arXiv subjects

Xin Sun

Publications and source records attributed to Xin Sun.

At least 217 records · Page 12Linked to original sources

arXiv2019

Exploiting NOMA for UAV Communications in Large-Scale Cellular Networks

This paper advocates a pair of strategies in non-orthogonal multiple access (NOMA) in unmanned aerial vehicles (UAVs) communications, where multiple UAVs play as new aerial communications platforms for serving terrestrial NOMA users. A new multiple UAVs framework with invoking stochastic geometry technique is proposed, in which a pair of practical strategies are considered: 1) the UAV-centric strategy for offloading actions and 2) the user-centric strategy for providing emergency communications. In order to provide practical insights for the proposed NOMA assisted UAV framework, an imperfect successive interference cancelation (ipSIC) scenario is taken into account. For both UAV-centric strategy and user-centric strategy, we derive new exact expressions for the coverage probability. We also derive new analytical results for orthogonal multiple access (OMA) for providing a benchmark scheme. The derived analytical results in both user-centric strategy and UAV-centric strategy explicitly indicate that the ipSIC coefficient is a dominant component in terms of coverage probability. Numerical results are provided to confirm that i) for both user-centric strategy and UAV-centric strategy, NOMA assisted UAV cellular networks is capable of outperforming OMA by setting power allocation factors and targeted rate properly; and ii) the coverage probability of NOMA assisted UAV cellular framework is affected to a large extent by ipSIC coefficient, target rates and power allocations factors of paired NOMA users.

cs.IT↗

arXiv2019

Liouville dynamical percolation

We construct and analyze a continuum dynamical percolation process which evolves in a random environment given by a $γ$-Liouville measure. The homogeneous counterpart of this process describes the scaling limit of discrete dynamical percolation on the rescaled triangular lattice. Our focus here is to study the same limiting dynamics, but where the speed of microscopic updates is highly inhomogeneous in space and is driven by the $γ$-Liouville measure associated with a two-dimensional log-correlated field $h$. Roughly speaking, this continuum percolation process evolves very rapidly where the field $h$ is high and barely moves where the field $h$ is low. Our main results can be summarized as follows. 1. First, we build this inhomogeneous dynamical percolation which we call $γ$-Liouville dynamical percolation (LDP) by taking the scaling limit of the associated process on the triangular lattice. We work with three different regimes each requiring different tools: $γ\in [0,2-\sqrt{5/2})$, $γ\in [2-\sqrt{5/2}, \sqrt{3/2})$, and $γ\in(\sqrt{3/2},2)$. 2. When $γ<\sqrt{3/2}$, we prove that $γ$-LDP is mixing in the Schramm-Smirnov space as $t\to \infty$, quenched in the log-correlated field $h$. On the contrary, when $γ>\sqrt{3/2}$ the process is frozen in time. The ergodicity result is a crucial piece of the Cardy embedding project of the second and fourth coauthors, where LDP for $γ=\sqrt{1/6}$ is used to study the scaling limit of a variant of dynamical percolation on uniform triangulations. 3. When $γ<\sqrt{3/4}$, we obtain quantitative bounds on the mixing of quad crossing events.

math.PR↗

arXiv2018

Occupation measure of random walks and wired spanning forests in balls of Cayley graphs

We show that for finite-range, symmetric random walks on general transient Cayley graphs, the expected occupation time of any given ball of radius $r$ is $O(r^{5/2})$.. We also study the volume-growth property of the wired spanning forests on general Cayley graphs, showing that the expected number of vertices in the component of the identity inside any given ball of radius $r$ is $O(r^{11/2})$.

math.PR↗

arXiv2018

Four dimensional loop-erased random walk

The loop-erased random walk (LERW) in $\mathbb{Z}^4$ is the process obtained by erasing loops chronologically for simple random walk. We prove that the escape probability of the LERW renormalized by $(\log n)^{\frac{1}{3}}$ converges almost surely and in $L^{p}$ for all $p>0$. Along the way, we extend previous results by the first author building on slowly recurrent sets. We provide two applications for the escape probability. We construct the two-sided LERW, and we construct a $\pm 1$ spin model coupled with the wired spanning forests on $\mathbb{Z}^4$ with the bi-Laplacian Gaussian field on $\mathbb{R}^{4}$ as its scaling limit.

math.PR↗

arXiv2018

A Generalized Kinetic Model for Heterogeneous Gas-Solid Reactions

We present a generalized kinetic model for gas-solid heterogeneous reactions taking place at the interface between two phases. The model studies the reaction kinetics by taking into account the reactions at the interface, as well as the transport process within the product layer. The standard unreacted shrinking core model relies on the assumption of quasi-static diffusion that results in a steady-state concentration profile of gas reactant in the product layer. By relaxing this assumption and resolving the entire problem, general solutions can be obtained for reaction kinetics, including the reaction front velocity and the conversion (volume fraction of reacted solid). The unreacted shrinking core model is shown to be accurate and in agreement with the generalized model for slow reaction (or fast diffusion), low concentration of gas reactant, and small solid size. Otherwise, a generalized kinetic model should be used.

physics.chem-ph↗

arXiv2018

Quantum-enhanced Logic-based Blockchain I: Quantum Honest-success Byzantine Agreement and Qulogicoin

We proposed a framework of quantum-enhanced logic-based blockchain, which improves the efficiency and power of quantum-secured blockchain. The efficiency is improved by using a new quantum honest-success Byzantine agreement protocol to replace the classical Byzantine agreement protocol, while the power is improved by incorporating quantum protection and quantum certificate into the syntax of transactions. Our quantum-secured logic-based blockchain can already be implemented by the current technology. The cryptocurrency created and transferred in our blockchain is called qulogicoin. Incorporating quantum protection and quantum certificates into blockchain makes it possible to use blockchain to overcome the limitations of some quantum cryptographic protocols. As an illustration, we show that a significant shortcoming of cheat-sensitive quantum bit commitment protocols can be overcome with the help of our blockchain and qulogicoin.

quant-ph↗

arXiv2018

A distance exponent for Liouville quantum gravity

Let $γ\in (0,2)$ and let $h$ be the random distribution on $\mathbb C$ which describes a $γ$-Liouville quantum gravity (LQG) cone. Also let $κ= 16/γ^2 >4$ and let $η$ be a whole-plane space-filling SLE$_κ$ curve sampled independent from $h$ and parametrized by $γ$-quantum mass with respect to $h$. We study a family $\{\mathcal G^ε\}_{ε>0}$ of planar maps associated with $(h, η)$ called the \textit{LQG structure graphs} (a.k.a.\ \textit{mated-CRT maps}) which we conjecture converge in probability in the scaling limit with respect to the Gromov-Hausdorff topology to a random metric space associated with $γ$-LQG. In particular, $\mathcal G^ε$ is the graph whose vertex set is $ε\mathbb Z$, with two such vertices $x_1,x_2\in ε\mathbb Z$ connected by an edge if and only if the corresponding curve segments $η([x_1-ε, x_1])$ and $η([x_2-ε,x_2])$ share a non-trivial boundary arc. Due to the peanosphere description of SLE-decorated LQG due to Duplantier, Miller, and Sheffield (2014), the graph $\mathcal G^ε$ can equivalently be expressed as an explicit functional of a correlated two-dimensional Brownian motion, so can be studied without any reference to SLE or LQG. We prove non-trivial upper and lower bounds for the cardinality of a graph-distance ball of radius $n$ in $\mathcal G^ε$ which are consistent with the prediction of Watabiki (1993) for the Hausdorff dimension of LQG. Using subadditivity arguments, we also prove that there is an exponent $χ> 0$ for which the expected graph distance between generic points in the subgraph of $\mathcal G^ε$ corresponding to the segment $η([0,1])$ is of order $ε^{-χ+ o_ε(1)}$, and this distance is extremely unlikely to be larger than $ε^{-χ+ o_ε(1)}$.

math.PR↗

arXiv2018

A Simple Voting Protocol on Quantum Blockchain

This paper proposes a simple voting protocol based on quantum blockchain. Besides being simple, our voting protocol is anonymous, binding, non-reusable, verifiable, eligible, fair and self-tallying. Our protocol is also realizable by the current technology.

quant-ph↗

arXiv2018

Negative moments for Gaussian multiplicative chaos on fractal sets

The objective of this note is to study the probability that the total mass of a sub-critical Gaussian multiplicative chaos (GMC) with arbitrary base measure $σ$ is small. When $σ$ has some continuous density w.r.t Lebesgue measure, a scaling argument shows that the logarithm of the total GMC mass is sub-Gaussian near $-\infty$. However, when $σ$ has no scaling properties, the situation is much less clear. In this paper, we prove that for any base measure $σ$, the total GMC mass has negative moments of all orders.

math.PR↗

arXiv2018

Multiple Antenna Aided NOMA in UAV Networks: A Stochastic Geometry Approach

This article investigates the multiple-input multiple-output (MIMO) non-orthogonal multiple access (NOMA) assisted unmanned aerial vehicles (UAVs) networks. By utilizing a stochastic geometry model, a new 3-Dimension UAV framework for providing wireless service to randomly roaming NOMA users has been proposed. In an effort to evaluate the performance of the proposed framework, we derive analytical expressions for the outage probability and the ergodic rate of MIMO-NOMA enhanced UAV networks. We examine tractable upper bounds for the whole proposed framework, with deriving asymptotic results for scenarios that transmit power of interference sources being proportional or being fixed to the UAV. For obtaining more insights for the proposed framework, we investigate the diversity order and high signal-to-noise (SNR) slope of MIMO-NOMA assisted UAV networks. Our results confirm that: i) The outage probability of NOMA enhanced UAV networks is affected to a large extent by the targeted transmission rates and power allocation factors of NOMA users; and ii) For the case that the interference power is proportional to the UAV power, there are error floors for the outage probabilities.

cs.IT↗

arXiv2018

SLE as a mating of trees in Euclidean geometry

The mating of trees approach to Schramm-Loewner evolution (SLE) in the random geometry of Liouville quantum gravity (LQG) has been recently developed by Duplantier-Miller-Sheffield (2014). In this paper we consider the mating of trees approach to SLE in Euclidean geometry. Let $η$ be a whole-plane space-filling SLE with parameter $κ>4$, parameterized by Lebesgue measure. The main observable in the mating of trees approach is the contour function, a two-dimensional continuous process describing the evolution of the Minkowski content of the left and right frontier of $η$. We prove regularity properties of the contour function and show that (as in the LQG case) it encodes all the information about the curve $η$. We also prove that the uniform spanning tree on $\mathbb Z^2$ converges to $\mathrm{SLE}_8$ in the natural topology associated with the mating of trees approach.

math.PR↗

arXiv2017

Almost sure multifractal spectrum of SLE

Suppose that $η$ is a Schramm-Loewner evolution (SLE$_κ$) in a smoothly bounded simply connected domain $D \subset {\mathbb C}$ and that $ϕ$ is a conformal map from ${\mathbb D}$ to a connected component of $D \setminus η([0,t])$ for some $t>0$. The multifractal spectrum of $η$ is the function $(-1,1) \to [0,\infty)$ which, for each $s \in (-1,1)$, gives the Hausdorff dimension of the set of points $x \in \partial {\mathbb D}$ such that $|ϕ'( (1-ε) x)| = ε^{-s+o(1)}$ as $ε\to 0$. We rigorously compute the a.s. multifractal spectrum of SLE, confirming a prediction due to Duplantier. As corollaries, we confirm a conjecture made by Beliaev and Smirnov for the a.s. bulk integral means spectrum of SLE and we obtain a new derivation of the a.s. Hausdorff dimension of the SLE curve for $κ\leq 4$. Our results also hold for the SLE$_κ(\underline ρ)$ processes with general vectors of weight $\underlineρ$.

math.PR↗

arXiv2017

Two perspectives of the 2D unit area quantum sphere and their equivalence

2D Liouville quantum gravity (LQG) is used as a toy model for 4D quantum gravity and is the theory of world-sheet in string theory. Recently there has been growing interest in studying LQG in the realm of probability theory: David, Kupiainen, Rhodes, Vargas (2014) and Duplantier, Miller, Sheffield (2014) both provide a probabilistic perspective of the LQG on the 2D sphere. In particular, in each of them one may find a definition of the so-called unit area quantum sphere. We examine these two perspectives and prove their equivalence by showing that the respective unit area quantum spheres are the same. This is done by considering a unified limiting procedure for defining both objects.

math.PR↗

arXiv2017

Prediction of Sea Surface Temperature using Long Short-Term Memory

This letter adopts long short-term memory(LSTM) to predict sea surface temperature(SST), which is the first attempt, to our knowledge, to use recurrent neural network to solve the problem of SST prediction, and to make one week and one month daily prediction. We formulate the SST prediction problem as a time series regression problem. LSTM is a special kind of recurrent neural network, which introduces gate mechanism into vanilla RNN to prevent the vanished or exploding gradient problem. It has strong ability to model the temporal relationship of time series data and can handle the long-term dependency problem well. The proposed network architecture is composed of two kinds of layers: LSTM layer and full-connected dense layer. LSTM layer is utilized to model the time series relationship. Full-connected layer is utilized to map the output of LSTM layer to a final prediction. We explore the optimal setting of this architecture by experiments and report the accuracy of coastal seas of China to confirm the effectiveness of the proposed method. In addition, we also show its online updated characteristics.

cs.CV↗

arXiv2017

Scaling limits for the critical Fortuin-Kastelyn model on a random planar map II: local estimates and empty reduced word exponent

We continue our study of the inventory accumulation introduced by Sheffield (2011), which encodes a random planar map decorated by a collection of loops sampled from the critical Fortuin-Kasteleyn (FK) model. We prove various \emph{local estimates} for the inventory accumulation model, i.e., estimates for the precise number of symbols of a given type in a reduced word sampled from the model. Using our estimates, we obtain the scaling limit of the associated two-dimensional random walk conditioned on the event that it stays in the first quadrant for one unit of time and ends up at a particular position in the interior of the first quadrant. We also obtain the exponent for the probability that a word of length $2n$ sampled from the inventory accumulation model corresponds to an empty reduced word, which is equivalent to an asymptotic formula for the partition function of the critical FK planar map model. The estimates of this paper will be used in a subsequent paper to obtain the scaling limit of the lattice walk associated with a finite-volume FK planar map.

math.PR↗

arXiv2017

A Procedural Texture Generation Framework Based on Semantic Descriptions

Procedural textures are normally generated from mathematical models with parameters carefully selected by experienced users. However, for naive users, the intuitive way to obtain a desired texture is to provide semantic descriptions such as "regular," "lacelike," and "repetitive" and then a procedural model with proper parameters will be automatically suggested to generate the corresponding textures. By contrast, it is less practical for users to learn mathematical models and tune parameters based on multiple examinations of large numbers of generated textures. In this study, we propose a novel framework that generates procedural textures according to user-defined semantic descriptions, and we establish a mapping between procedural models and semantic texture descriptions. First, based on a vocabulary of semantic attributes collected from psychophysical experiments, a multi-label learning method is employed to annotate a large number of textures with semantic attributes to form a semantic procedural texture dataset. Then, we derive a low dimensional semantic space in which the semantic descriptions can be separated from one other. Finally, given a set of semantic descriptions, the diverse properties of the samples in the semantic space can lead the framework to find an appropriate generation model that uses appropriate parameters to produce a desired texture. The experimental results show that the proposed framework is effective and that the generated textures closely correlate with the input semantic descriptions.

cs.CV↗

arXiv2016

Deep Learning with Coherent Nanophotonic Circuits

Artificial Neural Networks are computational network models inspired by signal processing in the brain. These models have dramatically improved the performance of many learning tasks, including speech and object recognition. However, today's computing hardware is inefficient at implementing neural networks, in large part because much of it was designed for von Neumann computing schemes. Significant effort has been made to develop electronic architectures tuned to implement artificial neural networks that improve upon both computational speed and energy efficiency. Here, we propose a new architecture for a fully-optical neural network that, using unique advantages of optics, promises a computational speed enhancement of at least two orders of magnitude over the state-of-the-art and three orders of magnitude in power efficiency for conventional learning tasks. We experimentally demonstrate essential parts of our architecture using a programmable nanophotonic processor.

physics.optics↗

arXiv2016

Spinodal Decomposition-Enabled Halide Perovskite Double Heterostructure with Reduced Fröhlich Electron-Phonon Coupling

Epitaxial III-V semiconductor heterostructures are key components in modern microelectronics, electro-optics and optoelectronics. With superior semiconducting properties, halide perovskite materials are rising as promising candidates for coherent heterostructure devices. In this report, spinodal decomposition is proposed and experimentally implemented to produce epitaxial double heterostructures in halide perovskite system. Pristine epitaxial mixed halide perovskites rods and films were synthesized via Van der Waals epitaxy by chemical vapor deposition method. At room temperature, photon was applied as a knob to regulate the kinetics of spinodal decomposition and classic coarsening. By this approach, halide perovskite double heterostructures were created carrying epitaxial interfaces and outstanding optical properties. Reduced Fröhlich electron-phonon coupling was discovered in coherent halide double heterostructure, which is hypothetically attributed to the classic phonon confinement effect widely existing in III-V double heterostructures. The ability to develop coherent double heterostructures in halide perovskites paves an avenue to exploring halide perovskite-based quantum wells and superlattices for high-performance and low-cost optoelectronics, electro-optics and microelectronics.

cond-mat.mtrl-sci↗