arXiv subjects

Bin Han

Publications and source records attributed to Bin Han.

At least 163 records · Page 9Linked to original sources

arXiv2020

Eulerian polynomials and excedance statistics

A formula of Stembridge states that the permutation peak polynomials and descent polynomials are connected via a quadratique transformation. The aim of this paper is to establish the cycle analogue of Stembridge's formula by using cycle peaks and excedances of permutations. We prove a series of new general formulae expressing polynomials counting permutations by various excedance statistics in terms of refined Eulerian polynomials. Our formulae are comparable with Zhuang's generalizations [Adv. in Appl. Math. 90 (2017) 86-144] using descent statistics of permutations. Our methods include permutation enumeration techniques involving variations of classical bijections from permutations to Laguerre histories, explicit continued fraction expansions of combinatorial generating functions in Shin and Zeng [European J. Combin. 33 (2012), no. 2, 111--127] and cycle version of modified Foata-Strehl action. We also prove similar formulae for restricted permutations such as derangements and permutations avoiding certain patterns. Moreover, we provide new combinatorial interpretations for the $γ$-coefficients of the inversion polynomials restricted on $321$-avoiding permutations.

math.CO↗

arXiv2020

Equidistributions of mesh patterns of length two and Kitaev and Zhang's conjectures

A systematic study of avoidance of mesh patterns of length 2 was conducted by Hilmarsson et al. in 2015. In a recent paper Kitaev and Zhang examined the distribution of the aforementioned patterns. The aim of this paper is to prove more equidistributions of mesh pattern and confirm Kitaev and Zhang's four conjectures by constructing two involutions on permutations.

math.CO↗

arXiv2020

Multiservice-based Network Slicing Orchestration with Impatient Tenants

The combination of recent emerging technologies such as network function virtualization (NFV) and network programmability (SDN) gave birth to the novel Network Slicing paradigm. 5G networks consist of multi-tenant infrastructures capable of offering leased network "slices" to new customers (e.g., vertical industries) enabling a new telecom business model: Slice-as-a-Service (SlaaS). However, as the service demand gets increasingly dense, slice requests congestion may occur leading to undesired waiting periods. This may turn into impatient tenant behaviors that increase potential loss of the business attractiveness to customers. In this paper, we aim to i study the slicing admission control problem by means of a multi-queuing system for heterogeneous tenant requests, ii) derive its statistical behavior model, iii) find out the rational strategy of impatient tenants waiting in queue-based slice admission control systems, iv) prove mathematically and empirically the benefits of allowing infrastructure providers to share its information with the upcoming tenants, and v) provide a utility model for network slices admission optimization. Our results analyze the capability of the proposed SlaaS system to be approximately Markovian and evaluate its performance as compared to a baseline solution.

cs.NI↗

arXiv2020

Recursive Optimization of Finite Blocklength Allocation to Mitigate Age-of-Information Outage

As an emerging metric for the timeliness of information delivery, Age-of-Information (AoI) raises a special interest in the research area of tolerance-critical communications, wherein sufficiently short blocklength is usually adopted as an essential requirement. However, the interplay between AoI and finite blocklength is scantly treated. This paper studies the occurrence of high AoI, i.e., AoI outage, in TDMA systems with respect to the blocklength allocation among users. A Markov Decision Process model is set up for the problem, which enables a static state analysis, and therewith a policy iteration approach to improve the AoI robustness is proposed. The burstiness of outages is also analyzed to provide additional insights into this problem in the finite blocklength (FBL) regime. It is shown that, different from average AoI optimizations, a risk-sensitive approach is significantly beneficial for AoI outage optimizations, on account of the FBL regime.

cs.IT↗

arXiv2020

Robustness Analysis of Networked Control Systems with Aging Status

As an emerging metric of communication systems, Age of Information (AoI) has been derived to have a critical impact in networked control systems with unreliable information links. This work sets up a novel model of outage probability in a loosely constrained control system as a function of the feedback AoI, and conducts numerical simulations to validate the model.

cs.IT↗

arXiv2020

Machine Learning for Network Slicing Resource Management: A Comprehensive Survey

The emerging technology of multi-tenancy network slicing is considered as an essential feature of 5G cellular networks. It provides network slices as a new type of public cloud services, and therewith increases the service flexibility and enhances the network resource efficiency. Meanwhile, it raises new challenges of network resource management. A number of various methods have been proposed over the recent past years, in which machine learning and artificial intelligence techniques are widely deployed. In this article, we provide a survey to existing approaches of network slicing resource management, with a highlight on the roles played by machine learning in them.

cs.NI↗

arXiv2020

Compactly Supported Quasi-tight Multiframelets with High Balancing Orders and Compact Framelet Transforms

Framelets (a.k.a. wavelet frames) are of interest in both theory and applications. Quite often, tight or dual framelets with high vanishing moments are constructed through the popular oblique extension principle (OEP). Though OEP can increase vanishing moments for improved sparsity, it has a serious shortcoming for scalar framelets: the associated discrete framelet transform is often not compact and deconvolution is unavoidable. Here we say that a framelet transform is compact if it can be implemented by convolution using only finitely supported filters. On the other hand, in sharp contrast to the extensively studied scalar framelets, multiframelets (a.k.a. vector framelets) derived through OEP from refinable vector functions are much less studied and are far from well understood. Also, most constructed multiframelets often lack balancing property which reduces sparsity. In this paper, we are particularly interested in quasi-tight multiframelets, which are special dual multiframelets but behave almost identically as tight multiframelets. From any compactly supported \emph{refinable vector function having at least two entries}, we prove that we can always construct through OEP a compactly supported quasi-tight multiframelet such that (1) its associated discrete framelet transform is compact and has the highest possible balancing order; (2) all compactly supported framelet generators have the highest possible order of vanishing moments, matching the approximation/accuracy order of its underlying refinable vector function. This result demonstrates great advantages of OEP for multiframelets (retaining all the desired properties) over scalar framelets.

math.FA↗

arXiv2019

Rational Impatience Admission Control in 5G-sliced Networks: Shall I Bide my Slice Opportunity?

Recently, the specifications of the fifth generation (5G) of mobile networks have been released witnessing the industrial interest around the novel network slicing concept. This context is further enriched by the evolution of an emerging type of public cloud environment: the Slice-as-a-Service (SlaaS). Infrastructure providers or network operators deploy different admission strategy while processing network slice requests issued by infrastructure tenants based on service level agreements (SLAs) and current (and predicted) resource availability. However, when the service demand will reasonably get dense, congestions of slice requests may occur leading to long waiting periods. This may turn into impatient tenant behaviors that mitigate potential loss. This paper studies the rational strategies of impatient tenants waiting in queue-based slice admission control system, proving mathematically and empirically the benefits of allowing infrastructure provider to share its information with the upcoming tenants.

cs.NI↗

arXiv2019

Wavelet-based Methods for Numerical Solutions of Differential Equations

Wavelet theory has been well studied in recent decades. Due to their appealing features such as sparse multiscale representation and fast algorithms, wavelets have enjoyed many tremendous successes in the areas of signal/image processing and computational mathematics. This paper primarily intends to shed some light on the advantages of using wavelets in the context of numerical differential equations. We shall identify a few prominent problems in this field and recapitulate some important results along these directions. Wavelet-based methods for numerical differential equations offer the advantages of sparse matrices with uniformly bounded small condition numbers. We shall demonstrate wavelets' ability in solving some one-dimensional differential equations: the biharmonic equation and the Helmholtz equation with high wave numbers (of magnitude $O(10^4)$ or larger).

math.NA↗

arXiv2019

Optimal Blocklength Allocation towards Reduced Age of Information in Wireless Sensor Networks

The freshness or timeliness of data at server is a significant key performance indicator of sensor networks, especially in tolerance critical applications such as factory automation. As an effective and intuitive measurement to data timeliness, the metric of Age of Information (AoI) has attracted an intensive recent interest of research. This paper initiates a study on the AoI of wireless sensor networks working in the finite blocklength (FBL) regime as a resource allocation problem, and proposes to minimize the long-term discounted system AoI as a Markov decision process (MDP). The proposed method with its optimum solved by Reinforced Learning technique is verified by simulations to outperform benchmarks, including the conventional error rate minimizing policy.

eess.SP↗

arXiv2019

D2D-Based Grouped Random Access to Mitigate Mobile Access Congestion in 5G Sensor Networks

The Fifth Generation (5G) wireless service of sensor networks involves significant challenges when dealing with the coordination of ever-increasing number of devices accessing shared resources. This has drawn major interest from the research community as many existing works focus on the radio access network congestion control to efficiently manage resources in the context of device-to-device (D2D) interaction in huge sensor networks. In this context, this paper pioneers a study on the impact of D2D link reliability in group-assisted random access protocols, by shedding the light on beneficial performance and potential limitations of approaches of this kind against tunable parameters such as group size, number of sensors and reliability of D2D links. Additionally, we leverage on the association with a Geolocation Database (GDB) capability to assist the grouping decisions by drawing parallels with recent regulatory-driven initiatives around GDBs and arguing benefits of the suggested proposal. Finally, the proposed method is approved to significantly reduce the delay over random access channels, by means of an exhaustive simulation campaign.

cs.NI↗

arXiv2019

Automatic target positioning and tracking for image-guided radiotherapy without implanted fiducials

Current image-guided prostate radiotherapy often relies on the use of implanted fiducials or transducers for target localization. Fiducial or transducer insertion requires an invasive procedure that adds cost and risks for bleeding, infection, and discomfort to some patients. We are developing a novel markerless prostate localization strategy using a pre-trained deep learning model to interpret routine projection kV X-ray images without the need for daily cone-beam computed tomography (CBCT). A deep learning model was first trained by using several thousand annotated projection X-ray images. The trained model is capable of identifying the location of the prostate target for a given input X-ray projection image. To assess the accuracy of the approach, three patients with prostate cancer received volumetric modulated arc therapy (VMAT) were retrospectively studied. The results obtained by using the deep learning model and the actual position of the prostate were compared quantitatively. The deviations between the target positions obtained by the deep learning model and the corresponding annotations ranged from 1.66 mm to 2.77 mm for anterior-posterior (AP) direction, and from 1.15 mm to 2.88 mm for lateral direction. Target position provided by deep learning model for the kV images acquired using OBI is found to be consistent that derived from the fiducials. This study demonstrates, for the first time, that highly accurate markerless prostate localization based on deep learning is achievable. The strategy provides a clinically valuable solution to daily patient positioning and real-time target tracking for image-guided radiotherapy (IGRT) and interventions.

physics.med-ph↗

arXiv2019

Gibbs Phenomenon of Framelet Expansions and Quasi-projection Approximation

The Gibbs phenomenon is widely known for Fourier expansions of periodic functions and refers to the phenomenon that the $n$th Fourier partial sums overshoot a target function at jump discontinuities in such a way that such overshoots do not die out as $n$ goes to infinity. The Gibbs phenomenon for wavelet expansions using (bi)orthogonal wavelets has been studied in the literature. Framelets (also called wavelet frames) generalize (bi)orthogonal wavelets. Approximation by quasi-projection operators are intrinsically linked to approximation by truncated wavelet and framelet expansions. In this paper we shall establish a key identity for quasi-projection operators and then we use it to study the Gibbs phenomenon of framelet expansions and approximation by general quasi-projection operators. We shall also study and characterize the Gibbs phenomenon at an arbitrary point for approximation by quasi-projection operators. As a consequence, we show that the Gibbs phenomenon appears at all points for every tight or dual framelet having at least two vanishing moments and for quasi-projection operators having at least three accuracy orders. Our results not only improve current results in the literature on the Gibbs phenomenon for (bi)orthogonal wavelet expansions but also are new for framelet expansions and approximation by quasi-projection operators.

cs.IT↗

arXiv2019

A Utility-Driven Multi-Queue Admission Control Solution for Network Slicing

The combination of recent emerging technologies such as network function virtualization (NFV) and network programmability (SDN) gave birth to the Network Slicing revolution. 5G networks consist of multi-tenant infrastructures capable of offering leased network "slices" to new customers (e.g., vertical industries) enabling a new telecom business model: Slice-as-aService (SlaaS). In this paper, we aim i ) to study the slicing admission control problem by means of a multi-queuing system for heterogeneous tenant requests, ii ) to derive its statistical behavior model, and iii ) to provide a utility-based admission control optimization. Our results analyze the capability of the proposed SlaaS system to be approximately Markovian and evaluate its performance as compared to legacy solutions.

cs.NI↗

arXiv2019

Context-Awareness Enhances 5G Multi-Access Edge Computing Reliability

The fifth generation (5G) mobile telecommunication network is expected to support Multi- Access Edge Computing (MEC), which intends to distribute computation tasks and services from the central cloud to the edge clouds. Towards ultra-responsive, ultra-reliable and ultra-low-latency MEC services, the current mobile network security architecture should enable a more decentralized approach for authentication and authorization processes. This paper proposes a novel decentralized authentication architecture that supports flexible and low-cost local authentication with the awareness of context information of network elements such as user equipment and virtual network functions. Based on a Markov model for backhaul link quality, as well as a random walk mobility model with mixed mobility classes and traffic scenarios, numerical simulations have demonstrated that the proposed approach is able to achieve a flexible balance between the network operating cost and the MEC reliability.

cs.NI↗

arXiv2019

Merging the Bernoulli-Gaussian and Symmetric Alpha-Stable Models for Impulsive Noises in Narrowband Power Line Channels

To model impulsive noise in power line channels, both the Bernoulli-Gaussian model and the symmetric alpha-stable model are usually applied. Towards a merge of existing noise measurement databases and a simplification of communication system design, the compatibility between the two models is of interest. In this paper, we show that they can be approximately converted to each other under certain constrains, although never generally unified. Based on this, we propose a fast model conversion.

eess.SP↗

arXiv2018

$(q,t)$-Catalan numbers: gamma expansions, pattern avoidance and the $(-1)$-phenomenon

The aim of this paper is two-fold. We first prove several new interpretations of a kind of $(q,t)$-Catalan numbers along with their corresponding $γ$-expansions using pattern avoiding permutations. Secondly, we give a complete characterization of certain $(-1)$-phenomenon for each subset of permutations avoiding a single pattern of length three, and discuss their $q$-analogues utilizing the newly obtained $q$-$γ$-expansions, as well as the continued fraction of a quint-variate generating function due to Shin and the fourth author. Moreover, we enumerate the alternating permutations avoiding simultaneously two patterns, namely $(2413,3142)$ and $(1342,2431)$, of length four, and consider such $(-1)$-phenomenon for these two subsets as well.

math.CO↗

arXiv2018

Admission and Congestion Control for 5G Network Slicing

Network Slicing has been widely accepted as essential feature of future 5th Generation (5G) mobile communication networks. Accounting the potentially dense demand of network slices as a cloud service and the limited resource of mobile network operators (MNOs), an efficient inter-slice management and orchestration plays a key role in 5G networks. This calls advanced solutions for slice admission and congestion control. This paper proposes a novel approach of inter-slice control that well copes with existing pre-standardized 5G architectures

cs.NI↗