arXiv subjects

Jianping Pan

Publications and source records attributed to Jianping Pan.

At least 37 records · Page 2Linked to original sources

arXiv2023

Lightweight privacy-preserving truth discovery for vehicular air quality monitoring

Air pollution has become a global concern for many years. Vehicular crowdsensing systems make it possible to monitor air quality at a fine granularity. To better utilize the sensory data with varying credibility, truth discovery frameworks are introduced. However, in urban cities, there is a significant difference in traffic volumes of streets or blocks, which leads to a data sparsity problem for truth discovery. Protecting the privacy of participant vehicles is also a crucial task. We first present a data masking-based privacy-preserving truth discovery framework, which incorporates spatial and temporal correlations to solve the sparsity problem. To further improve the truth discovery performance of the presented framework, an enhanced version is proposed with anonymous communication and data perturbation. Both frameworks are more lightweight than the existing cryptography-based methods. We also evaluate the work with simulations and fully discuss the performance and possible extensions.

cs.NI↗

arXiv2022

RSK tableaux and the weak order on fully commutative permutations

For each fully commutative permutation, we construct a "boolean core," which is the maximal boolean permutation in its principal order ideal under the right weak order. We partition the set of fully commutative permutations into the recently defined crowded and uncrowded elements, distinguished by whether or not their RSK insertion tableaux satisfy a sparsity condition. We show that a fully commutative element is uncrowded exactly when it shares the RSK insertion tableau with its boolean core. We present the dynamics of the right weak order on fully commutative permutations, with particular interest in when they change from uncrowded to crowded. In particular, we use consecutive permutation patterns and descents to characterize the minimal crowded elements under the right weak order.

math.CO↗

arXiv2022

A bijection between $K$-Kohnert diagrams and reverse set-valued tableaux

Lascoux polynomials are $K$-theoretic analogues of the key polynomials. They both have combinatorial formulas involving tableaux: reverse set-valued tableaux ($\mathsf{RSVT}$) rule for Lascoux polynomials and reverse semistandard Young tableaux ($\mathsf{RSSYT}$) rule for key polynomials. Furthermore, key polynomials have a simple algorithmic model in terms of Kohnert diagrams, which are in bijection with $\mathsf{RSSYT}$. Ross and Yong introduced $K$-Kohnert diagrams, which are analogues of Kohnert diagrams. They conjectured a $K$-Kohnert diagram rule for Lascoux polynomials. We establish this conjecture by constructing a weight-preserving bijection between $\mathsf{RSVT}$ and $K$-Kohnert diagrams.

math.CO↗

arXiv2021

Random Distances Associated with Hexagons

In this report, the explicit probability density functions of the random Euclidean distances associated with regular hexagons are given, when the two endpoints of a link are randomly distributed in the same hexagon, and two adjacent hexagons sharing a side, respectively. Simulation results show the accuracy of the obtained closed-form distance distribution functions, which are important in a wide variety of applied sciences and engineering fields. In particular, hexagons are often used in wireless communication networks such as the cellular systems. The correctness of these distance distribution functions is validated by a recursion and a probabilistic sum. The first two statistical moments of the random distances, and the polynomial fits of the density functions are also given in this report for practical uses.

math.GM↗

arXiv2020

A Unified Model for the Two-stage Offline-then-Online Resource Allocation

With the popularity of the Internet, traditional offline resource allocation has evolved into a new form, called online resource allocation. It features the online arrivals of agents in the system and the real-time decision-making requirement upon the arrival of each online agent. Both offline and online resource allocation have wide applications in various real-world matching markets ranging from ridesharing to crowdsourcing. There are some emerging applications such as rebalancing in bike sharing and trip-vehicle dispatching in ridesharing, which involve a two-stage resource allocation process. The process consists of an offline phase and another sequential online phase, and both phases compete for the same set of resources. In this paper, we propose a unified model which incorporates both offline and online resource allocation into a single framework. Our model assumes non-uniform and known arrival distributions for online agents in the second online phase, which can be learned from historical data. We propose a parameterized linear programming (LP)-based algorithm, which is shown to be at most a constant factor of $1/4$ from the optimal. Experimental results on the real dataset show that our LP-based approaches outperform the LP-agnostic heuristics in terms of robustness and effectiveness.

cs.AI↗

arXiv2020

Optimal Caching for Low Latency in Distributed Coded Storage Systems

Erasure codes have been widely considered a promising solution to enhance data reliability at low storage costs. However, in modern geo-distributed storage systems, erasure codes may incur high data access latency as they require data retrieval from multiple remote storage nodes. This hinders the extensive application of erasure codes to data-intensive applications. This paper proposes novel caching schemes to achieve low latency in distributed coded storage systems. Experiments based on Amazon Simple Storage Service confirm the positive correlation between the latency and the physical distance of data retrieval. The average data access latency is used the performance metric to quantify the benefits of caching. Assuming that the future data popularity and network latency information is available, an offline caching scheme is proposed to find the optimal caching solution. Guided by the optimal scheme, an online caching scheme is proposed according to the measured data popularity and network latency information in real time. Experiment results demonstrate that the online scheme can approximate the optimal scheme well with dramatically reduced computation complexity.

cs.IT↗

arXiv2020

Thompson Sampling for Combinatorial Semi-bandits with Sleeping Arms and Long-Term Fairness Constraints

We study the combinatorial sleeping multi-armed semi-bandit problem with long-term fairness constraints~(CSMAB-F). To address the problem, we adopt Thompson Sampling~(TS) to maximize the total rewards and use virtual queue techniques to handle the fairness constraints, and design an algorithm called \emph{TS with beta priors and Bernoulli likelihoods for CSMAB-F~(TSCSF-B)}. Further, we prove TSCSF-B can satisfy the fairness constraints, and the time-averaged regret is upper bounded by $\frac{N}{2η} + O\left(\frac{\sqrt{mNT\ln T}}{T}\right)$, where $N$ is the total number of arms, $m$ is the maximum number of arms that can be pulled simultaneously in each round~(the cardinality constraint) and $η$ is the parameter trading off fairness for rewards. By relaxing the fairness constraints (i.e., let $η\rightarrow \infty$), the bound boils down to the first problem-independent bound of TS algorithms for combinatorial sleeping multi-armed semi-bandit problems. Finally, we perform numerical experiments and use a high-rating movie recommendation application to show the effectiveness and efficiency of the proposed algorithm.

cs.LG↗

arXiv2020

A crystal on decreasing factorizations in the $0$-Hecke monoid

We introduce a type $A$ crystal structure on decreasing factorizations of fully-commutative elements in the 0-Hecke monoid which we call $\star$-crystal. This crystal is a $K$-theoretic generalization of the crystal on decreasing factorizations in the symmetric group of the first and last author. We prove that under the residue map the $\star$-crystal intertwines with the crystal on set-valued tableaux recently introduced by Monical, Pechenik and Scrimshaw. We also define a new insertion from decreasing factorization to pairs of semistandard Young tableaux and prove several properties, such as its relation to the Hecke insertion and the uncrowding algorithm. The new insertion also intertwines with the crystal operators.

math.CO↗

arXiv2019

PhyCode: A Practical Wireless Communication System Exploiting Superimposed Signals

Superimposed signals are anticipated to improve wireless spectrum efficiency to support the ever-growing IoT applications. Implementing the superimposed signal demands on ideally aligned signals in both the time and frequency domains. Prior work applied an average carrier-frequency offset compensation to the superimposed signal under the assumptions of homogeneous devices and static environments. However, this will cause a significant signal distortion in practice when heterogeneous IoT devices are involved in a dynamic environment. This paper presents PhyCode, which exploits the nature of varying offsets across devices, and designs a dynamic decoding scheme which can react to the exact offsets from different signal sources simultaneously. We implement PhyCode via a software-defined radio platform and demonstrate that PhyCode achieves a lower raw BER compared with the existing state-of-the-art method.

eess.SP↗

arXiv2019

Distance Distribution Between Two Random Nodes in Arbitrary Polygons

Distance distributions are a key building block in stochastic geometry modelling of wireless networks and in many other fields in mathematics and science. In this paper, we propose a novel framework for analytically computing the closed form probability density function (PDF) of the distance between two random nodes each uniformly randomly distributed in respective arbitrary (convex or concave) polygon regions (which may be disjoint or overlap or coincide). The proposed framework is based on measure theory and uses polar decomposition for simplifying and calculating the integrals to obtain closed form results. We validate our proposed framework by comparison with simulations and published closed form results in the literature for simple cases. We illustrate the versatility and advantage of the proposed framework by deriving closed form results for a case not yet reported in the literature. Finally, we also develop a Mathematica implementation of the proposed framework which allows a user to define any two arbitrary polygons and conveniently determine the distance distribution numerically.

cs.IT↗

arXiv2018

Consensus-based Privacy-preserving Data Aggregation

Privacy-preserving data aggregation in ad hoc networks is a challenging problem, considering the distributed communication and control requirement, dynamic network topology, unreliable communication links, etc. Different from the widely used cryptographic approaches, in this paper, we address this challenging problem by exploiting the distributed consensus technique. We first propose a secure consensus-based data aggregation (SCDA) algorithm that guarantees an accurate sum aggregation while preserving the privacy of sensitive data. Then, we prove that the proposed algorithm converges accurately and is $(ε, σ)$-data-privacy, and the mathematical relationship between $ε$ and $σ$ is provided. Extensive simulations have shown that the proposed algorithm has high accuracy and low complexity, and they are robust against network dynamics.

eess.SY↗

arXiv2017

Beyond Powers of Two: Hexagonal Modulation and Non-Binary Coding for Wireless Communication Systems

Adaptive modulation and coding (AMC) is widely employed in modern wireless communication systems to improve the transmission efficiency by adjusting the transmission rate according to the channel conditions. Thus, AMC can provide very efficient use of channel resources especially over fading channels. Quadrature Amplitude Modulation (QAM) is an ef- ficient and widely employed digital modulation technique. It typically employs a rectangular signal constellation. Therefore the decision regions of the constellation are square partitions of the two-dimensional signal space. However, it is well known that hexagons rather than squares provide the most compact regular tiling in two dimensions. A compact tiling means a dense packing of the constellation points and thus more energy efficient data transmission. Hexagonal modulation can be difficult to implement because it does not fit well with the usual power- of-two symbol sizes employed with binary data. To overcome this problem, non-binary coding is combined with hexagonal modulation in this paper to provide a system which is compatible with binary data. The feasibility and efficiency are evaluated using a software-defined radio (SDR) based prototype. Extensive simulation results are presented which show that this approach can provide improved energy efficiency and spectrum utilization in wireless communication systems.

eess.SP↗

arXiv2017

Virtualization map for the Littelmann path model

We show the natural embedding of weight lattices from a diagram folding is a virtualization map for the Littelmann path model, which recovers a result of Kashiwara. As an application, we give a type independent proof that certain Kirillov--Reshetikhin crystals respect diagram foldings, which is a known result on a special case of a conjecture given by Okado, Schilling, and Shimozono.

math.RT↗

arXiv2016

Random Distances Associated with Arbitrary Polygons: An Algorithmic Approach between Two Random Points

This report presents a new, algorithmic approach to the distributions of the distance between two points distributed uniformly at random in various polygons, based on the extended Kinematic Measure (KM) from integral geometry. We first obtain such random Point Distance Distributions (PDDs) associated with arbitrary triangles (i.e., triangle-PDDs), including the PDD within a triangle, and that between two triangles sharing either a common side or a common vertex. For each case, we provide an algorithmic procedure showing the mathematical derivation process, based on which either the closed-form expressions or the algorithmic results can be obtained. The obtained triangle-PDDs can be utilized for modeling and analyzing the wireless communication networks associated with triangle geometries, such as sensor networks with triangle-shaped clusters and triangle-shaped cellular systems with highly directional antennas. Furthermore, based on the obtained triangle-PDDs, we then show how to obtain the PDDs associated with arbitrary polygons through the decomposition and recursion approach, since any polygons can be triangulated, and any geometry shapes can be approximated by polygons with a needed precision. Finally, we give the PDDs associated with ring geometries. The results shown in this report can enrich and expand the theory and application of the probabilistic distance models for the analysis of wireless communication networks.

cs.CG↗

arXiv2015

Recursion-based Analysis for Information Propagation in Vehicular Ad Hoc Networks

Effective inter-vehicle communication is fundamental to a decentralized traffic information system based on Vehicular Ad Hoc Networks (VANETs). To reflect the uncertainty of the information propagation, most of the existing work was conducted by assuming the inter-vehicle distance follows some specific probability models, e.g., the lognormal or exponential distribution, while reducing the analysis complexity. Aimed at providing more generic results, a recursive modeling framework is proposed for VANETs in this paper when the vehicle spacing can be captured by a general i.i.d. distribution. With the framework, the analytical expressions for a series of commonly discussed metrics are derived respectively, including the mean, variance, probability distribution of the propagation distance, and expectation for the number of vehicles included in a propagation process, when the transmission failures are mainly caused by MAC contentions. Moreover, a discussion is also made for demonstrating the efficiency of the recursive analysis method when the impact of channel fading is also considered. All the analytical results are verified by extensive simulations. We believe that this work is able to potentially reveal a more insightful understanding of information propagation in VANETs by allowing to evaluate the effect of any vehicle headway distributions.

cs.NI↗

arXiv2014

A Geometrical-Based Throughput Bound Analysis for Device-to-Device Communications in Cellular Networks

Device-to-device (D2D) communications in cellular networks are promising technologies for improving network throughput, spectrum efficiency, and transmission delay. In this paper, we first introduce the concept of guard distance to explore a proper system model for enabling multiple concurrent D2D pairs in the same cell. Considering the Signal to Interference Ratio (SIR) requirements for both macro-cell and D2D communications, a geometrical method is proposed to obtain the guard distances from a D2D user equipment (DUE) to the base station (BS), to the transmitting cellular user equipment (CUE), and to other communicating D2D pairs, respectively, when the uplink resource is reused. By utilizing the guard distances, we then derive the bounds of the maximum throughput improvement provided by D2D communications in a cell. Extensive simulations are conducted to demonstrate the impact of different parameters on the optimal maximum throughput. We believe that the obtained results can provide useful guidelines for the deployment of future cellular networks with underlaying D2D communications.

cs.NI↗

arXiv2013

Random Distances Associated with Arbitrary Triangles: A Systematic Approach between Two Random Points

It has been known that the distribution of the random distances between two uniformly distributed points within a convex polygon can be obtained based on its chord length distribution (CLD). In this report, we first verify the existing known CLD for arbitrary triangles, and then derive and verify the distance distribution between two uniformly distributed points within an arbitrary triangle by simulation. Furthermore, a decomposition and recursion approach is applied to obtain the random point distance distribution between two arbitrary triangles sharing a side. As a case study, the explicit distribution functions are derived when two congruent isosceles triangles with the acute angle equal to $\fracπ{6}$ form a rhombus or a concave 4-gon.

math.GM↗

arXiv2013

Random Distances Associated with Trapezoids

The distributions of the random distances associated with hexagons, rhombuses and triangles have been derived and verified in the existing work. All of these geometric shapes are related to each other and have various applications in wireless communications, transportation, etc. Hexagons are widely used to model the cells in cellular networks, while trapezoids can be utilized to model the edge users in a cellular network with a hexagonal tessellation. In this report, the distributions of the random distances associated with unit trapezoids are derived, when two random points are within a unit trapezoid or in two neighbor unit trapezoids. The mathematical expressions are verified through simulation. Further, we present the polynomial fit for the PDFs, which can be used to simplify the computation.

math.GM↗