periodicity

We establish a theoretical framework to address evolutionary dynamics of spatial games under strong selection. As the selection intensity tends to infinity, strategy competition unfolds in the deterministic way of winners taking all. We rigorously prove that the evolutionary process soon or later either enters a cycle and from then on repeats the cycle periodically, or stabilizes at some state almost everywhere. This conclusion holds for any population graph and a large class of finite games. This framework suffices to reveal the underlying mathematical rationale for the kaleidoscopic cooperation of Nowak and May's pioneering work on spatial games: highly symmetric starting configuration causes a very long transient phase covering a large number of extremely beautiful spatial patterns. For all starting configurations, spatial patterns transit definitely over generations, so cooperators and defectors persist definitely. This framework can be extended to explore games including the snowdrift game, the public goods games (with or without loner, punishment), and repeated games on graphs. Aspiration dynamics can also be fully addressed when players deterministically switch strategy for unmet aspirations by virtue of our framework. Our results have potential implications for exploring the dynamics of a large variety of spatially extended systems in biology and physics.

q-bio.PE↗
arXiv2022

The arrow of evolution when the offspring variance is large

The concept of fitness is central to evolution, but it quantifies only the expected number of offspring an individual will produce. The actual number of offspring is also subject to noise, arising from environmental or demographic stochasticity. In nature, individuals who are more fecund tend to have greater variance in their offspring number -- sometimes far greater than the Poisson variance assumed in classical models of population genetics. Here, we develop a model for the evolution of two types reproducing in a population of non-constant size. The frequency-dependent fitness of each type is determined by pairwise interactions in a prisoner's dilemma game, but the offspring number is subject to an exogenously controlled variance that may depend upon the mean. Whereas defectors are preferred by natural selection in classical well-mixed populations, since they always have greater fitness than cooperators, we show that large offspring variance can reverse the direction of evolution and favor cooperation. Reproductive over-dispersion produces qualitatively new dynamics for other types of social interactions, as well, which cannot arise in populations with a fixed size or Poisson offspring variance.

q-bio.PE↗
arXiv2022

Dynamical Origin for the Collinder 132-Gulliver 21 Stream: A Mixture of three Co-Moving Populations with an Age Difference of 250 Myr

We use Gaia DR3 data to study the Collinder 132-Gulliver 21 region via the machine learning algorithm StarGO, and find eight subgroups of stars (ASCC 32, Collinder 132 gp 1--6, Gulliver 21) located in close proximity. Three co-moving populations were identified among these eight subgroups: (i) a coeval 25 Myr-old moving group (Collinder 132); (ii) an intermediate-age (50--100 Myr) group; and (iii) the 275 Myr-old dissolving cluster Gulliver 21. These three populations form parallel diagonal stripe-shape over-densities in the U--V distribution, which differ from open clusters and stellar groups in the solar neighborhood. We name this kinematic structure the Collinder 132-Gulliver 21 stream, as it extends over 270 pc in the 3D space. The oldest population Gulliver21 is spatially surrounded by the Collinder 132 moving group and the intermediate-age group. Stars in the Collinder 132-Gulliver 21 stream have an age difference up to 250 Myr. Metallicity information shows a variation of 0.3 dex between the youngest and oldest populations. The formation of the Collinder132-Gulliver 21 stream involves both star formation and dynamical heating. The youngest population (Collinder 132 moving group) with homogeneous metallicity is probably formed through filamentary star formation. The intermediate-age and the oldest population were then scatted by the Galactic bar or spiral structure resonance to intercept Collinder 132's orbit. Without mutual interaction between each population, the three populations are flying by each other currently and will become distinct three groups again in approximately ~50Myr.

astro-ph.GA↗
arXiv2022

The Geometry of Zero-Determinant Strategies

The advent of Zero-Determinant (ZD) strategies has reshaped the study of reciprocity and cooperation in the iterated Prisoner's Dilemma games. The ramification of ZD strategies has been demonstrated through their ability to unilaterally enforce a linear relationship between their own average payoff and that of their co-player. Common practice conveniently represents this relationship by a straight line in the parametric plot of pairwise payoffs. Yet little attention has been paid to studying the actual geometry of the strategy space of all admissible ZD strategies. Here, our work offers intuitive geometric relationships between different classes of ZD strategies as well as nontrivial geometric interpretations of their specific parameterizations. Adaptive dynamics of ZD strategies further reveals the unforeseen connection between general ZD strategies and the so-called equalizers that can set any co-player's payoff to a fixed value. We show that the class of equalizers forming a hyperplane is the critical equilibrium manifold, only part of which is stable. The same hyperplane is also a separatrix of the cooperation-enhancing region where the optimum response is to increase cooperation for each of the four payoff outcomes. Our results shed light on the simple but elegant geometry of ZD strategies that is previously overlooked.

physics.soc-ph↗
arXiv2022

Gravitational wave of intermediate-mass black holes in Population III star clusters

Previous theoretical studies suggest that the Population III (Pop3) stars tend to form in extremely metal poor gas clouds with approximately $10^5 M_\odot$ embedded in mini dark matter halos. Very massive stars can form via multiple collisions in Pop3 star clusters and eventually evolve to intermediate-mass black holes (IMBHs). In this work, we conduct star-by-star $N$-body simulations for modelling the long-term evolution of Pop3 star clusters. We find that if the mini dark matter halos can survive today, these star clusters can avoid tidal disruption by the galactic environment and can efficiently produce IMBH-BH mergers among a wide range of redshift from 0 to 20. The average gravitational wave event rate is estimated to be $0.1-0.8~\mathrm{yr}^{-1} \mathrm{Gpc}^{-3}$, and approximately $40-80$ percent of the mergers occur at high redshift ($z>6$). The characteristic strain shows that a part of low-redshift mergers can be detected by LISA, TianQin, and Taiji, whereas most mergers can be covered by DECIGO and advanced LIGO/VIRGO/Kagra. Mergers with pair-instability BHs have a rate of approximately $0.01-0.15$~yr$^{-1}$~Gpc$^{-3}$, which can explain the GW190521-like events.

astro-ph.GA↗