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Fan Xu

Publications and source records attributed to Fan Xu.

At least 181 records · Page 10Linked to original sources
arXiv2018

Fundamental Limits of Decentralized Caching in Fog-RANs with Wireless Fronthaul

This paper aims to characterize the synergy of distributed caching and wireless fronthaul in a fog radio access network (Fog-RAN) where all edge nodes (ENs) and user equipments (UEs) have a local cache and store contents independently at random. The network operates in two phases, a file-splitting based decentralized cache placement phase and a fronthaul-aided content delivery phase. We adopt normalized delivery time (NDT) to characterize the asymptotic latency performance with respect to cache size and fronthaul capacity. Both an achievable upper bound and a theoretical lower bound of NDT are obtained, and their multiplicative gap is within 12. In the proposed delivery scheme, we utilize the fronthaul link, by exploiting coded multicasting, to fetch both non-cached and cached contents to boost EN cooperation in the access link. In particular, to fetch contents already cached at ENs, an additional layer of coded multicasting is added on the coded messages desired by UEs in the fronthaul link. Our analysis shows that the proposed delivery scheme can balance the delivery latency between the fronthaul link and access link, and is approximately optimum under decentralized caching.

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arXiv2018

Cluster multiplication theorem in the quantum cluster algebra of type $A_{2}^{(2)}$

The objective of the present paper is to prove cluster multiplication theorem in the quantum cluster algebra of type $A_{2}^{(2)}$. As corollaries, we obtain bar-invariant $\mathbb{Z}[q^{\pm\frac{1}{2}}]$-bases established in [6], and naturally deduce the positivity of the elements in these bases. One bar-invariant basis as the triangular basis of this quantum cluster algebra is also explicitly described.

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arXiv2017

Ringel-Hall algebras beyond their quantum groups I: Restriction functor and Green's formula

In this paper, we generalize the categorifical construction of a quantum group and its canonical basis introduced by Lusztig (\cite{Lusztig,Lusztig2}) to the generic form of the whole Ringel-Hall algebra. We clarify the explicit relation between the Green formula in \cite{Green} and the restriction functor in \cite{Lusztig2}. By a geometric way to prove the Green formula, we show that the Hopf structure of a Ringel-Hall algebra can be categorified under Lusztig's framework.

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arXiv2017

Fundamental Tradeoff between Storage and Latency in Cache-Aided Wireless Interference Networks

This paper studies the fundamental tradeoff between storage and latency in a general wireless interference network with caches equipped at all transmitters and receivers. The tradeoff is characterized by an information-theoretic metric, \emph{normalized delivery time} (NDT), which is the worst-case delivery time of the actual traffic load at a transmission rate specified by degrees of freedom (DoF) of a given channel. We obtain both an achievable upper bound and a theoretical lower bound of the minimum NDT for any number of transmitters, any number of receivers, and any feasible cache size tuple. We show that the achievable NDT is exactly optimal in certain cache size regions, and is within a bounded multiplicative gap to the theoretical lower bound in other regions. In the achievability analysis, we first propose a novel cooperative transmitter/receiver coded caching strategy. It offers the freedom to adjust file splitting ratios for NDT minimization. We then propose a delivery strategy which transforms the considered interference network into a new class of cooperative X-multicast channels. It leverages local caching gain, coded multicasting gain, and transmitter cooperation gain (via interference alignment and interference neutralization) opportunistically. Finally, the achievable NDT is obtained by solving a linear programming problem. This study reveals that with caching at both transmitter and receiver sides, the network can benefit simultaneously from traffic load reduction and transmission rate enhancement, thereby effectively reducing the content delivery latency.

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arXiv2017

Fundamental Storage-Latency Tradeoff in Cache-Aided MIMO Interference Networks

Caching is an effective technique to improve user perceived experience for content delivery in wireless networks. Wireless caching differs from traditional web caching in that it can exploit the broadcast nature of wireless medium and hence opportunistically change the network topologies. This paper studies a cache-aided MIMO interference network with 3 transmitters each equipped with M antennas and 3 receivers each with N antennas. With caching at both the transmitter and receiver sides, the network is changed to hybrid forms of MIMO broadcast channel, MIMO X channel, and MIMO multicast channels. We analyze the degrees of freedom (DoF) of these new channel models using practical interference management schemes. Based on the collective use of these DoF results, we then obtain an achievable normalized delivery time (NDT) of the network, an information-theoretic metric that evaluates the worst-case delivery time at given cache sizes. The obtained NDT is for arbitrary M, N and any feasible cache sizes. It is shown to be optimal in certain cases and within a multiplicative gap of 3 from the optimum in other cases. The extension to the network with arbitrary number of transmitters and receivers is also discussed.

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arXiv2017

An entity-driven recursive neural network model for chinese discourse coherence modeling

Chinese discourse coherence modeling remains a challenge taskin Natural Language Processing field.Existing approaches mostlyfocus on the need for feature engineering, whichadoptthe sophisticated features to capture the logic or syntactic or semantic relationships acrosssentences within a text.In this paper, we present an entity-drivenrecursive deep modelfor the Chinese discourse coherence evaluation based on current English discourse coherenceneural network model. Specifically, to overcome the shortage of identifying the entity(nouns) overlap across sentences in the currentmodel, Our combined modelsuccessfully investigatesthe entities information into the recursive neural network freamework.Evaluation results on both sentence ordering and machine translation coherence rating task show the effectiveness of the proposed model, which significantly outperforms the existing strong baseline.

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arXiv2017

A quantum analogue of generalized cluster algebras

We define a quantum analogue of a class of generalized cluster algebras which can be viewed as a generalization of quantum cluster algebras defined in \cite{berzel}. In the case of rank two, we extend some structural results from the classical theory of generalized cluster algebras obtained in \cite{CS}\cite{rupel} to the quantum case.

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arXiv2017

Sentence-level dialects identification in the greater China region

Identifying the different varieties of the same language is more challenging than unrelated languages identification. In this paper, we propose an approach to discriminate language varieties or dialects of Mandarin Chinese for the Mainland China, Hong Kong, Taiwan, Macao, Malaysia and Singapore, a.k.a., the Greater China Region (GCR). When applied to the dialects identification of the GCR, we find that the commonly used character-level or word-level uni-gram feature is not very efficient since there exist several specific problems such as the ambiguity and context-dependent characteristic of words in the dialects of the GCR. To overcome these challenges, we use not only the general features like character-level n-gram, but also many new word-level features, including PMI-based and word alignment-based features. A series of evaluation results on both the news and open-domain dataset from Wikipedia show the effectiveness of the proposed approach.

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arXiv2016

Cooperative Tx/Rx Caching in Interference Channels: A Storage-Latency Tradeoff Study

This paper studies the storage-latency tradeoff in the $3\times3$ wireless interference network with caches equipped at all transmitters and receivers. The tradeoff is characterized by the so-called fractional delivery time (FDT) at given normalized transmitter and receiver cache sizes. We first propose a generic cooperative transmitter/receiver caching strategy with adjustable file splitting ratios. Based on this caching strategy, we then design the delivery phase carefully to turn the considered interference channel opportunistically into broadcast channel, multicast channel, X channel, or a hybrid form of these channels. After that, we obtain an achievable upper bound of the minimum FDT by solving a linear programming problem of the file splitting ratios. The achievable FDT is a convex and piece-wise linear decreasing function of the cache sizes. Receiver local caching gain, coded multicasting gain, and transmitter cooperation gain (interference alignment and interference neutralization) are leveraged in different cache size regions.

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arXiv2016

On positivity for generalized cluster variables of affine quivers

It has been proved in \cite{LS} that cluster variables in cluster algebras of every skew-symmetric cluster algebra are positive. We prove that any regular generalized cluster variable of an affine quiver is positive. As a corollary, we obtain that generalized cluster variables of affine quivers are positive and construct various positive bases. This generalizes the results in \cite{Dupont} and \cite{DXX}.

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arXiv2015

Realizing enveloping algebras via moduli stacks

Let $\mathop{\rm CF}\nolimits(\mathop{\mathfrak{Obj}\kern .05em}\nolimits_\mathcal{A})$ denote the vector space of $\mathbb{Q}$-valued constructible functions on a given stack $\mathop{\mathfrak{Obj}\kern .05em}\nolimits_\mathcal{A}$ for an exact category $\mathcal{A}$. By using the Ringel--Hall algebra approach, Joyce proved that $\mathop{\rm CF}\nolimits(\mathop{\mathfrak{Obj}\kern .05em}\nolimits_\mathcal{A})$ is an associative $\mathbb{Q}$-algebra via the convolution multiplication and the subspace $\mathop{\rm CF}\nolimits^{\rm ind}\mathop{\mathfrak{Obj}\kern .05em}\nolimits_\mathcal{A})$ of constructible functions supported on indecomposables is a Lie subalgebra of $\mathop{\rm CF}\nolimits(\mathop{\mathfrak{Obj}\kern .05em}\nolimits_\mathcal{A})$ in [10]. In this paper, we show that there is a subalgebra $\mathop{\rm CF}\nolimits^{\text{KS}}(\mathop{\mathfrak{Obj}\kern .05em}\nolimits_\mathcal{A})$ of $\mathop{\rm CF}\nolimits(\mathop{\mathfrak{Obj}\kern .05em}\nolimits_\mathcal{A})$ isomorphic to the universal enveloping algebra of $\mathop{\rm CF}\nolimits^{\rm ind}(\mathop{\mathfrak{Obj}\kern .05em}\nolimits_\mathcal{A})$. Moreover we construct a comultiplication on $\mathop{\rm CF}\nolimits^{\text{KS}}(\mathop{\mathfrak{Obj}\kern .05em}\nolimits_\mathcal{A})$ and a degenerate form of Green's theorem. This generalizes Joyce's work, as well as results of [3].

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arXiv2015

On homomorphisms from Ringel-Hall algebras to quantum cluster algebras

In \cite{rupel3},the authors defined algebra homomorphisms from the dual Ringel-Hall algebra of certain hereditary abelian category $\mathcal{A}$ to an appropriate $q$-polynomial algebra. In the case that $\mathcal{A}$ is the representation category of an acyclic quiver, we give an alternative proof by using the cluster multiplication formulas in \cite{DX}. Moreover, if the underlying graph of $Q$ is bipartite and the matrix $B$ associated to the quiver $Q$ is of full rank, we show that the image of the algebra homomorphisms is in the corresponding quantum cluster algebra.

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arXiv2013

Remarks on Hall algebras of triangulated categories

We introduce the notion of the Drinfeld dual of an algebra and show that Hall algebras defined by Kontsevich-Soibelman in \cite{KS} are the Drinfeld duals of derived Hall algebras defined in \cite{Toen2005} and \cite{XX2006}. Moreover, we construct the motivic analogue of a derived Hall algebra and prove that it is isomorphic to the motivic Hall algebra constructed in \cite{KS}.

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arXiv2010

The multiplication theorem and bases in finite and affine quantum cluster algebras

We prove a multiplication theorem for quantum cluster algebras of acyclic quivers. The theorem generalizes the multiplication formula for quantum cluster variables in \cite{fanqin}. We apply the formula to construct some $\mathbb{ZP}$-bases in quantum cluster algebras of finite and affine types. Under the specialization $q$ and coefficients to $1$, these bases are the integral bases of cluster algebra of finite and affine types (see \cite{CK1} and \cite{DXX}).

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arXiv2010

Bases of the quantum cluster algebra of the Kronecker quiver

We construct bar-invariant $\mathbb{Z}[q^{\pm 1/2}]-$bases of the quantum cluster algebra of the Kronecker quiver which are quantum analogues of the canonical basis, semicanonical basis and dual semicanonical basis of the cluster algebra of the Kronecker quiver in the sense of \cite{sherzel},\cite{calzel} and \cite{gls} respectively. As a byproduct, we prove the positivity of the elements in these bases.

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arXiv2010

Hall algebras for odd periodic triangulated categories

We define the Hall algebra associated to any triangulated category under some finiteness conditions with the $t$-periodic translation functor $T$ for odd $t>1.$ This generalizes the results in \cite{Toen2005} and \cite{XX2006}.

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