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Let \mu_{M,D} be the self-similar measure generated by the positive integer M=RN^q and the product-form digit set D=\{0,1,\dots,N-1\}\oplus N^{p_1}\{0,1,\dots,N-1\}\oplus \cdots \oplus N^{p_s}\{0,1,\dots,N-1\}, where R>1, N>1, q, p_i(1\leq i\leq s) are positive integers with gcd(R,N)=1 and p_1

Obesity is widely recognized as a critical and pervasive health concern. We strive to identify important genetic risk factors from hundreds of thousands of single nucleotide polymorphisms (SNPs) for obesity. We propose and apply a novel Quantile Regression with Insight Fusion (QRIF) approach that can integrate insights from established studies or domain knowledge to simultaneously select variables and modeling for ultra-high dimensional genetic data, focusing on high conditional quantiles of body mass index (BMI) that are of most interest. We discover interesting new SNPs and shed new light on a comprehensive view of the underlying genetic risk factors for different levels of BMI. This may potentially pave the way for more precise and targeted treatment strategies. The QRIF approach intends to balance the trade-off between the prior insights and the observed data while being robust to potential false information. We further establish the desirable asymptotic properties under the challenging non-differentiable check loss functions via Huber loss approximation and nonconvex SCAD penalty via local linear approximation. Finally, we develop an efficient algorithm for the QRIF approach. Our simulation studies further demonstrate its effectiveness., Comment: This article is submitted to Journal of the American Statistical Association

Model-based methods in reinforcement learning offer a promising approach to enhance data efficiency by facilitating policy exploration within a dynamics model. However, accurately predicting sequential steps in the dynamics model remains a challenge due to the bootstrapping prediction, which attributes the next state to the prediction of the current state. This leads to accumulated errors during model roll-out. In this paper, we propose the Any-step Dynamics Model (ADM) to mitigate the compounding error by reducing bootstrapping prediction to direct prediction. ADM allows for the use of variable-length plans as inputs for predicting future states without frequent bootstrapping. We design two algorithms, ADMPO-ON and ADMPO-OFF, which apply ADM in online and offline model-based frameworks, respectively. In the online setting, ADMPO-ON demonstrates improved sample efficiency compared to previous state-of-the-art methods. In the offline setting, ADMPO-OFF not only demonstrates superior performance compared to recent state-of-the-art offline approaches but also offers better quantification of model uncertainty using only a single ADM.

Silk damping is well known in the study of cosmic microwave background (CMB) and accounts for suppression of the angular power spectrum of CMB on large angular multipoles. In this Letter, we study the effect of Silk damping on the scalar-induced gravitational waves (SIGWs). Resulting from the dissipation of cosmic fluid, the Silk damping notably suppresses the energy-density spectrum of SIGWs on scales comparable to a diffusion scale at the decoupling time of feebly-interacting particles. The effect offers a novel observable for probing the underlying particle interaction, especially for those mediated by heavy gauge bosons beyond the standard model of particles. We anticipate that pulsar timing arrays are sensitive to gauge bosons with mass $\sim10^{3}-10^{4}\,\mathrm{GeV}$, while space- and ground-based interferometers to those with mass $\sim10^7-10^{12}\,\mathrm{GeV}$, leading to essential complements to on-going and future experiments of high-energy physics., Comment: 7 pages, 2 figures, additional references added

Although supervised machine learning is popular for information extraction from clinical notes, creating large annotated datasets requires extensive domain expertise and is time-consuming. Meanwhile, large language models (LLMs) have demonstrated promising transfer learning capability. In this study, we explored whether recent LLMs can reduce the need for large-scale data annotations. We curated a manually-labeled dataset of 769 breast cancer pathology reports, labeled with 13 categories, to compare zero-shot classification capability of the GPT-4 model and the GPT-3.5 model with supervised classification performance of three model architectures: random forests classifier, long short-term memory networks with attention (LSTM-Att), and the UCSF-BERT model. Across all 13 tasks, the GPT-4 model performed either significantly better than or as well as the best supervised model, the LSTM-Att model (average macro F1 score of 0.83 vs. 0.75). On tasks with high imbalance between labels, the differences were more prominent. Frequent sources of GPT-4 errors included inferences from multiple samples and complex task design. On complex tasks where large annotated datasets cannot be easily collected, LLMs can reduce the burden of large-scale data labeling. However, if the use of LLMs is prohibitive, the use of simpler supervised models with large annotated datasets can provide comparable results. LLMs demonstrated the potential to speed up the execution of clinical NLP studies by reducing the need for curating large annotated datasets. This may result in an increase in the utilization of NLP-based variables and outcomes in observational clinical studies.

The multi-drifting subpulse behaviors in PSR J2007+0910 have been studied carefully with the high sensitivity observations of the Five-hundred-meter Aperture Spherical radio Telescope (FAST) at 1250 MHz. We found that there are at least six different single emission modes in PSR J2007+0910 are observed, four of which show significant subpulse drifting behaviors (modes A, B, C, and D), and the remaining two (modes $E_1$ and $E_2$) show stationary subpulse structures. The subpulse drifting periods of modes A, B, C, and D are $P_{3, A} = 8.7 \pm 1.6 P$, $P_{3, B} = 15.8 \pm 1.2 P$, $P_{3, C} = 21.6 \pm 1.3 P$ and $P_{3, D} = 32.3 \pm 0.9 P$, respectively, where $P$ represents the pulse period of this pulsar. The subpulse separation is almost the same for all modes $P_2 = 6.01 \pm 0.18 ^\circ$. Deep analysis suggests that the appearance and significant changes in the drifting period of multi-drifting subpulse emission modes for a pulsar may originate from the aliasing effect. The observed non-drifting modes may be caused by the spark point move with a period ~P_2. Our statistical analysis shows that the drift mode of this pulsar almost always switches from slower to faster drifts in the mode change. The interesting subpulse emission phenomenon of PSR J2007+0910 provides a unique opportunity to understand the switching mechanism of multi-drift mode., Comment: 10 pages, 10 figures, 2 tables, Accepted to MNRAS

We propose a new model to generate large anisotropies in the scalar-induced gravitational wave (SIGW) background via sound speed resonance in the inflaton-curvaton mixed scenario. Cosmological curvature perturbations are not only exponentially amplified at a resonant frequency, but also preserve significant non-Gaussianity of local type described by $f_{\mathrm{nl}}$. Besides a significant enhancement of energy-density fraction spectrum, large anisotropies in SIGWs can be generated, because of super-horizon modulations of the energy density due to existence of primordial non-Gaussianity. A reduced angular power spectrum $\tilde{C}_{\ell}$ could reach an amplitude of $[\ell(\ell+1)\tilde{C}_{\ell}]^{1/2} \sim 10^{-2}$, leading to potential measurements via planned gravitational-wave detectors such as DECIGO. The large anisotropies in SIGWs would serve as a powerful probe of the early universe, shedding new light on the inflationary dynamics, primordial non-Gaussianity, and primordial black hole dark matter., Comment: 10 pages, 2 figures, 2 columns, additional references added

CNN-based object detection methods have achieved significant progress in recent years. The classic structures of CNNs produce pyramid-like feature maps due to the pooling or other re-scale operations. The feature maps in different levels of the feature pyramid are used to detect objects with different scales. For more accurate object detection, the highest-level feature, which has the lowest resolution and contains the strongest semantics, is up-scaled and connected with the lower-level features to enhance the semantics in the lower-level features. However, the classic mode of feature connection combines the feature of lower-level with all the features above it, which may result in semantics degradation. In this paper, we propose a skipped connection to obtain stronger semantics at each level of the feature pyramid. In our method, the lower-level feature only connects with the feature at the highest level, making it more reasonable that each level is responsible for detecting objects with fixed scales. In addition, we simplify the generation of anchor for bounding box regression, which can further improve the accuracy of object detection. The experiments on the MS COCO and Wider Face demonstrate that our method outperforms the state-of-the-art methods.

Imitation learning (IL) enables agents to mimic expert behaviors. Most previous IL techniques focus on precisely imitating one policy through mass demonstrations. However, in many applications, what humans require is the ability to perform various tasks directly through a few demonstrations of corresponding tasks, where the agent would meet many unexpected changes when deployed. In this scenario, the agent is expected to not only imitate the demonstration but also adapt to unforeseen environmental changes. This motivates us to propose a new topic called imitator learning (ItorL), which aims to derive an imitator module that can on-the-fly reconstruct the imitation policies based on very limited expert demonstrations for different unseen tasks, without any extra adjustment. In this work, we focus on imitator learning based on only one expert demonstration. To solve ItorL, we propose Demo-Attention Actor-Critic (DAAC), which integrates IL into a reinforcement-learning paradigm that can regularize policies' behaviors in unexpected situations. Besides, for autonomous imitation policy building, we design a demonstration-based attention architecture for imitator policy that can effectively output imitated actions by adaptively tracing the suitable states in demonstrations. We develop a new navigation benchmark and a robot environment for \topic~and show that DAAC~outperforms previous imitation methods \textit{with large margins} both on seen and unseen tasks.

We demonstrate transition between the fine structure splitting of the ground state of triply ionized zirconium (Zr IV) is suitable for a terahertz (THz) atomic clock. Its transition frequency is about 37.52 THz and is mainly guided by the magnetic dipole (M1) transition and can be accessible by a readily available laser. We suggest to consider stable even isotopes of Zr and $M_J= \pm 1/2$ sublevels (i.e. $|4D_{3/2},M_J=\pm 1/2\rangle \rightarrow |4D_{5/2},M_J=\pm 1/2\rangle$ clock transition) for the experimental advantage. By performing necessary calculations, we have estimated possible systematics due to blackbody radiation, ac Stark, electric quadrupole and second-order Zeeman shifts along with shifts due to the second-order Doppler effects. The proposed THz atomic clock can be very useful in quantum thermometry and frequency metrology., Comment: 1 figure, 11 pages, accepted for publication in Physical Review A

Laser cutting of semiconductor wafers and transparent dielectrics has become a dominant process in manufacturing industries, encompassing a wide range of applications from flat display panels to microelectronic chips. Limited by the diffraction barrier imposed on the beam width and its longitudinal extend of laser focus, a trade-off must be made between cutting accuracy and aspect ratio in conventional laser processing, with accuracy typically approaching a micron and the aspect ratio on the order of $10^2$. Herein, we propose a method to circumvent this limitation. It is based on the laser modification induced by a back-scattering interference crawling mechanism, which creates a positive feedback for homogenizing longitudinal energy deposition and lateral sub-wavelength light confinement during laser-matter interaction. Consequently, cutting width on the scale of tens of nanometers and aspect ratio $10^3 \sim 10^4$ were simultaneously achieved. We refer to this technique as ``super stealth dicing'', which is validated through numerical simulations, ensuring its broad applicability. It can be applied to various transparent functional solids, such as glass, laser crystal, ferroelectric, and semiconductor, and is elevating the precision of future advanced laser dicing, patterning, and drilling into the nanometric era., Comment: 32 pages, 5 figures

We examine energy level-crossings of fine-structure (FS) levels in the heavier highly charged ions (HCIs) with $d^6$ and $d^8$ configurations. From the analysis, we find that some of these HCIs are tailor-made for atomic clocks with quality factors ranging from $10^{16}$ to $10^{18}$ and fractional uncertainties below $10^{-19}$ level. Many of them are also realized to be highly sensitive to the observation of temporal variation of FS constant ($\alpha$) and testing violation of local Lorentz symmetry invariance (LLI). To probe variations of $\alpha$ and LLI, we have determined their corresponding sensitivity coefficients in the investigated HCIs. Similarly, we have estimated orders of magnitudes of the Zeeman, Stark, black-body radiation and electric quadrupole shifts of the clock transitions of the considered HCIs in order to demonstrate them as the potential candidates for atomic clocks., Comment: 5 pages, 1 figure

Robust regression has attracted a great amount of attention in the literature recently, particularly for taking asymmetricity into account simultaneously and for high-dimensional analysis. However, the majority of research on the topics falls in frequentist approaches, which are not capable of full probabilistic uncertainty quantification. This paper first proposes a new Huberised-type of asymmetric loss function and its corresponding probability distribution which is shown to have the scale-mixture of normals. Then we introduce a new Bayesian Huberised regularisation for robust regression. A by-product of the research is that a new Bayesian Huberised regularised quantile regression is also derived. We further present their theoretical posterior properties. The robustness and effectiveness of the proposed models are demonstrated in the simulation studies and the real data analysis.

We predict a scheme for the creation of isotropic three-dimensional droplets in Rydbeg-dressed Bose gases, which contain both repulsive contact interactions and attractive van der Waals interactions causing the quantum fluctuation effect non-negligible. We present detailed beyond mean-field calculations with Lee-Huang-Yang correction and demonstrate the existence of isotropic droplets under realistic experimental conditions. Stable droplets possess flat-top density distribution, and their chemical potentials decrease with the particle number expansion towarding a critical value. We distinguish droplets from bright solitons through peak density, width of condensate and quantum depletion calculations. We summarize a phase diagram of realizing droplets, and subsequently highlight the stability of droplets by real time evolution as well as collisions. Our work provides a novel platform for investigating excitation spectrum and superfluid nature of droplets.