Miracle-dz/UniFAR-FTUs huggingface dataset:
The heat flow, GAF, and SL(2;R)

We establish basic properties of the heat flow on entire holomorphic functions that have order at most 2. We then look specifically at the action of the heat flow on the Gaussian analytic function (GAF). We show that applying the heat flow to a GAF and then rescaling and multiplying by an exponential of a quadratic function gives another GAF. It follows that the zeros of the GAF are invariant in distribution under the heat flow, up to a simple rescaling. We then show that the zeros of the GAF evolve under the heat flow approximately along straight lines, with an error whose distribution is independent of the starting point. Finally, we connect the heat flow on the GAF to the metaplectic representation of the double cover of the group $SL(2;\mathbb{R}). $
SepicNet: Sharp Edges Recovery by Parametric Inference of Curves in 3D Shapes

3D scanning as a technique to digitize objects in reality and create their 3D models, is used in many fields and areas. Though the quality of 3D scans depends on the technical characteristics of the 3D scanner, the common drawback is the smoothing of fine details, or the edges of an object. We introduce SepicNet, a novel deep network for the detection and parametrization of sharp edges in 3D shapes as primitive curves. To make the network end-to-end trainable, we formulate the curve fitting in a differentiable manner. We develop an adaptive point cloud sampling technique that captures the sharp features better than uniform sampling. The experiments were conducted on a newly introduced large-scale dataset of 50k 3D scans, where the sharp edge annotations were extracted from their parametric CAD models, and demonstrate significant improvement over state-of-the-art methods.
Finite Temperature Dynamics of Spin Solitons with Applications in Thermocouples and Refrigerators

The exploitation of spin Berry phases to generate emergent fields for producing miniaturized and high-quality inductors has enjoyed considerable popularity among proponents of quantum technologies [Nature 586, 202 (2020)}]. Inspired by this breakthrough, we extend its mechanism to spin thermoelectrics by probing responses of ferrimagnetic domain walls (DWs) to thermal gradients. Similarly, voltages here stem from DW-spin collective motion, in contrast to normal electron transport phenomena. We further develop finite-temperature dynamics to investigate thermoelectric figures of merit and attribute corresponding quantum superiority to ultrafast spin evolution of ferrimagnetism with tunable non-Abelian phases. We propose a more likely cause of DW motion towards hot or cold regions (contrary to conclusions of previous reports) and verify existence of efficient magnon-momentum transfers. These findings deepen our understanding of heat-driven DW kinetics and suggest profitable new directions in an emerging realm of spincaloritronics.
Effect of hydraulic conductivity and permeability on drug distribution, an investigation based on a part of a real tissue

In this study, a computational simulation is employed to place two essential parameters, the permeability of vessels and hydraulic conductivity, under assessment. These parameters impact the movement of drug particles through vessels, and normal and tumoral tissue to examine the concentration of nanoparticles, interstitial pressure, and velocity. To provide a geometric model detailing the capillary network under normal and tumoral tissue conditions, the geometry is extracted via real image processing. Subsequently, the real conditions were considered to solve the equations pertaining to drug transport and intravascular and interstitial flows in the tissue. The results showed that an increase in permeability and hydraulic conductivity leads to an increase in drug concentration in the tumor. Finally, Methotrexate drug has the most effect in the treatment of tumors. Overall, the computational model for anti-cancer delivery provides a powerful tool for understanding and optimizing drug delivery strategies for the treatment of cancer.
Inelastic freeze-in

Dark matter (DM) could be a nonthermal relic that freezes in from extremely weak, sub-Hubble annihilation and decay of Standard Model (SM) particles. The case of Dirac DM freezing in via a dark photon mediator is a well-studied benchmark for DM direct detection experiments. Here, we extend prior work to take into account the possibility that DM is pseudo-Dirac with a small mass splitting. If the mass splitting is greater than twice the electron mass but less than the dark photon mass, there will be distinct cosmological signatures. The excited state $\chi_2$ is initially produced in equal abundance to the ground state $\chi_1$. Subsequently, the excited state population decays at relatively late cosmological times, primarily via the three-body process $\chi_2 \rightarrow \chi_1 e^+ e^-$. This process injects energetic electrons into the ambient environment, providing observable signatures involving Big Bang nucleosynthesis, cosmic microwave background spectral distortions and anisotropies, and the Lyman-$\alpha$ forest. Furthermore, the ground state particles that are populated from the three-body decay receive a velocity kick, with implications for DM clustering on small scales. We find that cosmological probes and accelerator experiments are highly complementary, with future coverage of much of the parameter space of the model.
Flashlights: Properties of Highly Magnified Images Near Cluster Critical Curves in the Presence of Dark Matter Subhalos

Dark matter subhalos with extended profiles and density cores, and globular star clusters of mass 106–108 M ⊙ that live near the critical curves in galaxy cluster lenses can potentially be detected through their lensing magnification of stars in background galaxies. In this work, we study the effect such subhalos have on lensed images, and compare to the case of more well-studied microlensing by stars and black holes near critical curves. We find that the cluster density gradient and the extended mass distribution of subhalos are important in determining image properties. Both lead to an asymmetry between the image properties on the positive- and negative-parity sides of the cluster that is more pronounced than in the case of microlensing. For example, on the negative-parity side, subhalos with cores larger than about 50 pc do not generate any images with magnification above ∼100 outside of the immediate vicinity of the cluster critical curve. We discuss these factors using analytical and numerical analysis, and exploit them to identify observable signatures of subhalos: Subhalos create pixel-to-pixel flux variations of ≳0.1 mag on the positive-parity side of clusters. These pixels tend to cluster around (otherwise invisible) subhalos. Unlike in the case of microlensing, signatures of subhalo lensing can be found up to 1″ away from the critical curves of massive clusters.
One Small Step for Generative AI, One Giant Leap for AGI: A Complete Survey on ChatGPT in AIGC Era

OpenAI has recently released GPT-4 (a.k.a. ChatGPT plus), which is demonstrated to be one small step for generative AI (GAI), but one giant leap for artificial general intelligence (AGI). Since its official release in November 2022, ChatGPT has quickly attracted numerous users with extensive media coverage. Such unprecedented attention has also motivated numerous researchers to investigate ChatGPT from various aspects. According to Google scholar, there are more than 500 articles with ChatGPT in their titles or mentioning it in their abstracts. Considering this, a review is urgently needed, and our work fills this gap. Overall, this work is the first to survey ChatGPT with a comprehensive review of its underlying technology, applications, and challenges. Moreover, we present an outlook on how ChatGPT might evolve to realize general-purpose AIGC (a.k.a. AI-generated content), which will be a significant milestone for the development of AGI.
When do homomorphism counts help in query algorithms?

A query algorithm based on homomorphism counts is a procedure for determining whether a given instance satisfies a property by counting homomorphisms between the given instance and finitely many predetermined instances. In a left query algorithm, we count homomorphisms from the predetermined instances to the given instance, while in a right query algorithm we count homomorphisms from the given instance to the predetermined instances. Homomorphisms are usually counted over the semiring N of non-negative integers; it is also meaningful, however, to count homomorphisms over the Boolean semiring B, in which case the homomorphism count indicates whether or not a homomorphism exists. We first characterize the properties that admit a left query algorithm over B by showing that these are precisely the properties that are both first-order definable and closed under homomorphic equivalence. After this, we turn attention to a comparison between left query algorithms over B and left query algorithms over N. In general, there are properties that admit a left query algorithm over N but not over B. The main result of this paper asserts that if a property is closed under homomorphic equivalence, then that property admits a left query algorithm over B if and only if it admits a left query algorithm over N. In other words and rather surprisingly, homomorphism counts over N do not help as regards properties that are closed under homomorphic equivalence. Finally, we characterize the properties that admit both a left query algorithm over B and a right query algorithm over B.
Investigating the asymmetric chemistry in the disk around the young star HD 142527

The atmospheric composition of planets is determined by the chemistry of the disks in which they form. Studying the gas-phase molecular composition of disks thus allows us to infer what the atmospheric composition of forming planets might be. Recent observations of the IRS 48 disk have shown that (asymmetric) dust traps can directly impact the observable chemistry, through radial and vertical transport, and the sublimation of ices. The asymmetric HD 142527 disk provides another good opportunity to investigate the role of dust traps in setting the disk's chemical composition. In this work, we use archival ALMA observations of the HD 142527 disk to obtain an as large as possible molecular inventory, which allows us to investigate the possible influence of the asymmetric dust trap on the disk's chemistry. We present the first ALMA detections of [C I], 13C18O, DCO+, H2CO and additional transition of HCO+ and CS in this disk. In addition, we have acquired upper limits for non-detected species such as SO and CH3OH. For the majority of the observed molecules, a decrement in the emission at the location of the dust trap is found. For the main CO isotopologues continuum over-subtraction likely causes the observed asymmetry, while for CS and HCN we propose that the observed asymmetries are likely due to shadows cast by the misaligned inner disk. As the emission of the observed molecules is not co-spatial with the dust trap and no SO or CH3OH are found, thermal sublimation of icy mantles does not appear to play a major role in changing the gas-phase composition of the outer disk in HD 142527 disk. Using our observations of 13C18O and DCO+ and a RADMC-3D model, we determine the CO snowline to be located beyond the dust traps, favouring cold gas-phase formation of H2CO, rather than the hydrogenation of CO-ice and subsequent sublimation.
Impact of Assimilating Wind Profiling Radar Observations on Convection-Permitting Quantitative Precipitation Forecasts during SCMREX

AbstractTo improve the prediction of heavy rainfall in southern China during the prerainy season, horizontal wind data from wind profiling radars (WPRs) were assimilated in the partial-cycle data assimilation (DA) system based on a three-dimensional variational method. The analyses from the DA system are used as initial conditions for the convection-permitting Global/Regional Assimilation and Prediction System (GRAPES) model. The impact of assimilating WPR data on the quantitative precipitation forecast (QPF) in southern China was evaluated over the period of the Southern China Monsoon Rainfall Experiment (SCMREX) in May 2014, by comparing the results of a control experiment with WPR data assimilated and a denial experiment without WPR data. The positive impact of WPR DA was significant on the forecasts of atmospheric variables in the vertical and diagnostic fields at the surface, especially those of surface wind fields in the 0–6-h range. The inclusion of WPR data also improved the QPF skill of light and.
Empirical likelihood for a class of functionals of survival distribution with censored data

The empirical likelihood was first introduced by Owen in 1990 in the complete data case.Wang applied this method to a class of functionals of survival function in the presence of censoring.In this paper, a generally adjusted empirical likelihood is defined.It is showed that the adjusted empirical likelihood asymptotically follows a chi square distribution also.Some simulation studies indicate that the better results than those of Wang may be get.
Accuracy in LP electromagnetic seismograph calibration by least-squares inversion of the calibration pulse

abstract Uncertainties in the instrumental constants for the standard LP instruments of the WWSSN, arising from errors in amplitude measurements of the calibration pulse, are analytically quantified assuming that such measurement errors may be approximated by a perturbing Gaussian noise distribution. More importantly, for the practicing seismologist, uncertainties in magnification and phase delay of the entire instrumental transfer function are deduced from least-squares inversion of the seismogram calibration pulse. It is emphasized that reliable estimates of instrumental transfer functions are obtained by least-squares inversion of the calibration pulse, particularly for underdamped or near critically damped seismographs, where the Gaussian noise distribution is the dominant source of error.
A note on Gupta's co-density conjecture

Let $G$ be a multigraph. A subset $F$ of $E(G)$ is an edge cover of $G$ if every vertex of $G$ is incident to an edge of $F$. The cover index, $\xi(G)$, is the largest number of edge covers into which the edges of $G$ can be partitioned. Clearly $\xi(G) \le \delta(G)$, the minimum degree of $G$. For $U\subseteq V(G)$, denote by $E^+(U)$ the set of edges incident to a vertex of $U$. When $|U|$ is odd, to cover all the vertices of $U$, any edge cover needs to contain at least $(|U|+1)/2$ edges from $E^+(U)$, indicating $ \xi(G) \le |E^+(U)|/ (|U|+1)/2$. Let $\rho_c(G)$, the co-density of $G$, be defined as the minimum of $|E^+(U)|/((|U|+1)/2)$ ranging over all $U\subseteq V(G)$ with $|U| $ odd and at least 3. Then $\rho_c(G)$ provides another upper bound on $\xi(G)$. Thus $\xi(G) \le \min\{\delta(G), \lfloor \rho_c(G) \rfloor \}$. For a lower bound on $\xi(G)$, in 1967, Gupta conjectured that $\xi(G) \ge \min\{\delta(G)-1, \lfloor \rho_c(G) \rfloor \}$. Gupta showed that the conjecture is true when $G$ is simple, and Cao et al. verified this conjecture when $\rho_c(G)$ is not an integer. In this note, we confirm the conjecture when the maximum multiplicity of $G$ is at most two or $ \min\{\delta(G)-1, \lfloor \rho_c(G) \rfloor \} \le 6$.
TransHP: Image Classification with Hierarchical Prompting

This paper explores a hierarchical prompting mechanism for the hierarchical image classification (HIC) task. Different from prior HIC methods, our hierarchical prompting is the first to explicitly inject ancestor-class information as a tokenized hint that benefits the descendant-class discrimination. We think it well imitates human visual recognition, i.e., humans may use the ancestor class as a prompt to draw focus on the subtle differences among descendant classes. We model this prompting mechanism into a Transformer with Hierarchical Prompting (TransHP). TransHP consists of three steps: 1) learning a set of prompt tokens to represent the coarse (ancestor) classes, 2) on-the-fly predicting the coarse class of the input image at an intermediate block, and 3) injecting the prompt token of the predicted coarse class into the intermediate feature. Though the parameters of TransHP maintain the same for all input images, the injected coarse-class prompt conditions (modifies) the subsequent feature extraction and encourages a dynamic focus on relatively subtle differences among the descendant classes. Extensive experiments show that TransHP improves image classification on accuracy (e.g., improving ViT-B/16 by +2.83% ImageNet classification accuracy), training data efficiency (e.g., +12.69% improvement under 10% ImageNet training data), and model explainability. Moreover, TransHP also performs favorably against prior HIC methods, showing that TransHP well exploits the hierarchical information. The code is available at: https://github.com/WangWenhao0716/TransHP.
Temporal Knowledge Sharing enable Spiking Neural Network Learning from Past and Future

Spiking Neural Networks (SNNs) have attracted significant attention from researchers across various domains due to their brain-like information processing mechanism. However, SNNs typically grapple with challenges such as extended time steps, low temporal information utilization, and the requirement for consistent time step between testing and training. These challenges render SNNs with high latency. Moreover, the constraint on time steps necessitates the retraining of the model for new deployments, reducing adaptability. To address these issues, this paper proposes a novel perspective, viewing the SNN as a temporal aggregation model. We introduce the Temporal Knowledge Sharing (TKS) method, facilitating information interact between different time points. TKS can be perceived as a form of temporal self-distillation. To validate the efficacy of TKS in information processing, we tested it on static datasets like CIFAR10, CIFAR100, ImageNet-1k, and neuromorphic datasets such as DVS-CIFAR10 and NCALTECH101. Experimental results demonstrate that our method achieves state-of-the-art performance compared to other algorithms. Furthermore, TKS addresses the temporal consistency challenge, endowing the model with superior temporal generalization capabilities. This allows the network to train with longer time steps and maintain high performance during testing with shorter time steps. Such an approach considerably accelerates the deployment of SNNs on edge devices. Finally, we conducted ablation experiments and tested TKS on fine-grained tasks, with results showcasing TKS's enhanced capability to process information efficiently.
Growing Pains: Understanding the Impact of Likelihood Uncertainty on Hierarchical Bayesian Inference for Gravitational-Wave Astronomy

Observations of gravitational waves emitted by merging compact binaries have provided tantalising hints about stellar astrophysics, cosmology, and fundamental physics. However, the physical parameters describing the systems, (mass, spin, distance) used to extract these inferences about the Universe are subject to large uncertainties. The current method of performing these analyses requires performing many Monte Carlo integrals to marginalise over the uncertainty in the properties of the individual binaries and the survey selection bias. These Monte Carlo integrals are subject to fundamental statistical uncertainties. Previous treatments of this statistical uncertainty has focused on ensuring the precision of the inferred inference is unaffected, however, these works have neglected the question of whether sufficient accuracy can also be achieved. In this work, we provide a practical exploration of the impact of uncertainty in our analyses and provide a suggested framework for verifying that astrophysical inferences made with the gravitational-wave transient catalogue are accurate. Applying our framework to models used by the LIGO-Virgo-Kagra collaboration, we find that Monte Carlo uncertainty in estimating the survey selection bias is the limiting factor in our ability to probe narrow populations model and this will rapidly grow more problematic as the size of the observed population increases.
Single-Stage Diffusion NeRF: A Unified Approach to 3D Generation and Reconstruction

3D-aware image synthesis encompasses a variety of tasks, such as scene generation and novel view synthesis from images. Despite numerous task-specific methods, developing a comprehensive model remains challenging. In this paper, we present SSDNeRF, a unified approach that employs an expressive diffusion model to learn a generalizable prior of neural radiance fields (NeRF) from multi-view images of diverse objects. Previous studies have used two-stage approaches that rely on pretrained NeRFs as real data to train diffusion models. In contrast, we propose a new single-stage training paradigm with an end-to-end objective that jointly optimizes a NeRF auto-decoder and a latent diffusion model, enabling simultaneous 3D reconstruction and prior learning, even from sparsely available views. At test time, we can directly sample the diffusion prior for unconditional generation, or combine it with arbitrary observations of unseen objects for NeRF reconstruction. SSDNeRF demonstrates robust results comparable to or better than leading task-specific methods in unconditional generation and single/sparse-view 3D reconstruction.6
Reduced-order particle-in-cell simulations of a high-power magnetically shielded Hall thruster

High-power magnetically shielded Hall thrusters have emerged in recent years to meet the needs of the next-generation on-orbit servicing and exploration missions. Even though a few such thrusters are currently undergoing their late-stage development and qualification campaigns, many unanswered questions yet exist concerning the behavior and evolution of the plasma in these large-size thrusters that feature an unconventional magnetic field topology. Noting the complex, multi-dimensional nature of plasma processes in Hall thrusters, high-fidelity particle-in-cell (PIC) simulations are optimal tools to study the intricate plasma behavior. Nonetheless, the significant computational cost of traditional multi-dimensional PIC schemes renders simulating the high-power thrusters without any physics-altering speed-up factors unfeasible. The novel reduced-order ‘quasi-2D’ PIC scheme enables a significant reduction in the computational cost requirement of the PIC simulations. Thus, in this article, we demonstrate the applicability of the reduced-order PIC for a cost-efficient, self-consistent study of the physics in high-power Hall thrusters by performing simulations of a 20 kW-class magnetically shielded Hall thruster along the axial-azimuthal and radial-azimuthal coordinates. The axial-azimuthal quasi-2D simulations are performed for three operating conditions in a rather simplified representation of the thruster’s inherently 3D configuration. Nevertheless, we have resolved self-consistently an unprecedented 650 µs of the discharge evolution without any ad-hoc electron mobility model, capturing several breathing cycles and approximating the experimental performance parameters with an accuracy of 70%–80% across the operating conditions. The radial-azimuthal simulations, carried out at three cross-sections corresponding to different axial locations within the discharge channel, have casted further light on the evolution of the azimuthal instabilities and the resulting variations in the electrons’ cross-field mobility and the plasma-wall interactions. Particularly, we observed the development of a long-wavelength, relatively low-frequency wave mode near the exit plane of the thruster’s channel that induces a notable electron transport and a significant ion heating.