arXiv subjects

Bin Han

Publications and source records attributed to Bin Han.

At least 145 records · Page 8Linked to original sources

arXiv2021

Equidistributions around special kinds of descents and excedances

We consider a sequence of four variable polynomials by refining Stieltjes' continued fraction for Eulerian polynomials. Using combinatorial theory of Jacobi-type continued fractions and bijections we derive various combinatorial interpretations in terms of permutation statistics for these polynomials, which include special kinds of descents and excedances in a recent paper of Baril and Kirgizov. As a by-product, we derive several equidistribution results for permutation statistics, which enables us to confirm and strengthen a recent conjecture of Vajnovszki and also to obtain several compagnion permutation statistics for two bistatistics in a conjecture of Baril and Kirgizov.

math.CO↗

arXiv2021

CLARQ: A Dynamic ARQ Solution for Ultra-high Closed-loop Reliability

Emerging wireless control applications demand for extremely high closed-loop reliability under strict latency constraints, which the conventional Automatic Repeat reQuest (ARQ) solutions with static schedules fail to provide. To overcome this issue and enable data-link layer error control for ultra reliable low-latency communication (URLLC) services, we propose a novel protocol: the Closed-Loop ARQ (CLARQ), which forces to accomplish an information exchange round within a fixed loop-back latency, and dynamically re-allocates the remaining resource between uplink and downlink slots upon the result of last uplink transmission. The proposed method guarantees to meet the latency requirement, while delivering high communication reliability and power efficiency. It can be efficiently offline optimized by means of dynamic programming techniques, and is capable of real-time deployment with a low-cost implementation based on look-up tables. Numerical evaluations have verified that CLARQ outperforms baselines with significantly improved closed-loop reliability and reduced energy consumption. Especially, over a Rayleigh channel with 0dB mean SNR, it is able to provide a closed-loop error rate below 1e-7 within 10ms loop-back latency, which makes our proposal competitive for practical URLLC applications in future 5G-and-beyond networks.

cs.IT↗

arXiv2021

Dirac Assisted Tree Method for 1D Heterogeneous Helmholtz Equations with Arbitrary Variable Wave Numbers

In this paper we introduce a new method called the Dirac Assisted Tree (DAT) method, which can handle 1D heterogeneous Helmholtz equations with arbitrarily large variable wave numbers. DAT breaks an original global problem into many parallel tree-structured small local problems, which are linked together to form a global solution by solving small linking problems. To solve the local problems in DAT, we propose a compact finite difference method (FDM) with arbitrarily high accuracy order and low numerical dispersion for piecewise smooth coefficients and variable wave numbers. This compact FDM is particularly appealing for DAT, because the local problems and their fluxes in DAT can be computed with high accuracy. DAT with such compact FDMs can solve heterogeneous Helmholtz equations with arbitrarily large variable wave numbers accurately by solving small linear systems - $4 \times 4$ matrices in the extreme case - with tridiagonal coefficient matrices in a parallel fashion. Several numerical examples are provided to illustrate the effectiveness of DAT using the $M$th order compact FDMs with $M=6,8$ for numerically solving heterogeneous Helmholtz equations with variable wave numbers. We shall also discuss how to solve some special 2D Helmholtz equations using DAT.

math.NA↗

arXiv2021

Online Estimation of Resource Overload Risk in 5G Multi-Tenancy Network

The technology of network slicing, as the most characteristic feature of the fifth generation (5G) wireless networks, manages the resources and network functions in heterogeneous and logically isolated slices on the top of a shared physical infrastructure, where every slice can be independently customized to fulfill the specific requirements of its devoted service type. It enables a new paradigm of multi-tenancy networking, where the network slices can be leased by the mobile network operator (MNO) to tenants in form of public cloud computing service, known as Slice-asa- Service (SlaaS). Similar to classical cloud computing scenarios, SlaaS benefits from overbooking its resources to numerous tenants, taking advantage of the resource elasticity and diversity, at a price of risking overloading network resources and violating the service-level agreements (SLAs), which stipulate the quality of service (QoS) that shall be guaranteed to the network slices. Thus, it becomes a critical challenge to the MNOs, accurately estimating the resource overload risk - especially under the sophisticated network dynamics - for monitoring and enhancing the reliability of SlaaS business.

cs.NI↗

arXiv2021

Fairness for Freshness: Optimal Age of Information Based OFDMA Scheduling with Minimal Knowledge

It is becoming increasingly clear that an important task for wireless networks is to minimize the age of information (AoI), i.e., the timeliness of information delivery. While mainstream approaches generally rely on the real-time observation of user AoI and channel state, there has been little attention to solve the problem in a complete (or partial) absence of such knowledge. In this article, we present a novel study to address the optimal blind radio resource scheduling problem in orthogonal frequency division multiplexing access (OFDMA) systems towards minimizing long-term average AoI, which is proven to be the composition of time-domain-fair clustered round-robin and frequency-domain-fair intra-cluster sub-carrier assignment. Heuristic solutions that are near-optimal as shown by simulation results are also proposed to effectively improve the performance upon presence of various degrees of extra knowledge, e.g., channel state and AoI.

cs.IT↗

arXiv2021

A High Order Compact Finite Difference Scheme for Elliptic Interface Problems with Discontinuous and High-Contrast Coefficients

The elliptic interface problems with discontinuous and high-contrast coefficients appear in many applications and often lead to huge condition numbers of the corresponding linear systems. Thus, it is highly desired to construct high order schemes to solve the elliptic interface problems with discontinuous and high-contrast coefficients. Let $Γ$ be a smooth curve inside a rectangular region $Ω$. In this paper, we consider the elliptic interface problem $-\nabla\cdot (a \nabla u)=f$ in $Ω\setminus Γ$ with Dirichlet boundary conditions, where the coefficient $a$ and the source term $f$ are smooth in $Ω\setminus Γ$ and the two nonzero jump condition functions $[u]$ and $[a\nabla u\cdot \vec{n}]$ across $Γ$ are smooth along $Γ$. To solve such elliptic interface problems, we propose a high order compact finite difference scheme for numerically computing both the solution $u$ and the gradient $\nabla u$ on uniform Cartesian grids without changing coordinates into local coordinates. Our numerical experiments confirm the fourth order accuracy for computing the solution $u$, the gradient $\nabla u$ and the velocity $a \nabla u$ of the proposed compact finite difference scheme on uniform meshes for the elliptic interface problems with discontinuous and high-contrast coefficients.

math.NA↗

arXiv2021

Users' Perception of Search Engine Biases and Satisfaction

Search engines could consistently favor certain values over the others, which is considered as biased due to the built-in infrastructures. Many studies have been dedicated to detect, control, and mitigate the impacts of the biases from the perspectives of search engines themselves. In our study, we take the perspective from end-users to analyze their perceptions of search engine biases and their satisfaction when the biases are regulated. In the study, we paired a real search page from search engine Bing with a synthesized page that has more diversities in the results (i.e. less biased). Both pages show the top-10 search items given search queries and we asked participants which one do they prefer and why do they prefer the one selected. Statistical analyses revealed that overall, participants prefer the original Bing pages and the locations where the diversities are introduced are also associated with users' preferences. We found out that users prefer results that are more consistent and relevant to the search queries. Introducing diversities undermines the relevance of the search results and impairs users' satisfaction to some degree. Additionally, we confirmed that users tend to pay more attention to the top portion of the results than the bottom ones.

cs.IR↗

arXiv2021

Sixth Order Compact Finite Difference Scheme for Poisson Interface Problem with Singular Sources

Let $Γ$ be a smooth curve inside a two-dimensional rectangular region $Ω$. In this paper, we consider the Poisson interface problem $-\nabla^2 u=f$ in $Ω\setminus Γ$ with Dirichlet boundary condition such that $f$ is smooth in $Ω\setminus Γ$ and the jump functions $[u]$ and $[\nabla u\cdot \vec{n}]$ across $Γ$ are smooth along $Γ$. This Poisson interface problem includes the weak solution of $-\nabla^2 u=f+gδ_Γ$ in $Ω$ as a special case. Because the source term $f$ is possibly discontinuous across the interface curve $Γ$ and contains a delta function singularity along the curve $Γ$, both the solution $u$ of the Poisson interface problem and its flux $\nabla u\cdot \vec{n}$ are often discontinuous across the interface. To solve the Poisson interface problem with singular sources, in this paper we propose a sixth order compact finite difference scheme on uniform Cartesian grids. Our proposed compact finite difference scheme with explicitly given stencils extends the immersed interface method (IIM) to the highest possible accuracy order six for compact finite difference schemes on uniform Cartesian grids, but without the need to change coordinates into the local coordinates as in most papers on IIM in the literature. Also in contrast with most published papers on IIM, we explicitly provide the formulas for all involved stencils. The coefficient matrix $A$ in the resulting linear system $Ax=b$, following from the proposed scheme, is independent of any source term $f$, jump condition $gδ_Γ$, interface curve $Γ$ and Dirichlet boundary conditions. Our numerical experiments confirm the sixth accuracy order of the proposed compact finite difference scheme on uniform meshes for the Poisson interface problems with various singular sources.

math.NA↗

arXiv2021

How Should Network Slice Instances be Provided to Multiple Use Cases of a Single Vertical Industry?

There are a large number of vertical industries implementing multiple use cases, each use case characterized by diverging service, network, and connectivity requirements such as automobile, manufacturing, power grid, etc. Such heterogeneity cannot be effectively managed and efficiently mapped onto a single type of network slice instance (NSI). Thus the tailored provisioning of an end-to-end network slicing solution to a vertical industry that consists of multiple use cases is a critical issue, which motivates this article, aimed at exploring this never-addressed and challenging research problem by proposing the Use-case Specific Network Slicing and the SubNetwork Slicing concepts that enable the provisioning of Use-case-specific NSI(US-NSI) and GeNeric NSI(GN-NSI), respectively. Both approaches tackle the same technical issue of provisioning, management, and orchestration of per vertical per use case NSIs in order to improve resource allocation and enhance network performance. The article also presents the architectural frameworks for managing US-NSI and GN-NSI, which extend the service deployment concept and system architecture of network slicing for vertical customers of fifth-generation (5G) mobile networks.

cs.NI↗

arXiv2021

Edge-Assisted Congestion Control Mechanism for 5G Network Using Software-Defined Networking

In order to cope with the explosive growth of data traffic which is associated with a wide plethora of emerging applications and services that are expected to be used by both ordinary users and vertical industries, the congestion control mechanism is considered to be vital. In this paper, we proposed a congestion control mechanism that could function within the framework of Multi-Access Edge Computing (MEC). The proposed mechanism is aiming to make real-time decisions for selectively buffering traffic while taking network condition and Quality of Service (QoS) into consideration. In order to support a MEC-assisted scheme, the MEC server is expected to locally store delay-tolerant data traffics until the delay conditions expire. This enables the network to have better control over the radio resource provisioning of higher priority data. To achieve this, we introduced a dedicated function known as Congestion Control Engine (CCE), which can capture Radio Access Network (RAN) condition through Radio Network Information Service (RNIS) function, and use this knowledge to make the real-time decision for selectively offloading traffic so that it can perform more intelligently. Analytical evaluation results of our proposed mechanism confirm that it can alleviate network congestion more efficiently.

cs.NI↗

arXiv2021

Wavelets on Intervals Derived from Arbitrary Compactly Supported Biorthogonal Multiwavelets

(Bi)orthogonal (multi)wavelets on the real line have been extensively studied and employed in applications with success. A lot of problems in applications are defined on bounded intervals or domains. Therefore, it is important in both theory and application to construct all possible wavelets on intervals with some desired properties from (bi)orthogonal (multi)wavelets on the real line. Vanishing moments of compactly supported wavelets are the key property for sparse wavelet representations and are closely linked to polynomial reproduction of their underlying refinable (vector) functions. Boundary wavelets with low order vanishing moments often lead to undesired boundary artifacts as well as reduced sparsity and approximation orders near boundaries in applications. From any arbitrarily given compactly supported (bi)orthogonal multiwavelet on the real line, in this paper we propose two different approaches to construct/derive all possible locally supported (bi)orthogonal (multi)wavelets on $[0,\infty)$ or $[0,1]$ with or without prescribed vanishing moments, polynomial reproduction, and/or homogeneous boundary conditions. The first approach generalizes the classical approach from scalar wavelets to multiwavelets, while the second approach is direct without explicitly involving any dual refinable functions and dual multiwavelets. (Multi)wavelets on intervals satisfying homogeneous boundary conditions will also be addressed. Though constructing orthogonal (multi)wavelets on intervals is much easier than their biorthogonal counterparts, we show that some boundary orthogonal wavelets cannot have any vanishing moments if these orthogonal (multi)wavelets on intervals satisfy the homogeneous Dirichlet boundary condition. Several examples of orthogonal and biorthogonal multiwavelets on the interval $[0,1]$ will be provided to illustrate our construction approaches and proposed algorithms.

math.NA↗

arXiv2021

The Road Towards 6G: A Comprehensive Survey

As of today, the fifth generation (5G) mobile communication system has been rolled out in many countries and the number of 5G subscribers already reaches a very large scale. It is time for academia and industry to shift their attention towards the next generation. At this crossroad, an overview of the current state of the art and a vision of future communications are definitely of interest. This article thus aims to provide a comprehensive survey to draw a picture of the sixth generation (6G) system in terms of drivers, use cases, usage scenarios, requirements, key performance indicators (KPIs), architecture, and enabling technologies. First, we attempt to answer the question of "Is there any need for 6G?" by shedding light on its key driving factors, in which we predict the explosive growth of mobile traffic until 2030, and envision potential use cases and usage scenarios. Second, the technical requirements of 6G are discussed and compared with those of 5G with respect to a set of KPIs in a quantitative manner. Third, the state-of-the-art 6G research efforts and activities from representative institutions and countries are summarized, and a tentative roadmap of definition, specification, standardization, and regulation is projected. Then, we identify a dozen of potential technologies and introduce their principles, advantages, challenges, and open research issues. Finally, the conclusions are drawn to paint a picture of "What 6G may look like?". This survey is intended to serve as an enlightening guideline to spur interests and further investigations for subsequent research and development of 6G communications systems.

eess.SP↗

arXiv2021

AI-Empowered VNF Migration as a Cost-Loss-Effective Solution for Network Resilience

With a wide deployment of Multi-Access Edge Computing (MEC) in the Fifth Generation (5G) mobile networks, virtual network functions (VNF) can be flexibly migrated between difference locations, and therewith significantly enhances the network resilience to counter the degradation in quality of service (QoS) due to network function outages. A balance has to be taken carefully, between the loss reduced by VNF migration and the operations cost generated thereby. To achieve this in practical scenarios with realistic user behavior, it calls for models of both cost and user mobility. This paper proposes a novel cost model and a AI-empowered approach for a rational migration of stateful VNFs, which minimizes the sum of operations cost and potential loss caused by outages, and is capable to deal with the complex realistic user mobility patterns.

cs.NI↗

arXiv2021

An Abstracted Survey on 6G: Drivers, Requirements, Efforts, and Enablers

As of today, 5G mobile systems have been already widely rolled out, it is the right time for academia and industry to explore the next generation mobile communication system beyond 5G. To this end, this paper provides an abstracted survey for the 6G mobile system. We shed light on the key driving factors for 6G through predicting the growth trend of mobile traffic and mobile service subscriptions until the year of 2030, envisioning the potential use cases and applications, as well as deriving the potential use scenarios. Then, a number of key performance indicators to support the 6G use cases are identified and their target values are estimated in a quantitatively manner, which is compared with those of 5G clearly in a visualized way. An investigation of the efforts spent on 6G research in different countries and institutions until now is summarized, and a potential roadmap in terms of the definition, specification, standardization, and spectrum regulation is given. Finally, an introduction to potential key 6G technologies is provided. The principle, technical advantages, challenges, and open research issues for each identified technology are discussed.

cs.NI↗

arXiv2020

Multivariate Quasi-tight Framelets with High Balancing Orders Derived from Any Compactly Supported Refinable Vector Functions

Generalizing wavelets by adding desired redundancy and flexibility,framelets are of interest and importance in many applications such as image processing and numerical algorithms. Several key properties of framelets are high vanishing moments for sparse multiscale representation, fast framelet transforms for numerical efficiency, and redundancy for robustness. However, it is a challenging problem to study and construct multivariate nonseparable framelets, mainly due to their intrinsic connections to factorization and syzygy modules of multivariate polynomial matrices. In this paper, we circumvent the above difficulties through the approach of quasi-tight framelets, which behave almost identically to tight framelets. Employing the popular oblique extension principle (OEP), from an arbitrary compactly supported $\dm$-refinable vector function $ϕ$ with multiplicity greater than one, we prove that we can always derive from $ϕ$ a compactly supported multivariate quasi-tight framelet such that (i) all the framelet generators have the highest possible order of vanishing moments;(ii) its associated fast framelet transform is compact with the highest balancing order.For a refinable scalar function $ϕ$, the above item (ii) often cannot be achieved intrinsically but we show that we can always construct a compactly supported OEP-based multivariate quasi-tight framelet derived from $ϕ$ satisfying item (i).This paper provides a comprehensive investigation on OEP-based multivariate quasi-tight multiframelets and their associated framelet transforms with high balancing orders. This deepens our theoretical understanding of multivariate quasi-tight multiframelets and their associated fast multiframelet transforms.

math.FA↗

arXiv2020

Microlocal analysis and characterization of Sobolev wavefront sets using shearlets

Sobolev wavefront sets and $2$-microlocal spaces play a key role in describing and analyzing the singularities of distributions in microlocal analysis and solutions of partial differential equations. Employing the continuous shearlet transform to Sobolev spaces, in this paper we characterize the microlocal Sobolev wavefront sets, the $2$-microlocal spaces, and local Hölder spaces of distributions/functions. We then establish the connections among Sobolev wavefront sets, $2$-microlocal spaces, and local Hölder spaces through the continuous shearlet transform.

math.FA↗

arXiv2020

Beam data modeling of linear accelerators (linacs) through machine learning and its potential applications in fast and robust linac commissioning and quality assurance

Background and purpose: To propose a novel machine learning-based method for reliable and accurate modeling of linac beam data applicable to the processes of linac commissioning and QA. Materials and methods: We hypothesize that the beam data is a function of inherent linac features and percentage depth doses (PDDs) and profiles of different field sizes are correlated with each other. The correlation is formulated as a multivariable regression problem using a machine learning framework. Varian TrueBeam beam data sets (n=43) acquired from multiple institutions were used to evaluate the framework. The data sets included PDDs and profiles across different energies and field sizes. A multivariate regression model was trained for prediction of beam specific PDDs and profiles of different field sizes using a 10x10cm$^2$ field as input. Results: Predictions of PDDs were achieved with a mean absolute percent relative error (%RE) of 0.19-0.35% across the different beam energies investigated. The maximum mean absolute %RE was 0.93%. For profile prediction, the mean absolute %RE was 0.66-0.93% with a maximum absolute %RE of 3.76%. The largest uncertainties in the PDD and profile predictions were found at the build-up region and at the field penumbra, respectively. The prediction accuracy increased with the number of training sets up to around 20 training sets. Conclusions: Through this novel machine learning-based method we have shown accurate and reproducible generation of beam data for linac commissioning for routine radiation therapy. This method has the potential to simplify the linac commissioning procedure, save time and manpower while increasing the accuracy of the commissioning process.

physics.med-ph↗

arXiv2020

Analysis and convergence of Hermite subdivision schemes

Hermite interpolation property is desired in applied and computational mathematics. Hermite and vector subdivision schemes are of interest in CAGD for generating subdivision curves and in computational mathematics for building Hermite wavelets to numerically solve partial differential equations. In contrast to well-studied scalar subdivision schemes, Hermite and vector subdivision schemes employ matrix-valued masks and vector input data, which make their analysis much more complicated and difficult than their scalar counterparts. Despite recent progresses on Hermite subdivision schemes, several key questions still remain unsolved, for example, characterization of Hermite masks, factorization of matrix-valued masks, and convergence of Hermite subdivision schemes. In this paper, we shall study Hermite subdivision schemes through investigating vector subdivision operators acting on vector polynomials and establishing the relations among Hermite subdivision schemes, vector cascade algorithms and refinable vector functions. This approach allows us to resolve several key problems on Hermite subdivision schemes including characterization of Hermite masks, factorization of matrix-valued masks, and convergence of Hermite subdivision schemes.

math.NA↗