arXiv subjects

Ting Yang

Publications and source records attributed to Ting Yang.

At least 37 records · Page 2Linked to original sources

arXiv2025

PoVF: Empowering Decentralized Blockchain Systems with Verifiable Function Consensus

Consensus mechanism is the core technology for blockchain to ensure that transactions are executed in sequence. It also determines the decentralization, security, and efficiency of blockchain. Existing mechanisms all have certain centralization issues and fail to ensure the decentralization of blockchain networks. A decentralized and efficient mechanism is required to improve blockchain systems. This paper proposes a fair consensus mechanism called Proof of Verifiable Functions (PoVF), based on the verifiability and unpredictability of verifiable functions. PoVF provides a sufficiently fair mechanism, ensuring that all nodes in blockchain network have equal opportunity to participate in consensus. In addition, a structure called "Delay buffer" is proposed to ensure transactions are executed sequentially. It delay the selection of blocks to avoid blockchain forks caused by broadcasting and transaction execution confusion. According to our security analysis, PoVF is provably secure and has the ability to resist potential adversaries. According to the experiments, PoVF-based blockchain can process up to 4000 transactions per second with nodes configured with only 4-core CPUs. This paper uses the Gini coefficient to measure the decentralization of blockchains, and the PoVF-based blockchain achieves the lowest Gini coefficient of 0.39 among all sampled blockchains. PoVF has been shown to provide sufficient efficiency while ensuring decentralization and security through experiments.

cs.CR↗

arXiv2024

Stationary measures and the continuous-state branching process conditioned on extinction

We consider continuous-state branching processes (CB processes) which become extinct almost surely. First, we tackle the problem of describing the stationary measures on $(0,+\infty)$ for such CB processes. We give a representation of the stationary measure in terms of scale functions of related Lévy processes. Then we prove that the stationary measure can be obtained from the vague limit of the potential measure, and, in the critical case, can also be obtained from the vague limit of a normalized transition probability. Next, we prove some limit theorems for the CB process conditioned on extinction in a near future and on extinction at a fixed time. We obtain non-degenerate limit distributions which are of the size-biased type of the stationary measure in the critical case and of the Yaglom's distribution in the subcritical case. Finally we explore some further properties of the limit distributions.

math.PR↗

arXiv2024

Weak slice regular functions on the $n$-dimensional quadratic cone of octonions

In the literature on slice analysis in the hypercomplex setting, there are two main approaches to define slice regular functions in one variable: one consists in requiring that the restriction to any complex plane is holomorphic (with the same complex structure of the complex plane), the second one makes use of stem and slice functions. So far, in the setting of several hypercomplex variables, only the second approach has been considered, i.e. the one based on stem functions. In this paper, we use instead the first definition on the so-called $n$-dimensional quadratic cone of octonions. These two approaches yield the same class of slice regular functions on axially symmetric slice-domains, however, they are different on other types of domains. We call this new class of functions weak slice regular. We show that there exist weak slice regular functions which are not slice regular in the second approach. Moreover, we study various properties of these functions, including a Taylor expansion.

math.CV↗

arXiv2024

Navigating User Experience of ChatGPT-based Conversational Recommender Systems: The Effects of Prompt Guidance and Recommendation Domain

Conversational recommender systems (CRS) enable users to articulate their preferences and provide feedback through natural language. With the advent of large language models (LLMs), the potential to enhance user engagement with CRS and augment the recommendation process with LLM-generated content has received increasing attention. However, the efficacy of LLM-powered CRS is contingent upon the use of prompts, and the subjective perception of recommendation quality can differ across various recommendation domains. Therefore, we have developed a ChatGPT-based CRS to investigate the impact of these two factors, prompt guidance (PG) and recommendation domain (RD), on the overall user experience of the system. We conducted an online empirical study (N = 100) by employing a mixed-method approach that utilized a between-subjects design for the variable of PG (with vs. without) and a within-subjects design for RD (book recommendations vs. job recommendations). The findings reveal that PG can substantially enhance the system's explainability, adaptability, perceived ease of use, and transparency. Moreover, users are inclined to perceive a greater sense of novelty and demonstrate a higher propensity to engage with and try recommended items in the context of book recommendations as opposed to job recommendations. Furthermore, the influence of PG on certain user experience metrics and interactive behaviors appears to be modulated by the recommendation domain, as evidenced by the interaction effects between the two examined factors. This work contributes to the user-centered evaluation of ChatGPT-based CRS by investigating two prominent factors and offers practical design guidance.

cs.HC↗

arXiv2024

Fluctuations of the additive martingales related to super-Brownian motion

Let $(W_{t}(λ))_{t\ge 0}$, parametrized by $λ\in\mathbb{R}$, be the additive martingale related to a supercritical super-Brownian motion on the real line and let $W_{\infty}(λ)$ be its limit. Under a natural condition for the martingale limit to be non-degenerate, we investigate the rate at which the martingale approaches its limit. Indeed, assuming certain moment conditions on the branching mechanism, we show that the tail martingale $W_{\infty}(λ)-W_{t}(λ)$, properly normalized, converges in distribution to a non-degenerate random variable, and we identify the limit laws. We find that, for parameters with small absolute value, the fluctuations are affected by the behaviour of the branching mechanism $ψ$ around $0$. In fact, we prove that, in the case of small $|λ|$, when $ψ$ is secondly differentiable at $0$, the limit laws are scale mixtures of the standard normal laws, and when $ψ$ is `stable-like' near $0$ in some proper sense, the limit laws are scale mixtures of the stable laws. However, the effect of the branching mechanism is limited in the case of large $|λ|$. In the latter case, we show that the fluctuations and limit laws are determined by the limiting extremal process of the super-Brownian motion.

math.PR↗

arXiv2024

Path-slice star-product on non-axially symmetric domains in several quaternionic variables

This paper extends the $*$-product from slice analysis to weakly slice analysis in several quaternionic variables, focusing on non-axially symmetric domains. It diverges from traditional applications in axially symmetric domains to address slice regularity in more complicated cases. The approach involves redefining the $*$-product for path-slice functions, borrowing techniques from strongly slice analysis. Key to this work is the introduction of relative stem-preserving set pairs and real-path-connected sets, which help establish a direct link between path-slice functions and their stem functions. The study culminates in conditions under which weakly slice regular functions form an algebra in specific slice domains, broadening the scope of slice analysis.

math.CV↗

arXiv2023

Limiting distributions for a class of super-Brownian motions with spatially dependent branching mechanisms

In this paper we consider a large class of super-Brownian motions in $\mathbb{R}$ with spatially dependent branching mechanisms. We establish the almost sure growth rate of the mass located outside a time-dependent interval $(-δt,δt)$ for $δ>0$. The growth rate is given in terms of the principal eigenvalue $λ_{1}$ of the Schödinger type operator associated with the branching mechanism. From this result we see the existence of phase transition for the growth order at $δ=\sqrt{λ_{1}/2}$. We further show that the super-Brownian motion shifted by $\sqrt{λ_{1}/2}\,t$ converges in distribution to a random measure with random density mixed by a martingale limit.

math.PR↗

arXiv2023

Multi-MEC Cooperation Based VR Video Transmission and Cache using K-Shortest Paths Optimization

In recent network architectures, multi-MEC cooperative caching has been introduced to reduce the transmission latency of VR videos, in which MEC servers' computing and caching capability are utilized to optimize the transmission process. However, many solutions that use the computing capability of MEC servers ignore the additional arithmetic power consumed by the codec process, thus making them infeasible. Besides, the minimum cache unit is usually the entire VR video, which makes caching inefficient. To address these challenges, we split VR videos into tile files for caching based on the current popular network architecture and provide a reliable transmission mechanism and an effective caching strategy. Since the number of different tile files N is too large, the current cooperative caching algorithms do not cope with such large-scale input data. We further analyze the problem and propose an optimized k-shortest paths (OKSP) algorithm with an upper bound time complexity of O((K * M + N) * M * logN)), and suitable for shortest paths with restricted number of edges, where K is the total number of tiles that all M MEC servers can cache in the collaboration domain. And we prove the OKSP algorithm can compute the caching scheme with the lowest average latency in any case, which means the solution given is the exact solution. The simulation results show that the OKSP algorithm has excellent speed for solving large-scale data and consistently outperforms other caching algorithms in the experiments.

cs.NI↗

arXiv2022

The extremal process of super-Brownian motion: a probabilistic approach via skeletons

Recently Ren et al. [Stoch. Proc. Appl., 137 (2021)] have proved that the extremal process of the super-Brownian motion converges in distribution in the limit of large times. Their techniques rely heavily on the study of the convergence of solutions to the Kolmogorov-Petrovsky-Piscounov equation along the lines of [M. Bramson, Mem. Amer. Math. Soc., 44 (1983)]. In this paper we take a different approach. Our approach is based on the skeleton decomposition of super-Brownian motion. The skeleton may be interpreted as immortal particles that determine the large time behaviour of the process. We exploit this fact and carry asymptotic properties from the skeleton over to the super-Brownian motion. Some new results concerning the probabilistic representations of the limiting process are obtained, which cannot be directly obtained through the results of [Y.-X. Ren et al., Stoch. Proc. Appl., 137 (2021)]. Apart from the results, our approach offers insights into the driving force behind the limiting process for super-Brownian motions.

math.PR↗

arXiv2022

Multiple-antenna Placement Delivery Array for Cache-aided MISO Systems

We consider the cache-aided multiple-input single-output (MISO) broadcast channel, which consists of a server with $L$ antennas and $K$ single-antenna users, where the server contains $N$ files of equal length and each user is equipped with a local cache of size $M$ files. Each user requests an arbitrary file from library. The objective is to design a coded caching scheme based on uncoded placement and one-shot linear delivery, to achieve the maximum sum Degree-of-Freedom (sum-DoF) with low subpacketization. It was shown in the literature that under the constraint of uncoded placement and one-shot linear delivery, the optimal sum-DoF is $L+\frac{KM}{N}$. However, previously proposed schemes for this setting incurred either an exponential subpacketization order in $K$, or required specific conditions in the system parameters $L$, $K$, $M$ and $N$. In this paper, we propose a new combinatorial structure called multiple-antenna placement delivery array (MAPDA). Based on MAPDA and Latin square, the first proposed scheme achieves the optimal sum-DoF $L+\frac{KM}{N}$ with the subpacketization of $K$ when $\frac{KM}{N}+L=K$. Subsequently, for the general case we propose a transformation approach to construct an MAPDA from any $g$-regular PDA (a class of PDA where each integer in the array occurs $g$ times) for the original shared-link coded caching problem. When the original PDA corresponds to the Maddah-Ali and Niesen coded caching scheme, the resulting scheme under the combinatorial structure of MAPDA can achieve the optimal sum-DoF $L+\frac{KM}{N}$ with reduced subpacketization with respect to the existing schemes. The work can be extended to the multiple independent single-antenna transmitters (servers) corresponding to the cache-aided interference channel proposed by Naderializadeh et al. and the scenario of transmitters equipped with multiple antennas.

cs.IT↗

arXiv2021

Collective Intelligence: Decentralized Learning for Android Malware Detection in IoT with Blockchain

The widespread significance of Android IoT devices is due to its flexibility and hardware support features which revolutionized the digital world by introducing exciting applications almost in all walks of daily life, such as healthcare, smart cities, smart environments, safety, remote sensing, and many more. Such versatile applicability gives incentive for more malware attacks. In this paper, we propose a framework which continuously aggregates multiple user trained models on non-overlapping data into single model. Specifically for malware detection task, (i) we propose a novel user (local) neural network (LNN) which trains on local distribution and (ii) then to assure the model authenticity and quality, we propose a novel smart contract which enable aggregation process over blokchain platform. The LNN model analyzes various static and dynamic features of both malware and benign whereas the smart contract verifies the malicious applications both for uploading and downloading processes in the network using stored aggregated features of local models. In this way, the proposed model not only improves malware detection accuracy using decentralized model network but also model efficacy with blockchain. We evaluate our approach with three state-of-the-art models and performed deep analyses of extracted features of the relative model.

cs.CR↗

arXiv2021

Blockchain based Privacy-Preserved Federated Learning for Medical Images: A Case Study of COVID-19 CT Scans

Medical health care centers are envisioned as a promising paradigm to handle the massive volume of data of COVID-19 patients using artificial intelligence (AI). Traditionally, AI techniques often require centralized data collection and training the model in a single organization, which is most common weakness due to the privacy and security of raw data communication. To solve this challenging task, we propose a blockchain-based federated learning framework that provides collaborative data training solutions by coordinating multiple hospitals to train and share encrypted federated models without leakage of data privacy. The blockchain ledger technology provides the decentralization of federated learning model without any central server. The proposed homomorphic encryption scheme encrypts and decrypts the gradients of model to preserve the privacy. More precisely, the proposed framework: i) train the local model by a novel capsule network to segmentation and classify COVID-19 images, ii) then use the homomorphic encryption scheme to secure the local model that encrypts and decrypts the gradients, and finally the model is shared over a decentralized platform through proposed blockchain-based federated learning algorithm. The integration of blockchain and federated learning leads to a new paradigm for medical image data sharing in the decentralized network. The conducted experimental resultsdemonstrate the performance of the proposed scheme.

cs.CR↗

arXiv2021

Nordhaus-Gaddum type inequality for the fractional matching number of a graph

The fractional matching number of a graph G, is the maximum size of a fractional matching of G. The following sharp lower bounds for a graph G of order n are proved, and all extremal graphs are characterized in this paper. (1)The sum of the fractional matching number of a graph G and the fractional matching number of its complement is not less than n/2 , where n is not less than 2. (2) If G and its complement are non-empty, then the sum of the fractional matching number of a graph G and the fractional matching number of its complement is not less than (n+1)/2, where n is not less than 28. (3) If G and its complement have no isolated vertices, then the sum of the fractional matching number of a graph G and the fractional matching number of its complement is not less than (n+4)/2, where n is not less than 28.

math.CO↗

arXiv2020

Blockchain-Federated-Learning and Deep Learning Models for COVID-19 detection using CT Imaging

With the increase of COVID-19 cases worldwide, an effective way is required to diagnose COVID-19 patients. The primary problem in diagnosing COVID-19 patients is the shortage and reliability of testing kits, due to the quick spread of the virus, medical practitioners are facing difficulty identifying the positive cases. The second real-world problem is to share the data among the hospitals globally while keeping in view the privacy concerns of the organizations. Building a collaborative model and preserving privacy are major concerns for training a global deep learning model. This paper proposes a framework that collects a small amount of data from different sources (various hospitals) and trains a global deep learning model using blockchain based federated learning. Blockchain technology authenticates the data and federated learning trains the model globally while preserving the privacy of the organization. First, we propose a data normalization technique that deals with the heterogeneity of data as the data is gathered from different hospitals having different kinds of CT scanners. Secondly, we use Capsule Network-based segmentation and classification to detect COVID-19 patients. Thirdly, we design a method that can collaboratively train a global model using blockchain technology with federated learning while preserving privacy. Additionally, we collected real-life COVID-19 patients data, which is, open to the research community. The proposed framework can utilize up-to-date data which improves the recognition of computed tomography (CT) images. Finally, our results demonstrate a better performance to detect COVID-19 patients.

eess.IV↗

arXiv2020

State sharding model on the blockchain

Blockchain is an incrementally updated ledger maintained by distributed nodes rather than centralized organizations. The current blockchain technology faces scalability issues, which include two aspects: low transaction throughput and high storage capacity costs. This paper studies the blockchain structure based on state sharding technology, and mainly solves the problem of non-scalability of block chain storage. This paper designs and implements the blockchain state sharding scheme, proposes a specific state sharding data structure and algorithm implementation, and realizes a complete blockchain structure so that the blockchain has the advantages of high throughput, processing a large number of transactions and saving storage costs. Experimental results show that a blockchain network with more than 100,000 nodes can be divided into 1024 shards. A blockchain network with this structure can process 500,000 transactions in about 5 seconds. If the consensus time of the blockchain is about 10 seconds, and the block generation time of the blockchain system of the sharding mechanism is 15 seconds, the transaction throughput can reach 33,000 tx/sec. Experimental results show that the throughput of the proposed protocol increases with the increase of the network node size. This confirms the scalability of the blockchain structure based on sharding technology.

cs.CR↗

arXiv2020

Spine decomposition and $L\log L$ criterion for superprocesses with non-local branching mechanisms

In this paper, we provide a pathwise spine decomposition for superprocesses with both local and non-local branching mechanisms under a martingale change of measure. This result complements the related results obtained in Evans (1993), Kyprianou et al. (2012) and Liu, Ren and Song (2009) for superprocesses with purely local branching mechanisms and in Chen, Ren and Song (2016) and Kyprianou and Palau (2016) for multitype superprocesses. As an application of this decomposition, we obtain necessary/sufficient conditions for the limit of the fundamental martingale to be non-degenerate. In particular, we obtain extinction properties of superprocesses with non-local branching mechanisms as well as a Kesten-Stigum $L\log L$ theorem for the fundamental martingale.

math.PR↗

arXiv2019

Entrance laws at the origin of self-similar Markov processes in high dimensions

In this paper we consider the problem of finding entrance laws at the origin for self-similar Markov processes in $\mathbb{R}^d$, killed upon hitting the origin. Under mild assumptions, we show the existence of an entrance law and the convergence to this law when the process is started close to the origin. We obtain an explicit description of the process started from the origin as the time reversal of the original self-similar Markov process conditioned to hit the origin.

math.PR↗

arXiv2019

Hierarchical Total Variations and Doubly Penalized ANOVA Modeling for Multivariate Nonparametric Regression

For multivariate nonparametric regression, functional analysis-of-variance (ANOVA) modeling aims to capture the relationship between a response and covariates by decomposing the unknown function into various components, representing main effects, two-way interactions, etc. Such an approach has been pursued explicitly in smoothing spline ANOVA modeling and implicitly in various greedy methods such as MARS. We develop a new method for functional ANOVA modeling, based on doubly penalized estimation using total-variation and empirical-norm penalties, to achieve sparse selection of component functions and their knots. For this purpose, we formulate a new class of hierarchical total variations, which measures total variations at different levels including main effects and multi-way interactions, possibly after some order of differentiation. Furthermore, we derive suitable basis functions for multivariate splines such that the hierarchical total variation can be represented as a regular Lasso penalty, and hence we extend a previous backfitting algorithm to handle doubly penalized estimation for ANOVA modeling. We present extensive numerical experiments on simulations and real data to compare our method with existing methods including MARS, tree boosting, and random forest. The results are very encouraging and demonstrate considerable gains from our method in both prediction or classification accuracy and simplicity of the fitted functions.

stat.ME↗