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Dawei Chen

Publications and source records attributed to Dawei Chen.

At least 55 records · Page 3Linked to original sources
arXiv2023

CoMap: Proactive Provision for Crowdsourcing Map in Automotive Edge Computing

Crowdsourcing data from connected and automated vehicles (CAVs) is a cost-efficient way to achieve high-definition maps with up-to-date transient road information. Achieving the map with deterministic latency performance is, however, challenging due to the unpredictable resource competition and distributional resource demands. In this paper, we propose CoMap, a new crowdsourcing high definition (HD) map to minimize the monetary cost of network resource usage while satisfying the percentile requirement of end-to-end latency. We design a novel CROP algorithm to learn the resource demands of CAV offloading, optimize offloading decisions, and proactively allocate temporal network resources in a fully distributed manner. In particular, we create a prediction model to estimate the uncertainty of resource demands based on Bayesian neural networks and develop a utilization balancing scheme to resolve the imbalanced resource utilization in individual infrastructures. We evaluate the performance of CoMap with extensive simulations in an automotive edge computing network simulator. The results show that CoMap reduces up to 80.4% average resource usage as compared to existing solutions.

cs.NI↗
arXiv2023

Metamobility: Connecting Future Mobility with Metaverse

A Metaverse is a perpetual, immersive, and shared digital universe that is linked to but beyond the physical reality, and this emerging technology is attracting enormous attention from different industries. In this article, we define the first holistic realization of the metaverse in the mobility domain, coined as ``metamobility". We present our vision of what metamobility will be and describe its basic architecture. We also propose two use cases, tactile live maps and meta-empowered advanced driver-assistance systems (ADAS), to demonstrate how the metamobility will benefit and reshape future mobility systems. Each use case is discussed from the perspective of the technology evolution, future vision, and critical research challenges, respectively. Finally, we identify multiple concrete open research issues for the development and deployment of the metamobility.

cs.NI↗
arXiv2022

Nonvarying, affine, and extremal geometry of strata of differentials

We prove that the nonvarying strata of abelian and quadratic differentials in [CM1, CM2] have trivial tautological rings and are affine varieties. We also prove that strata of $k$-differentials of infinite area are affine varieties for all $k$. Vanishing of homology in degree higher than the complex dimension follows as a consequence for these affine strata. Moreover we prove that the stratification of the Hodge bundle for abelian and quadratic differentials of finite area is extremal in the sense that merging two zeros in each stratum leads to an extremal effective divisor in the boundary. A common feature throughout these results is a relation of divisor classes in strata of differentials as well as its incarnation in Teichmüller dynamics.

math.AG↗
arXiv2022

Complete curves in the strata of differentials

Gendron proved that the strata of holomorphic differentials with prescribed orders of zeros do not contain complete algebraic curves by applying the maximum modulus principle to saddle connections. Here we provide an alternative proof for this result by using positivity of divisor classes on moduli spaces of curves.

math.AG↗
arXiv2022

Discrete Boltzmann modeling of Rayleigh-Taylor instability: effects of interfacial tension, viscosity and heat conductivity

The Rayleigh-Taylor Instability (RTI) in compressible flow with inter-molecular interactions is probed via the Discrete Boltzmann Method (DBM). The effects of interfacial tension, viscosity and heat conduction are investigated. It is found that the influences of interfacial tension on the perturbation amplitude, bubble velocity, and two kinds of entropy production rates all show differences at different stages of RTI evolution. It inhibits the RTI evolution at the bubble acceleration stage, while at the asymptotic velocity stage, it first promotes and then inhibits the RTI evolution. Viscosity and heat conduction inhibit the RTI evolution. Viscosity shows a suppressive effect on entropy generation rate related to heat flow at the early stage but a first promotive and then suppressive effect on entropy generation rate related to heat flow at a later stage. Heat conduction shows a promotive effect on entropy generation rate related to heat flow at an early stage. Still, it offers a first promotive and then suppressive effect on entropy generation rate related to heat flow at a later stage. By introducing the morphological boundary length, we found that the stage of exponential growth of interface length with time corresponds to the bubble acceleration stage. The first maximum point of interface length change rate and the first maximum point of the change rate of entropy generation rate related to viscous stress can be used as a new criterion for RTI to enter the asymptotic velocity stage.

physics.flu-dyn↗
arXiv2022

On the Kodaira dimension of moduli spaces of Abelian differentials

This paper lays the foundation for determining the Kodaira dimension of the projectivized strata of Abelian differentials with prescribed zero and pole orders in large genus. We work with the moduli space of multi-scale differentials constructed in [BCGGM2] which provides an orbifold compactification of these strata. We establish the projectivity of the moduli space of multi-scale differentials, describe the locus of canonical singularities, and compute a series of effective divisor classes. Moreover, we exhibit a perturbation of the canonical class which allows the corresponding pluri-canonical forms to extend over the locus of non-canonical singularities. As applications, we certify general type for strata with few zeros as well as for strata with equidistributed zero orders when g is sufficiently large. In particular, we show general type for the odd spin components of the minimal strata for g > 12.

math.AG↗
arXiv2021

Dynamical invariants and intersection theory on the flex and gothic loci

The flex locus parameterizes plane cubics with three collinear cocritical points under a projection, and the gothic locus arises from quadratic differentials with zeros at a fiber of the projection and with poles at the cocritical points. The flex and gothic loci provide the first example of a primitive, totally geodesic subvariety of moduli space and new ${\rm SL}_2(\mathbb{R})$-invariant varieties in Teichmüller dynamics, as discovered by McMullen-Mukamel-Wright. In this paper we determine the divisor class of the flex locus as well as various tautological intersection numbers on the gothic locus. For the case of the gothic locus our result confirms numerically a conjecture of Chen-Möller-Sauvaget about computing sums of Lyapunov exponents for ${\rm SL}_2(\mathbb{R})$-invariant varieties via intersection theory.

math.AG↗
arXiv2021

Towards a classification of connected components of the strata of $k$-differentials

A $k$-differential on a Riemann surface is a section of the $k$-th power of the canonical bundle. Loci of $k$-differentials with prescribed number and multiplicities of zeros and poles form a natural stratification for the moduli space of $k$-differentials. The classification of connected components of the strata of $k$-differentials was known for holomorphic differentials, meromorphic differentials and quadratic differentials with at worst simple poles by Kontsevich--Zorich, Boissy and Lanneau, respectively. Built on their work we develop new techniques to study connected components of the strata of $k$-differentials for general $k$. As an application, we give a complete classification of connected components of the strata of quadratic differentials with arbitrary poles. Moreover, we distinguish certain components of the strata of $k$-differentials by generalizing the hyperelliptic structure and spin parity for higher $k$. We also describe an approach to determine explicitly parities of $k$-differentials in genus zero and one, which inspires an amusing conjecture in number theory. A key viewpoint we use is the notion of multi-scale $k$-differentials introduced by Bainbridge--Chen--Gendron--Grushevsky--Möller for $k = 1$ and extended by Costantini--Möller--Zachhuber for all $k$.

math.GT↗
arXiv2020

The WYSIWYG compactification

We show that the partial compactification of a stratum of Abelian differentials previously considered by Mirzakhani and Wright is not an algebraic variety. Despite this, we use a combination of algebro-geometric and other methods to provide a short, unconditional proof of Mirzakhani and Wright's formula for the tangent space to the boundary of a GL(2,R) orbit closure, and give new results on the structure of the boundary.

math.DS↗
arXiv2020

Enabling Cost-Effective Population Health Monitoring By Exploiting Spatiotemporal Correlation: An Empirical Study

Because of its important role in health policy-shaping, population health monitoring (PHM) is considered a fundamental block for public health services. However, traditional public health data collection approaches, such as clinic-visit-based data integration or health surveys, could be very costly and time-consuming. To address this challenge, this paper proposes a cost-effective approach called Compressive Population Health (CPH), where a subset of a given area is selected in terms of regions within the area for data collection in the traditional way, while leveraging inherent spatial correlations of neighboring regions to perform data inference for the rest of the area. By alternating selected regions longitudinally, this approach can validate and correct previously assessed spatial correlations. To verify whether the idea of CPH is feasible, we conduct an in-depth study based on spatiotemporal morbidity rates of chronic diseases in more than 500 regions around London for over ten years. We introduce our CPH approach and present three extensive analytical studies. The first confirms that significant spatiotemporal correlations do exist. In the second study, by deploying multiple state-of-the-art data recovery algorithms, we verify that these spatiotemporal correlations can be leveraged to do data inference accurately using only a small number of samples. Finally, we compare different methods for region selection for traditional data collection and show how such methods can further reduce the overall cost while maintaining high PHM quality.

stat.AP↗
arXiv2020

Moduli of Differentials and Teichmüller Dynamics

An increasingly important area of interest for mathematicians is the study of Abelian differentials. This growing interest can be attributed to the interdisciplinary role this subject plays in modern mathematics, as various problems of algebraic geometry, dynamical systems, geometry and topology lead to the study of such objects. It comes as a natural consequence that we can employ in our study algebraic, analytic, combinatorial and dynamical perspectives. These lecture notes aim to provide an expository introduction to this subject that will emphasize the aforementioned links between different areas of mathematics. We will associate to an Abelian differential a flat surface with conical singularities such that the underlying Riemann surface is obtained from a polygon by identifying edges with one another via translation. We will focus on studying these objects in families and describe some properties of the orbit as we vary the polygon by the action of $GL_2^{+}(\mathbb{R})$ on the plane.

math.AG↗
arXiv2019

Cold-start Playlist Recommendation with Multitask Learning

Playlist recommendation involves producing a set of songs that a user might enjoy. We investigate this problem in three cold-start scenarios: (i) cold playlists, where we recommend songs to form new personalised playlists for an existing user; (ii) cold users, where we recommend songs to form new playlists for a new user; and (iii) cold songs, where we recommend newly released songs to extend users' existing playlists. We propose a flexible multitask learning method to deal with all three settings. The method learns from user-curated playlists, and encourages songs in a playlist to be ranked higher than those that are not by minimising a bipartite ranking loss. Inspired by an equivalence between bipartite ranking and binary classification, we show how one can efficiently approximate an optimal solution of the multitask learning objective by minimising a classification loss. Empirical results on two real playlist datasets show the proposed approach has good performance for cold-start playlist recommendation.

cs.IR↗
arXiv2019

Masur-Veech volumes and intersection theory on moduli spaces of abelian differentials

We show that the Masur-Veech volumes and area Siegel-Veech constants can be obtained by intersection numbers on the strata of Abelian differentials with prescribed orders of zeros. As applications, we evaluate their large genus limits and compute the saddle connection Siegel-Veech constants for all strata. We also show that the same results hold for the spin and hyper-elliptic components of the strata.

math.AG↗
arXiv2018

Positivity of divisor classes on the strata of differentials

Three decades ago Cornalba-Harris proved a fundamental positivity result for divisor classes associated to families of stable curves. In this paper we establish an analogous positivity result for divisor classes associated to families of stable differentials.

math.AG↗
arXiv2018

Quasimodularity and large genus limits of Siegel-Veech constants

Quasimodular forms were first studied in the context of counting torus coverings. Here we show that a weighted version of these coverings with Siegel-Veech weights also provides quasimodular forms. We apply this to prove conjectures of Eskin and Zorich on the large genus limits of Masur-Veech volumes and of Siegel-Veech constants. In Part I we connect the geometric definition of Siegel-Veech constants both with a combinatorial counting problem and with intersection numbers on Hurwitz spaces. We introduce modified Siegel-Veech weights whose generating functions will later be shown to be quasimodular. Parts II and III are devoted to the study of the quasimodularity of the generating functions arising from weighted counting of torus coverings. The starting point is the theorem of Bloch and Okounkov saying that q-brackets of shifted symmetric functions are quasimodular forms. In Part II we give an expression for their growth polynomials in terms of Gaussian integrals and use this to obtain a closed formula for the generating series of cumulants that is the basis for studying large genus asymptotics. In Part III we show that the even hook-length moments of partitions are shifted symmetric polynomials and prove a formula for the q-bracket of the product of such a hook-length moment with an arbitrary shifted symmetric polynomial. This formula proves quasimodularity also for the (-2)-nd hook-length moments by extrapolation, and implies the quasimodularity of the Siegel-Veech weighted counting functions. Finally, in Part IV these results are used to give explicit generating functions for the volumes and Siegel-Veech constants in the case of the principal stratum of abelian differentials. To apply these exact formulas to the Eskin-Zorich conjectures we provide a general framework for computing the asymptotics of rapidly divergent power series.

math.NT↗
arXiv2018

Compactification of strata of abelian differentials

We describe the closure of the strata of abelian differentials with prescribed type of zeros and poles, in the projectivized Hodge bundle over the Deligne-Mumford moduli space of stable curves with marked points. We provide an explicit characterization of pointed stable differentials in the boundary of the closure, both a complex analytic proof and a flat geometric proof for smoothing the boundary differentials, and numerous examples. The main new ingredient in our description is a global residue condition arising from a full order on the dual graph of a stable curve.

math.AG↗
arXiv2017

Strata of $k$-differentials

A $k$-differential on a Riemann surface is a section of the $k$-th power of the canonical line bundle. Loci of $k$-differentials with prescribed number and multiplicities of zeros and poles form a natural stratification of the moduli space of $k$-differentials. In this paper we give a complete description for the compactification of the strata of $k$-differentials in terms of pointed stable $k$-differentials, for all $k$. The upshot is a global $k$-residue condition that can also be reformulated in terms of admissible covers of stable curves. Moreover, we study properties of $k$-differentials regarding their deformations, residues, and flat geometric structure.

math.AG↗