An asymptotic local-global theorem on heights of some Kleinian group orbits
We use circle method prove an asymptotic local-global theorem on the heights of point orbits of thin subgroups of Bianchi groups in $\mathbb H^3$.
math.NT↗
arXiv subjects
Xin Zhang
Publications and source records attributed to Xin Zhang.
Two person non-zero-sum linear-quadratic differential game with Markovian jumps in infinite horizon
This paper investigates an inhomogeneous non-zero-sum linear-quadratic (LQ, for short) differential game problem whose state process and cost functional are regulated by a Markov chain. Under the $L^2$ stabilizability framework, we first provide a sufficient condition to ensure the $L^2$-integrability of the state process and study a class of linear backward stochastic differential equation (BSDE, for short) in infinite horizon. Then, we seriously discuss the LQ problem and show that the closed-loop optimal control is characterized by the solutions to coupled algebra Riccati equations (CAREs, for short) with some stabilizing conditions and a linear BSDE. Based on those results, we further analyze the non-zero-sum stochastic differential game problem and give the closed-loop Nash equilibrium through the solution to a system of two cross-coupled CAREs and two cross-coupled BSDEs. Finally, some related numerical
math.OC↗
Conditional probability tensor decompositions for multivariate categorical response regression
In many modern regression applications, the response consists of multiple categorical random variables whose probability mass is a function of a common set of predictors. In this article, we propose a new method for modeling such a probability mass function in settings where the number of response variables, the number of categories per response, and the dimension of the predictor are large. Our method relies on a functional probability tensor decomposition: a decomposition of a tensor-valued function such that its range is a restricted set of low-rank probability tensors. This decomposition is motivated by the connection between the conditional independence of responses, or lack thereof, and their probability tensor rank. We show that the model implied by such a low-rank functional probability tensor decomposition can be interpreted in terms of a mixture of regressions and can thus be fit using maximum likelihood. We derive an efficient and scalable penalized expectation maximization algorithm to fit this model and examine its statistical properties. We demonstrate the encouraging performance of our method through both simulation studies and an application to modeling the functional classes of genes.
stat.ME↗
Fast radio burst energy function in the presence of $\rm DM_{host}$ variation
Fast radio bursts (FRBs) have been found in great numbers, but the physical mechanism of these sources is still a mystery. The redshift evolutions of the FRB energy distribution function and the volumetric rate shed light on the origin of FRBs. However, such estimations rely on the dispersion measurement (DM)-redshift ($z$) relationship. A few FRBs that have been detected recently show large excess DMs beyond the expectation from the cosmological and Milky Way contributions, which indicates large spread of DMs from their host galaxies. In this work, we adopt two lognormal-distributed ${\rm DM}_{\rm host}$ models and estimate the energy function using the non-repeating FRBs selected from the Canadian Hydrogen Intensity Mapping Experiment (CHIME)/FRB Catalog 1. By comparing the lognormal-distributed ${\rm DM}_{\rm host}$ models to a constant ${\rm DM}_{\rm host}$ model, the FRB energy function results are consistent within the measurement uncertainty. We also estimate the volumetric rate of the non-repeating FRBs in three different redshift bins. The volumetric rate shows that the trend is consistent with the stellar-mass density redshift evolution. Since the lognormal-distributed ${\rm DM}_{\rm host}$ model increases the measurement errors, the inference of FRBs tracking the stellar-mass density is nonetheless undermined.
astro-ph.HE↗
E2GNN: Efficient Graph Neural Network Ensembles for Semi-Supervised Classification
This work studies ensemble learning for graph neural networks (GNNs) under the popular semi-supervised setting. Ensemble learning has shown superiority in improving the accuracy and robustness of traditional machine learning by combining the outputs of multiple weak learners. However, adopting a similar idea to integrate different GNN models is challenging because of two reasons. First, GNN is notorious for its poor inference ability, so naively assembling multiple GNN models would deteriorate the inference efficiency. Second, when GNN models are trained with few labeled nodes, their performance are limited. In this case, the vanilla ensemble approach, e.g., majority vote, may be sub-optimal since most base models, i.e., GNNs, may make the wrong predictions. To this end, in this paper, we propose an efficient ensemble learner--E2GNN to assemble multiple GNNs in a learnable way by leveraging both labeled and unlabeled nodes. Specifically, we first pre-train different GNN models on a given data scenario according to the labeled nodes. Next, instead of directly combing their outputs for label inference, we train a simple multi-layer perceptron--MLP model to mimic their predictions on both labeled and unlabeled nodes. Then the unified MLP model is deployed to infer labels for unlabeled or new nodes. Since the predictions of unlabeled nodes from different GNN models may be incorrect, we develop a reinforced discriminator to effectively filter out those wrongly predicted nodes to boost the performance of MLP. By doing this, we suggest a principled approach to tackle the inference issues of GNN ensembles and maintain the merit of ensemble learning: improved performance. Comprehensive experiments over both transductive and inductive settings, across different GNN backbones and 8 benchmark datasets, demonstrate the superiority of E2GNN.
cs.LG↗
Exploring Text-based Realistic Building Facades Editing Applicaiton
This paper explores the utilization of diffusion models and textual guidance for achieving localized editing of building facades, addressing the escalating demand for sophisticated editing methodologies in architectural design and urban planning. Leveraging the robust generative capabilities of diffusion models, this study presents a promising avenue for realistically synthesizing and modifying architectural facades. Through iterative diffusion and text descriptions, these models adeptly capture both the intricate global and local structures inherent in architectural facades, thus effectively navigating the complexity of such designs. Additionally, the paper examines the expansive potential of diffusion models in various facets, including the generation of novel facade designs, the enhancement of existing facades, and the realization of personalized customization. Despite their promise, diffusion models encounter obstacles such as computational resource constraints and data imbalances. To address these challenges, the study introduces the innovative Blended Latent Diffusion method for architectural facade editing, accompanied by a comprehensive visual analysis of its viability and efficacy. Through these endeavors, we aims to propel forward the field of architectural facade editing, contributing to its advancement and practical application.
cs.HC↗
Spatial Heterogeneous Additive Partial Linear Model: A Joint Approach of Bivariate Spline and Forest Lasso
Identifying spatial heterogeneous patterns has attracted a surge of research interest in recent years, due to its important applications in various scientific and engineering fields. In practice the spatially heterogeneous components are often mixed with components which are spatially smooth, making the task of identifying the heterogeneous regions more challenging. In this paper, we develop an efficient clustering approach to identify the model heterogeneity of the spatial additive partial linear model. Specifically, we aim to detect the spatially contiguous clusters based on the regression coefficients while introducing a spatially varying intercept to deal with the smooth spatial effect. On the one hand, to approximate the spatial varying intercept, we use the method of bivariate spline over triangulation, which can effectively handle the data from a complex domain. On the other hand, a novel fusion penalty termed the forest lasso is proposed to reveal the spatial clustering pattern. Our proposed fusion penalty has advantages in both the estimation and computation efficiencies when dealing with large spatial data. Theoretically properties of our estimator are established, and simulation results show that our approach can achieve more accurate estimation with a limited computation cost compared with the existing approaches. To illustrate its practical use, we apply our approach to analyze the spatial pattern of the relationship between land surface temperature measured by satellites and air temperature measured by ground stations in the United States.
stat.ME↗
Early Autism Diagnosis based on Path Signature and Siamese Unsupervised Feature Compressor
Autism Spectrum Disorder (ASD) has been emerging as a growing public health threat. Early diagnosis of ASD is crucial for timely, effective intervention and treatment. However, conventional diagnosis methods based on communications and behavioral patterns are unreliable for children younger than 2 years of age. Given evidences of neurodevelopmental abnormalities in ASD infants, we resort to a novel deep learning-based method to extract key features from the inherently scarce, class-imbalanced, and heterogeneous structural MR images for early autism diagnosis. Specifically, we propose a Siamese verification framework to extend the scarce data, and an unsupervised compressor to alleviate data imbalance by extracting key features. We also proposed weight constraints to cope with sample heterogeneity by giving different samples different voting weights during validation, and we used Path Signature to unravel meaningful developmental features from the two-time point data longitudinally. We further extracted machine learning focused brain regions for autism diagnosis. Extensive experiments have shown that our method performed well under practical scenarios, transcending existing machine learning methods and providing anatomical insights for autism early diagnosis.
cs.CV↗
Revealing the working mechanism of quantum neural networks by mutual information
Quantum neural networks (QNNs) is a parameterized quantum circuit model, which can be trained by gradient-based optimizer, can be used for supervised learning, regression tasks, combinatorial optimization, etc. Although many works have demonstrated that QNNs have better learnability, generalizability, etc. compared to classical neural networks. However, as with classical neural networks, we still can't explain their working mechanism well. In this paper, we reveal the training mechanism of QNNs by mutual information. Unlike traditional mutual information in neural networks, due to quantum computing remains information conserved, the mutual information is trivial of the input and output of U operator. In our work, in order to observe the change of mutual information during training, we divide the quantum circuit (U operator) into two subsystems, discard subsystem (D) and measurement subsystem (M) respectively. We calculate two mutual information, I(Di : Mo) and I(Mi : Mo) (i and o means input or output of the corresponding subsystem), and observe their behavior during training. As the epochs increases, I(Di : Mo) gradually increases, this may means some information of discard subsystem is continuously pushed into the measurement subsystem, the information should be label-related. What's more, I(Mi : Mo) exist two-phase behavior in training process, this consistent with the information bottleneck anticipation. The first phase, I(Mi : Mo) is increasing, this means the measurement subsystem perform feature fitting. The second phase, I(Mi : Mo) is decreasing, this may means the system is generalizing, the measurement subsystem discard label-irrelevant information into the discard subsystem as many as possible. Our work discussed the working mechanism of QNNs by mutual information, further, it can be used to analyze the accuracy and generalization of QNNs.
quant-ph↗
Real-fluid Transport Property Computations Based on the Boltzmann-weighted Full-dimensional Potential Model
The intermolecular potential plays crucial roles in real-fluid interactions away from the ideal-gas equilibrium, such as supercritical fluid, high-enthalpy fluid, plasma interactions, etc. We propose a Boltzmann-weighted Full-dimensional (BWF) potential model for real-fluid computations. It includes diverse intermolecular interactions so as to determine the potential well, molecular diameter, dipole moment, polarizability of species without introducing bath gases, allowing more accurate descriptions of potential surfaces with more potential parameters. The anisotropy and temperature dependence of potential parameters are also considered by applying the Boltzmann weighting on all orientations. Through the high-level Symmetry-Adapted Perturbation Theory calculations, full-dimensional potential energy surface datasets are obtained in 432 orientations for each species. Subsequently, the Boltzmann-weighted Full-dimensional potential parameters are derived by training the dataset exceeding 5*106 data, including nonpolar and polar molecules, radicals, long-chain molecules, and ions. These BWF transport properties calculated by the BWF potential have been compared against the Lennard-Jones transport properties as well as experimental viscosity, mass diffusivity, and thermal conductivity coefficients. It shows discrepancies of viscosity coefficients within 1% and 5% for nonpolar and polar molecules, respectively. Furthermore, this potential model is applied to study radicals, long-chain molecules, and ions, for which the experimental data is rarely accessed in high accuracy. It indicates significant prediction improvements of complex interactions between various particles. The new transport properties are also embedded to predict the laminar flame speeds and the flame extinction limits of methane, dimethyl ether, and n-heptane at elevated pressures, confirming its predictivity and effectiveness.
physics.app-ph↗
Joint Service Caching, Communication and Computing Resource Allocation in Collaborative MEC Systems: A DRL-based Two-timescale Approach
Meeting the strict Quality of Service (QoS) requirements of terminals has imposed a signiffcant challenge on Multiaccess Edge Computing (MEC) systems, due to the limited multidimensional resources. To address this challenge, we propose a collaborative MEC framework that facilitates resource sharing between the edge servers, and with the aim to maximize the long-term QoS and reduce the cache switching cost through joint optimization of service caching, collaborative offfoading, and computation and communication resource allocation. The dual timescale feature and temporal recurrence relationship between service caching and other resource allocation make solving the problem even more challenging. To solve it, we propose a deep reinforcement learning (DRL)-based dual timescale scheme, called DGL-DDPG, which is composed of a short-term genetic algorithm (GA) and a long short-term memory network-based deep deterministic policy gradient (LSTM-DDPG). In doing so, we reformulate the optimization problem as a Markov decision process (MDP) where the small-timescale resource allocation decisions generated by an improved GA are taken as the states and input into a centralized LSTM-DDPG agent to generate the service caching decision for the large-timescale. Simulation results demonstrate that our proposed algorithm outperforms the baseline algorithms in terms of the average QoS and cache switching cost.
cs.NI↗
Chiral basis for qubits and spin-helix decay
We propose a qubit basis composed of transverse spin helices with kinks. Unlike the usual computational basis, this chiral basis is well suited for describing quantum states with nontrivial topology. Choosing appropriate parameters the operators of the transverse spin components, $σ_n^x$ and $σ_n^y$, become diagonal in the chiral basis, which facilitates the study of problems focused on transverse spin components. As an application, we study the temporal decay of the transverse polarization of a spin helix in the XX model that has been measured in recent cold atom experiments. We obtain an explicit universal function describing the relaxation of helices of arbitrary wavelength.
quant-ph↗
FRB dark sirens: Measuring the Hubble constant with unlocalized fast radio bursts
Fast radio bursts (FRBs) can be used to measure cosmological parameters by employing the Macquart relation. However, at present, only a small number of FRB events are localized to host galaxies with known redshifts. Inspired by the dark siren method in gravitational wave cosmology, we develop a Bayesian method to statistically measure the Hubble constant using unlocalized FRBs and galaxy catalog data, which makes it possible to constrain cosmological parameters from a large number of FRB data without known redshifts, meanwhile including the real galaxy information. We assume that the probability for a galaxy to host an FRB is proportional to the luminosity of this galaxy and use the results from the IllustrisTNG simulation as the priors of FRB host galaxy parameters. Ignoring some systematic errors, we obtain the first statistical $H_0$ measurement only using twelve unlocalized FRB events combined with the big bang nucleosynthesis result, i.e., $H_0=80.4^{+24.1}_{-19.4}$ km s$^{-1}$ Mpc$^{-1}$, ($68\%$ highest-density interval). This method can also be refined to constrain other cosmological and FRB parameters. It is applicable to well-localized FRBs that still have several potential hosts.
astro-ph.CO↗
Boosting Architectural Generation via Prompts: Report
In the realm of AI architectural design, the importance of prompts is becoming increasingly prominent. With advancements in artificial intelligence and large-scale model technology, more design tasks are being delegated to machine learning algorithms. This necessitates a method for designers to guide algorithms in producing their desired designs. Prompts serve as a guiding and motivational mechanism, playing a crucial role in AI-generated architectural design. This paper categorizes and summarizes common vocabulary used in architectural design, discussing how to craft effective prompts and their impact on the quality and creativity of generated results. Through careful prompt design, designers can better control the generated architectural design images, thereby achieving designs that are more aligned with requirements and innovative.
cs.HC↗
Hypotheses regarding Baxter's $T-Q$ relation for the periodic XYZ chain
Baxter's $T-Q$ relation for the periodic spin-$\frac12$ XYZ chain is studied. We extensively perform numerical calculations for the $T-Q$ relation and the Bethe ansatz equations. Numerical based hypotheses are then proposed to answer some open questions regarding Baxter's $T-Q$ relation and the XYZ chain.
math-ph↗
Calibration of the Cryogenic Measurement System of a Resonant Haloscope Cavity
Possible light bosonic dark matter interactions with the Standard Model photon have been searched by microwave resonant cavities. In this paper, we demonstrate the cryogenic readout system calibration of a 7.138 GHz copper cavity with a loaded quality factor $Q_l=10^4$, operated at 22 mK temperature based on a dilution refrigerator. Our readout system consists of High Electron Mobility Transistors as cryogenic amplifiers at 4 K, plus room-temperature amplifiers and a spectrum analyzer for signal power detection. We test the system with a superconducting two-level system as a single-photon source in the microwave frequency regime and report an overall 95.6 dB system gain and -71.4 dB attenuation in the cavity's input channel. The effective noise temperature of the measurement system is 7.5 K.
hep-ex↗
A spin-refrigerated cavity quantum electrodynamic sensor
Quantum sensors based on solid-state defects, in particular nitrogen-vacancy (NV) centers in diamond, enable precise measurement of magnetic fields, temperature, rotation, and electric fields. However, the sensitivity of leading NV spin ensemble sensors remains far from the intrinsic spin-projection noise limit. Here we move towards this quantum limit of performance by introducing (i) a cavity quantum electrodynamic (cQED) hybrid system operating in the strong coupling regime, which enables high readout fidelity of an NV ensemble using microwave homodyne detection; (ii) a comprehensive nonlinear model of the cQED sensor operation, including NV ensemble inhomogeneity and optical polarization; and (iii) ``spin refrigeration'' where the optically-polarized spin ensemble sharply reduces the ambient-temperature microwave thermal noise, resulting in enhanced sensitivity. Applying these advances to magnetometry, we demonstrate a broadband sensitivity of 580 fT/$\sqrt{\mathrm{Hz}}$ around 15 kHz in ambient conditions. We then discuss the implications of this model for design of future magnetometers, including devices approaching 12 fT/$\sqrt{\mathrm{Hz}}$ sensitivity. Applications of these techniques extend to the fields of gyroscope and clock technologies.
quant-ph↗
Every subcubic graph is packing $(1,1,2,2,3)$-colorable
For a sequence $S=(s_1, \ldots, s_k)$ of non-decreasing integers, a packing $S$-coloring of a graph $G$ is a partition of its vertex set $V(G)$ into $V_1, \ldots, V_k$ such that for every pair of distinct vertices $u,v \in V_i$, where $1 \le i \le k$, the distance between $u$ and $v$ is at least $s_i+1$. The packing chromatic number, $χ_p(G)$, of a graph $G$ is the smallest integer $k$ such that $G$ has a packing $(1,2, \ldots, k)$-coloring. Gastineau and Togni asked an open question ``Is it true that the $1$-subdivision ($D(G)$) of any subcubic graph $G$ has packing chromatic number at most $5$?'' and later Brešar, Klavžar, Rall, and Wash conjectured that it is true. In this paper, we prove that every subcubic graph has a packing $(1,1,2,2,3)$-coloring and it is sharp due to the existence of subcubic graphs that are not packing $(1,1,2,2)$-colorable. As a corollary of our result, $χ_p(D(G)) \le 6$ for every subcubic graph $G$, improving a previous bound ($8$) due to Balogh, Kostochka, and Liu in 2019, and we are now just one step away from fully solving the conjecture.
math.CO↗