Miracle-dz/UniFAR-FTUs huggingface dataset:
Far–field asymptotics of the Green's tensor for a transversely isotropic solid

The dynamic time–harmonic Green's tensor for a transversely isotropic homogeneous linearly elastic solid is studied. First, the representation of the Green's tensor as an integral over the unit sphere is obtained. It consists of three parts: quasi–longitudinal (P), shear–horizontal (SH) and quasi–shear (SV). Then, an exact analytical solution for the SH part in terms of elementary functions is derived. The complete far–field asymptotic approximation of P and SV parts is obtained next, using the uniform stationary phase method. For the P wave it involves the leading term of the ray series since there is only one arrival of this wave. The wave surface for the SV wave contains conical points and cuspidal edges. The asymptotic description applicable near these singular directions is derived involving the Airy and Bessel functions. The directions close to the points of tangential contact of the SH and SV sheets of the wave surface are also treated. At the end of the paper numerical results in both frequency and time domain are presented. They show that the agreement between the outputs of the asymptotic and direct numerical codes is very good throughout all regions but the former can be orders of magnitude faster.
Forbidden transition properties in the ground-state configurations of singly ionized noble gas atoms for stellar and interstellar media

High-accuracy calculations of the forbidden transition amplitudes for the np 2 P 1 / 2 → np 2 P 3 / 2 transitions with the ground-state principal quantum number n in singly charged inert gas atoms, which are of astrophysical interest, have been carried out using sophisticated relativistic many-body methods. Using these amplitudes, the line strengths, oscillator strengths and transition probabilities of the above transitions and lifetimes of the np 2 P 1 / 2 states are estimated precisely. Most of these transition wavelengths lie in the infrared region, while the corresponding Rn II line is the optical one, and they can be observed in the stellar and interstellar media, where the abundances of these ions have already been identiﬁed. The above forbidden transitions can also be very useful for astrophysical plasma diagnostics and can guide experiments to measure the lifetimes of the above np 2 P 1 / 2 states.
Methods for Default and Robust Bayesian Model Comparison: the Fractional Bayes Factor Approach

In the Bayesian approach to model selection and hypothesis testing, the Bayes factor plays a central role. However, the Bayes factor is very sensitive to prior distributions of parameters. This is a problem especially in the presence of weak prior information on the parameters of the models. The most radical consequence of this fact is that the Bayes factor is undetermined when improper priors are used. Nonetheless, extending the non‐informative approach of Bayesian analysis to model selection/testing procedures is important both from a theoretical and an applied viewpoint. The need to develop automatic and robust methods for model comparison has led to the introduction of several alternative Bayes factors. In this paper we review one of these methods: the fractional Bayes factor (O'Hagan, 1995). We discuss general properties of the method, such as consistency and coherence. Furthermore, in addition to the original, essentially asymptotic justifications of the fractional Bayes factor, we provide further finite‐sample motivations for its use. Connections and comparisons to other automatic methods are discussed and several issues of robustness with respect to priors and data are considered. Finally, we focus on some open problems in the fractional Bayes factor approach, and outline some possible answers and directions for future research.
Lipedema patients show a distinctly altered Quantitative Sensory Testing (QST) profile

Lipohyperplasia dolorosa (LiDo), also known as lipedema, is a painful subcutaneous adipose tissue disorder. While the characteristic bilateral accumulation of adipocytes in extremities sparing hands and feet is investigated, an objective characterization of pain and the sensory system of LiDo patients is missing. Accordingly, progress to overcome the unsatisfying response to pain-therapeutics of patients of this widespread, lifelong, and severe disease is missing. We characterized the sensory detection profile of painful and non-painful stimuli in 20 non-obese LiDo patients and 20 waist-to-height-ratio matched controls using the clinically approved QST-protocol of the German Research Association on Neuropathic Pain (DFNS e.V.). Further, pain-reports and participants'-psychometry was assessed using the German Pain Questionnaire. LiDo patients showed no overt psychometric abnormalities. LiDo pain appeared as somatic rather than neuropathic or psychosomatic aversive. All QST measurements were normal with the selective exception of two: The pressure pain threshold (PPT) was strongly reduced and the vibration detection threshold (VDT) was strongly increased selectively at the affected thigh. In contrast, sensory profiles at the dorsum of the hand were normal. ROC-analysis of the combination of PPT and VDT of thigh versus hand shows high sensitivity and specificity, categorizing correctly 96.5% of the measured participants as LiDo patients or healthy controls, respectively. Thus, we propose to assess both, PPT and VDT, at the painful thigh and the pain-free hand as basis to develop a combined PVTH-score for differential diagnosis as a fast and convenient bedside test for the identification of non-obese LiDo patients.
A Comprehensive Study on the Relation between the Metal Enrichment of Ionized and Atomic Gas in Star-forming Galaxies

We study the relation between the metallicities of ionized and atomic gas in star-forming galaxies at z = 0–3 using the Evolution and Assembly of GaLaxies and their Environments (EAGLE) cosmological, hydrodynamical simulations. This is done by constructing a dense grid of sight lines through the simulated galaxies and obtaining the star formation rate- and H i column density-weighted metallicities, Z SFR and Z H I, for each sightline as proxies for the metallicities of ionized and atomic gas, respectively. We find Z SFR ≳ Z H I for almost all sight lines, with their difference generally increasing with decreasing metallicity. The stellar masses of galaxies do not have a significant effect on this trend, but the positions of the sight lines with respect to the galaxy centers play an important role: the difference between the two metallicities decreases when moving toward the galaxy centers, and saturates to a minimum value in the central regions of galaxies, irrespective of redshift and stellar mass. This implies that the mixing of the two gas phases is most efficient in the central regions of galaxies where sight lines generally have high column densities of H i. However, a high H i column density alone does not guarantee a small difference between the two metallicities. In galaxy outskirts, the inefficiency of the mixing of star-forming gas with H i seems to dominate over the dilution of heavy elements in H i through mixing with the pristine gas. We find good agreement between the available observational data and the Z SFR–Z H I relation predicted by the EAGLE simulations. Though, observed regions with a nuclear starburst mode of star formation appear not to follow the same relation.
A minimal face constant rank constraint qualification for reducible conic programming

In a previous paper [R. Andreani, G. Haeser, L. M. Mito, H. Ram\'irez, T. P. Silveira. First- and second-order optimality conditions for second-order cone and semidefinite programming under a constant rank condition. Mathematical Programming, 2023. DOI: 10.1007/s10107-023-01942-8] we introduced a constant rank constraint qualification for nonlinear semidefinite and second-order cone programming by considering all faces of the underlying cone. This condition is independent of Robinson's condition and it implies a strong second-order necessary optimality condition which depends on a single Lagrange multiplier instead of the full set of Lagrange multipliers. In this paper we expand on this result in several directions, namely, we consider the larger class of $\mathcal{C}^2-$cone reducible constraints and we show that it is not necessary to consider all faces of the cone; instead a single specific face should be considered (which turns out to be weaker than Robinson's condition) in order for the first order necessary optimality condition to hold. This gives rise to a notion of facial reduction for nonlinear conic programming, that allows locally redefining the original problem only in terms of this specific face instead of the whole cone, providing a more robust formulation of the problem in which Robinson's condition holds. We were also able to prove the strong second-order necessary optimality condition in this context by considering only the subfaces of this particular face, which is a new result even in nonlinear programming.
Powers in finite unitary groups

Let $\text{U}(n,\mathbb{F}_{q^2})$ denote the subgroup of unitary matrices of the general linear group $\text{GL}(n,\mathbb{F}_{q^2})$ which fixes a Hermitian form and $M\geq 2$ an integer. This is a companion paper to the previous works where the elements of the groups $\text{GL}(n,\mathbb{F}_{q})$, $\text{Sp}(2n,\mathbb{F}_{q})$, $\text{O}^{\pm}(2n,\mathbb{F}_{q})$ and $\text{O}(2n+1,\mathbb{F}_{q})$ which has an $M$-th root in the concerned group, have been described. Here we will describe the $M$-th powers in unitary groups for the regular semisimple, semisimple and cyclic elements. Our methods are parallel to those of the Memoir ``A generating function approach to the enumeration of matrices in classical groups over finite fields"by Fulman, Neumann and Praeger.
A novel measurement of the neutron magnetic form factor from A=3 mirror nuclei

The electromagnetic form factors of the proton and neutron encode information on the spatial structure of their charge and magnetization distributions. While measurements of the proton are relatively straightforward, the lack of a free neutron target makes measurements of the neutron's electromagnetic structure more challenging and more sensitive to experimental or model-dependent uncertainties. Various experiments have attempted to extract the neutron form factors from scattering from the neutron in deuterium, with different techniques providing different, and sometimes large, systematic uncertainties. We present results from a novel measurement of the neutron magnetic form factor using quasielastic scattering from the mirror nuclei $^3$H and $^3$He, where the nuclear effects are larger than for deuterium but expected to largely cancel in the cross-section ratios. We extracted values of the neutron magnetic form factor for low-to-modest momentum transfer, $0.6<Q^2<2.9$ GeV$^2$, where existing measurements give inconsistent results. The precision and $Q^2$ range of this data allow for a better understanding of the current world's data, and suggest a path toward further improvement of our overall understanding of the neutron's magnetic form factor.
ChatLog: Recording and Analyzing ChatGPT Across Time

While there are abundant researches about evaluating ChatGPT on natural language understanding and generation tasks, few studies have investigated how ChatGPT's behavior changes over time. In this paper, we collect a coarse-to-fine temporal dataset called ChatLog, consisting of two parts that update monthly and daily: ChatLog-Monthly is a dataset of 38,730 question-answer pairs collected every month including questions from both the reasoning and classification tasks. ChatLog-Daily, on the other hand, consists of ChatGPT's responses to 1000 identical questions for long-form generation every day. We conduct comprehensive automatic and human evaluation to provide the evidence for the existence of ChatGPT evolving patterns. We further analyze the unchanged characteristics of ChatGPT over time by extracting its knowledge and linguistic features. We find some stable features to improve the robustness of a RoBERTa-based detector on new versions of ChatGPT. We will continuously maintain our project at https://github.com/THU-KEG/ChatLog.
On Propagation Characteristics of Reconfigurable Surface Wave Platform: Simulation and Experimental Verification

Reconfigurable intelligent surface (RIS) as a smart reflector is revolutionizing research for next-generation wireless communications. Complementing this is a concept of using RIS as an efficient propagation medium for potentially superior path loss characteristics. Motivated by a recent porous surface architecture that facilitates reconfigurable pathways with cavities filled with fluid metal, this paper studies the propagation characteristics of different pathway configurations in different lossy materials on the reconfigurable surface wave platform by using a commercial full electromagnetic simulation software and S-parameters experiments. This paper also looks into the best scheme to switch between a straight pathway and a $90^\circ$-bend and attempts to quantify the additional path loss when making a turn. Our experimental results verify the simulation results, showing the effectiveness of the proposed reconfigurable surface wave platform for a wide-band, low path loss and highly programmable communications.
A Simple and Efficient Parallel Laplacian Solver

A symmetric matrix is called a Laplacian if it has nonpositive off-diagonal entries and zero row sums. Since the seminal work of Spielman and Teng (2004) on solving Laplacian linear systems in nearly linear time, several algorithms have been designed for the task. Yet, the work of Kyng and Sachdeva (2016) remains the simplest and most practical sequential solver. They presented a solver purely based on random sampling and without graph-theoretic constructions such as low-stretch trees and sparsifiers. In this work, we extend the result of Kyng and Sachdeva to a simple parallel Laplacian solver with O(m log3 nlog log n) or O((m + n log5 n)log n log log n) work and O(log2 n log log n) depth using the ideas of block Cholesky factorization from Kyng et al. (2016). Compared to the best known parallel Laplacian solvers that achieve polylogarithmic depth due to Lee et al. (2015), our solver achieves both better depth and, for dense graphs, better work.
Multicast Transmission Design with Enhanced DoF for MIMO Coded Caching Systems

Integrating coded caching (CC) into multi-input multi-output (MIMO) setups significantly enhances the achievable degrees of freedom (DoF). We consider a cache-aided MIMO configuration with a CC gain $t$, where a server with $L$ Tx-antennas communicates with $K$ users, each equipped with $G$ Rx-antennas. Similar to existing works, we also extend a core CC approach, designed initially for multi-input single-output (MISO) scenarios, to the MIMO setup. However, in the proposed MIMO strategy, rather than replicating the transmit scheme from the MISO setup, the number of users $\Omega$ served in each transmission is fine-tuned to maximize DoF. As a result, an optimized DoF of ${\max_{\beta, \Omega }}{\Omega \beta}$ is achieved, where ${\beta \le \mathrm{min}\big(G,L \binom{\Omega-1}{t}}\Big/{1 + (\Omega - t-1)\binom{\Omega-1}{t}}\big)$ is the number of parallel streams decoded by each user. For the considered MIMO-CC setup, we also introduce an effective multicast transmit covariance matrix design for the symmetric rate maximization objective solved iteratively via successive convex approximation (SCA). Finally, numerical simulations verify the enhanced DoF and improved performance of the proposed design.
Wavelength-resolved reverberation mapping of intermediate-redshift quasars HE 0413-4031 and HE 0435-4312: Dissecting Mg II, optical Fe II, and UV Fe II emission regions

We present the wavelength-resolved reverberation mapping (RM) of combined MgII and UV FeII broad-line emissions for two intermediate redshifts (z$\sim$1), luminous quasars - HE 0413-4031 and HE 0435-4312, monitored by the SALT and 1-m class telescopes between 2012-2022. Through this technique, we aim to disentangle the Mg II and FeII emission regions and to build a radius-luminosity relation for UV FeII emission, which has so far remained unconstrained. Several methodologies have been applied to constrain the time delays for total MgII and FeII emissions. In addition, this technique is performed to quantify the inflow or outflow of broad-line region gas around the supermassive black hole and to disentangle the emission/emitting regions from lines produced in proximity to each other. The mean total FeII time delay is nearly equal to the mean total Mg II time delay for HE 0435-4312 suggesting a co-spatiality of their emissions. However, in HE 0413-4031, the mean FeII time delay is found to be longer than the mean MgII time delay, suggesting that FeII is produced at longer distances from the black hole. The UV Fe II R-L relation is updated with these two quasars and compared with the optical FeII relation, which suggests that the optical FeII region is located further than the UV FeII by a factor of 1.7-1.9 i.e. $R_{\rm FeII-opt}\sim(1.7-1.9)R_{\rm FeII-UV}$. We detected a weak pattern in the time delay vs. wavelength relation, suggesting that the MgII broad-line originates a bit closer to the SMBH than the UV FeII, however, the difference is not very significant. Comparison of MgII, UV, and optical FeII R-L relations suggests that the difference may be larger for lower-luminosity sources, possibly with the MgII emission originating further from the SMBH. In the future, more RM data will be acquired to put better constraints on these trends, in particular the UV FeII R-L relation.
Text-to-Audio Generation using Instruction-Tuned LLM and Latent Diffusion Model

The immense scale of the recent large language models (LLM) allows many interesting properties, such as, instruction- and chain-of-thought-based fine-tuning, that has significantly improved zero- and few-shot performance in many natural language processing (NLP) tasks. Inspired by such successes, we adopt such an instruction-tuned LLM Flan-T5 as the text encoder for text-to-audio (TTA) generation -- a task where the goal is to generate an audio from its textual description. The prior works on TTA either pre-trained a joint text-audio encoder or used a non-instruction-tuned model, such as, T5. Consequently, our latent diffusion model (LDM)-based approach TANGO outperforms the state-of-the-art AudioLDM on most metrics and stays comparable on the rest on AudioCaps test set, despite training the LDM on a 63 times smaller dataset and keeping the text encoder frozen. This improvement might also be attributed to the adoption of audio pressure level-based sound mixing for training set augmentation, whereas the prior methods take a random mix.
Rotating Bardeen black hole surrounded by perfect fluid dark matter as a particle accelerator

We study the event horizon of a rotating Bardeen black hole surrounded by perfect fluid dark matter and the black hole as a particle accelerator. The black hole is represented by four parameters: mass M, rotation parameter a, dark matter parameter α and magnetic charge g. It is interesting that when we determine the values of magnetic charge g and dark matter parameters α we can get a critical rotation parameter a E and then we get a contour plane with Δ = 0 taking three parameters as coordinates. We also derive the effective potential of the particle and the center-of-mass (CM) energy of the two particles outside the black hole by using the motion equations of the particle in the equatorial plane of the black hole. We find that the CM energy depends not only on the rotation parameter a, but also on the parameters g and α. We discuss the CM energy for two particles colliding at the black hole horizon in the extreme and non-extreme cases, respectively. It is found that the CM energy can become arbitrarily high when the angular momentum of one of the two particles is the critical angular momentum under the background of extreme black holes and there is no such result for non-extreme black holes, because the particles do not reach the black hole horizon when the angular momentum of the particles is critical angular momentum. Therefore, we prove that the rotating Bardeen black hole surrounded by perfect fluid dark matter can be used as a particle accelerator.
Asymptotics for the site frequency spectrum associated with the genealogy of a birth and death process

Consider a birth and death process started from one individual in which each individual gives birth at rate $\lambda$ and dies at rate $\mu$, so that the population size grows at rate $r = \lambda - \mu$. Lambert and Harris, Johnston, and Roberts came up with methods for constructing the exact genealogy of a sample of size $n$ taken from this population at time $T$. We use the construction of Lambert, which is based on the coalescent point process, to obtain asymptotic results for the site frequency spectrum associated with this sample. In the supercritical case $r>0$, our results extend results of Durrett for exponentially growing populations. In the critical case $r = 0$, our results parallel those that Dahmer and Kersting obtained for Kingman's coalescent.
Structure-Aware Lower Bounds and Broadening the Horizon of Tractability for QBF

The QSAT problem, which asks to evaluate a quantified Boolean formula (QBF), is of fundamental interest in approximation, counting, decision, and probabilistic complexity and is also considered the prototypical PSPACE-complete problem. As such, it has previously been studied under various structural restrictions (parameters), most notably parameterizations of the primal graph representation of instances. Indeed, it is known that QSAT remains PSPACE-complete even when restricted to instances with constant treewidth of the primal graph, but the problem admits a double-exponential fixed-parameter algorithm parameterized by the vertex cover number (primal graph). However, prior works have left a gap in our understanding of the complexity of QSAT when viewed from the perspective of other natural representations of instances, most notably via incidence graphs. In this paper, we develop structure-aware reductions which allow us to obtain essentially tight lower bounds for highly restricted instances of QSAT, including instances whose incidence graphs have bounded treedepth or feedback vertex number. We complement these lower bounds with novel algorithms for QSAT which establish a nearly-complete picture of the problem's complexity under standard graph-theoretic parameterizations. We also show implications for other natural graph representations, and obtain novel upper as well as lower bounds for QSAT under more fine-grained parameterizations of the primal graph.