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Lu Liu

Publications and source records attributed to Lu Liu.

At least 217 records · Page 12Linked to original sources
arXiv2018

Hot Streaks in Artistic, Cultural, and Scientific Careers

The hot streak, loosely defined as winning begets more winnings, highlights a specific period during which an individual's performance is substantially higher than her typical performance. While widely debated in sports, gambling, and financial markets over the past several decades, little is known if hot streaks apply to individual careers. Here, building on rich literature on lifecycle of creativity, we collected large-scale career histories of individual artists, movie directors and scientists, tracing the artworks, movies, and scientific publications they produced. We find that, across all three domains, hit works within a career show a high degree of temporal regularity, each career being characterized by bursts of high-impact works occurring in sequence. We demonstrate that these observations can be explained by a simple hot-streak model we developed, allowing us to probe quantitatively the hot streak phenomenon governing individual careers, which we find to be remarkably universal across diverse domains we analyzed: The hot streaks are ubiquitous yet unique across different careers. While the vast majority of individuals have at least one hot streak, hot streaks are most likely to occur only once. The hot streak emerges randomly within an individual's sequence of works, is temporally localized, and is unassociated with any detectable change in productivity. We show that, since works produced during hot streaks garner significantly more impact, the uncovered hot streaks fundamentally drives the collective impact of an individual, ignoring which leads us to systematically over- or under-estimate the future impact of a career. These results not only deepen our quantitative understanding of patterns governing individual ingenuity and success, they may also have implications for decisions and policies involving predicting and nurturing individuals with lasting impact.

physics.soc-ph↗
arXiv2018

A computable analysis of variable words theorems

The Carlson-Simpson lemma is a combinatorial statement occurring in the proof of the Dual Ramsey theorem. Formulated in terms of variable words, it informally asserts that given any finite coloring of the strings, there is an infinite sequence with infinitely many variables such that for every valuation, some specific set of initial segments is homogeneous. Friedman, Simpson, and Montalban asked about its reverse mathematical strength. We study the computability-theoretic properties and the reverse mathematics of this statement, and relate it to the finite union theorem. In particular, we prove the Ordered Variable word for binary strings in ACA0.

math.LO↗
arXiv2018

Typicality at quantum-critical points

We discuss the concept of typicality of quantum states at quantum-critical points, using projector Monte Carlo simulations of an $S=1/2$ bilayer Heisenberg antiferromagnet as an illustration. With the projection (imaginary) time $τ$ scaled as $τ=aL^z$, $L$ being the system length and $z$ the dynamic critical exponent (which takes the value $z=1$ in the bilayer model studied here), a critical point can be identified which asymptotically flows to the correct location and universality class with increasing $L$, independently of the prefactor $a$ and the initial state. Varying the proportionality factor $a$ and the initial state only changes the cross-over behavior into the asymptotic large-$L$ behavior. In some cases, choosing an optimal factor $a$ may also lead to the vanishing of the leading finite-size corrections. The observation of typicality can be used to speed up simulations of quantum criticality, not only within the Monte Carlo approach but also with other numerical methods where imaginary-time evolution is employed, e.g., tensor network states, as it is not necessary to evolve fully to the ground state but only for sufficiently long times to reach the typicality regime.

cond-mat.str-el↗
arXiv2018

On the Transition of the Galaxy Quenching Mode at 0.5<z<1 in CANDELS

We investigate the galaxy quenching process at intermediate redshift using a sample of $\sim4400$ galaxies with $M_{\ast} > 10^{9}M_{\odot}$ between redshift 0.5 and 1.0 in all five CANDELS fields. We divide this sample, using the integrated specific star formation rate (sSFR), into four sub-groups: star-forming galaxies (SFGs) above and below the ridge of the star-forming main sequence (SFMS), transition galaxies and quiescent galaxies. We study their $UVI$ ($U-V$ versus $V-I$) color gradients to infer their sSFR gradients out to twice effective radii. We show that on average both star-forming and transition galaxies at all masses are not fully quenched at any radii, whereas quiescent galaxies are fully quenched at all radii. We find that at low masses ($M_{\ast} = 10^{9}-10^{10}M_{\odot}$) SFGs both above and below the SFMS ridge generally have flat sSFR profiles, whereas the transition galaxies at the same masses generally have sSFRs that are more suppressed in their outskirts. In contrast, at high masses ($M_{\ast} > 10^{10.5}M_{\odot}$), SFGs above and below the SFMS ridge and transition galaxies generally have varying degrees of more centrally-suppressed sSFRs relative to their outskirts. These findings indicate that at $z\sim~0.5-1.0$ the main galaxy quenching mode depends on its already formed stellar mass, exhibiting a transition from "the outside-in" at $M_{\ast} \leq 10^{10}M_{\odot}$ to "the inside-out" at $M_{\ast} > 10^{10.5}M_{\odot}$. In other words, our findings support that internal processes dominate the quenching of massive galaxies, whereas external processes dominate the quenching of low-mass galaxies.

astro-ph.GA↗
arXiv2018

Detecting high-dimensional multipartite entanglement via some classes of measurements

Mutually unbiased bases, mutually unbiased measurements and general symmetric informationally complete measurements are three related concepts in quantum information theory. We investigate multipartite systems using these notions and present some criteria detecting entanglement of arbitrary high dimensional multi-qudit systems and multipartite systems of subsystems with different dimensions. It is proved that these criteria can detect the $k$-nonseparability ($k$ is even) of multipartite qudit systems and arbitrary high dimensional multipartite systems of $m$ subsystems with different dimensions. We show that they are more efficient and wider of application range than the previous ones. They provide experimental implementation in detecting entanglement without full quantum state tomography.

quant-ph↗
arXiv2018

The Isophotal Structure of Star-forming Galaxies at $0.5< z <1.8$ in CANDELS: Implications for the Evolution of Galaxy Structure

We have measured the radial profiles of isophotal ellipticity ($\varepsilon$) and disky/boxy parameter A$_4$ out to radii of about three times the semi-major axes for $\sim4,600$ star-forming galaxies (SFGs) at intermediate redshifts $0.5 1$. Moreover, the median A$_4$ values at all radii are almost zero. In contrast, the highly-inclined, low-mass LSFGs in the same mass-redshift bins generally have monotonically increasing $\varepsilon$ with radius and are dominated by disky values at intermediate radii. These findings at intermediate redshifts imply that low-mass SSFGs are not disk-like, while low-mass LSFGs appear to harbour disk-like components flattened by significant rotation. At high masses ($M_{\ast} > 10^{10}M_{\odot}$), highly-inclined SSFGs and LSFGs both exhibit a general, distinct trend for both $\varepsilon$ and A$_4$ profiles: increasing values with radius at lower radii, reaching maxima at intermediate radii, and then decreasing values at larger radii. Such a trend is more prevalent for more massive ($M_{\ast} > 10^{10.5}M_{\odot}$) galaxies or those at lower redshifts ($z<1.4$). The distinct trend in $\varepsilon$ and A$_4$ can be simply explained if galaxies possess all three components: central bulges, disks in the intermediate regions, and halo-like stellar components in the outskirts.

astro-ph.GA↗
arXiv2017

Durable Bistable Auxetics Made of Rigid Solids

Bistable Auxetic Metamaterials (BAMs) are a class of monolithic perforated periodic structures with negative Poisson's ratio. Under tension, a BAM can expand and reach a second state of equilibrium through a globally large shape transformation that is ensured by the flexibility of its elastomeric base material. However, if made from a rigid polymer, or metal, BAM ceases to function due to the inevitable rupture of its ligaments. The goal of this work is to extend the unique functionality of the original kirigami architecture of BAM to a rigid solid base material. We use experiments and numerical simulations to assess performance, bistability and durability of rigid BAMs at 10,000 cycles. Geometric maps are presented to elucidate the role of the main descriptors of BAM architecture. The proposed design enables the realization of BAM from a large palette of materials, including elastic-perfectly plastic materials and potentially brittle materials.

physics.app-ph↗
arXiv2017

Link Quality Aware Channel Allocation for Multichannel Body Sensor Networks

Body Sensor Network (BSN) is a typical Internet-of-Things (IoT) application for personalized health care. It consists of economically powered, wireless and implanted medical monitoring sensor nodes, which are designed to continually collect the medical information of the target patients. Multichannel is often used in BSNs to reduce the spectrum competition of the tremendous sensor nodes and the problem of channel assignment has attracted much research attention. The health sensing data in BSNs is often required to be delivered to a sink node (or server) before a certain deadline for real time monitoring or health emergency alarm. Therefore, deadline is of significant importance for multichannel allocation and scheduling. The existing works, though designed to meet the deadline, often overlook the impact of the unreliable wireless links. As a result, the health sensing data can still be overdue because of the scheduled lossy links. Besides, potential collisions in the schedules also incur considerable delay in delivering the sensing data. In this paper, we propose a novel deadline- driven Link quality Aware Channel Assignment scheme (LACA), where link quality, deadlines and collisions are jointly considered. LACA prioritizes links with urgent deadlines and heavy collisions. Besides, LACA allows the exploition of the spare slots for retransmissions on lossy links, which can further reduce the retransmission delay. Extensive simulation experiments show that compared to the existing approaches, LACA can better utilize the wireless spectrum and achieve higher packet delivery ratio before the deadline.

cs.NI↗
arXiv2017

Uniform Consistency in Stochastic Block Model with Continuous Community Label

\cite{bickel2009nonparametric} developed a general framework to establish consistency of community detection in stochastic block model (SBM). In most applications of this framework, the community label is discrete. For example, in \citep{bickel2009nonparametric,zhao2012consistency} the degree corrected SBM is assumed to have a discrete degree parameter. In this paper, we generalize the method of \cite{bickel2009nonparametric} to give consistency analysis of maximum likelihood estimator (MLE) in SBM with continuous community label. We show that there is a standard procedure to transform the $||\cdot||_2$ error bound to the uniform error bound. We demonstrate the application of our general results by proving the uniform consistency (strong consistency) of the MLE in the exponential network model with interaction effect. Unfortunately, in the continuous parameter case, the condition ensuring uniform consistency we obtained is much stronger than that in the discrete parameter case, namely $nμ_n^5/(\log n)^{8}\rightarrow\infty$ versus $nμ_n/\log n\rightarrow\infty$. Where $nμ_n$ represents the average degree of the network. But continuous is the limit of discrete. So it is not surprising as we show that by discretizing the community label space into sufficiently small (but not too small) pieces and applying the MLE on the discretized community label space, uniform consistency holds under almost the same condition as in discrete community label space. Such a phenomenon is surprising since the discretization does not depend on the data or the model. This reminds us of the thresholding method.

stat.ME↗
arXiv2017

On the Log Partition Function of Ising Model on Stochastic Block Model

A sparse stochastic block model (SBM) with two communities is defined by the community probability $π_0,π_1$, and the connection probability between communities $a,b\in\{0,1\}$, namely $q_{ab} = \frac{α_{ab}}{n}$. When $q_{ab}$ is constant in $a,b$, the random graph is simply the Erdős-Rény random graph. We evaluate the log partition function of the Ising model on sparse SBM with two communities. As an application, we give consistent parameter estimation of the sparse SBM with two communities in a special case. More specifically, let $d_0,d_1$ be the average degree of the two communities, i.e., $d_0\overset{def}{=}π_0α_{00}+π_1α_{01},d_1\overset{def}{=}π_0α_{10}+π_1α_{11}$. We focus on the regime $d_0=d_1$ (the regime $d_0\ne d_1$ is trivial). In this regime, there exists $d,λ$ and $r\geq 0$ with $π_0=\frac{1}{1+r}, π_1=\frac{r}{1+r}$, $α_{00}=d(1+rλ), α_{01}=α_{10} = d(1-λ), α_{11} = d(1+\fracλ{r})$. We give a consistent estimator of $r$ when $λ<0$. The estimator of $λ$ given by \citep{mossel2015reconstruction} is valid in the general situation. We also provide a random clustering algorithm which does not require knowledge of parameters and which is positively correlated with the true community label when $λ<0$.

stat.ME↗
arXiv2017

Separability criteria via some classes of measurements

Mutually unbiased bases (MUBs) and symmetric informationally complete (SIC) positive operator-valued measurements (POVMs) are two related topics in quantum information theory. They are generalized to mutually unbiased measurements (MUMs) and general symmetric informationally complete (GSIC) measurements, respectively, that are both not necessarily rank 1. We study the quantum separability problem by using these measurements and present separability criteria for bipartite systems with arbitrary dimensions and multipartite systems of multi-level subsystems. These criteria are proved to be more effective than previous criteria especially when the dimensions of the subsystems are different. Furthermore, full quantum state tomography is not needed when these criteria are implemented in experiment.

quant-ph↗
arXiv2017

The Origins of UV-optical Color Gradients in Star-forming Galaxies at z ~ 2: Predominant Dust Gradients But Negligible sSFR Gradients

The rest-frame UV-optical (i.e., $NUV-B$) color is sensitive to both low-level recent star formation (specific star formation rate - sSFR) and dust. In this Letter, we extend our previous work on the origins of $NUV-B$ color gradients in star-forming galaxies (SFGs) at $z\sim1$ to those at $z\sim2$. We use a sample of 1335 large (semi-major axis radius $R_{\rm SMA}>0.''18$) SFGs with extended UV emission out to $2R_{\rm SMA}$ in the mass range $M_{\ast} = 10^{9}-10^{11}M_{\odot}$ at $1.5<z<2.8$ in the CANDELS/GOODS-S and UDS fields. We show that these SFGs generally have negative $NUV-B$ color gradients (redder centres), and their color gradients strongly increase with galaxy mass. We also show that the global rest-frame $FUV-NUV$ color is approximately linear with $A_{\rm V}$, which is derived by modeling the observed integrated FUV to NIR spectral energy distributions of the galaxies. Applying this integrated calibration to our spatially-resolved data, we find a negative dust gradient (more dust extinguished in the centers), which steadily becomes steeper with galaxy mass. We further find that the $NUV-B$ color gradients become nearly zero after correcting for dust gradients regardless of galaxy mass. This indicates that the sSFR gradients are negligible and dust reddening is likely the principal cause of negative UV-optical color gradients in these SFGs. Our findings support that the buildup of the stellar mass in SFGs at the Cosmic Noon is self-similar inside $2R_{\rm SMA}$.

astro-ph.GA↗
arXiv2017

Joint Optimization of Scheduling and Power Control in Wireless Networks: Multi-Dimensional Modeling and Decomposition

The energy efficiency of future networks is becoming a significant and urgent issue, calling for greener network designs. At the same time, rapid development of wireless networks shows a trend of increasing complexity in network structure and resource space, leading to that optimizing the energy efficiency of such networks requires a joint solution over multi-dimensional resource space. However, the coupled resource dimensions and growing problem scales bring great challenges in obtaining the optimal solutions. In this paper, we develop a multi-dimensional network model on the basis of tuple-links associated with transmission patterns (TPs) and formulate the optimization problem as a TP based scheduling problem which jointly solves transmission scheduling, routing, power control, radio and channel assignment. In order to tackle the complexity issues raised from coupled resource dimensions, we propose a novel algorithm that decomposes the coupling scheduling and power control by exploiting the delay column generation technique to recursively solve a master problem for scheduling and a sub-problem for power allocation. Further, we theoretically prove that the performance gap between the proposed algorithm and the optimum is upper bounded by that for the sub-problem solution, where the latter is derived by solving a relaxed version of the sub-problem. Numerical results demonstrate the effectiveness of the multi-dimensional framework and the benefit of the proposed joint optimization in improving network energy efficiency.

cs.NI↗
arXiv2016

Representation Learning with Deconvolution for Multivariate Time Series Classification and Visualization

We propose a new model based on the deconvolutional networks and SAX discretization to learn the representation for multivariate time series. Deconvolutional networks fully exploit the advantage the powerful expressiveness of deep neural networks in the manner of unsupervised learning. We design a network structure specifically to capture the cross-channel correlation with deconvolution, forcing the pooling operation to perform the dimension reduction along each position in the individual channel. Discretization based on Symbolic Aggregate Approximation is applied on the feature vectors to further extract the bag of features. We show how this representation and bag of features helps on classification. A full comparison with the sequence distance based approach is provided to demonstrate the effectiveness of our approach on the standard datasets. We further build the Markov matrix from the discretized representation from the deconvolution to visualize the time series as complex networks, which show more class-specific statistical properties and clear structures with respect to different labels.

cs.LG↗
arXiv2016

All passive photonic power divider with arbitrary split ratio

Integrated optical power splitter is one of the fundamental building blocks in photonic integrated circuits (PIC). Conventional multimode interferometer based power splitter is widely used as it has reasonable footprint and is easy to fabricate. However, it is challenging to realize arbitrary split ratio especially for multi-outputs. In this work, an ultra-compact power splitter with a QR code-like nanostructure is designed by a nonlinear fast search method (FSM). The highly functional structure is composed of a number of freely designed square pixels with the size of 120nm x 120nm which could be either dielectric or air. The lightwaves are scattered by a number of etched squares with optimized locations and the scattered waves superimpose at the outputs with the desired power ratio. We demonstrate 1x2 splitters with 1:1, 1:2, 1:3 split ratios and a 1x3 splitter with the ratio of 1:2:1. The footprint for all the devices is only 3.6umx3.6 um. Well-controlled split ratios are measured for all the cases. The measured transmission efficiencies of all the splitters are close to 80% over 30 nm wavelength range.

physics.optics↗
arXiv2016

Generalized low solution of $\mathsf{RT}_k^1$ problem

We study the "coding power" of an arbitrary $\mathsf{RT}_k^1$-instance. We prove that every $\mathsf{RT}_k^1$-instance admit non trivial generalized low solution. This is somewhat related to a problem proposed by Patey. We also answer a question proposed by Liu, i.e., we prove that there exists a $\mathbf{0}'$-computable $\mathsf{RT}_3^1$-instance, $I_3^1$, such that every $\mathsf{RT}_2^1$-instance admit a non trivial solution that does not compute any non trivial solution of $I_3^1$.

math.LO↗
arXiv2016

Cone avoiding closed sets

We prove that for an arbitrary subtree $T$ of $2^{<ω}$ with each element extendable to a path, a given countable class $\mathcal{M}$ closed under disjoint union, and any set $A$, if none of the members of $\mathcal{M}$ strongly $k$-enumerate $T$ for any $k$, then there exists an infinite set contained in either $A$ or $\bar{A}$ such that for every $C\in\mathcal{M}$, $C\oplus G$ also does not strongly $k$-enumerate $T$. We give applications of this result, which include: (1) $\mathsf{RT_2^2}$ doesn't imply $\mathsf{WWKL_0}$; (2) (Ambos-Spies et al.2004) $\mathsf{DNR}$ is strictly weaker than $\mathsf{WWKL_0}$; (3) (Kjos-Hanssen 2009) for any Martin-Löf random set $A$ either $A$ or $\bar{A}$ contains an infinite subset that does not compute any Martin-Löf random set; etc. We also discuss further generalizations of this result.

math.LO↗