arXiv subjects

Minyi Huang

Publications and source records attributed to Minyi Huang.

36 records · Page 2Linked to original sources

arXiv2020

Mean-Field Transmission Power Control in Dense Networks

We consider uplink power control in wireless communication when a large number of users compete over the channel resources. The CDMA protocol, as a supporting technology of 3G networks accommodating signal from different sources over the code domain, represents the orthogonal multiple access (OMA) techniques. With the development of 5G wireless networks, non-orthogonal multiple access (NOMA) is introduced to improve the efficiency of channel allocation. Our goal is to investigate whether the power-domain NOMA protocol can introduce performance improvement when the users interact with each other in a non-cooperative manner. It is compared with the CDMA protocol, where the fierce competition among users jeopardizes the efficiency of channel usage. In this work, we conduct analysis with an aggregative game model, and show the existence and uniqueness of an equilibrium strategy. Next, we adopt the social welfare of the population as the performance metric, which is the average utility achieved by the user population. It is shown that under the corresponding equilibrium strategies, NOMA outperforms CDMA by higher efficiency of channel access for uplink communications.

eess.SY↗

arXiv2020

Three Party Quantum Networks Created by Quantum Cloning

With progress in quantum technologies, the field of quantum networks has emerged as an important area of research. In the last few years, there has been substantial progress in understanding the correlations present in quantum networks. In this article, we study cloning as a prospective method to generate three party quantum networks which can be further used to create larger networks. We analyze various quantum network topologies that can be created using cloning transformations. This would be useful in the situations wherever the availability of entangled pairs is limited. In addition to that we focus on the problem of distinguishing networks created by cloning from those which are created by distributing independently generated entangled pairs. We find that there are several states which cannot be distinguished using the Finner inequalities in the standard way. For such states, we propose an extension to the existing Finner inequality for triangle networks by further increasing the number of observers from three to four or six depending on the network topology. This takes into account the additional correlations that exist in the case of cloned networks. In the last part of the article we have used tripartite mutual information to distinguish cloned networks from networks created by independent sources and have further used squashed entanglement as a measure to quantify the amount of dependence in the cloned networks.

quant-ph↗

arXiv2020

Mean-Field Transmission Power Control in Dense Networks, Part II -- Social Welfare Evaluation

We consider uplink power control in wireless communication when massive users compete over the channel resources. In Part I, we have formulated massive transmission power control contest in a mean-field game framework. In this part, our goal is to investigate whether the power-domain non-orthogonal multiple access (NOMA) protocol can regulate the non-cooperative channel access behaviors, i.e., steering the competition among the non-cooperative users in a direction with improved efficiency and fairness. It is compared with the CDMA protocol, which drives each user to fiercely compete against the population, hence the efficiency of channel usage is sacrificed. The existence and uniqueness of an equilibrium strategy under CDMA and NOMA have already been characterized in Part I. In this paper, we adopt the social welfare of the population as the performance metric, which is defined as the expectation of utility over the distribution of different types of channel users. It is shown that under the corresponding equilibrium strategies, NOMA outperforms CDMA in the social welfare achieved, which is illustrated through simulation with different unit price for power consumption. Moreover, it can be observed from numerical results that NOMA can improve the fairness of the achieved data rates among different users.

eess.SY↗

arXiv2019

Linear quadratic mean field games with a major player: The multi-scale approach

This paper considers linear quadratic (LQ) mean field games with a major player and analyzes an asymptotic solvability problem. It starts with a large-scale system of coupled dynamic programming equations and applies a re-scaling technique introduced in Huang and Zhou (2018a, 2018b) to derive a set of Riccati equations in lower dimensions, the solvability of which determines the necessary and sufficient condition for asymptotic solvability. We next derive the mean field limit of the strategies and the value functions. Finally, we show that the two decentralized strategies can be interpreted as the best responses of a major player and a representative minor player embedded in an infinite population, which have the property of consistent mean field approximations.

math.OC↗

arXiv2019

Simulating broken $\cal PT$-symmetric Hamiltonian systems by weak measurement

By embedding a $\cal PT$-symmetric (pseudo-Hermitian) system into a large Hermitian one, we disclose the relations between $\cal{PT}$-symmetric Hamiltonians and weak measurement theory. We show that the amplification effect in weak measurement on a conventional quantum system can be used to effectively simulate a local broken $\cal PT$-symmetric Hamiltonian system, with the pre-selected state in the $\cal PT$-symmetric Hamiltonian system and its post-selected state resident in the dilated Hamiltonian system.

quant-ph↗

arXiv2019

The geometry properties of parity and time reversal operators in two dimensional spaces

The parity operator $\cal P$ and time reversal operator $\cal T$ are two important operators in the quantum theory, in particular, in the $\cal PT$-symmetric quantum theory. By using the concrete forms of $\cal P$ and $\cal T$, we discuss their geometrical properties in two dimensional spaces. It is showed that if $\cal T$ is given, then all $\cal P$ links with the quadric surfaces; if $\cal P$ is given, then all $\cal T$ links with the quadric curves. Moreover, we give out the generalized unbroken $\cal PT$-symmetric condition of an operator. The unbroken $\cal PT$-symmetry of a Hermitian operator is also showed in this way.

quant-ph↗

arXiv2019

Linear quadratic mean field games: Asymptotic solvability and relation to the fixed point approach

Mean field game theory has been developed largely following two routes. One of them, called the direct approach, starts by solving a large-scale game and next derives a set of limiting equations as the population size tends to infinity. The second route is to apply mean field approximations and formalize a fixed point problem by analyzing the best response of a representative player. This paper addresses the connection and difference of the two approaches in a linear quadratic (LQ) setting. We first introduce an asymptotic solvability notion for the direct approach, which means for all sufficiently large population sizes, the corresponding game has a set of feedback Nash strategies in addition to a mild regularity requirement. We provide a necessary and sufficient condition for asymptotic solvability and show that in this case the solution converges to a mean field limit. This is accomplished by developing a re-scaling method to derive a low dimensional ordinary differential equation (ODE) system, where a non-symmetric Riccati ODE has a central role. We next compare with the fixed point approach which determines a two point boundary value (TPBV) problem, and show that asymptotic solvability implies feasibility of the fixed point approach, but the converse is not true. We further address non-uniqueness in the fixed point approach and examine the long time behavior of the non-symmetric Riccati ODE in the asymptotic solvability problem.

math.OC↗

arXiv2019

Linear-Quadratic Mean Field Social Optimization with a Major Player

This paper considers a linear-quadratic (LQ) mean field control problem involving a major player and a large number of minor players, where the dynamics and costs depend on random parameters. The objective is to optimize a social cost as a weighted sum of the individual costs under decentralized information. We apply the person-by-person optimality principle in team decision theory to the finite population model to construct two limiting variational problems whose solutions, subject to the requirement of consistent mean field approximations, yield a system of forward-backward stochastic differential equations (FBSDEs). We show the existence and uniqueness of a solution to the FBSDEs and obtain decentralized strategies nearly achieving social optimality in the original large but finite population model.

math.OC↗

arXiv2019

Partial coherence and quantum correlation with fidelity and affinity distances

A fundamental task in any physical theory is to quantify certain physical quantity in a meaningful way. In this paper we show that both fidelity distance and affinity distance satisfy the strong contractibility, and the corresponding resource quantifiers can be used to characterize a large class of resource theories. Under two assumptions, namely, convexity of "free states" and closure of free states under "selective free operations", our general framework of resource theory includes quantum resource theories of entanglement, coherence, partial coherence and superposition. In partial coherence theory, we show that fidelity partial coherence of a bipartite state is equal to the minimal error probability of a mixed quantum state discrimination (QSD) task and vice versa, which complements the main result in [Xiong and Wu, J. Phys. A: Math. Theor. 51, 414005 (2018)]. We also compute the analytic expression of fidelity partial coherence for $(2,n)$ bipartite X-states. At last, we study the correlated coherence in the framework of partial coherence theory. We show that partial coherence of a bipartite state, with respect to the eigenbasis of a subsystem, is actually a measure of quantum correlation.

quant-ph↗

arXiv2018

Linear-Quadratic Mean Field Control: The Hamiltonian Matrix and Invariant Subspace Method

This paper studies the existence and uniqueness of a solution to linear quadratic (LQ) mean field social optimization problems with uniform agents. We exploit a Hamiltonian matrix structure of the associated ordinary differential equation (ODE) system and apply a subspace decomposition method to find the solution. This approach is effective for both the existence analysis and numerical computations. We further extend the decomposition method to LQ mean field games.

math.OC↗

arXiv2018

Linear Quadratic Mean Field Games -- Part I: The Asymptotic Solvability Problem

This paper investigates the so-called asymptotic solvability problem in linear quadratic (LQ) mean field games. The model has asymptotic solvability if for all sufficiently large population sizes, the corresponding game has a set of feedback Nash strategies subject to a mild regularity requirement. We provide a necessary and sufficient condition and show that in this case the solution converges to a mean field limit. This is accomplished by developing a re-scaling method to derive a low dimensional ordinary differential equation (ODE) system, where a non-symmetric Riccati ODE has a central role.

math.OC↗

arXiv2018

Mean Field Production Output Control with Sticky Prices: Nash and Social Solutions

This paper presents an application of mean field control to dynamic production optimization. Both noncooperative and cooperative solutions are considered. We first introduce a market of a large number of agents (firms) with sticky prices and adjustment costs. By solving auxiliary limiting optimal control problems subject to consistent mean field approximations, two sets of decentralized strategies are obtained and further shown to asymptotically attain Nash equilibria and social optima, respectively. The performance estimate of the social optimum strategies exploits a passivity property of the underlying model. A numerical example is given to compare market prices, firms' outputs and costs under two two solution frameworks.

math.OC↗

arXiv2018

Embedding, simulation and consistency of $\cal PT$ -symmetric quantum Theory

A physical requirement on the Hamiltonian operator in quantum mechanics is that it must generate real energy spectrum and unitary time evolution. While the Hamiltonians are Dirac Hermitian in conventional quantum mechanics, they observe $\cal PT$-symmetry in $\cal PT$-symmetric quantum theory. The embedding property was first studied by Günther and Samsonov to visualize the evolution of unbroken $\cal PT$-symmetric Hamiltonians on $\mathbb C^2$ by Hermitian Hamiltonians on $\mathbb C^4$. This paper investigates the properties of $\cal PT$-symmetric quantum systems including the embedding property. We provide a full characterization of the embedding property in the general case and show that only unbroken $\cal PT$-symmetric quantum systems admit this property in a finite dimensional space. Furthermore, utilizing this property, we establish a physically realizable simulation process of the unbroken $\cal PT$-symmetric Hamiltonians. An observation that the unbroken $\cal PT$-symmetric quantum systems can be viewed as open systems in the conventional quantum mechanics accounts for the consistency of $\cal PT$-symmetric quantum theory.

math-ph↗

arXiv2018

Manifestation of Superposition and Coherence in $\cal PT$-symmetry through the $η$-inner Product

Through the $η$-inner product, we investigate $\cal PT$-symmetric quantum mechanics from the viewpoint of superposition and coherence theory. It is argued that $\cal PT$-symmetric quantum systems are endowed with stationary superposition or superposition-free properties. A physical interpretation of $η$-inner product in $\mathbb C^2$ is given through the Stokes parameters, showing the difference between broken and unbroken $\cal PT$-symmetric quantum systems.

quant-ph↗

arXiv2017

Mean Field Stochastic Games with Binary Action Spaces and Monotone Costs

This paper considers mean field games in a multi-agent Markov decision process (MDP) framework. Each player has a continuum state and binary action. By active control, a player can bring its state to a resetting point. All players are coupled through their cost functions. The structural property of the individual strategies is characterized in terms of threshold policies when the mean field game admits a solution. We further introduce a stationary equation system of the mean field game and analyze uniqueness of its solution under positive externalities.

math.OC↗

arXiv2017

Robust Mean Field Linear-Quadratic-Gaussian Games with Unknown $L^2$-Disturbance

This paper considers a class of mean field linear-quadratic-Gaussian (LQG) games with model uncertainty. The drift term in the dynamics of the agents contains a common unknown function. We take a robust optimization approach where a representative agent in the limiting model views the drift uncertainty as an adversarial player. By including the mean field dynamics in an augmented state space, we solve two optimal control problems sequentially, which combined with consistent mean field approximations provides a solution to the robust game. A set of decentralized control strategies is derived by use of forward-backward stochastic differential equations (FBSDE) and shown to be a robust epsilon-Nash equilibrium.

math.OC↗

arXiv2014

A characterization of sub-game perfect Nash equilibria for SDEs of mean field type

We study a class of dynamic decision problems of mean field type with time inconsistent cost functionals, and derive a stochastic maximum principle to characterize subgame perfect Nash equilibrium points. Subsequently, this approach is extended to a mean field game to construct decentralized strategies and obtain an estimate of their performance.

math.OC↗

arXiv2011

Distributed Cooperative Spectrum Sensing in Mobile Ad Hoc Networks with Cognitive Radios

In cognitive radio mobile ad hoc networks (CR-MANETs), secondary users can cooperatively sense the spectrum to detect the presence of primary users. In this chapter, we propose a fully distributed and scalable cooperative spectrum sensing scheme based on recent advances in consensus algorithms. In the proposed scheme, the secondary users can maintain coordination based on only local information exchange without a centralized common receiver. We use the consensus of secondary users to make the final decision. The proposed scheme is essentially based on recent advances in consensus algorithms that have taken inspiration from complex natural phenomena including flocking of birds, schooling of fish, swarming of ants and honeybees. Unlike the existing cooperative spectrum sensing schemes, there is no need for a centralized receiver in the proposed schemes, which make them suitable in distributed CR-MANETs. Simulation results show that the proposed consensus schemes can have significant lower missing detection probabilities and false alarm probabilities in CR-MANETs. It is also demonstrated that the proposed scheme not only has proven sensitivity in detecting the primary user's presence, but also has robustness in choosing a desirable decision threshold.

cs.IT↗