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Yi Ouyang

Publications and source records attributed to Yi Ouyang.

At least 55 records · Page 3Linked to original sources
arXiv2019

Endomorphism rings of supersingular elliptic curves over $\mathbb{F}_p$

Let $p>3$ be a fixed prime. For a supersingular elliptic curve $E$ over $\mathbb{F}_p$ with $j$-invariant $j(E)\in \mathbb{F}_p\backslash\{0, 1728\}$, it is well known that the Frobenius map $π=((x,y)\mapsto (x^p, y^p))\in \mathrm{End}(E)$ satisfies $π^2=-p$. A result of Ibukiyama tells us that $\mathrm{End}(E)$ is a maximal order in $\mathrm{End}(E)\otimes \mathbb{Q}$ associated to a (minimal) prime $q$ satisfying $q\equiv 3 \bmod 8$ and the quadratic residue $\bigl(\frac{p}{q}\bigr)=-1$ according to $\frac{1+π}{2}\notin \mathrm{End}(E)$ or $\frac{1+π}{2}\in \mathrm{End}(E)$. Let $q_j$ denote the minimal $q$ for $E$ with $j=j(E)$. Firstly, we determine the neighborhood of the vertex $[E]$ in the supersingular $\ell$-isogeny graph if $\frac{1+π}{2}\notin \mathrm{End}(E)$ and $p>q\ell^2$ or $\frac{1+π}{2}\in \mathrm{End}(E)$ and $p>4q\ell^2$. In particular, under our assumption, we show that there are at most two vertices defined over $\mathbb{F}_p$ adjacent to $[E]$. Next, under GRH, we obtain the bound $M(p)$ of $q_j$ for all $j$ and estimate the number of supersingular elliptic curves with $q_j \sqrt{p}$ except $p=11,23$ and $M(p)<p\log^2 p$ for all $p$.

math.NT↗
arXiv2019

Learning Cross-Domain Representation with Multi-Graph Neural Network

Learning effective embedding has been proved to be useful in many real-world problems, such as recommender systems, search ranking and online advertisement. However, one of the challenges is data sparsity in learning large-scale item embedding, as users' historical behavior data are usually lacking or insufficient in an individual domain. In fact, user's behaviors from different domains regarding the same items are usually relevant. Therefore, we can learn complete user behaviors to alleviate the sparsity using complementary information from correlated domains. It is intuitive to model users' behaviors using graph, and graph neural networks (GNNs) have recently shown the great power for representation learning, which can be used to learn item embedding. However, it is challenging to transfer the information across domains and learn cross-domain representation using the existing GNNs. To address these challenges, in this paper, we propose a novel model - Deep Multi-Graph Embedding (DMGE) to learn cross-domain representation. Specifically, we first construct a multi-graph based on users' behaviors from different domains, and then propose a multi-graph neural network to learn cross-domain representation in an unsupervised manner. Particularly, we present a multiple-gradient descent optimizer for efficiently training the model. We evaluate our approach on various large-scale real-world datasets, and the experimental results show that DMGE outperforms other state-of-art embedding methods in various tasks.

cs.LG↗
arXiv2019

Quantum Tomography of the Photon-Plasmon Conversion Process in a Metal Hole Array

In the past decades, quantum plasmonics has become an active area due to its potential applications in on-chip plasmonic devices for quantum information processing. However, the fundamental physical process, i.e., how a quantum state of light evolves in the photon-plasmon conversion process, has not been clearly understood. Here, we report a complete characterization of the plasmon-assisted extraordinary optical transmission process through quantum process tomography. By inputting various coherent states to interact with the plasmonic structure and detecting the output states with a homodyne detector, we reconstruct the process tensor of the photon-plasmon conversion process. Both the amplitude and phase information of the process are extracted, which explains the evolution of the quantum-optical state after the coupling with plasmons. Our experimental demonstration constitutes a fundamental block for future on-chip applications of quantum plasmonic circuits.

quant-ph↗
arXiv2019

An Approximation Algorithm for Optimal Clique Cover Delivery in Coded Caching

Coded caching can significantly reduce the communication bandwidth requirement for satisfying users' demands by utilizing the multicasting gain among multiple users. Most existing works assume that the users follow the prescriptions for content placement made by the system. However, users may prefer to decide what files to cache. To address this issue, we consider a network consisting of a file server connected through a shared link to $K$ users, each equipped with a cache which has been already filled arbitrarily. Given an arbitrary content placement, the goal is to find a delivery strategy for the server that minimizes the load of the shared link. In this paper, we focus on a specific class of coded multicasting delivery schemes known as the "clique cover delivery scheme". We first formulate the optimal clique cover delivery problem as a combinatorial optimization problem. Using a connection with the weighted set cover problem, we propose an approximation algorithm and show that it provides an approximation ratio of $(1 + \log K)$, while the approximation ratio for the existing coded delivery schemes is linear in $K$. Numerical simulations show that our proposed algorithm provides a considerable bandwidth reduction over the existing coded delivery schemes for almost all content placement schemes.

cs.IT↗
arXiv2019

Worst-case Guarantees for Remote Estimation of an Uncertain Source

Consider a remote estimation problem where a sensor wants to communicate the state of an uncertain source to a remote estimator over a finite time horizon. The uncertain source is modeled as an autoregressive process with bounded noise. Given that the sensor has a limited communication budget, the sensor must decide when to transmit the state to the estimator who has to produce real-time estimates of the source state. In this paper, we consider the problem of finding a scheduling strategy for the sensor and an estimation strategy for the estimator to jointly minimize the worst-case maximum instantaneous estimation error over the time horizon. This leads to a decentralized minimax decision-making problem. We obtain a complete characterization of optimal strategies for this decentralized minimax problem. In particular, we show that an open loop communication scheduling strategy is optimal and the optimal estimate depends only on the most recently received sensor observation.

eess.SY↗
arXiv2018

A Unified Approach to Dynamic Decision Problems with Asymmetric Information - Part I: Non-Strategic Agents

We study a general class of dynamic multi-agent decision problems with asymmetric information and non-strategic agents, which includes dynamic teams as a special case. When agents are non-strategic, an agent's strategy is known to the other agents. Nevertheless, the agents' strategy choices and beliefs are interdependent over times, a phenomenon known as signaling. We introduce the notions of private information that effectively compresses the agents' information in a mutually consistent manner. Based on the notions of sufficient information, we propose an information state for each agent that is sufficient for decision making purposes. We present instances of dynamic multi-agent decision problems where we can determine an information state with a time-invariant domain for each agent. Furthermore, we present a generalization of the policy-independence property of belief in Partially Observed Markov Decision Processes (POMDP) to dynamic multi-agent decision problems. Within the context of dynamic teams with asymmetric information, the proposed set of information states leads to a sequential decomposition that decouples the interdependence between the agents' strategies and beliefs over time, and enables us to formulate a dynamic program to determine a globally optimal policy via backward induction.

cs.MA↗
arXiv2018

A Unified Approach to Dynamic Decision Problems with Asymmetric Information - Part II: Strategic Agents

We study a general class of dynamic games with asymmetric information where agents' beliefs are strategy dependent, i.e. signaling occurs. We show that the notion of sufficient information, introduced in the companion paper team, can be used to effectively compress the agents' information in a mutually consistent manner that is sufficient for decision-making purposes. We present instances of dynamic games with asymmetric information where we can characterize a time-invariant information state for each agent. Based on the notion of sufficient information, we define a class of equilibria for dynamic games called Sufficient Information Based Perfect Bayesian Equilibrium (SIB-PBE). Utilizing the notion of SIB-PBE, we provide a sequential decomposition of dynamic games with asymmetric information over time; this decomposition leads to a dynamic program that determines SIB-PBE of dynamic games. Furthermore, we provide conditions under which we can guarantee the existence of SIB-PBE.

cs.MA↗
arXiv2018

Optimal Infinite Horizon Decentralized Networked Controllers with Unreliable Communication

We consider a decentralized networked control system (DNCS) consisting of a remote controller and a collection of linear plants, each associated with a local controller. Each local controller directly observes the state of its co-located plant and can inform the remote controller of the plant's state through an unreliable uplink channel. The downlink channels from the remote controller to local controllers were assumed to be perfect. The objective of the local controllers and the remote controller is to cooperatively minimize the infinite horizon time average of expected quadratic cost. The finite horizon version of this problem was solved in our prior work [2]. The optimal strategies in the finite horizon case were shown to be characterized by coupled Riccati recursions. In this paper, we show that if the link failure probabilities are below certain critical thresholds, then the coupled Riccati recursions of the finite horizon solution reach a steady state and the corresponding decentralized strategies are optimal. Above these thresholds, we show that no strategy can achieve finite cost. We exploit a connection between our DNCS Riccati recursions and the coupled Riccati recursions of an auxiliary Markov jump linear system to obtain our results. Our main results in Theorems 1 and 2 explicitly identify the critical thresholds for the link failure probabilities and the optimal decentralized control strategies when all link failure probabilities are below their thresholds.

eess.SY↗
arXiv2018

Optimal Local and Remote Controllers with Unreliable Uplink Channels

We consider a networked control system consisting of a remote controller and a collection of linear plants, each associated with a local controller. Each local controller directly observes the state of its co-located plant and can inform the remote controller of the plant's state through an unreliable uplink channel. We assume that the downlink channels from the remote controller to local controllers are perfect. The objective of the local controllers and the remote controller is to cooperatively minimize a quadratic performance cost. We provide a dynamic program for this decentralized control problem using the common information approach. Although our problem is not a partially nested problem, we obtain explicit optimal strategies for all controllers. In the optimal strategies, all controllers compute common estimates of the states of the plants based on the common information obtained from the communication network. The remote controller's action is linear in the common state estimates, and the action of each local controller is linear in both the actual state of its co-located plant and the common state estimates. We illustrate our results with numerical experiments using randomly generated models.

eess.SY↗
arXiv2018

CompetitiveBike: Competitive Prediction of Bike-Sharing Apps Using Heterogeneous Crowdsourced Data

In recent years, bike-sharing systems have been deployed in many cities, which provide an economical lifestyle. With the prevalence of bike-sharing systems, a lot of companies join the market, leading to increasingly fierce competition. To be competitive, bike-sharing companies and app developers need to make strategic decisions for mobile apps development. Therefore, it is significant to predict and compare the popularity of different bike-sharing apps. However, existing works mostly focus on predicting the popularity of a single app, the popularity contest among different apps has not been explored yet. In this paper, we aim to forecast the popularity contest between Mobike and Ofo, two most popular bike-sharing apps in China. We develop CompetitiveBike, a system to predict the popularity contest among bike-sharing apps. Moreover, we conduct experiments on real-world datasets collected from 11 app stores and Sina Weibo, and the experiments demonstrate the effectiveness of our approach.

cs.HC↗
arXiv2018

Decentralized Control of Stochastically Switched Linear System with Unreliable Communication

We consider a networked control system (NCS) consisting of two plants, a global plant and a local plant, and two controllers, a global controller and a local controller. The global (resp. local) plant follows discrete-time stochastically switched linear dynamics with a continuous global (resp. local) state and a discrete global (resp. local) mode. We assume that the state and mode of the global plant are observed by both controllers while the state and mode of the local plant are only observed by the local controller. The local controller can inform the global controller of the local plant's state and mode through an unreliable TCP-like communication channel where successful transmissions are acknowledged. The objective of the controllers is to cooperatively minimize a modes-dependent quadratic cost over a finite time horizon. Following the method developed in [1] and [2], we construct a dynamic program based on common information and a decomposition of strategies, and use it to obtain explicit optimal strategies for the controllers. In the optimal strategies, both controllers compute a common estimate of the local plant's state. The global controller's action is linear in the state of the global plant and the common estimated state, and the local controller's action is linear in the actual states of both plants and the common estimated state. Furthermore, the gain matrices for the global controller depend on the global mode and its observation about the local mode, while the gain matrices for the local controller depend on the actual modes of both plants and the global controller's observation about the local mode.

eess.SY↗
arXiv2017

Learning Unknown Markov Decision Processes: A Thompson Sampling Approach

We consider the problem of learning an unknown Markov Decision Process (MDP) that is weakly communicating in the infinite horizon setting. We propose a Thompson Sampling-based reinforcement learning algorithm with dynamic episodes (TSDE). At the beginning of each episode, the algorithm generates a sample from the posterior distribution over the unknown model parameters. It then follows the optimal stationary policy for the sampled model for the rest of the episode. The duration of each episode is dynamically determined by two stopping criteria. The first stopping criterion controls the growth rate of episode length. The second stopping criterion happens when the number of visits to any state-action pair is doubled. We establish $\tilde O(HS\sqrt{AT})$ bounds on expected regret under a Bayesian setting, where $S$ and $A$ are the sizes of the state and action spaces, $T$ is time, and $H$ is the bound of the span. This regret bound matches the best available bound for weakly communicating MDPs. Numerical results show it to perform better than existing algorithms for infinite horizon MDPs.

cs.LG↗
arXiv2017

Learning-based Control of Unknown Linear Systems with Thompson Sampling

We propose a Thompson sampling-based learning algorithm for the Linear Quadratic (LQ) control problem with unknown system parameters. The algorithm is called Thompson sampling with dynamic episodes (TSDE) where two stopping criteria determine the lengths of the dynamic episodes in Thompson sampling. The first stopping criterion controls the growth rate of episode length. The second stopping criterion is triggered when the determinant of the sample covariance matrix is less than half of the previous value. We show under some conditions on the prior distribution that the expected (Bayesian) regret of TSDE accumulated up to time T is bounded by O(\sqrt{T}). Here O(.) hides constants and logarithmic factors. This is the first O(\sqrt{T} ) bound on expected regret of learning in LQ control. By introducing a reinitialization schedule, we also show that the algorithm is robust to time-varying drift in model parameters. Numerical simulations are provided to illustrate the performance of TSDE.

eess.SY↗
arXiv2017

Counting the solutions of $λ_1 x_1^{k_1}+\cdots +λ_t x_t^{k_t}\equiv c\bmod{n}$

Given a polynomial $Q(x_1,\cdots, x_t)=λ_1 x_1^{k_1}+\cdots +λ_t x_t^{k_t}$, for every $c\in \mathbb{Z}$ and $n\geq 2$, we study the number of solutions $N_J(Q;c,n)$ of the congruence equation $Q(x_1,\cdots, x_t)\equiv c\bmod{n}$ in $(\mathbb{Z}/n\mathbb{Z})^t$ such that $x_i\in (\mathbb{Z}/n\mathbb{Z})^\times$ for $i\in J\subseteq I= \{1,\cdots, t\}$. We deduce formulas and an algorithm to study $N_J(Q; c,p^a)$ for $p$ any prime number and $a\geq 1$ any integer. As consequences of our main results, we completely solve: the counting problem of $Q(x_i)=\sum\limits_{i\in I}λ_i x_i$ for any prime $p$ and any subset $J$ of $I$; the counting problem of $Q(x_i)=\sum\limits_{i\in I}λ_i x^2_i$ in the case $t=2$ for any $p$ and $J$, and the case $t$ general for any $p$ and $J$ satisfying $\min\{v_p(λ_i)\mid i\in I\}=\min\{v_p(λ_i)\mid i\in J\}$; the counting problem of $Q(x_i)=\sum\limits_{i\in I}λ_i x^k_i$ in the case $t=2$ for any $p\nmid k$ and any $J$, and in the case $t$ general for any $p\nmid k$ and $J$ satisfying $\min\{v_p(λ_i)\mid i\in I\}=\min\{v_p(λ_i)\mid i\in J\}$.

math.NT↗
arXiv2016

Optimal Local and Remote Controllers with Unreliable Communication

We consider a decentralized optimal control problem for a linear plant controlled by two controllers, a local controller and a remote controller. The local controller directly observes the state of the plant and can inform the remote controller of the plant state through a packet-drop channel. We assume that the remote controller is able to send acknowledgments to the local controller to signal the successful receipt of transmitted packets. The objective of the two controllers is to cooperatively minimize a quadratic performance cost. We provide a dynamic program for this decentralized control problem using the common information approach. Although our problem is not a partially nested LQG problem, we obtain explicit optimal strategies for the two controllers. In the optimal strategies, both controllers compute a common estimate of the plant state based on the common information. The remote controller's action is linear in the common estimated state, and the local controller's action is linear in both the actual state and the common estimated state.

eess.SY↗