arXiv subjects

Lu Liu

Publications and source records attributed to Lu Liu.

At least 145 records · Page 8Linked to original sources

arXiv2022

Fully Distributed Continuous-Time Algorithm for Nonconvex Optimization over Unbalanced Directed Networks

This paper investigates the distributed continuous-time nonconvex optimization problem over unbalanced directed networks. The objective is to cooperatively drive all the agent states to an optimal solution that minimizes the sum of the local cost functions. Based on the topology balancing technique and adaptive control approach, a novel fully distributed algorithm is developed for each agent with neither prior global information concerning network connectivity nor convexity of local cost functions. By viewing the proposed algorithm as a perturbed system, its input-to-state stability with a vanishing perturbation is first established, and asymptotic convergence of the decision variables toward the optimal solution is then proved under the relaxed condition. A key feature of the algorithm design is that it removes the dependence on the smallest strong convexity constant of local cost functions, and the left eigenvector corresponding to the zero eigenvalue of the Laplacian matrix of unbalanced directed topologies. The effectiveness of the proposed fully distributed algorithm is illustrated with two examples.

math.OC↗

arXiv2022

Dirac Equation under Modified Hylleraas Potential in Noncommutative Spaces

In this paper, we study the interaction of spin 1/2 Dirac particles with the Hylleraas potential based on the noncommutative space framework. Solving the first-order correction of the energy level caused by the noncommutation parameter $θ$ in the wave equation. The problem of energy level correction under the action of additional weak electric field is further analyzed. Due to the non-commutation parameter, the energy levels are split. The noncommutation parameter $θ$ has a significant effect on the energy eigenvalues. The effect of $θ$ on the energy level splitting caused by the electric field is reflected by adding a slight numerical change to the energy level after splitting.

quant-ph↗

arXiv2022

Primitive recursive reverse mathematics

We use a second-order analogy $\mathsf{PRA}^2$ of $\mathsf{PRA}$ to investigate the proof-theoretic strength of theorems in countable algebra, analysis, and infinite combinatorics. We compare our results with similar results in the fast-developing field of primitive recursive (\lq punctual\rq) algebra and analysis, and with results from \lq online\rq\ combinatorics. We argue that $\mathsf{PRA}^2$ is sufficiently robust to serve as an alternative base system below $\mathsf{RCA}_0$ to study the proof-theoretic content of theorems in ordinary mathematics. (The most popular alternative is perhaps $\mathsf{RCA}_0^*$.) We discover that many theorems that are known to be true in $\mathsf{RCA}_0$ either hold in $\mathsf{PRA}^2$ or are equivalent to $\mathsf{RCA}_0$ or its weaker (but natural) analogy $2^N-\mathsf{RCA}_0$ over $\mathsf{PRA}^2$. However, we also discover that some standard mathematical and combinatorial facts are incomparable with these natural subsystems.

math.LO↗

arXiv2022

Proximate deconfined quantum critical point in SrCu2(BO3)2

The deconfined quantum critical point (DQCP) represents a paradigm shift in quantum matter studies, presenting a "beyond Landau" scenario for order--order transitions. Its experimental realization, however, has remained elusive. Using high-pressure $^{11}$B NMR measurements on the quantum magnet SrCu$_2$(BO$_3$)$_2$, we here demonstrate a magnetic-field induced plaquette-singlet to antiferromagnetic transition above 1.8 GPa at a remarkably low temperature, $T_{\rm c}\simeq 0.07$ K. First-order signatures of the transition weaken with increasing pressure, and we observe quantum critical scaling at the highest pressure, 2.4 GPa. Supported by model calculations, we suggest that these observations can be explained by a proximate DQCP inducing critical quantum fluctuations and emergent O(3) symmetry of the order parameters. Our findings take the DQCP from a theoretical concept to a concrete experimental platform.

cond-mat.str-el↗

arXiv2022

Federated Learning from Pre-Trained Models: A Contrastive Learning Approach

Federated Learning (FL) is a machine learning paradigm that allows decentralized clients to learn collaboratively without sharing their private data. However, excessive computation and communication demands pose challenges to current FL frameworks, especially when training large-scale models. To prevent these issues from hindering the deployment of FL systems, we propose a lightweight framework where clients jointly learn to fuse the representations generated by multiple fixed pre-trained models rather than training a large-scale model from scratch. This leads us to a more practical FL problem by considering how to capture more client-specific and class-relevant information from the pre-trained models and jointly improve each client's ability to exploit those off-the-shelf models. In this work, we design a Federated Prototype-wise Contrastive Learning (FedPCL) approach which shares knowledge across clients through their class prototypes and builds client-specific representations in a prototype-wise contrastive manner. Sharing prototypes rather than learnable model parameters allows each client to fuse the representations in a personalized way while keeping the shared knowledge in a compact form for efficient communication. We perform a thorough evaluation of the proposed FedPCL in the lightweight framework, measuring and visualizing its ability to fuse various pre-trained models on popular FL datasets.

cs.CR↗

arXiv2022

Imaging the quantum melting of Wigner crystal with electronic quasicrystal order

Wigner crystal, as the most fundamental exemplification where the many-body interaction forges the electrons into a solid, experiences an intriguing quantum melting where diverse intermediate phases are predicted to emerge near the quantum critical point. Indications of exotic Wigner orders like bubble phase, liquid-solid phase, and anisotropic Wigner phase have been established by optical or transport measurements. However, the direct visualization of lattice-scale melting order, which is of paramount importance to unequivocally uncover the melting nature, remains challenging and lacking. Noting that Wigner crystals have been achieved in the fractionally filled moire superlattice recently, here, via scanning tunneling microscope, we image the quantum melting of Wigner solid realized by further varying the moire superstructure in monolayer YbCl3/graphene heterostructure. The Wigner solid is constructed on the two-dimensional ensemble of interfacial electron-hole pairs derived from charge transfer. The interplay between certain moire potential and ionic potential leads to the quantum melting of Wigner solid evidenced by the emergence of electron-liquid characteristic, verifying the theoretical predictions. Particularly, akin to the classical quasicrystal made of atoms, a dodecagonal quasicrystal made of electrons, i.e., the Wigner quasicrytal, is visualized at the quantum melting point. In stark contrast to the incompressible Wigner solid, the Wigner quasicrytal hosts considerable liquefied nature unraveled by the interference ripples caused by scattering. By virtue of the two-dimensional charge transfer interface composed of monolayer heavy electron material and graphene, our discovery not only enriches the exploration and understanding of quantum solid-liquid melting, but also paves the way to directly probe the quantum critical order of correlated many-body system.

cond-mat.str-el↗

arXiv2022

The least-used key selection method for information retrieval in large-scale Cloud-based service repositories

As the number of devices connected to the Internet of Things (IoT) increases significantly, it leads to an exponential growth in the number of services that need to be processed and stored in the large-scale Cloud-based service repositories. An efficient service indexing model is critical for service retrieval and management of large-scale Cloud-based service repositories. The multilevel index model is the state-of-art service indexing model in recent years to improve service discovery and combination. This paper aims to optimize the model to consider the impact of unequal appearing probability of service retrieval request parameters and service input parameters on service retrieval and service addition operations. The least-used key selection method has been proposed to narrow the search scope of service retrieval and reduce its time. The experimental results show that the proposed least-used key selection method improves the service retrieval efficiency significantly compared with the designated key selection method in the case of the unequal appearing probability of parameters in service retrieval requests under three indexing models.

cs.IR↗

arXiv2022

Limit Complexities, Minimal Descriptions, and $n$-Randomness

Let $K$ denote prefix-free Kolmogorov Complexity, and $K^A$ denote it relative to an oracle $A$. We show that for any $n$, $K^{\emptyset^{(n)}}$ is definable purely in terms of the unrelativized notion $K$. It was already known that 2-randomness is definable in terms of $K$ (and plain complexity $C$) as those reals which infinitely often have maximal complexity. We can use our characterization to show that $n$-randomness is definable purely in terms of $K$. To do this we extend a certain ``limsup'' formula from the literature, and apply Symmetry of Information. This extension entails a novel use of semilow sets, and a more precise analysis of the complexity of $Δ_2^0$ sets of mimimal descriptions.

math.LO↗

arXiv2022

The reverse mathematics of Carlson's theorem for located words

In this article, we give two proofs of Carlson's theorem for located words in~$\mathsf{ACA}^+_0$. The first proof is purely combinatorial, in the style of Towsner's proof of Hindman's theorem. The second uses topological dynamics to show that an iterated version of Hindman's theorem for bounded sums implies Carlson's theorem for located words.

math.CO↗

arXiv2022

Spin-Orbital States and Strong Antiferromagnetism of Layered Eu$_2$SrFe$_2$O$_6$ and Sr$_3$Fe$_2$O$_4$Cl$_2$

The insulating iron compounds Eu$_2$SrFe$_2$O$_6$ and Sr$_3$Fe$_2$O$_4$Cl$_2$ have high-temperature antiferromagnetic (AF) order despite their different layered structures. Here we carry out density functional calculations and Monte Carlo simulations to study their electronic structures and magnetic properties aided with analyses of the crystal field, magnetic anisotropy, and superexchange. We find that both compounds are Mott insulators and in the high-spin (HS) Fe$^{2+}$ state ($S$ = 2) accompanied by the weakened crystal field. Although they have different local coordination and crystal fields, the Fe$^{2+}$ ions have the same level sequence and ground-state configuration $(3z^2-r^2)^2(xz,yz)^2(xy)^1(x^2-y^2)^1$. Then, the multiorbital superexchange produces strong AF couplings, and the $(3z^2-r^2)/(xz,yz)$ mixing via the spin-orbit coupling (SOC) yields a small in-plane orbital moment and anisotropy. Indeed, by tracing a set of different spin-orbital states, our density functional calculations confirm the strong AF couplings and the easy planar magnetization for both compounds. Moreover, using the derived magnetic parameters, our Monte Carlo simulations give the Néel temperature $T_{\rm N}$ = 420 K (372 K) for the former (the latter), which well reproduce the experimental results. Therefore, the present study provides a unified picture for Eu$_2$SrFe$_2$O$_6$ and Sr$_3$Fe$_2$O$_4$Cl$_2$ concerning their electronic and magnetic properties.

cond-mat.str-el↗

arXiv2022

Omni-Scale CNNs: a simple and effective kernel size configuration for time series classification

The Receptive Field (RF) size has been one of the most important factors for One Dimensional Convolutional Neural Networks (1D-CNNs) on time series classification tasks. Large efforts have been taken to choose the appropriate size because it has a huge influence on the performance and differs significantly for each dataset. In this paper, we propose an Omni-Scale block (OS-block) for 1D-CNNs, where the kernel sizes are decided by a simple and universal rule. Particularly, it is a set of kernel sizes that can efficiently cover the best RF size across different datasets via consisting of multiple prime numbers according to the length of the time series. The experiment result shows that models with the OS-block can achieve a similar performance as models with the searched optimal RF size and due to the strong optimal RF size capture ability, simple 1D-CNN models with OS-block achieves the state-of-the-art performance on four time series benchmarks, including both univariate and multivariate data from multiple domains. Comprehensive analysis and discussions shed light on why the OS-block can capture optimal RF sizes across different datasets. Code available [https://github.com/Wensi-Tang/OS-CNN]

cs.LG↗

arXiv2022

Unique electronic state in ferromagnetic semiconductor FeCl$_{2}$ monolayer

Two-dimensional (2D) van der Waals (vdW) magnetic materials could be an ideal platform for ultracompact spintronic applications. Among them, FeCl$_{2}$ monolayer in the triangular lattice is subject to a strong debate. Thus, we critically examine its spin-orbital state, electronic structure, and magnetic properties, using a set of delicate first-principles calculations, crystal field level analyses, and Monte Carlo simulations. Our work reveals that FeCl$_{2}$ monolayer is a ferromagnetic (FM) semiconductor in which the electron correlation of the narrow Fe $3d$ bands determines the band gap of about 1.2 eV. Note that only when the spin-orbit coupling (SOC) is properly handled, the unique $d$$^{5\uparrow}$$l$$^\downarrow_{z+}$ electronic ground state is achieved. Then, both the orbital and spin contributions (0.59 $μ_{\rm B}$ plus 3.56 $μ_{\rm B}$) to the total magnetic moment well account for, for the first time, the experimental perpendicular moment of 4.3 $μ_{\rm B}$/Fe. Moreover, we find that a compressive strain further stabilizes the $d$$^{5\uparrow}$$l$$^\downarrow_{z+}$ ground state, and that the enhanced magnetic anisotropy and exchange coupling would boost the Curie temperature ($T_{\rm C}$) from 25 K for the pristine FeCl$_{2}$ monolayer to 69-102 K under 3$\%$-5$\%$ compressive strain. Therefore, FeCl$_{2}$ monolayer is indeed an appealing 2D FM semiconductor.

cond-mat.mtrl-sci↗

arXiv2022

Magnetic frustration in the cubic double perovskite Ba2NiIrO6

Hybrid transition metal oxides continue to attract attention due to their multiple degrees of freedom ($e.g.$, lattice, charge, spin, and orbital) and versatile properties. Here we investigate the magnetic and electronic properties of the newly synthesized double perovskite Ba$_2$NiIrO$_6$, using crystal field theory, superexchange model analysis, density functional calculations, and parallel tempering Monte Carlo (PTMC) simulations. Our results indicate that Ba$_2$NiIrO$_6$ has the Ni$^{2+}$ ($t_{2g}^{6}e_{g}^{2}$)-Ir$^{6+}$ ($t_{2g}^{3}$) charge states. The first nearest-neighboring (1NN) Ni$^{2+}$-Ir$^{6+}$ ions prefer a ferromagnetic (FM) coupling as expected from the Goodenough-Kanamori-Anderson rules, which contradicts the experimental antiferromagnetic (AF) order in Ba$_2$NiIrO$_6$. We find that the strong 2NN AF couplings are frustrated in the fcc sublattices, and they play a major role in determining the observed AF ground state. We also prove that the $J_{\rm eff}$ = 3/2 and $J_{\rm eff}$ = 1/2 states induced by spin-orbit coupling, which would be manifested in low-dimensional (e.g., layered) iridates, are however not the case for cubic Ba$_2$NiIrO$_6$. Our PTMC simulations show that when the long-range (2NN and 3NN) AF interactions are included, an AF transition with $T_{\rm N}$ = 66 K would be obtained and it is well comparable with the experimental 51 K. Meanwhile, we propose a possible 2$\times$2$\times$2 noncollinear AF structure for Ba$_2$NiIrO$_6$.

cond-mat.str-el↗

arXiv2022

Distantly Supervised Relation Extraction via Recursive Hierarchy-Interactive Attention and Entity-Order Perception

Wrong-labeling problem and long-tail relations severely affect the performance of distantly supervised relation extraction task. Many studies mitigate the effect of wrong-labeling through selective attention mechanism and handle long-tail relations by introducing relation hierarchies to share knowledge. However, almost all existing studies ignore the fact that, in a sentence, the appearance order of two entities contributes to the understanding of its semantics. Furthermore, they only utilize each relation level of relation hierarchies separately, but do not exploit the heuristic effect between relation levels, i.e., higher-level relations can give useful information to the lower ones. Based on the above, in this paper, we design a novel Recursive Hierarchy-Interactive Attention network (RHIA) to further handle long-tail relations, which models the heuristic effect between relation levels. From the top down, it passes relation-related information layer by layer, which is the most significant difference from existing models, and generates relation-augmented sentence representations for each relation level in a recursive structure. Besides, we introduce a newfangled training objective, called Entity-Order Perception (EOP), to make the sentence encoder retain more entity appearance information. Substantial experiments on the popular (NYT) dataset are conducted. Compared to prior baselines, our RHIA-EOP achieves state-of-the-art performance in terms of precision-recall (P-R) curves, AUC, Top-N precision and other evaluation metrics. Insightful analysis also demonstrates the necessity and effectiveness of each component of RHIA-EOP.

cs.CL↗

arXiv2022

See further upon the giants: Quantifying intellectual lineage in science

Newton's centuries-old wisdom of standing on the shoulders of giants raises a crucial yet underexplored question: Out of all the prior works cited by a discovery, which one is its giant? Here, we develop a novel, discipline-independent method to identify the giant for any individual paper, allowing us to systematically examine the role and characteristics of giants in science. We find that across disciplines, about 95% of papers stand on the shoulders of giants, yet the weight of scientific progress rests on relatively few shoulders. Defining a new measure of giant index, we find that, while papers with high citations are more likely to be giants, for papers with the same citations, their giant index sharply predicts a paper's future impact and prize-winning probabilities. Giants tend to originate from both small and large teams, being either highly disruptive or highly developmental. And papers that did not have a giant but later became a giant tend to be home-run papers that are highly disruptive to science. Given the crucial importance of citation-based measures in science, the developed concept of giants may offer a useful new dimension in assessing scientific impact that goes beyond sheer citation counts.

cs.DL↗

arXiv2022

Irreducibility of enumerable betting strategies

We study the problem of whether a betting-strategy can be decomposed into an equivalent set of simpler betting-strategies, such as betting-strategies that bet on a restricted set of stages or bet on a restricted of favorable outcomes. We show that the class of effectively enumerable betting-strategies has irreducible members which cannot be decomposed into an equivalent set of simpler betting-strategies. We answer questions of Kastermans and Hitchcock by constructing a real on which no kastergale (which is a left-c.e. supermartingale whose favorable outcomes are effectively determined) succeeds, but some unrestricted left-c.e. supermartingale succeeds on it. We generalize a result of Muchnick by showing that there is a non-1-random real such that no muchgale (which is a left-c.e. supermartingale who does not bet on certain stages) succeeds on it. Our methodology is then used to obtain further irreducibility results, strongly supporting a conjecture that if a natural class of left-c.e. supermartingales defines 1-randomness, then a single member of that class can do so. In another word, the class of left-c.e. supermartingales cannot be reduced to a simpler, natural subclass of it. For example, we show that there is a non-1-random real such that no kastergale or muchgale succeeds on it.

math.PR↗

arXiv2022

FedProto: Federated Prototype Learning across Heterogeneous Clients

Heterogeneity across clients in federated learning (FL) usually hinders the optimization convergence and generalization performance when the aggregation of clients' knowledge occurs in the gradient space. For example, clients may differ in terms of data distribution, network latency, input/output space, and/or model architecture, which can easily lead to the misalignment of their local gradients. To improve the tolerance to heterogeneity, we propose a novel federated prototype learning (FedProto) framework in which the clients and server communicate the abstract class prototypes instead of the gradients. FedProto aggregates the local prototypes collected from different clients, and then sends the global prototypes back to all clients to regularize the training of local models. The training on each client aims to minimize the classification error on the local data while keeping the resulting local prototypes sufficiently close to the corresponding global ones. Moreover, we provide a theoretical analysis to the convergence rate of FedProto under non-convex objectives. In experiments, we propose a benchmark setting tailored for heterogeneous FL, with FedProto outperforming several recent FL approaches on multiple datasets.

cs.LG↗

arXiv2022

Experimental investigation of quantum uncertainty relations with classical shadows

The quantum component in uncertainty relation can be naturally characterized by the quantum coherence of a quantum state, which is of paramount importance in quantum information science. Here, we experimentally investigate quantum uncertainty relations construed with relative entropy of coherence, $l_1$ norm of coherence and coherence of formation. In stead of quantum state tomographic technology, we employ the classical shadow algorithm for the detection of lower bounds in quantum uncertainty relations. With an all optical setup, we prepare a family of quantum states whose purity can be fully controlled. We experimentally explore the tightness of various lower bounds in different reference bases on the prepared states. Our results indicate the tightness of quantum coherence lower bounds dependents on the reference bases as well as the purity of quantum state.

quant-ph↗