arXiv subjects

Lei You

Publications and source records attributed to Lei You.

At least 37 records · Page 2Linked to original sources

arXiv2025

Thermodynamic properties and Joule-Thomson expansion of AdS black hole with Gaussian distribution in non-commutative geometry

The thermodynamics and Joule-Thomson expansion of anti-de Sitter black hole (AdS BH) with Gaussian distribution in non-commutative geometry is systematically studied. The metric of Gaussian-distributed BH is obtained, showing a dS geometry at the core of BH. The research indicates that the BH characterized by a Gaussian distribution exhibit thermodynamic properties that are remarkably similar to those of BH with a Lorentzian distribution in non-commutative geometry. This similarity is specifically manifested in the small BH-large BH phase transition, the corrected first law of thermodynamics, the criticality, the heat capacity, the zeroth-order phase transition and the Joule-Thomson process. Notably, the critical ratio of Gaussian-distributed BH (0.46531) is significantly larger than those observed in Van der Waals fluids (0.375), and indeed, it is also substantially exceed those of Lorentzian-distributed BH (0.36671). Moreover, compared to the case of Lorentzian source, the zeroth-order phase transition effect in Gaussian-distributed BH is exceedingly subtle (accompanied by a relative increase in the Gibbs free energy on the order of $10^{-3}\!\sim\!\!10^{-2}$) and is difficult to detect distinctly.

gr-qc↗

arXiv2025

Distributional Counterfactual Explanations With Optimal Transport

Counterfactual explanations (CE) are the de facto method for providing insights into black-box decision-making models by identifying alternative inputs that lead to different outcomes. However, existing CE approaches, including group and global methods, focus predominantly on specific input modifications, lacking the ability to capture nuanced distributional characteristics that influence model outcomes across the entire input-output spectrum. This paper proposes distributional counterfactual explanation (DCE), shifting focus to the distributional properties of observed and counterfactual data, thus providing broader insights. DCE is particularly beneficial for stakeholders making strategic decisions based on statistical data analysis, as it makes the statistical distribution of the counterfactual resembles the one of the factual when aligning model outputs with a target distribution\textemdash something that the existing CE methods cannot fully achieve. We leverage optimal transport (OT) to formulate a chance-constrained optimization problem, deriving a counterfactual distribution aligned with its factual counterpart, supported by statistical confidence. The efficacy of this approach is demonstrated through experiments, highlighting its potential to provide deeper insights into decision-making models.

cs.AI↗

arXiv2025

Thermodynamics of Schwarzschild-AdS black hole in non-commutative geometry

In this paper, we study the thermodynamics of Schwarzschild-anti-de Sitter black holes within the framework of non-commutative geometry. By solving the Einstein's equations, we derive the corrected Schwarzschild-AdS black hole with Lorentzian distribution and analyze the thermodynamics. Our results confirm that if the energy-momentum tensor outside the event horizon is related to the mass of the black hole, the conventional first law of thermodynamics will be violated. The study of criticality reveals that the black hole undergoes a small black hole-large black hole phase transition similar to that of the Van der Waals system, with a critical point and a critical ratio slightly smaller than that of the Van der Waals fluid. As the non-commutative parameter increases, the phase transition process shortens, leading to a critical point, and ultimately to the disappearance of the phase transition. The violation of the conventional first law results in a discontinuity of the Gibbs free energy during the phase transition, indicating the occurrence of zeroth-order phase transition. Moreover, we investigate the Joule-Thomson expansion, obtaining the minimum inversion temperature and the minimum inversion mass.

gr-qc↗

arXiv2024

Thermodynamics of AdS-Schwarzschild-like black hole in loop quantum gravity

We obtained the metric of the Schwarzschild-like black hole with loop quantum gravity (LQG) corrections in anti-de Sitter (AdS) space-time, under the assumption that the cosmological constant is decoupled in LQG. We investigated its thermodynamics, including the equation of state, criticality, heat capacity, and Gibbs free energy. The $P-v$ graph was plotted, and the critical behavior was calculated. It was found that, due to the LQG effect, the quantum-corrected Schwarzschild-AdS black hole exhibits a critical point and a critical ratio of $7/18$, which differs from the Reissner-Nordstr$\ddot{\mathrm{o}}$m-AdS black hole's ratio of $3/8$ (the same as that of the Van der Waals system) slightly. However, there are still some similarities compared to the Van der Waals system, such as the same critical exponents and a similar $P-v$ graph. Moreover, it is concluded that the energy-momentum tensor related to the black hole's mass could violate the conventional first law of thermodynamics. This modified first law may violate the conservation of Gibbs free energy during the small black hole-large black hole phase transitions, potentially indicating the occurrence of the zeroth-order phase transition. The Joule-Thomson expansion was also studied. Interestingly, compared to the Schwarzschild-AdS black hole, the LQG effect leads to inversion points. The inversion curve divides the $\left(P,T\right)$ coordinate system into two regions: a heating region and a cooling region, as shown in detail by the inversion curves and isenthalpic curves. The results indicated that there is a minimum inversion mass, below which any black hole will not possess an inversion point.

gr-qc↗

arXiv2024

Thermal chaos of quantum-corrected-AdS black hole in the extended phase space

We briefly analyzed the equation of state and critical points of the quantum-corrected Schwarzschild-like black hole and used the Melnikov method to study its thermal chaotic behavior in the extended phase space of flat, closed, and open universes. The results show that the black hole's thermodynamic behavior is similar to that of the Van der Waals system. Although the critical ratios at the critical points differ among the three universes, they are all independent of the quantum correction parameter. For chaos, time perturbations will lead to chaotic behavior when their amplitude exceeds a critical value that depends on the quantum correction parameter and the radius of the dust sphere in the FRW model. Based on this, we found that the chaotic behavior of the black hole varies across different universes depending on the quantum correction parameter, but this parameter always makes chaos more likely. Using the value of the quantum correction parameter determined by Meissner, chaos is always more difficult to occur in an open universe compared to the other two types of universes. Which universe is most prone to chaos depends on the radius of the dust sphere. Finally, chaotic behavior is always present under spatial perturbations.

gr-qc↗

arXiv2024

Self-Supervised Learning of Time Series Representation via Diffusion Process and Imputation-Interpolation-Forecasting Mask

Time Series Representation Learning (TSRL) focuses on generating informative representations for various Time Series (TS) modeling tasks. Traditional Self-Supervised Learning (SSL) methods in TSRL fall into four main categories: reconstructive, adversarial, contrastive, and predictive, each with a common challenge of sensitivity to noise and intricate data nuances. Recently, diffusion-based methods have shown advanced generative capabilities. However, they primarily target specific application scenarios like imputation and forecasting, leaving a gap in leveraging diffusion models for generic TSRL. Our work, Time Series Diffusion Embedding (TSDE), bridges this gap as the first diffusion-based SSL TSRL approach. TSDE segments TS data into observed and masked parts using an Imputation-Interpolation-Forecasting (IIF) mask. It applies a trainable embedding function, featuring dual-orthogonal Transformer encoders with a crossover mechanism, to the observed part. We train a reverse diffusion process conditioned on the embeddings, designed to predict noise added to the masked part. Extensive experiments demonstrate TSDE's superiority in imputation, interpolation, forecasting, anomaly detection, classification, and clustering. We also conduct an ablation study, present embedding visualizations, and compare inference speed, further substantiating TSDE's efficiency and validity in learning representations of TS data.

cs.LG↗

arXiv2024

Decoding quantum gravity information with black hole accretion disk

The combination of Loop Quantum Gravity theory with the classical gravitational collapse model has effectively addressed the singularity problem of black holes and predicted the emergence of white holes in the late stages of collapse. The quantum extension of Kruskal spacetime suggests that the appearance of white holes may carry information from companion black holes in the universe earlier than ours. Photons emitted from the accretion disk of companion black holes will enter the companion black hole, traverse through quantum regions from the white hole to our universe, and produce imaging of accretion disk carrying quantum gravity information. In our work, we have obtained the accretion disk images of black hole from a universe earlier than ours, transported by a white hole within our universe, along with the positions and widths of these images exactly. Remarkably, behaviours of white hole and black hole imaging are similar in photon sphere and contrary to some cases of outside. This will provide valuable references for astronomical observations to validate quantum gravity theory.

gr-qc↗

arXiv2024

Optical properties of Euler-Heisenberg black hole in the Cold Dark Matter Halo

The optical properties of Euler-Heisenberg (EH) black hole (BH) surrounded by Cold Dark Matter (CDM) halo are investigated. By changing BH's parameters, we found that the radius of horizon r_{h} and radius of photon sphere r_{ph} will transparently increase as CDM halo parameters R and ρincrease. To show the influence of CDM halo on the BH's optical characteristics, we took two sets of R and ρwith prominent differences and plot the first four orders of images for thin accretion disk with different angle of inclination θof observer. The images with light intensity distributions using Novikov-Thorne (N-T) model are also derived, as well as the effective potential, photon orbits. Especially, analysis of intersection behaviors between photon trajectories with different impact parameters and circular time-like orbits in accretion disk will help better understand the image of thin accretion disk. Our results showed that CDM halo will make BH become more larger and dimmer distinctly.

gr-qc↗

arXiv2024

SWAP: Sparse Entropic Wasserstein Regression for Robust Network Pruning

This study addresses the challenge of inaccurate gradients in computing the empirical Fisher Information Matrix during neural network pruning. We introduce SWAP, a formulation of Entropic Wasserstein regression (EWR) for pruning, capitalizing on the geometric properties of the optimal transport problem. The ``swap'' of the commonly used linear regression with the EWR in optimization is analytically demonstrated to offer noise mitigation effects by incorporating neighborhood interpolation across data points with only marginal additional computational cost. The unique strength of SWAP is its intrinsic ability to balance noise reduction and covariance information preservation effectively. Extensive experiments performed on various networks and datasets show comparable performance of SWAP with state-of-the-art (SoTA) network pruning algorithms. Our proposed method outperforms the SoTA when the network size or the target sparsity is large, the gain is even larger with the existence of noisy gradients, possibly from noisy data, analog memory, or adversarial attacks. Notably, our proposed method achieves a gain of 6% improvement in accuracy and 8% improvement in testing loss for MobileNetV1 with less than one-fourth of the network parameters remaining.

cs.AI↗

arXiv2023

Less Carbon Footprint in Edge Computing by Joint Task Offloading and Energy Sharing

In sprite the state-of-the-art, significantly reducing carbon footprint (CF) in communications systems remains urgent. We address this challenge in the context of edge computing. The carbon intensity of electricity supply largely varies spatially as well as temporally. This, together with energy sharing via a battery management system (BMS), justifies the potential of CF-oriented task offloading, by redistributing the computational tasks in time and space. In this paper, we consider optimal task scheduling and offloading, as well as battery charging to minimize the total CF. We formulate this CF minimization problem as an integer linear programming model. However, we demonstrate that, via a graph-based reformulation, the problem can be cast as a minimum-cost flow problem. This finding reveals that global optimum can be admitted in polynomial time. Numerical results using real-world data show that optimization can reduce up to 83.3% of the total CF.

cs.DC↗

arXiv2023

Weighted Sum-Rate Maximization With Causal Inference for Latent Interference Estimation

The paper investigates the weighted sum-rate maximization (WSRM) problem with latent interfering sources outside the known network, whose power allocation policy is hidden from and uncontrollable to optimization. The paper extends the famous alternate optimization algorithm weighted minimum mean square error (WMMSE) [1] under a causal inference framework to tackle with WSRM. Specifically, with the possibility of power policy shifting in the hidden network, computing an iterating direction based only on the observed interference inherently implies that counterfactual is ignored in decision making. A method called synthetic control (SC) is used to estimate the counterfactual. For any link in the known network, SC constructs a convex combination of the interference on other links and uses it as an estimate for the counterfactual. Power iteration in the proposed SC-WMMSE is performed taking into account both the observed interference and its counterfactual. SC-WMMSE requires no more information than the original WMMSE in the optimization stage. To our best knowledge, this is the first paper explores the potential of SC in assisting mathematical optimization in addressing classic wireless optimization problems. Numerical results suggest the superiority of the SC-WMMSE over the original in both convergence and objective.

cs.IT↗

arXiv2021

Gaussian Mixture Model Based Distributionally Robust Optimal Power Flow With CVaR Constraints

This paper proposes a distributionally robust optimal power flow (OPF) model for transmission grids with wind power generation. The model uses the conditional value-at-risk (CVaR) constraints to control the reserve and branch flow limit violations caused by wind power forecast errors. Meanwhile, the Gaussian mixture model (GMM) is integrated into the CVaR constraints to guard against the non-Gaussian forecast error distributions. Unlike the previous studies considering the GMM with fixed parameters, this paper allows the GMM parameters to be variable within some credible regions and develops a data-driven GMM-based ambiguity set to achieve the distributional robustness. Also, rather than using the traditional sample-based approximation of CVaR with high computational burden, this paper designs a scalable cutting-plane algorithm to handle the distributionally robust CVaR constraints. Case studies on the IEEE 2736-bus system show the effectiveness and scalability of the proposed OPF model.

eess.SY↗

arXiv2021

User-centric Performance Optimization with Remote Radio Head Cooperation in C-RAN

In a cloud radio access network (C-RAN), distributed remote radio heads (RRHs) are coordinated by baseband units (BBUs) in the cloud. The centralization of signal processing provides flexibility for coordinated multi-point transmission (CoMP) of RRHs to cooperatively serve user equipments (UEs). We target enhancing UEs' capacity performance, by jointly optimizing the selection of RRHs for serving UEs, i.e., resource allocation (and CoMP selection). We analyze the computational complexity of the problem. Next, we prove that under fixed CoMP selection, the optimal resource allocation amounts to solving a so-called iterated function. Towards user-centric network optimization, we propose an algorithm for the joint optimization problem, aiming at maximumly scaling up the capacity for any target UE group of interest. The proposed algorithm enables network-level performance evaluation for quality of experience.

cs.IT↗

arXiv2020

Resource Optimization with Load Coupling in Multi-cell NOMA

Optimizing non-orthogonal multiple access (NOMA) in multi-cell scenarios is much more challenging than the single-cell case because inter-cell interference must be considered. Most papers addressing NOMA consider a single cell. We take a significant step of analyzing NOMA in multi-cell scenarios. We explore the potential of NOMA networks in achieving optimal resource utilization with arbitrary topologies. Towards this goal, we investigate a broad class of problems consisting in optimizing power allocation and user pairing for any cost function that is monotonically increasing in time-frequency resource consumption. We propose an algorithm that achieves global optimality for this problem class. The basic idea is to prove that solving the joint optimization problem of power allocation, user pair selection, and time-frequency resource allocation amounts to solving a so-called iterated function without a closed form. We prove that the algorithm approaches optimality with fast convergence. Numerically, we evaluate and demonstrate the performance of NOMA for multi-cell scenarios in terms of resource efficiency and load balancing.

cs.IT↗

arXiv2020

A Note on Decoding Order in User Grouping and Power Optimization for Multi-Cell NOMA with Load Coupling

In this technical note, we present a new theoretical result for resource optimization with non-orthogonal multiple access (NOMA). For multi-cell scenarios, a so-called load-coupling model has been proposed to characterize the presence of mutual interference for NOMA, and resource optimization relies on the use of fixed-point iterations [1], [2] across cells. One difficulty here is that the order of decoding for successive interference cancellation (SIC) in NOMA is generally not known a priori. This is because the decoding order in one cell depends on interference, which, in turn, is governed by resource allocation in other cells, and vice versa. To achieve convergence, previous works have used workarounds that pose restrictions to NOMA, such that the SIC decoding order remains in optimization. As a comment to [1], [2], we derive and prove the following result: The convergence is guaranteed, even if the order changes over the iterations. The result not only waives the need of previous workarounds, but also implies that a wide class of resource optimization problems for multi-cell NOMA is tractable, as long as that for single cell is.

cs.IT↗

arXiv2018

Resource Optimization with Flexible Numerology and Frame Structure for Heterogeneous Services

We explore the potential of optimizing resource allocation with flexible numerology in frequency domain and variable frame structure in time domain, in presence of services with different types of requirements. We analyze the computational complexity and propose a scalable optimization algorithm based on searching in both the primal space and dual space that are complementary to each other. Numerical results show significant advantages of adopting flexibility in both time and frequency domains for capacity enhancement and meeting the requirements of mission critical services.

cs.IT↗

arXiv2018

Device Caching for Network Offloading: Delay Minimization with Presence of User Mobility

A delay-optimal caching problem (DOCP) in deviceto- device (D2D) networks with moblity is modelled. The problem arises in the context of achieving offloading using device caching, and the offloading effect is represented by the expected network load ratio (NLR) which is the percentage of data that has to be downloaded from the network. Compared with the related studies, this work considers minimizing delay with NLR guarantee in mobility scenarios. A lower bound of global optimum is derived, thus enabling performance benchmarking of any sub-optimal algorithm. For problem-solving, an effective search algorithm (ESA) is proposed based on the bound. Simulations are conducted to evaluate the effectiveness of the ESA algorithm.

cs.NI↗

arXiv2017

A Framework for Optimizing Multi-cell NOMA: Delivering Demand with Less Resource

Non-orthogonal multiple access (NOMA) allows multiple users to simultaneously access the same time-frequency resource by using superposition coding and successive interference cancellation (SIC). Thus far, most papers on NOMA have focused on performance gain for one or sometimes two base stations. In this paper, we study multi-cell NOMA and provide a general framework for user clustering and power allocation, taking into account inter-cell interference, for optimizing resource allocation of NOMA in multi-cell networks of arbitrary topology. We provide a series of theoretical analysis, to algorithmically enable optimization approaches. The resulting algorithmic notion is very general. Namely, we prove that for any performance metric that monotonically increases in the cells' resource consumption, we have convergence guarantee for global optimum. We apply the framework with its algorithmic concept to a multi-cell scenario to demonstrate the gain of NOMA in achieving significantly higher efficiency.

cs.IT↗