arXiv subjects

Tian Lan

Publications and source records attributed to Tian Lan.

At least 253 records · Page 14Linked to original sources

arXiv2018

The EDGE-CALIFA Survey: Molecular and Ionized Gas Kinematics in Nearby Galaxies

We present a comparative study of molecular and ionized gas kinematics in nearby galaxies. These results are based on observations from the EDGE survey, which measured spatially resolved $^{12}$CO(J=1-0) in 126 nearby galaxies. Every galaxy in EDGE has corresponding resolved ionized gas measurements from CALIFA. Using a sub-sample of 17 rotation dominated, star-forming galaxies where precise molecular gas rotation curves could be extracted, we derive CO and H$α$ rotation curves using the same geometric parameters out to $\gtrsim$1 $R_e$. We find that $\sim$75% of our sample galaxies have smaller ionized gas rotation velocities than the molecular gas in the outer part of the rotation curve. In no case is the molecular gas rotation velocity measurably lower than that of the ionized gas. We suggest that the lower ionized gas rotation velocity can be attributed to a significant contribution from extraplanar diffuse ionized gas in a thick, turbulence supported disk. Using observations of the H$γ$ transition also available from CALIFA, we measure ionized gas velocity dispersions and find that these galaxies have sufficiently large velocity dispersions to support a thick ionized gas disk. Kinematic simulations show that a thick disk with a vertical rotation velocity gradient can reproduce the observed differences between the CO and H$α$ rotation velocities. Observed line ratios tracing diffuse ionized gas are elevated compared to typical values in the midplane of the Milky Way. In galaxies affected by this phenomenon, dynamical masses measured using ionized gas rotation curves will be systematically underestimated.

astro-ph.GA↗

arXiv2018

Chronos: A Unifying Optimization Framework for Speculative Execution of Deadline-critical MapReduce Jobs

Meeting desired application deadlines in cloud processing systems such as MapReduce is crucial as the nature of cloud applications is becoming increasingly mission-critical and deadline-sensitive. It has been shown that the execution times of MapReduce jobs are often adversely impacted by a few slow tasks, known as stragglers, which result in high latency and deadline violations. While a number of strategies have been developed in existing work to mitigate stragglers by launching speculative or clone task attempts, none of them provides a quantitative framework that optimizes the speculative execution for offering guaranteed Service Level Agreements (SLAs) to meet application deadlines. In this paper, we bring several speculative scheduling strategies together under a unifying optimization framework, called Chronos, which defines a new metric, Probability of Completion before Deadlines (PoCD), to measure the probability that MapReduce jobs meet their desired deadlines. We systematically analyze PoCD for popular strategies including Clone, Speculative-Restart, and Speculative-Resume, and quantify their PoCD in closed-form. The result illuminates an important tradeoff between PoCD and the cost of speculative execution, measured by the total (virtual) machine time required under different strategies. We propose an optimization problem to jointly optimize PoCD and execution cost in different strategies, and develop an algorithmic solution that is guaranteed to be optimal. Chronos is prototyped on Hadoop MapReduce and evaluated against three baseline strategies using both experiments and trace-driven simulations, achieving 50% net utility increase with up to 80% PoCD and 88% cost improvements.

cs.DC↗

arXiv2018

A classification of 3+1D bosonic topological orders (I): the case when point-like excitations are all bosons

Topological orders are new phases of matter beyond Landau symmetry breaking. They correspond to patterns of long-range entanglement. In recent years, it was shown that in 1+1D bosonic systems there is no nontrivial topological order, while in 2+1D bosonic systems the topological orders are classified by a pair: a modular tensor category and a chiral central charge. In this paper, we propose a partial classification of topological orders for 3+1D bosonic systems: If all the point-like excitations are bosons, then such topological orders are classified by unitary pointed fusion 2-categories, which are one-to-one labeled by a finite group $G$ and its group 4-cocycle $ω_4 \in \mathcal H^4[G;U(1)]$ up to group automorphisms. Furthermore, all such 3+1D topological orders can be realized by Dijkgraaf-Witten gauge theories.

cond-mat.str-el↗

arXiv2018

A Classification of (2+1)D Topological Phases with Symmetries

This thesis aims at concluding the classification results for topological phases with symmetry in 2+1 dimensions. The main result is that topological phases are classified by a triple of unitary braided fusion categories $\mathcal E\subset\mathcal C\subset\mathcal M$ plus the chiral central charge $c$. Here $\mathcal E$ is a symmetric fusion category, $\mathcal E=\mathrm{Rep}(G)$ for boson systems or $\mathcal E=\mathrm{sRep}(G^f)$ for fermion systems, consisting of the representations of the symmetry group and describing the local excitations with symmetry; $\mathcal C$ is the category of all the quasiparticle excitations in the bulk, containing $\mathcal E$ as its Müger center; $\mathcal M$ is a minimal modular extension of $\mathcal C$, that also includes the gauged symmetry defects. We also study the stacking of topological phases with symmetry and two types of anyon condensations based on such classification.

cond-mat.str-el↗

arXiv2017

Tiered cloud storage via two-stage, latency-aware bidding

In cloud storage, the digital data is stored in logical storage pools, backed by heterogeneous physical storage media and computing infrastructure that are managed by a Cloud Service Provider (CSP). To balance the tradeoff between service performance and cost, CSPs often employ different storage tiers, for instance, cold storage and hot storage. Storing data in hot storage incurs high storage cost yet delivers low access latency, whereas cold storage is able to inexpensively store massive amounts of data and thus provides lower cost with higher latency. In this paper, we address a major challenge confronting the CSPs utilizing such tiered storage architecture - how to maximize their overall profit over a variety of storage tiers that offer distinct characteristics, as well as file placement and access request scheduling policies. To this end, we propose a scheme where the CSP offers a two-stage auction process for (a) requesting storage capacity, and (b) requesting accesses with latency requirements. Our two-stage bidding scheme provides a hybrid storage and access optimization framework with the objective of maximizing the CSP's total net profit over four dimensions: file acceptance decision, placement of accepted files, file access decision and access request scheduling policy. The proposed optimization is a mixed-integer nonlinear program that is hard to solve. We propose an efficient heuristic to relax the integer optimization and to solve the resulting nonlinear stochastic programs. The algorithm is evaluated under different scenarios and with different storage system parameters, and insightful numerical results are reported by comparing the proposed approach with other profit-maximization models. We see a profit increase of over 60% of our proposed method compared to other schemes in certain simulation scenarios.

cs.NI↗

arXiv2017

Hierarchy construction and non-Abelian families of generic topological orders

We generalize the hierarchy construction to generic 2+1D topological orders (which can be non-Abelian) by condensing Abelian anyons in one topological order to construct a new one. We show that such construction is reversible and leads to a new equivalence relation between topological orders. We refer to the corresponding equivalent class (the orbit of the hierarchy construction) as "the non-Abelian family". Each non-Abelian family has one or a few root topological orders with the smallest number of anyon types. All the Abelian topological orders belong to the trivial non-Abelian family whose root is the trivial topological order. We show that Abelian anyons in root topological orders must be bosons or fermions with trivial mutual statistics between them. The classification of topological orders is then greatly simplified, by focusing on the roots of each family: those roots are given by non-Abelian modular extensions of representation categories of Abelian groups.

cond-mat.str-el↗

arXiv2017

Tail Index for a Distributed Storage System with Pareto File Size Distribution

Distributed storage systems often employ erasure codes to achieve high data reliability while attaining space efficiency. Such storage systems are known to be susceptible to long tails in response time. It has been shown that in modern online applications such as Bing, Facebook, and Amazon, the long tail of latency is of particular concern, with $99.9$th percentile response times that are orders of magnitude worse than the mean. Taming tail latency is very challenging in erasure-coded storage systems since quantify tail latency (i.e., $x$th-percentile latency for arbitrary $x\in[0,1]$) has been a long-standing open problem. In this paper, we propose a mathematical model to quantify {\em tail index} of service latency for arbitrary erasure-coded storage systems, by characterizing the asymptotic behavior of latency distribution tails. When file size has a heavy tailed distribution, we find tail index, defined as the exponent at which latency tail probability diminishes to zero, in closed-form, and further show that a family of probabilistic scheduling algorithms are (asymptotically) optimal since they are able to achieve the exact tail index.

cs.IT↗

arXiv2017

Sprout: A functional caching approach to minimize service latency in erasure-coded storage

Modern distributed storage systems often use erasure codes to protect against disk and node failures to increase reliability, while trying to meet the latency requirements of the applications and clients. Storage systems may have caches at the proxy or client ends in order to reduce the latency. In this paper, we consider a novel caching framework with erasure code called functional caching. Functional Caching involves using erasure-coded chunks in the cache such that the code formed by the chunks in storage nodes and cache combined are maximal-distance-separable (MDS) erasure codes. Based on the arrival rates of different files, placement of file chunks on the servers, and service time distribution of storage servers, an optimal functional caching placement and the access probabilities of the file request from different disks are considered. The proposed algorithm gives significant latency improvement in both simulations and a prototyped solution in an open-source, cloud storage deployment.

cs.DC↗

arXiv2017

Taming Tail Latency for Erasure-coded, Distributed Storage Systems

Distributed storage systems are known to be susceptible to long tails in response time. In modern online storage systems such as Bing, Facebook, and Amazon, the long tails of the service latency are of particular concern. with 99.9th percentile response times being orders of magnitude worse than the mean. As erasure codes emerge as a popular technique to achieve high data reliability in distributed storage while attaining space efficiency, taming tail latency still remains an open problem due to the lack of mathematical models for analyzing such systems. To this end, we propose a framework for quantifying and optimizing tail latency in erasure-coded storage systems. In particular, we derive upper bounds on tail latency in closed form for arbitrary service time distribution and heterogeneous files. Based on the model, we formulate an optimization problem to jointly minimize the weighted latency tail probability of all files over the placement of files on the servers, and the choice of servers to access the requested files. The non-convex problem is solved using an efficient, alternating optimization algorithm. Numerical results show significant reduction of tail latency for erasure-coded storage systems with a realistic workload.

cs.DC↗

arXiv2017

Classification of 2+1D topological orders and SPT orders for bosonic and fermionic systems with on-site symmetries

Gapped quantum liquids (GQL) include both topologically ordered states (with long range entanglement) and symmetry protected topological (SPT) states (with short range entanglement). In this paper, we propose a classification of 2+1D GQL for both bosonic and fermionic systems: 2+1D bosonic/fermionic GQLs with finite on-site symmetry are classified by non-degenerate unitary braided fusion categories over a symmetric fusion category (SFC) $\cal E$, abbreviated as $\text{UMTC}_{/\cal E}$, together with their modular extensions and total chiral central charges. The SFC $\cal E$ is $\text{Rep}(G)$ for bosonic symmetry $G$, or $\text{sRep}(G^f)$ for fermionic symmetry $G^f$. As a special case of the above result, we find that the modular extensions of $\text{Rep}(G)$ classify the 2+1D bosonic SPT states of symmetry $G$, while the $c=0$ modular extensions of $\text{sRep}(G^f)$ classify the 2+1D fermionic SPT states of symmetry $G^f$. Many fermionic SPT states are studied based on the constructions from free-fermion models. But it is not clear if free-fermion constructions can produce all fermionic SPT states. Our classification does not have such a drawback. We show that, for interacting 2+1D fermionic systems, there are exactly 16 superconducting phases with no symmetry and no fractional excitations (up to $E_8$ bosonic quantum Hall states). Also, there are exactly 8 $Z_2\times Z_2^f$-SPT phases, 2 $Z_8^f$-SPT phases, and so on. Besides, we show that two topological orders with identical bulk excitations and central charge always differ by the stacking of the SPT states of the same symmetry.

cond-mat.str-el↗

arXiv2017

Experimental Identification of Non-Abelian Topological Orders on a Quantum Simulator

Topological orders can be used as media for topological quantum computing --- a promising quantum computation model due to its invulnerability against local errors. Conversely, a quantum simulator, often regarded as a quantum computing device for special purposes, also offers a way of characterizing topological orders. Here, we show how to identify distinct topological orders via measuring their modular $S$ and $T$ matrices. In particular, we employ a nuclear magnetic resonance quantum simulator to study the properties of three topologically ordered matter phases described by the string-net model with two string types, including the $\Z_2$ toric code, doubled semion, and doubled Fibonacci. The third one, non-Abelian Fibonacci order is notably expected to be the simplest candidate for universal topological quantum computing. Our experiment serves as the basic module, built on which one can simulate braiding of non-Abelian anyons and ultimately topological quantum computation via the braiding, and thus provides a new approach of investigating topological orders using quantum computers.

cond-mat.str-el↗

arXiv2016

Modular extensions of unitary braided fusion categories and 2+1D topological/SPT orders with symmetries

A finite bosonic or fermionic symmetry can be described uniquely by a symmetric fusion category $\mathcal{E}$. In this work, we propose that 2+1D topological/SPT orders with a fixed finite symmetry $\mathcal{E}$ are classified, up to $E_8$ quantum Hall states, by the unitary modular tensor categories $\mathcal{C}$ over $\mathcal{E}$ and the modular extensions of each $\mathcal{C}$. In the case $\mathcal{C}=\mathcal{E}$, we prove that the set $\mathcal{M}_{ext}(\mathcal{E})$ of all modular extensions of $\mathcal{E}$ has a natural structure of a finite abelian group. We also prove that the set $\mathcal{M}_{ext}(\mathcal{C})$ of all modular extensions of $\mathcal{C}$, if not empty, is equipped with a natural $\mathcal{M}_{ext}(\mathcal{E})$-action that is free and transitive. Namely, the set $\mathcal{M}_{ext}(\mathcal{C})$ is an $\mathcal{M}_{ext}(\mathcal{E})$-torsor. As special cases, we explain in details how the group $\mathcal{M}_{ext}(\mathcal{E})$ recovers the well-known group-cohomology classification of the 2+1D bosonic SPT orders and Kitaev's 16 fold ways. We also discuss briefly the behavior of the group $\mathcal{M}_{ext}(\mathcal{E})$ under the symmetry-breaking processes and its relation to Witt groups.

math.QA↗

arXiv2016

Spatio-temporal Aware Non-negative Component Representation for Action Recognition

This paper presents a novel mid-level representation for action recognition, named spatio-temporal aware non-negative component representation (STANNCR). The proposed STANNCR is based on action component and incorporates the spatial-temporal information. We first introduce a spatial-temporal distribution vector (STDV) to model the distributions of local feature locations in a compact and discriminative manner. Then we employ non-negative matrix factorization (NMF) to learn the action components and encode the video samples. The action component considers the correlations of visual words, which effectively bridge the sematic gap in action recognition. To incorporate the spatial-temporal cues for final representation, the STDV is used as the part of graph regularization for NMF. The fusion of spatial-temporal information makes the STANNCR more discriminative, and our fusion manner is more compact than traditional method of concatenating vectors. The proposed approach is extensively evaluated on three public datasets. The experimental results demonstrate the effectiveness of STANNCR for action recognition.

cs.CV↗

arXiv2016

Differentiated latency in data center networks with erasure coded files through traffic engineering

This paper proposes an algorithm to minimize weighted service latency for different classes of tenants (or service classes) in a data center network where erasure-coded files are stored on distributed disks/racks and access requests are scattered across the network. Due to limited bandwidth available at both top-of-the-rack and aggregation switches and tenants in different service classes need differentiated services, network bandwidth must be apportioned among different intra- and inter-rack data flows for different service classes in line with their traffic statistics. We formulate this problem as weighted queuing and employ a class of probabilistic request scheduling policies to derive a closed-form upper-bound of service latency for erasure-coded storage with arbitrary file access patterns and service time distributions. The result enables us to propose a joint weighted latency (over different service classes) optimization over three entangled "control knobs": the bandwidth allocation at top-of-the-rack and aggregation switches for different service classes, dynamic scheduling of file requests, and the placement of encoded file chunks (i.e., data locality). The joint optimization is shown to be a mixed-integer problem. We develop an iterative algorithm which decouples and solves the joint optimization as 3 sub-problems, which are either convex or solvable via bipartite matching in polynomial time. The proposed algorithm is prototyped in an open-source, distributed file system, {\em Tahoe}, and evaluated on a cloud testbed with 16 separate physical hosts in an Openstack cluster using 48-port Cisco Catalyst switches. Experiments validate our theoretical latency analysis and show significant latency reduction for diverse file access patterns. The results provide valuable insights on designing low-latency data center networks with erasure coded storage.

cs.DC↗

arXiv2015

Advanced Post-Processing Techniques of Molecular Dynamics Simulations in Studying Strong Anharmonic Thermodynamics of Solids

While the vibrational thermodynamics of materials with small anharmonicity at low temperatures has been understood well based on the harmonic phonons approximation; at high temperatures, this understanding must accommodate how phonons interact with other phonons or with other excitations. We shall see that the phonon-phonon interactions give rise to interesting coupling problems, and essentially modify the equilibrium and non-equilibrium properties of materials, e.g., thermal expansion, thermodynamic stability, heat capacity, optical properties, thermal transport and other nonlinear properties of materials. To date the anharmonic lattice dynamics is poorly understood despite its great importance, and most studies on lattice dynamics still rely on the harmonic or quasiharmonic models. With recent developement of computational models, the anharmonic information can be extracted from the atomic trajectories of molecular dynamics simulations. For example, the vibrational energy spectra, the effective potential energy surface and the phonon-phonon interaction channels can be derived from these trajectories which appear stochastic. These inter-dependent methods are adopted to successfully uncover the strong anharmonic phenomena while the traditional harmonic models fail dramatically, e.g., the negative thermal expansion of cuprite and the high temperature thermal stability of rutile.

cond-mat.mtrl-sci↗

arXiv2015

Action Recognition by Hierarchical Mid-level Action Elements

Realistic videos of human actions exhibit rich spatiotemporal structures at multiple levels of granularity: an action can always be decomposed into multiple finer-grained elements in both space and time. To capture this intuition, we propose to represent videos by a hierarchy of mid-level action elements (MAEs), where each MAE corresponds to an action-related spatiotemporal segment in the video. We introduce an unsupervised method to generate this representation from videos. Our method is capable of distinguishing action-related segments from background segments and representing actions at multiple spatiotemporal resolutions. Given a set of spatiotemporal segments generated from the training data, we introduce a discriminative clustering algorithm that automatically discovers MAEs at multiple levels of granularity. We develop structured models that capture a rich set of spatial, temporal and hierarchical relations among the segments, where the action label and multiple levels of MAE labels are jointly inferred. The proposed model achieves state-of-the-art performance in multiple action recognition benchmarks. Moreover, we demonstrate the effectiveness of our model in real-world applications such as action recognition in large-scale untrimmed videos and action parsing.

cs.CV↗

arXiv2015

A theory of 2+1D fermionic topological orders and fermionic/bosonic topological orders with symmetries

We propose that, up to invertible topological orders, 2+1D fermionic topological orders without symmetry and 2+1D fermionic/bosonic topological orders with symmetry $G$ are classified by non-degenerate unitary braided fusion categories (UBFC) over a symmetric fusion category (SFC); the SFC describes a fermionic product state without symmetry or a fermionic/bosonic product state with symmetry $G$, and the UBFC has a modular extension. We developed a simplified theory of non-degenerate UBFC over a SFC based on the fusion coefficients $N^{ij}_k$ and spins $s_i$. This allows us to obtain a list that contains all 2+1D fermionic topological orders (without symmetry). We find explicit realizations for all the fermionic topological orders in the table. For example, we find that, up to invertible $p+\hspace{1pt}\mathrm{i}\hspace{1pt} p$ fermionic topological orders, there are only four fermionic topological orders with one non-trivial topological excitation: (1) the $K={\scriptsize \begin{pmatrix} -1&0\\0&2\end{pmatrix}}$ fractional quantum Hall state, (2) a Fibonacci bosonic topological order $2^B_{14/5}$ stacking with a fermionic product state, (3) the time-reversal conjugate of the previous one, (4) a primitive fermionic topological order that has a chiral central charge $c=\frac14$, whose only topological excitation has a non-abelian statistics with a spin $s=\frac14$ and a quantum dimension $d=1+\sqrt{2}$. We also proposed a categorical way to classify 2+1D invertible fermionic topological orders using modular extensions.

cond-mat.str-el↗

arXiv2015

Phonon quarticity induced by changes in phonon-tracked hybridization during lattice expansion and its stabilization of rutile TiO$_2$

Although the rutile structure of TiO$_2$ is stable at high temperatures, the conventional quasiharmonic approximation predicts that several acoustic phonons decrease anomalously to zero frequency with thermal expansion, incorrectly predicting a structural collapse at temperatures well below 1000\,K. Inelastic neutron scattering was used to measure the temperature dependence of the phonon density of states (DOS) of rutile TiO$_2$ from 300 to 1373\,K. Surprisingly, these anomalous acoustic phonons were found to increase in frequency with temperature. First-principles calculations showed that with lattice expansion, the potentials for the anomalous acoustic phonons transform from quadratic to quartic, stabilizing the rutile phase at high temperatures. In these modes, the vibrational displacements of adjacent Ti and O atoms cause variations in hybridization of $3d$ electrons of Ti and $2p$ electrons of O atoms. With thermal expansion, the energy variation in this "phonon-tracked hybridization" flattens the bottom of the interatomic potential well between Ti and O atoms, and induces a quarticity in the phonon potential.

cond-mat.mtrl-sci↗