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Source author record

Ling Wang

Ling Wang appears in the imported research catalog. Authorship, coauthor and topic links are available while profile ownership is still unclaimed.

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cond-mat.str-elcond-mat.stat-mechMachine LearningComputer Visionquant-phArtificial IntelligenceNeural and Evolutionary ComputingComputation and Languagecond-mat.dis-nncond-mat.mtrl-scicond-mat.othereess.IVeess.SYInformation Theorymath-phmath.APmath.ITmath.MPMolecular Networksphysics.app-phphysics.comp-phphysics.ins-detq-fin.MFq-fin.RMQuantitative MethodsSystems and Control

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Published work

33 published item(s)

preprint2026arXiv

Hypergraph Enterprise Agentic Reasoner over Heterogeneous Business Systems

Applying Large Language Models (LLMs) to heterogeneous enterprise systems is hindered by hallucinations and failures in multi-hop, n-ary reasoning. Existing paradigms (e.g., GraphRAG, NL2SQL) lack the semantic grounding and auditable execution required for these complex environments. We introduce HEAR, an enterprise agentic reasoner built on a Stratified Hypergraph Ontology. Its base Graph Layer virtualizes provenance-aware data interfaces, while the Hyperedge Layer encodes n-ary business rules and procedural protocols. Operating an evidence-driven reasoning loop, HEAR dynamically orchestrates ontology tools for structured multi-hop analysis without requiring LLM retraining. Evaluations on supply-chain tasks, including order fulfillment blockage root cause analysis (RCA), show HEAR achieves up to 94.7% accuracy. Crucially, HEAR demonstrates adaptive efficiency: utilizing procedural hyperedges to minimize token costs, while leveraging topological exploration for rigorous correctness on complex queries. By matching proprietary model performance with open-weight backbones and automating manual diagnostics, HEAR establishes a scalable, auditable foundation for enterprise intelligence.

0 citations0 reviewsNo code linkedOpen access
preprint2026arXiv

Interactive State Space Model with Cross-Modal Local Scanning for Depth Super-Resolution

Guided depth super-resolution (GDSR) reconstructs HR depth maps from LR inputs with HR RGB guidance. Existing methods either model each modality independently or rely on computationally expensive attention mechanisms with quadratic complexity, hindering the establishment of efficient and semantically interactive joint representations. In this paper, we observe that feature maps from different modalities exhibit semantic-level correlations during feature extraction. This motivates us to develop a more flexible approach enabling dense, semantically-aware deep interactions between modalities. To this end, we propose a novel GDSR framework centered around the Interactive State Space Model. Specifically, we design a cross-modal local scanning mechanism that enables fine-grained semantic interactions between RGB and depth features. Leveraging the Mamba architecture, our framework achieves global modeling with linear complexity. Furthermore, a cross-modal matching transform module is introduced to enhance interactive modeling quality by utilizing representative features from both modalities. Extensive experiments demonstrate competitive performance against state-of-the-art methods.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Crystal growth engineering and origin of the weak ferromagnetism in antiferromagnetic matrix of orthochromates from $t$-$e$ orbital hybridization

We report a combined experimental and theoretical study on intriguing magnetic properties of quasiferroelectric orthochromates. Large single crystals of the family of RECrO$_3$ (RE = Y, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, and Lu) compounds were successfully grown. Neutron Laue study indicates a good quality of the obtained single crystals. Applied magnetic-field and temperature dependent magnetization measurements reveal their intrinsic magnetic properties, especially the antiferromagnetic (AFM) transition temperatures. Density functional theory studies of the electronic structures were carried out using the Perdew-Burke-Ernzerhof functional plus Hubbard $U$ method. Crystallographic information and magnetism were theoretically optimized systematically. When RE$^{3+}$ cations vary from Y$^{3+}$ and Eu$^{3+}$ to Lu$^{3+}$ ions, the calculated $t$-$e$ orbital hybridization degree and Néel temperature behave similarly to the experimentally-determined AFM transition temperature with variation in cationic radius. We found that the $t$-$e$ hybridization is anisotropic, causing a magnetic anisotropy of Cr$^{3+}$ sublattices. This was evaluated with the nearest-neighbour $J_1$-$J_2$ model. Our research provides a picture of the electronic structures during the $t$-$e$ hybridization process while changing RE ions and sheds light on the nature of the weak ferromagnetism coexisting with predominated antiferromagnetism. The available large RECrO$_3$ single crystals build a platform for further studies of orthochromates.

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preprint2022arXiv

Deep Reinforcement Learning for Online Routing of Unmanned Aerial Vehicles with Wireless Power Transfer

The unmanned aerial vehicle (UAV) plays an vital role in various applications such as delivery, military mission, disaster rescue, communication, etc., due to its flexibility and versatility. This paper proposes a deep reinforcement learning method to solve the UAV online routing problem with wireless power transfer, which can charge the UAV remotely without wires, thus extending the capability of the battery-limited UAV. Our study considers the power consumption of the UAV and the wireless charging process. Unlike the previous works, we solve the problem by a designed deep neural network. The model is trained using a deep reinforcement learning method offline, and is used to optimize the UAV routing problem online. On small and large scale instances, the proposed model runs from four times to 500 times faster than Google OR-tools, the state-of-the-art combinatorial optimization solver, with identical solution quality. It also outperforms different types of heuristic and local search methods in terms of both run-time and optimality. In addition, once the model is trained, it can scale to new generated problem instances with arbitrary topology that are not seen during training. The proposed method is practically applicable when the problem scale is large and the response time is crucial.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

FP-GNN: a versatile deep learning architecture for enhanced molecular property prediction

Deep learning is an important method for molecular design and exhibits considerable ability to predict molecular properties, including physicochemical, bioactive, and ADME/T (absorption, distribution, metabolism, excretion, and toxicity) properties. In this study, we advanced a novel deep learning architecture, termed FP-GNN, which combined and simultaneously learned information from molecular graphs and fingerprints. To evaluate the FP-GNN model, we conducted experiments on 13 public datasets, an unbiased LIT-PCBA dataset, and 14 phenotypic screening datasets for breast cell lines. Extensive evaluation results showed that compared to advanced deep learning and conventional machine learning algorithms, the FP-GNN algorithm achieved state-of-the-art performance on these datasets. In addition, we analyzed the influence of different molecular fingerprints, and the effects of molecular graphs and molecular fingerprints on the performance of the FP-GNN model. Analysis of the anti-noise ability and interpretation ability also indicated that FP-GNN was competitive in real-world situations.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

HiGNN: Hierarchical Informative Graph Neural Networks for Molecular Property Prediction Equipped with Feature-Wise Attention

Elucidating and accurately predicting the druggability and bioactivities of molecules plays a pivotal role in drug design and discovery and remains an open challenge. Recently, graph neural networks (GNN) have made remarkable advancements in graph-based molecular property prediction. However, current graph-based deep learning methods neglect the hierarchical information of molecules and the relationships between feature channels. In this study, we propose a well-designed hierarchical informative graph neural networks framework (termed HiGNN) for predicting molecular property by utilizing a co-representation learning of molecular graphs and chemically synthesizable BRICS fragments. Furthermore, a plug-and-play feature-wise attention block is first designed in HiGNN architecture to adaptively recalibrate atomic features after the message passing phase. Extensive experiments demonstrate that HiGNN achieves state-of-the-art predictive performance on many challenging drug discovery-associated benchmark datasets. In addition, we devise a molecule-fragment similarity mechanism to comprehensively investigate the interpretability of HiGNN model at the subgraph level, indicating that HiGNN as a powerful deep learning tool can help chemists and pharmacists identify the key components of molecules for designing better molecules with desired properties or functions. The source code is publicly available at https://github.com/idruglab/hignn.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Interior estimates for Monge-Ampère type fourth order equations

In this paper, we give several new approaches to study interior estimates for a class of fourth order equations of Monge-Ampère type. First, we prove interior estimates for the homogeneous equation in dimension two by using the partial Legendre transform. As an application, we obtain a new proof of the Bernstein theorem without using Caffarelli-Gutiérrez's estimate, including the Chern conjecture on affine maximal surfaces. For the inhomogeneous equation, we also obtain a new proof in dimension two by an integral method relying on the Monge-Ampère Sobolev inequality. This proof works even when the right hand side is singular. In higher dimensions, we obtain the interior regularity in terms of integral bounds on the second derivatives and the inverse of the determinant.

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preprint2022arXiv

LAI Estimation of Cucumber Crop Based on Improved Fully Convolutional Network

LAI (Leaf Area Index) is of great importance for crop yield estimation in agronomy. It is directly related to plant growth status, net assimilation rate, plant photosynthesis, and carbon dioxide in the environment. How to measure LAI accurately and efficiently is the key to the crop yield estimation problem. Manual measurement consumes a lot of human resources and material resources. Remote sensing technology is not suitable for near-Earth LAI measurement. Besides, methods based on traditional digital image processing are greatly affected by environmental noise and image exposure. Nowadays, deep learning is widely used in many fields. The improved FCN (Fully Convolutional Network) is proposed in our study for LAI measure task. Eighty-two cucumber images collected from our greenhouse are labeled to fine-tuning the pre-trained model. The result shows that the improved FCN model performs well on our dataset. Our method's mean IoU can reach 0.908, which is 11% better than conventional methods and 4.7% better than the basic FCN model.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Quantum Criticality and Spin Liquid Phase in the Shastry-Sutherland model

Using the density-matrix renormalization group method for the ground state and excitations of the Shastry- Sutherland spin model, we demonstrate the existence of a narrow quantum spin liquid phase between the previously known plaquette-singlet and antiferromagnetic states. Our conclusions are based on finite-size scaling of excited level crossings and order parameters. Together with previous results on candidate models for deconfined quantum criticality and spin liquid phases, our results point to a unified quantum phase diagram where the deconfined quantum-critical point separates a line of first-order transitions and a gapless spin liquid phase. The frustrated Shastry-Sutherland model is close to the critical point but slightly inside the spin liquid phase, while previously studied unfrustrated models cross the first-order line. We also argue that recent heat capacity measurements in SrCu2(BO3)2 show evidence of the proposed spin liquid at pressures between 2.6 and 3 GPa.

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preprint2022arXiv

Quantum spin liquid phase in the Shastry-Sutherland model detected by an improved level spectroscopic method

We study the spin-$1/2$ two-dimensional Shastry-Sutherland spin model by exact diagonalization of clusters with periodic boundary conditions. We develop an improved level spectroscopic technique using energy gaps between states with different quantum numbers. The crossing points of some of the relative (composite) gaps have much weaker finite-size drifts than the normally used gaps defined only with respect to the ground state, thus allowing precise determination of quantum critical points even with small clusters. Our results support the picture of a spin liquid phase intervening between the well known plaquette-singlet and antiferromagnetic ground states, with phase boundaries in almost perfect agreement with a recent density matrix renormalization group study, where much larger cylindrical lattices were used [J. Yang et al., Phys. Rev. B {\bf 105}, L060409 (2022)]. The method of using composite low-energy gaps to reduce scaling corrections has potentially broad applications in numerical studies of quantum critical phenomena.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Temporal Convolution Domain Adaptation Learning for Crops Growth Prediction

Existing Deep Neural Nets on crops growth prediction mostly rely on availability of a large amount of data. In practice, it is difficult to collect enough high-quality data to utilize the full potential of these deep learning models. In this paper, we construct an innovative network architecture based on domain adaptation learning to predict crops growth curves with limited available crop data. This network architecture overcomes the challenge of data availability by incorporating generated data from the developed crops simulation model. We are the first to use the temporal convolution filters as the backbone to construct a domain adaptation network architecture which is suitable for deep learning regression models with very limited training data of the target domain. We conduct experiments to test the performance of the network and compare our proposed architecture with other state-of-the-art methods, including a recent LSTM-based domain adaptation network architecture. The results show that the proposed temporal convolution-based network architecture outperforms all benchmarks not only in accuracy but also in model size and convergence rate.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

A Deep Learning-Based Approach to Extracting Periosteal and Endosteal Contours of Proximal Femur in Quantitative CT Images

Automatic CT segmentation of proximal femur is crucial for the diagnosis and risk stratification of orthopedic diseases; however, current methods for the femur CT segmentation mainly rely on manual interactive segmentation, which is time-consuming and has limitations in both accuracy and reproducibility. In this study, we proposed an approach based on deep learning for the automatic extraction of the periosteal and endosteal contours of proximal femur in order to differentiate cortical and trabecular bone compartments. A three-dimensional (3D) end-to-end fully convolutional neural network, which can better combine the information between neighbor slices and get more accurate segmentation results, was developed for our segmentation task. 100 subjects aged from 50 to 87 years with 24,399 slices of proximal femur CT images were enrolled in this study. The separation of cortical and trabecular bone derived from the QCT software MIAF-Femur was used as the segmentation reference. We randomly divided the whole dataset into a training set with 85 subjects for 10-fold cross-validation and a test set with 15 subjects for evaluating the performance of models. Two models with the same network structures were trained and they achieved a dice similarity coefficient (DSC) of 97.87% and 96.49% for the periosteal and endosteal contours, respectively. To verify the excellent performance of our model for femoral segmentation, we measured the volume of different parts of the femur and compared it with the ground truth and the relative errors between predicted result and ground truth are all less than 5%. It demonstrated a strong potential for clinical use, including the hip fracture risk prediction and finite element analysis.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Balancing Common Treatment and Epidemic Control in Medical Procurement during COVID-19: Transform-and-Divide Evolutionary Optimization

Balancing common disease treatment and epidemic control is a key objective of medical supplies procurement in hospitals during a pandemic such as COVID-19. This problem can be formulated as a bi-objective optimization problem for simultaneously optimizing the effects of common disease treatment and epidemic control. However, due to the large number of supplies, difficulties in evaluating the effects, and the strict budget constraint, it is difficult for existing evolutionary multiobjective algorithms to efficiently approximate the Pareto front of the problem. In this paper, we present an approach that first transforms the original high-dimensional, constrained multiobjective optimization problem to a low-dimensional, unconstrained multiobjective optimization problem, and then evaluates each solution to the transformed problem by solving a set of simple single-objective optimization subproblems, such that the problem can be efficiently solved by existing evolutionary multiobjective algorithms. We applied the transform-and-divide evolutionary optimization approach to six hospitals in Zhejiang Province, China, during the peak of COVID-19. Results showed that the proposed approach exhibits significantly better performance than that of directly solving the original problem. Our study has also shown that transform-and-divide evolutionary optimization based on problem-specific knowledge can be an efficient solution approach to many other complex problems and, therefore, enlarge the application field of evolutionary algorithms.

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preprint2020arXiv

Existence of a Spectral Gap in the Affleck-Kennedy-Lieb-Tasaki Model on the Hexagonal Lattice

The $S=1$ Affleck-Kennedy-Lieb-Tasaki (AKLT) quantum spin chain was the first rigorous example of an isotropic spin system in the Haldane phase. The conjecture that the $S=3/2$ AKLT model on the hexagonal lattice is also in a gapped phase has remained open, despite being a fundamental problem of ongoing relevance to condensed-matter physics and quantum information theory. Here we confirm this conjecture by demonstrating the size-independent lower bound $Δ>0.006$ on the spectral gap of the hexagonal model with periodic boundary conditions in the thermodynamic limit. Our approach consists of two steps combining mathematical physics and high-precision computational physics. We first prove a mathematical finite-size criterion which gives an analytical, size-independent bound on the spectral gap if the gap of a particular cut-out subsystem of 36 spins exceeds a certain threshold value. Then we verify the finite-size criterion numerically by performing state-of-the-art DMRG calculations on the subsystem.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Experimental and modelling evidence for structural crossover in supercritical CO$_2$

Physics of supercritical state is understood to a much lesser degree compared to subcritical liquids. Carbon dioxide in particular has been intensely studied, yet little is known about the supercritical part of its phase diagram. Here, we combine neutron scattering experiments and molecular dynamics simulations and demonstrate the structural crossover at the Frenkel line. The crossover is seen at pressures as high as 14 times the critical pressure and is evidenced by changes of the main features of the structure factor and pair distribution functions.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Quantum phases of SrCu2(BO3)2 from high-pressure thermodynamics

We report heat capacity measurements of SrCu$_2$(BO$_3$)$_2$ under high pressure along with simulations of relevant quantum spin models and map out the $(P,T)$ phase diagram of the material. We find a first-order quantum phase transition between the low-pressure quantum dimer paramagnet and a phase with signatures of a plaquette-singlet state below T = $2$ K. At higher pressures, we observe a transition into a previously unknown antiferromagnetic state below $4$ K. Our findings can be explained within the two-dimensional Shastry-Sutherland quantum spin model supplemented by weak inter-layer couplings. The possibility to tune SrCu$_2$(BO$_3$)$_2$ between the plaquette-singlet and antiferromagnetic states opens opportunities for experimental tests of quantum field theories and lattice models involving fractionalized excitations, emergent symmetries, and gauge fluctuations.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Volterra mortality model: Actuarial valuation and risk management with long-range dependence

While abundant empirical studies support the long-range dependence (LRD) of mortality rates, the corresponding impact on mortality securities are largely unknown due to the lack of appropriate tractable models for valuation and risk management purposes. We propose a novel class of Volterra mortality models that incorporate LRD into the actuarial valuation, retain tractability, and are consistent with the existing continuous-time affine mortality models. We derive the survival probability in closed-form solution by taking into account of the historical health records. The flexibility and tractability of the models make them useful in valuing mortality-related products such as death benefits, annuities, longevity bonds, and many others, as well as offering optimal mean-variance mortality hedging rules. Numerical studies are conducted to examine the effect of incorporating LRD into mortality rates on various insurance products and hedging efficiency.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

A tensor product state approach to spin-1/2 square $J_1$-$J_2$ antiferromagnetic Heisenberg model: evidence for deconfined quantum criticality

The ground state phase of spin-1/2 $J_1$-$J_2$ antiferromagnetic Heisenberg model on square lattice around the maximally frustrated regime ($J_2\sim 0.5J_1$) has been debated for decades. Here we study this model using the cluster update algorithm for tensor product states (TPSs). The ground state energies at finite sizes and in the thermodynamic limit (with finite size scaling) are in good agreement with exact diagonalization study. Through finite size scaling of the spin correlation function, we find the critical point $J_2^{c_1}=0.572(5)J_1$ and critical exponents $ν=0.50(8)$, $η_s=0.28(6)$. In the range of $0.572 < J_2/J_1 \leqslant 0.6 $ we find a paramagnetic ground state with exponentially decaying spin-spin correlation. Up to $24\times 24$ system size, we observe power law decaying dimer-dimer and plaquette-plaquette correlations with an anomalous plaquette scaling exponent $η_p=0.24(1)$ and an anomalous columnar scaling exponent $η_c=0.28(1)$ at $J_2/J_1=0.6$. These results are consistent with a potential gapless $U(1)$ spin liquid phase. However, since the $U(1)$ spin liquid is unstable due to the instanton effect, a VBS order with very small amplitude might develop in the thermodynamic limit. Thus, our numerical results strongly indicate a deconfined quantum critical point (DQCP) at $J_2^{c_1}$. Remarkably, all the observed critical exponents are consistent with the $J-Q$ model.

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preprint2015arXiv

Numerical detection of symmetry enriched topological phases with space group symmetry

Topologically ordered phases of matter, in particular so-called symmetry enriched topological (SET) phases, can exhibit quantum number fractionalization in the presence of global symmetry. In Z_2 topologically ordered states in two dimensions, fundamental translations T_x and T_y acting on anyons can either commute or anticommute. This property, crystal momentum fractionalization, can be seen in a periodicity of the excited-state spectrum in the Brillouin zone. We present a numerical method to detect the presence of this form of symmetry enrichment given a projected entangled pair state (PEPS); we study the minima of spectrum of correlation lengths of the transfer matrix for a cylinder. As a benchmark, we demonstrate our method using a modified toric code model with perturbation. An enhanced periodicity in momentum clearly reveals the anticommutation relation {T_x,T_y}=0$ for the corresponding quasiparticles in the system.

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preprint2014arXiv

Correlated valence bond state and its study of the spin-1/2 J1-J2 Anti-ferromagnetic Heisenberg model on a square lattice

We propose a class of variational wave functions, namely the correlated valence bond states, for the frustrated Hamiltonian in the paramagnetic phase. This class of wave functions admits negative amplitude and the same sub-lattice pairing when a bipartite lattice is considered, thus suffers from the negative sign problem. However if applied to small systems, the sign problem is manageable using the standard variational Monte Carlo method. We optimize the wave functions for the J1-J2 Anti ferromagnetic Heisenberg model on a square lattice in the coupling region J2/J1 \in [0.45 : 0.56] for system sizes L = 4, 6, 8. To calculate the correlation functions and the order parameters for larger systems, we make the extensive Monte Carlo samplings using the variational parameters optimized at system size L = 8. We find that the paramagnetic phase is a gap-less spin liquid in the entire range of J2/J1 \in [0.45 : 0.56] with a gap-less singlet excitation and a gaped triplet excitation.

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preprint2013arXiv

Bistatic Synthetic Aperture Radar Imaging of Moving Targets using Ultra-Narrowband Continuous Waveforms

We consider a synthetic aperture radar (SAR) system that uses ultra-narrowband continuous waveforms (CW) as an illumination source. Such a system has many practical advantages, such as the use of relatively simple, low-cost and low-power transmitters, and in some cases, using the transmitters of opportunity, such as TV, radio stations. Additionally, ultra-narrowband CW signals are suitable for motion estimation due to their ability to acquire high resolution Doppler information. In this paper, we present a novel synthetic aperture imaging method for moving targets using a bi-static SAR system transmitting ultra-narrowband continuous waveforms. Our method exploits the high Doppler resolution provided by ultra-narrowband CW signals to image both the scene reflectivity and to determine the velocity of multiple moving targets. Starting from the first principle, we develop a novel forward model based on the temporal Doppler induced by the movement of antennas and moving targets. We form the reflectivity image of the scene and estimate the motion parameters using a filtered-backprojection technique combined with a contrast optimization method. Analysis of the point spread function of our image formation method shows that reflectivity images are focused when the motion parameters are estimated correctly. We present analysis of the velocity resolution and the resolution of reconstructed reflectivity images. We analyze the error between the correct and reconstructed position of targets due to errors in velocity estimation. Extensive numerical simulations demonstrate the performance of our method and validate the theoretical results.

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preprint2013arXiv

Constructing gapless spin liquid state for the spin-1/2 J1-J2 Heisenberg model on a square lattice

We construct a class of projected entangled pair states (PEPS) which is exactly the resonating valence bond (RVB) wavefunctions endowed with both short range and long range valence bonds. With an energetically preferred RVB pattern, the wavefunction is simplified to live in a one parameter variational space. We tune this variational parameter to minimize the energy for the frustrated spin 1/2 J1-J2 antiferromagnetic Heisenberg model on the square lattice. Taking a cylindrical geometry, we are able to construct four topological sectors with even or odd number of fluxes penetrating the cylinder and even or odd number of spinons on the boundary. The energy splitting in different topological sectors is exponentially small with the cylinder perimeter. We find a power law decay of the dimer correlation function on a torus, and a lnL correction to the entanglement entropy, indicating a gapless spin liquid phase at the optimum parameter.

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preprint2012arXiv

Low-Speed ADC Sampling Based High-Resolution Compressive Channel Estimation

Broadband channel is often characterized by a sparse multipath channel where dominant multipath taps are widely separated in time, thereby resulting in a large delay spread. Traditionally, accurate channel estimation is done by sampling received signal by analog-to-digital converter (ADC) at Nyquist rate (high-speed ADC sampling) and then estimate all channel taps with high-resolution. However, traditional linear estimation methods have two mainly disadvantages: 1) demand of the high-speed ADC sampling rate which already exceeds the capability of current ADC and also the high-speed ADC is very expensive for regular wireless communications; 2) neglect the inherent channel sparsity and the low spectral efficiency wireless communication is unavoidable. To solve these challenges, in this paper, we propose a high-resolution compressive channel estimation method by using low-speed ADC sampling. Our proposed method can achieve close performance comparing with traditional sparse channel estimation methods. At the same time, the proposed method has following advantages: 1) reduce communication cost by utilizing cheap low-speed ADC; 2) improve spectral efficiency by extracting potential training signal resource. Numerical simulations confirm our proposed method using low-speed ADC sampling.

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preprint2012arXiv

Total Variation and Euler's Elastica for Supervised Learning

In recent years, total variation (TV) and Euler's elastica (EE) have been successfully applied to image processing tasks such as denoising and inpainting. This paper investigates how to extend TV and EE to the supervised learning settings on high dimensional data. The supervised learning problem can be formulated as an energy functional minimization under Tikhonov regularization scheme, where the energy is composed of a squared loss and a total variation smoothing (or Euler's elastica smoothing). Its solution via variational principles leads to an Euler-Lagrange PDE. However, the PDE is always high-dimensional and cannot be directly solved by common methods. Instead, radial basis functions are utilized to approximate the target function, reducing the problem to finding the linear coefficients of basis functions. We apply the proposed methods to supervised learning tasks (including binary classification, multi-class classification, and regression) on benchmark data sets. Extensive experiments have demonstrated promising results of the proposed methods.

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preprint2011arXiv

Cluster update for tensor network states

We propose a novel recursive way of updating the tensors in projected entangled pair states by evolving the tensor in imaginary time evolution on clusters of different sizes. This generalizes the so- called simple update method of Jiang et al. [Phys. Rev. Lett. 101, 090603 (2008)] and the updating schemes in the single layer picture of Pižorn et al. [Phys. Rev. A 83, 052321 (2011)]. A finite-size scaling of the observables as a function of the cluster size provides a remarkable improvement in the accuracy as compared to the simple update scheme. We benchmark our results on the hand of the spin 1/2 staggered dimerized antiferromagnetic model on the square lattice, and accurate results for the magnetization and the critical exponents are determined.

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preprint2011arXiv

Monte Carlo simulation with Tensor Network States

It is demonstrated that Monte Carlo sampling can be used to efficiently extract the expectation value of projected entangled pair states with large virtual bond dimension. We use the simple update rule introduced by Xiang et al. to obtain the tensors describing the ground state wavefunction of the antiferromagnetic Heisenberg model and evaluate the finite size energy and staggered magnetization for square lattices with periodic boundary conditions of sizes up to L=16 and virtual bond dimensions up to D=16. The finite size magnetization errors are 0.003(2) and 0.013(2) at D=16 for a system of size L=8,16 respectively. Finite D extrapolation provides exact finite size magnetization for L=8, and reduces the magnetization error to 0.005(3) for L=16, significantly improving the previous state of the art results.

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preprint2011arXiv

Plaquette Renormalization Scheme for Tensor Network States

We present a method for contracting a square-lattice tensor network in two dimensions, based on auxiliary tensors accomplishing successive truncations (renormalization) of 8-index tensors for 2 by 2 plaquettes into 4-index tensors. The scheme is variational, and thus the tensors can be optimized by minimizing the energy. Test results for the quantum phase transition of the transverse-field Ising model confirm that even the smallest possible tensors (two values for each tensor index at each renormalization level) produce much better results than the simple product (mean-field) state.

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preprint2011arXiv

Time evolution of projected entangled pair states in the single layer picture

We propose an efficient algorithm for simulating quantum many-body systems in two spatial dimensions using projected entangled pair states. This is done by approximating the environment, arising in the context of updating tensors in the process of time evolution, using a single-layered tensor network structure. This significantly reduces the computational costs and allows simulations in a larger submanifold of the Hilbert space as bounded by the bond dimension of the tensor network. We present numerical evidence for stability of the method on an antiferromagnetic isotropic Heisenberg model where good agreement is found with the available accurate results.

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preprint2010arXiv

Effects of edge disorder in nano-scale antiferromagnetic clusters

We study the distribution of local magnetic susceptibilities in the two-dimensional antiferromagnetic S=1/2 Heisenberg model on various random clusters, in order to determine whether effects of edge disorder could be detected in NMR experiments (through the line shape, as given by the distribution of local Knight shifts). Although the effects depend strongly on the nature of the edge and the cluster size, our results indicate that line widths broader than the average shift should be expected even in clusters as large as $\approx 1000$ lattice spacing in diameter. Experimental investigations of the NMR line width should give insights into the magnetic structure of the edges.

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preprint2010arXiv

Symmetry breaking and criticality in tensor-product states

We discuss variationally optimized matrix-product states for the transverse-field Ising chain, using D*D matrices with small D=2-10. For finite system size N there are energy minimums for symmetric as well as symmetry-broken states, which cross each other at a field value hc(N,D); thus the transition is first-order. A continuous transition develops as N->infinity. The asymptotic critical behavior is then always of mean-field type (the magnetization exponent beta=1/2), but a window of field strengths where true Ising scaling holds (beta=1/8) emerges with increasing D. We also demonstrate asymptotic mean-field behavior for infinite-size two-dimensional tensor-product (iPEPS) states with small tensors.

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preprint2009arXiv

Nature of the low-energy excitations of two-dimensional diluted Heisenberg quantum antiferromagnets

We present several different calculations pertaining to the nature of the low-energy excitations of the site-diluted S=1/2 Heisenberg antiferromagnet, in particular at the percolation point. We present a picture of excitations originating from an effective low-energy subsystem consisting of localized magnetic moments. At the percolation point, these moments lead to an anomalously large dynamic exponent; z=3.6(1). The magnetic moments are shown to originate from local sublattice imbalance, which we study quantitatively using a classical dimer-monomer model. The localization properties of triplet excitations of clusters with singlet ground state are examined using simulations in the valence bond basis. The triplet is shown to affect predominantly sites on the classical monomer regions. The number of sites affected grows as a non-trivial power of the cluster size. We also study a bilayer model, where there is no sublattice imbalance. Accordingly, we find a much smaller dynamic exponent, consistent with quantum rotor (or possibly fracton) excitations.

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preprint2006arXiv

Low-energy dynamics of the two-dimensional S=1/2 Heisenberg antiferromagnet on percolating clusters

We investigate the quantum dynamics of site diluted S=1/2 Heisenberg antiferromagnetic clusters at the percolation threshold. We use Lanczos diagonalization to calculate the lowest excitation gap Delta and, to reach larger sizes, study an upper bound for Delta obtained from sum rules involving the staggered structure factor and susceptibility, which we evaluate by quantum Monte Carlo simulations. Scaling the gap distribution with the cluster length L, Delta sim 1/L^z, we obtain a dynamic exponent z approximate 2D_f, where D_f=91/48 is the fractal dimensionality of the percolating cluster. This is in contrast to previous expectations of z=D_f. We argue that the low-energy excitations are due to weakly coupled effective moments formed due to local imbalance in sublattice occupation.

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preprint2005arXiv

High-precision finite-size scaling analysis of the quantum-critical point of S=1/2 Heisenberg antiferromagnetic bilayers

We use quantum Monte Carlo (stochastic series expansion) and finite-size scaling to study the quantum critical points of two S=1/2 Heisenberg antiferromagnets in two dimensions: a bilayer and a Kondo-lattice-like system (incomplete bilayer), each with intra- and inter-plane couplings J and J_perp. We discuss the ground-state finite-size scaling properties of three different quantities--the Binder moment ratio, the spin stiffness, and the long-wavelength magnetic susceptibility--which we use to extract the critical value of the coupling ratio g=J_perp/J. The individual estimates of g_c are consistent provided that subleading finite-size corrections are properly taken into account. In the case of the complete bilayer, the Binder ratio leads to the most precise estimate of the critical coupling, although the subleading finite-size corrections to the stiffness are considerably smaller. For the incomplete bilayer, the subleading corrections to the stiffness are extremely small, and this quantity then gives the best estimate of the critical point. Contrary to predictions, we do not find a universal prefactor of the 1/L spin stiffness scaling at the critical point, whereas the Binder ratio is consistent with a universal value. Our results for the critical coupling ratios are g_c=2.52181(3) (full bilayer) and g_c=1.38882(2) (incomplete bilayer), which represent improvements of two orders of magnitude relative to the previous best estimates. For the correlation length exponent we obtain nu = 0.7106(9), consistent with the expected 3D Heisenberg universality class.

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