Cyclone rapid intensification is the rapid increase in cyclone wind intensity, exceeding a threshold of 30 knots, within 24 hours. Rapid intensification is considered an extreme event during a cyclone, and its occurrence is relatively rare, contributing to a class imbalance in the dataset. A diverse array of factors influences the likelihood of a cyclone undergoing rapid intensification, further complicating the task for conventional machine learning models. In this paper, we evaluate deep learning, ensemble learning and data augmentation frameworks to detect cyclone rapid intensification based on wind intensity and spatial coordinates. We note that conventional data augmentation methods cannot be utilised for generating spatiotemporal patterns replicating cyclones that undergo rapid intensification. Therefore, our framework employs deep learning models to generate spatial coordinates and wind intensity that replicate cyclones to address the class imbalance problem of rapid intensification. We also use a deep learning model for the classification module within the data augmentation framework to differentiate between rapid and non-rapid intensification events during a cyclone. Our r
This paper addresses the problem of quantitative rapid stabilization via the linear quadratic (LQ) theory. Specifically, for non-self-adjoint parabolic equations, by virtue of the LQ theory, we derive the quantitative rapid stabilization by selecting a special cost functional and combining it with a quantitative observability inequality. Furthermore, this approach reveals the equivalence between the quantitative rapid stabilization and the quantitative observability inequality for linear systems. In addition, we apply this framework to the Navier--Stokes equations and establish the quantitative rapid stabilization around nontrivial steady states. Finally, we extend this methodology to finite-dimensional feedback laws in self-adjoint cases.
We study the rapid stabilization of general linear systems, when the differential operator $\mathcal{A}$ has a Riesz basis of eigenvectors. We find simple sufficient conditions for the rapid stabilization and the construction of a relatively explicit feedback operator. We use an $F$-equivalence approach \textcolor{black}{relying on Fredholm transformation} to show a stronger result: under these sufficient conditions the system is equivalent to a simple exponentially stable system, with arbitrarily large decay rate. In particular, our conditions improve the existing conditions of rapid stabilization for non-parabolic operators such as skew-adjoint systems.
In this paper, we investigate the rapid stabilizability of linear infinite-dimensional control systems with a constant time delay. Under the assumptions that the state operator generates an immediately compact semigroup and that the delay coefficient is constant, we establish two main results: (i) The presence of a time-delay term does not affect the rapid stabilizability of the control system; that is, this property depends only on the state and control operators; (ii) Static feedback is sufficient to achieve rapid stabilization of the system. Applications are also presented.
With rapid urbanisation and the accompanying increase in traffic density, traffic noise has become a major concern in urban planning. However, traditional grid noise mapping methods have limitations in terms of time consumption, software costs, and a lack of parameter integration interfaces. These limitations hinder their ability to meet the need for iterative updates and rapid performance feedback in the early design stages of street-scale urban planning. Herein, we developed a rapid urban traffic noise mapping technique that leverages generative adversarial networks (GANs) as a surrogate model. This approach enables the rapid assessment of urban traffic noise distribution by using urban elements such as roads and buildings as the input. The mean values for the mean squared error (RMSE) and structural similarity index (SSIM) are 0.3024 dB(A) and 0.8528, respectively, for the validation dataset. The trained model is integrated into Grasshopper as a tool, facilitating the rapid generation of traffic noise maps. This integration allows urban designers and planners, even those without expertise in acoustics, to easily anticipate changes in acoustics impacts caused by design in the ear
Regular and rapid variation have been extensively studied in the literature and applied across various fields, particularly in extreme value theory. In this paper, we examine regular and rapid variation through the lens of generalized hazard rates, with a focus on the behavior of survival and density functions of random variables. Motivated by the von Mises condition, our hazard rate based framework offers a unified approach that spans from slow to rapid variation, providing in particular new insights into the relationship between hazard rate functions and the right tail decays of random variables.
In this paper, we focus on the rapid boundary stabilization of 1D nonlinear parabolic equations via the modal decomposition method. The nonlinear term is assumed to satisfy certain local Lipschitz continuity and global growth conditions. Through the modal decomposition, we construct a feedback control that modifies only the unstable eigenvalues to achieve spectral reduction. Under this control, we establish locally rapid stabilization by estimating the nonlinearity in Lyapunov stability analysis. Furthermore, utilizing the dissipative property, we derive a globally rapid stabilization result for dissipative systems such as the Burgers equation and the Allen-Cahn equation.
Partially Observable Markov Decision Processes (POMDPs) are a general and principled framework for motion planning under uncertainty. Despite tremendous improvement in the scalability of POMDP solvers, long-horizon POMDPs remain difficult to solve. To alleviate the difficulty, this paper proposes a new approximate online POMDP solver, called Reference-Based Online POMDP Planning via Rapid State Space Sampling (ROP-RAS3). ROP-RAS3 uses novel extremely fast sampling-based motion planning techniques to sample the state space and generate a diverse set of macro actions online, which are then used to bias belief-space sampling and infer high-quality policies without requiring exhaustive enumeration of the action space -- a fundamental constraint for modern online POMDP solvers. ROP-RAS3 converges to a near-optimal reference-based solution at a rate that depends on the number of sampled actions, rather than the size of the action space. ROP-RAS3 is evaluated on various long-horizon POMDPs with up to 3000 lookahead steps and 35-dimensional state spaces, where the state, action and observation spaces can be continuous, discrete, or a hybrid of discrete and continuous. Although the referenc
Dissipative quantum algorithms for state preparation in many-body systems are increasingly recognised as promising candidates for achieving large quantum advantages in application-relevant tasks. Recent advances in algorithmic, detailed-balance Lindbladians enable the efficient simulation of open-system dynamics converging towards desired target states. However, the overall complexity of such schemes is governed by system-size dependent mixing times. In this work, we analyse algorithmic Lindbladians for Gibbs state preparation and prove that they exhibit rapid mixing, i.e., convergence in time poly-logarithmic in the system size. We first establish this for non-interacting spin systems, free fermions, and free bosons, and then show that these rapid mixing results are stable under perturbations, covering weakly interacting qudits and perturbed non-hopping fermions. Further, we adapt the techniques from separable qudits to the fermionic setting and prove rapid mixing of the strongly-interacting regime of the Fermi-Hubbard model, for which we also explicitly evaluate the guaranteed parameter regimes. Our results constitute the first efficient mixing bounds for non-commuting qudit mode
Over the past decade, the rapid updating of resource knowledge and the integration of real-time sensor information have gained attention in both industry and academia. However, most studies on rapid resource model updating have focused on continuous variables, such as grade variables and coal quality parameters. Geological domain modelling is an essential component of resource estimation, which is why it is crucial to extend data assimilation techniques to enable the rapid updating of categorical variables. In this paper, a methodology inspired by pluri-Gaussian simulation is proposed for near-real-time updating of geological domains, followed by updating grade variables within these domain boundaries. The proposed algorithm consists of a Gibbs sampler for converting geological domains into Gaussian random fields, an ensemble Kalman filter with multiple data assimilations for rapid updating, and rotation based iterative Gaussianisation for multi-Gaussian transformation. We demonstrate the algorithm by using a synthetic case study with observations sampled from the ground truth, as well as a real case study that uses production drilling samples to jointly update geological domains a
Recent studies, in the context of consistency conditions for rapid-turn and third order slow-roll inflation in two-field models, raised the question whether this regime can be sustained for more than a few e-folds of expansion. We answer this question in the affirmative by showing that the consistency conditions themselves ensure the longevity of the rapid-turn regime. Furthermore, we prove this for the most general definition of rapid turning (i.e., with a turning rate that is large compared to the slow-roll parameters, but not necessarily large compared to unity), using in the process a generalized consistency condition. We also show that a special class of rapid-turn models, including angular inflation, satisfy a large-(compared to $1$)-turn-rate condition even for non-large turning rates.
We prove rapid mixing for almost all random walks generated by $m$ translations on an arbitrary nilmanifold under mild assumptions on the size of $m$. For several classical classes of nilmanifolds, we show $m=2$ suffices. This provides a partial answer to the question raised in \cite{D02} about the prevalence of rapid mixing for random walks on homogeneous spaces.
We generalize the notion of rapid decay property for a group $G$ to pairs of groups $(G,H)$ where $H$ is a finitely generated subgroup of $G$, where typically the subgroup $H$ does not have rapid decay. We deduce some isomorphisms in $K$-theory, and investigate relatively spectral injections in the reduced group $C^*$-algebra. Rapid decay property for the pair $(G,H)$ also gives a lower bound for the probability of return to $H$ of symmetric random walks on $G$.
The existence of massive quiescent galaxies at high redshift seems to require rapid quenching, but it is unclear whether all quiescent galaxies have gone through this phase and what physical mechanisms are involved. To study rapid quenching, we use rest-frame colors to select 12 young quiescent galaxies at $z \sim 1.5$. From spectral energy distribution fitting, we find that they all experienced intense starbursts prior to rapid quenching. We confirm this with deep Magellan/FIRE spectroscopic observations for a subset of seven galaxies. Broad emission lines are detected for two galaxies and are most likely caused by AGN activity. The other five galaxies do not show any emission features, suggesting that gas has already been removed or depleted. Most of the rapidly quenched galaxies are more compact than normal quiescent galaxies, providing evidence for a central starburst in the recent past. We estimate an average transition time of $300\,\rm Myr$ for the rapid quenching phase. Approximately $4\%$ of quiescent galaxies at $z=1.5$ have gone through rapid quenching; this fraction increases to $23\%$ at $z=2.2$. We identify analogs in the TNG100 simulation and find that rapid quenchin
The success of Computer Vision (CV) relies heavily on manually annotated data. However, it is prohibitively expensive to annotate images in key domains such as healthcare, where data labeling requires significant domain expertise and cannot be easily delegated to crowd workers. To address this challenge, we propose a neuro-symbolic approach called Rapid, which infers image labeling rules from a small amount of labeled data provided by domain experts and automatically labels unannotated data using the rules. Specifically, Rapid combines pre-trained CV models and inductive logic learning to infer the logic-based labeling rules. Rapid achieves a labeling accuracy of 83.33% to 88.33% on four image labeling tasks with only 12 to 39 labeled samples. In particular, Rapid significantly outperforms finetuned CV models in two highly specialized tasks. These results demonstrate the effectiveness of Rapid in learning from small data and its capability to generalize among different tasks. Code and our dataset are publicly available at https://github.com/Neural-Symbolic-Image-Labeling/
We discuss rapid decay functions on odometer Cantor spaces and their noncommutative geometry applications.
In the realm of daily services, the deployment of deep neural networks underscores the paramount importance of their reliability. However, the vulnerability of these networks to adversarial attacks, primarily evasion-based, poses a concerning threat to their functionality. Common methods for enhancing robustness involve heavy adversarial training or leveraging learned knowledge from clean data, both necessitating substantial computational resources. This inherent time-intensive nature severely limits the agility of large foundational models to swiftly counter adversarial perturbations. To address this challenge, this paper focuses on the Rapid Plug-in Defender (RaPiD) problem, aiming to rapidly counter adversarial perturbations without altering the deployed model. Drawing inspiration from the generalization and the universal computation ability of pre-trained transformer models, we propose a novel method termed CeTaD (Considering Pre-trained Transformers as Defenders) for RaPiD, optimized for efficient computation. CeTaD strategically fine-tunes the normalization layer parameters within the defender using a limited set of clean and adversarial examples. Our evaluation centers on as
Rapid and robust parameter estimation of gravitational-wave sources is a key component of modern multi-messenger astronomy. We present a novel and straightforward method for rapid parameter estimation of gravitational-wave sources that uses metric-based importance sampling. The method enables robust parameter estimation of binary neutron star and binary black hole binaries and is trivially parallelized, enabling parameter estimation in seconds with modest resources. The algorithm achieves a median $35\%$ effective sampling efficiency for a population of aligned-spin neutron star binaries sources. Surprisingly, this approach is also highly efficient for analyzing the full 15-dimensional parameter space of typical binary black holes, with a population median $20\%$ efficiency achieved for a source detected primarily by the twin LIGO observatories and $9\%$ for a network of three comparable sensitivity observatories. This method can serve immediate use to improve the low-latency data products of the gravitational-wave observatory network and may be a key component of how the millions of sources observed by next-generation observatories could be analyzed. The approach can also be broad
Integrating research evidence into practice is one of the main goals of Evidence-Based Software Engineering (EBSE). Secondary studies, one of the main EBSE products, are intended to summarize the best research evidence and make them easily consumable by practitioners. However, recent studies show that some secondary studies lack connections with software engineering practice. In this chapter, we present the concept of Rapid Reviews, which are lightweight secondary studies focused on delivering evidence to practitioners in a timely manner. Rapid reviews support practitioners in their decision-making, and should be conducted bounded to a practical problem, inserted into a practical context. Thus, Rapid Reviews can be easily integrated in a knowledge/technology transfer initiative. After describing the basic concepts, we present the results and experiences of conducting two Rapid Reviews. We also provide guidelines to help researchers and practitioners who want to conduct Rapid Reviews, and we finally discuss topics that my concern the research community about the feasibility of Rapid Reviews as an Evidence-Based method. In conclusion, we believe Rapid Reviews might interest researche
We present the results of a search for unusually rapidly rotating giant stars in a large sample of K giants (~1300 stars) that had been spectroscopically monitored as potential targets for the Space Interferometry Mission's Astrometric Grid. The stars in this catalog are much fainter and typically more metal-poor than those of other catalogs of red giant star rotational velocities, but the spectra generally only have signal-to-noise (S/N) of ~20-60, making the measurement of the widths of individual lines difficult. To compensate for this, we have developed a cross-correlation method to derive rotational velocities in moderate S/N echelle spectra to efficiently probe this sample for rapid rotator candidates. We have discovered 28 new red giant rapid rotators as well as one extreme rapid rotator with a vsini of 86.4 km/s. Rapid rotators comprise 2.2% of our sample, which is consistent with other surveys of brighter, more metal-rich K giant stars. Although we find that the temperature distribution of rapid rotators is similar to that of the slow rotators, this may not be the case with the distributions of surface gravity and metallicity. The rapid rotators show a slight overabundance