arXiv subjects

Enzhi Li

Publications and source records attributed to Enzhi Li.

7 recordsLinked to original sources

arXiv2024

Frustrated Random Walks: A Fast Method to Compute Node Distances on Hypergraphs

A hypergraph is a generalization of a graph that arises naturally when attribute-sharing among entities is considered. Compared to graphs, hypergraphs have the distinct advantage that they contain explicit communities and are more convenient to manipulate. An open problem in hypergraph research is how to accurately and efficiently calculate node distances on hypergraphs. Estimating node distances enables us to find a node's nearest neighbors, which has important applications in such areas as recommender system, targeted advertising, etc. In this paper, we propose using expected hitting times of random walks to compute hypergraph node distances. We note that simple random walks (SRW) cannot accurately compute node distances on highly complex real-world hypergraphs, which motivates us to introduce frustrated random walks (FRW) for this task. We further benchmark our method against DeepWalk, and show that while the latter can achieve comparable results, FRW has a distinct computational advantage in cases where the number of targets is fairly small. For such cases, we show that FRW runs in significantly shorter time than DeepWalk. Finally, we analyze the time complexity of our method, and show that for large and sparse hypergraphs, the complexity is approximately linear, rendering it superior to the DeepWalk alternative.

cs.SI↗

arXiv2020

Frustrated Random Walks: A Faster Algorithm to Evaluate Node Distances on Connected and Undirected Graphs

Researchers have designed many algorithms to measure the distances between graph nodes, such as average hitting times of random walks, cosine distances from DeepWalk, personalized PageRank, etc. Successful although these algorithms are, still they are either underperforming or too time-consuming to be applicable to huge graphs that we encounter daily in this big data era. To address these issues, here we propose a faster algorithm based on an improved version of random walks that can beat DeepWalk results with more than ten times acceleration. The reason for this significant acceleration is that we can derive an analytical formula to calculate the expected hitting times of this random walk quickly. There is only one parameter (the power expansion order) in our algorithm, and the results are robust with respect to its changes. Therefore, we can directly find the optimal solution without fine-tuning of model parameters. Our method can be widely used for fraud detection, targeted ads, recommendation systems, topic-sensitive search, etc.

cs.DM↗

arXiv2019

Schwinger-Dyson Equation Method to Calculate Total Energy in Periodic Anderson Model with Electron-Phonon Interactions

We have recently employed periodic Anderson model with electron-phonon interactions to describe Cerium volume collapse ($γ\rightarrow α$ transition) under pressure. To describe the volume collapse transition in Cerium, we have tried to plot the pressure versus volume curves and see when a kink structure emerges. One way to obtain the pressure versus volume curve is to calculate the total energy of the system at different temperatures. In order to solve the periodic Anderson model with electron-phonon interactions, we have used the continuous time quantum Monte Carlo algorithm by integrating out the phonons to obtain a retarded electron-electron interaction. Monte Carlo simulation results give us the model's electronic Green function and self energy, from which we can calculate the system's total energy. A well known formula for calculating total energy through the knowledge of electron's self energy and Green function is derived from the model's Hamiltonian, which is not available for our case. Here, we have devised a new method to derive the total energy formula purely from a path integral description of the system, without resort to its Hamiltonian formulation. Since not all systems can be described by a Hamiltonian, thus our method has a wider applicability. It is noteworthy that the total energy formula that we derived here takes an identical form with that obtained from a model's Hamiltonian.

cond-mat.str-el↗

arXiv2019

Periodic Anderson model with Holstein phonons for the description of the Cerium volume collapse

Recent experiments have suggested that the electron-phonon coupling may play an important role in the $γ\rightarrow α$ volume collapse transition in Cerium. A minimal model for the description of such transition is the periodic Anderson model. In order to better understand the effect of the electron-phonon interaction on the volume collapse transition, we study the periodic Anderson model with coupling between Holstein phonons and electrons in the conduction band. We find that the electron-phonon coupling enhances the volume collapse, which is consistent with experiments in Cerium. While we start with the Kondo Volume Collapse scenario in mind, our results capture some interesting features of the Mott scenario, such as a gap in the conduction electron spectra which grows with the effective electron-phonon coupling.

cond-mat.str-el↗

arXiv2018

Integral Equation Approach to Stationary Stochastic Counting Process with Independent Increments

Stationary stochastic processes with independent increments, of which the Poisson process is a prominent example, are widely used to describe real world events. With the basic assumption that a counting process is stationary and has independent increments, here I derive two integral equations to capture the time evolution of any such process. In order to solve these two integral equations explicitly, I need to introduce one more restriction condition. For sake of simplicity, I have imposed the Poisson condition on the two equations and successfully reproduced the renown Poisson results. The methods proposed here may also be applicable for investigating other stationary processes with independent increments.

math.PR↗

arXiv2018

Suppression of Overfitting in Extraction of Spectral Data from Imaginary Frequency Green Function Using Maximum Entropy Method

Although maximum entropy method (maxEnt method) is currently the standard algorithm for extracting real frequency information from imaginary frequency Green function, still this method is beset with overfitting problem, which manifests itself as the spurious spikes in the resultant spectral functions. To address this issue and motivated by the regularization techniques widely used in machine learning and statistics, here we propose to add one more regularization term into the original maxEnt loss function to suppress these redundant spikes. The essence of this extra regularization term is to demand that the resultant spectral functions should pay a price for being spiky. We test our algorithm with both artificial and real data, and find that spurious spikes in the resultant spectral functions can be effectively suppressed by this method.

physics.comp-ph↗

arXiv2018

Variational Neural Networks: Every Layer and Neuron Can Be Unique

The choice of activation function can significantly influence the performance of neural networks. The lack of guiding principles for the selection of activation function is lamentable. We try to address this issue by introducing our variational neural networks, where the activation function is represented as a linear combination of possible candidate functions, and an optimal activation is obtained via minimization of a loss function using gradient descent method. The gradient formulae for the loss function with respect to these expansion coefficients are central for the implementation of gradient descent algorithm, and here we derive these gradient formulae.

cs.LG↗