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In this study, we present a novel analytical approach to solving large-scale Ising problems by reformulating the discrete Ising Hamiltonian into a continuous framework. This transformation enables us to derive exact solutions for a non-trivial class of fully connected Ising models. To validate our method, we conducted numerical experiments comparing our analytical solutions with those obtained from a quantum-inspired Ising algorithm and a quantum Ising machine. The results demonstrate that the quantum-inspired algorithm and brute-force method successfully align with our solutions, while the quantum Ising machine exhibits notable deviations. Our method offers promising avenues for analytically solving diverse Ising problem instances, while the class of Ising problems addressed here provides a robust framework for assessing the fidelity of Ising machines.

The bimodal metallicity distribution of globular clusters (GCs) in massive galaxies implies two distinct sub-populations: metal-poor and metal-rich. Using the recent data of \textit{Gaia} we highlighted three distinct dissimilarities between metal-poor and metal-rich GCs in the Milky Way (MW). Half-mass (light) radii of metal-poor GCs exhibit, on average, $\simeq 52 \pm$5 ($60 \pm$3) per cent more expansion than metal-rich ones. Furthermore, the lack of metal-poor GCs at low Galactocentric distances ($R_\mathrm{G}$) follows a triangular pattern in $R_\mathrm{G}$-[Fe/H] space, indicating that GCs with lower metallicities appear further away from the Galactic center. Metal-poor GCs are more susceptible to destruction by the tidal field in the inner part of the MW. We perform a series of \Nbody simulations of star clusters, to study the impact of the BHs' natal kicks on the long-term evolution of low- and high-metallicity GCs to explain these observational aspects. We found that the retention of BHs inside the cluster is crucial to reproducing the observed dissimilarities. The heavier and less expanded BH sub-system (BHSub) in metal-poor clusters leads to more intense few-body encounters, injecting more kinetic energy into the stellar population. Consequently, they experience larger expansion and higher evaporation rates rather than metal-rich clusters. The higher energy production within the BHSub of metal-poor GCs causes them to dissolve before a Hubble time near the Galactic center, leading to a triangular pattern in $R_\mathrm{G}$-[Fe/H] space., Comment: 11 pages, 9 figures, 1 table. Accepted for publication in MNRAS

The surface states of topological superconductors significantly influence electromagnetic fields within these materials. The interaction between gapless boundary states and electromagnetic fields induces a Berry phase, coupling electric and magnetic fields and introducing the axion term into the effective Lagrangian . In this paper, we utilize a model of a topological superconductor, represented as a Weyl superconductor-topological insulator-Weyl superconductor structure with a {\pi} phase difference between superconductors. By incorporating tilting of Weyl cones, we study the Meissner effect, demonstrating that the interplay between tilt and the axion field enhances surface state contributions. Furthermore, we show that an anisotropy in the Meissner effect arises from the anisotropic nature of the tilt vector. This anisotropy manifests as directional dependence in the magnetic response of the material. We derive a universal equation for magnetic penetration in topological superconductors and explore the impact of tilt on the planar Hall current at the surface., Comment: 9 pages, 6 figures

In recent years, few-shot segmentation (FSS) models have emerged as a promising approach in medical imaging analysis, offering remarkable adaptability to segment novel classes with limited annotated data. Existing approaches to few-shot segmentation have often overlooked the potential of the query itself, failing to fully utilize the valuable information it contains. However, treating the query as unlabeled data provides an opportunity to enhance prediction accuracy. Specifically in the domain of medical imaging, the volumetric structure of queries offers a considerable source of valuable information that can be used to improve the target slice segmentation. In this work, we present a novel strategy to efficiently leverage the intrinsic information of the query sample for final segmentation during inference. First, we use the support slices from a reference volume to generate an initial segmentation score for the query slices through a prototypical approach. Subsequently, we apply a confidence-aware pseudo-labeling procedure to transfer the most informative parts of query slices to the support set. The final prediction is performed based on the new expanded support set, enabling the prediction of a more accurate segmentation mask for the query volume. Extensive experiments show that the proposed method can effectively boost performance across diverse settings and datasets.

We examine a new scenario to model the outer halo globular cluster (GC) Pal 14 over its lifetime by performing a comprehensive set of direct N-body calculations. We assume Pal 14 was born in a now detached/disrupted dwarf galaxy with a strong tidal field. Pal 14 evolved there until the slope of the stellar mass function (MF) became close to the measured value which is observed to be significantly shallower than in most GCs. After about 2-3 Gyr, Pal 14 was then captured by the Milky Way (MW). Although the physical size of such a cluster is indistinguishable from a cluster that has lived its entire life in the MW, other parameters like its mass and the MF-slope, strongly depend on the time the cluster is taken from the dwarf galaxy. After being captured by the MW on a new orbit, the cluster expands and eventually reaches the appropriate mass and size of Pal 14 after 11.5 Gyr while reproducing the observed MF. These simulations thus suggest that Pal 14 may have formed in a dwarf galaxy with a post-gas-expulsion initial half-mass radius and mass of $r_h=7$ pc and $8

Classifiers trained with Empirical Risk Minimization (ERM) tend to rely on attributes that have high spurious correlation with the target. This can degrade the performance on underrepresented (or 'minority') groups that lack these attributes, posing significant challenges for both out-of-distribution generalization and fairness objectives. Many studies aim to enhance robustness to spurious correlation, but they sometimes depend on group annotations for training. Additionally, a common limitation in previous research is the reliance on group-annotated validation datasets for model selection. This constrains their applicability in situations where the nature of the spurious correlation is not known, or when group labels for certain spurious attributes are not available. To enhance model robustness with minimal group annotation assumptions, we propose Environment-based Validation and Loss-based Sampling (EVaLS). It uses the losses from an ERM-trained model to construct a balanced dataset of high-loss and low-loss samples, mitigating group imbalance in data. This significantly enhances robustness to group shifts when equipped with a simple post-training last layer retraining. By using environment inference methods to create diverse environments with correlation shifts, EVaLS can potentially eliminate the need for group annotation in validation data. In this context, the worst environment accuracy acts as a reliable surrogate throughout the retraining process for tuning hyperparameters and finding a model that performs well across diverse group shifts. EVaLS effectively achieves group robustness, showing that group annotation is not necessary even for validation. It is a fast, straightforward, and effective approach that reaches near-optimal worst group accuracy without needing group annotations, marking a new chapter in the robustness of trained models against spurious correlation.

We investigate the impact of primordial mass segregation on the formation and evolution of dark star clusters (DSCs). Considering a wide range of initial conditions, we conducted $N$-body simulations of globular clusters (GCs) around the Milky Way. In particular, we assume a canonical IMF for all GCs without natal kicks for supernovae remnants, namely neutron stars or black holes. Our results demonstrate that clusters with larger degrees of primordial mass segregation reach their DSC phase earlier and spend a larger fraction of their dissolution time in such a phase, compared to clusters without mass segregation. In primordially segregated clusters, the maximum Galactocentric distance that the clusters can have to enter the DSC phase is almost twice that of the clusters without primordial mass segregation. Primordially segregated clusters evolve with a higher number of stellar mass black holes, accelerating energy creation in their central regions and consequently increasing evaporation rates and cluster sizes during dark phases. The simulations reveal that aggregating heavy components at the centre doubles the time spent in the dark phase. Additionally, the study identifies potential links between simulated dark clusters and initial conditions of Milky Way globular clusters, suggesting some may transition to dark phases before dissolution. Higher primordial mass segregation coefficients amplify the average binary black hole formation rate by 2.5 times, raising higher expectations for gravitational wave emissions., Comment: 10 pages, 7 Figures, 1 Table, Accepted for publication in MNRAS

Autonomous vehicle navigation is a key challenge in artificial intelligence, requiring robust and accurate decision-making processes. This research introduces a new end-to-end method that exploits multimodal information from a single monocular camera to improve the steering predictions for self-driving cars. Unlike conventional models that require several sensors which can be costly and complex or rely exclusively on RGB images that may not be robust enough under different conditions, our model significantly improves vehicle steering prediction performance from a single visual sensor. By focusing on the fusion of RGB imagery with depth completion information or optical flow data, we propose a comprehensive framework that integrates these modalities through both early and hybrid fusion techniques. We use three distinct neural network models to implement our approach: Convolution Neural Network - Neutral Circuit Policy (CNN-NCP) , Variational Auto Encoder - Long Short-Term Memory (VAE-LSTM) , and Neural Circuit Policy architecture VAE-NCP. By incorporating optical flow into the decision-making process, our method significantly advances autonomous navigation. Empirical results from our comparative study using Boston driving data show that our model, which integrates image and motion information, is robust and reliable. It outperforms state-of-the-art approaches that do not use optical flow, reducing the steering estimation error by 31%. This demonstrates the potential of optical flow data, combined with advanced neural network architectures (a CNN-based structure for fusing data and a Recurrence-based network for inferring a command from latent space), to enhance the performance of autonomous vehicles steering estimation.

Autonomous driving holds great potential to transform road safety and traffic efficiency by minimizing human error and reducing congestion. A key challenge in realizing this potential is the accurate estimation of steering angles, which is essential for effective vehicle navigation and control. Recent breakthroughs in deep learning have made it possible to estimate steering angles directly from raw camera inputs. However, the limited available navigation data can hinder optimal feature learning, impacting the system's performance in complex driving scenarios. In this paper, we propose a shared encoder trained on multiple computer vision tasks critical for urban navigation, such as depth, pose, and 3D scene flow estimation, as well as semantic, instance, panoptic, and motion segmentation. By incorporating diverse visual information used by humans during navigation, this unified encoder might enhance steering angle estimation. To achieve effective multi-task learning within a single encoder, we introduce a multi-scale feature network for pose estimation to improve depth learning. Additionally, we employ knowledge distillation from a multi-backbone model pretrained on these navigation tasks to stabilize training and boost performance. Our findings demonstrate that a shared backbone trained on diverse visual tasks is capable of providing overall perception capabilities. While our performance in steering angle estimation is comparable to existing methods, the integration of human-like perception through multi-task learning holds significant potential for advancing autonomous driving systems. More details and the pretrained model are available at https://hi-computervision.github.io/uni-encoder/.

Brain tumor classification is a challenging task in medical image analysis. In this paper, we propose a novel approach to brain tumor classification using a vision transformer with a novel cross-attention mechanism. Our approach leverages the strengths of transformers in modeling long-range dependencies and multi-scale feature fusion. We introduce two new mechanisms to improve the performance of the cross-attention fusion module: Feature Calibration Mechanism (FCM) and Selective Cross-Attention (SCA). FCM calibrates the features from different branches to make them more compatible, while SCA selectively attends to the most informative features. Our experiments demonstrate that the proposed approach outperforms other state-of-the-art methods in brain tumor classification, achieving improved accuracy and efficiency. The proposed FCM and SCA mechanisms can be easily integrated into other vision transformer architectures, making them a promising direction for future research in medical image analysis. Experimental results confirm that our approach surpasses existing methods, achieving state-of-the-art performance in brain tumor classification tasks.

Simulators are powerful tools for autonomous robot learning as they offer scalable data generation, flexible design, and optimization of trajectories. However, transferring behavior learned from simulation data into the real world proves to be difficult, usually mitigated with compute-heavy domain randomization methods or further model fine-tuning. We present a method to improve generalization and robustness to distribution shifts in sim-to-real visual quadrotor navigation tasks. To this end, we first build a simulator by integrating Gaussian Splatting with quadrotor flight dynamics, and then, train robust navigation policies using Liquid neural networks. In this way, we obtain a full-stack imitation learning protocol that combines advances in 3D Gaussian splatting radiance field rendering, crafty programming of expert demonstration training data, and the task understanding capabilities of Liquid networks. Through a series of quantitative flight tests, we demonstrate the robust transfer of navigation skills learned in a single simulation scene directly to the real world. We further show the ability to maintain performance beyond the training environment under drastic distribution and physical environment changes. Our learned Liquid policies, trained on single target manoeuvres curated from a photorealistic simulated indoor flight only, generalize to multi-step hikes onboard a real hardware platform outdoors.

We approach designing a state-space model for deep learning applications through its dual representation, the transfer function, and uncover a highly efficient sequence parallel inference algorithm that is state-free: unlike other proposed algorithms, state-free inference does not incur any significant memory or computational cost with an increase in state size. We achieve this using properties of the proposed frequency domain transfer function parametrization, which enables direct computation of its corresponding convolutional kernel's spectrum via a single Fast Fourier Transform. Our experimental results across multiple sequence lengths and state sizes illustrates, on average, a 35% training speed improvement over S4 layers -- parametrized in time-domain -- on the Long Range Arena benchmark, while delivering state-of-the-art downstream performances over other attention-free approaches. Moreover, we report improved perplexity in language modeling over a long convolutional Hyena baseline, by simply introducing our transfer function parametrization. Our code is available at https://github.com/ruke1ire/RTF., Comment: Resubmission 02/06/2024: Fixed minor typo of recurrent form RTF

(Abridged) Observational estimates of galaxy properties rely on the inherent galaxy-wide initial mass function (gwIMF), which systematically varies with the global SFR and metallicity, as proposed by the integrated-galactic IMF (IGIMF) theory and supported by empirical evidence. We incorporate PARSEC and COLIBRI stellar isochrones into the GalIMF code, a galaxy chemical evolution (GCE) model featuring real-time updates of environment-dependent gwIMFs. This newly developed photometric GalIMF (photGalIMF) code allows the calculation of photometric properties for galaxies with diverse stellar populations. Subsequently, we analyze observed luminosities and metallicities of local star-forming galaxies to deduce their stellar masses assuming that they have constant SFRs over 13.6 Gyr. We also compute SFR$-$H$\alpha$ luminosity relations for varying stellar metallicities using a separate stellar population synthesis code based on PEGASE. Comparing the IGIMF theory to the canonical universal IMF, our analysis reveals that estimates of the stellar masses and SFRs for local star-forming galaxies differ by factors of $\approx 2$ and 10, respectively. The computed gas-depletion timescale increases with gas mass, implying lower star formation efficiencies in more massive galaxies, possibly due to stronger feedback regulation, aligning with theoretical expectations. Additionally, the characteristic stellar mass buildup timescale increases with stellar mass, indicating that massive disk galaxies initiate star formation earlier than their low-mass counterparts. The photGalIMF code enables self-consistent computations of galactic photometry, self-consistently with GCE modelling within the context of an environment-dependent gwIMF. Utilizing Ks-band and H$\alpha$ luminosities of galaxies, the outcomes include galaxy mass, SFR, and fitting functions for the SFR correction factor., Comment: Accepted for publication in Astronomy & Astrophysics (A&A), 19 pages, 11 figures, 2 tables. The photGalIMF code is publicly available on GitHub: https://github.com/juzikong/photGalIMF

The Spitzer instability leads to the formation of a black hole sub-system (BHSub) at the center of a star cluster providing energy to luminous stars (LSs) and increasing their rate of evaporation. When the self-depletion time of the BHSub exceeds the evaporation time of the LSs, a dark star cluster (DSC) will appear. Using the NBODY7 code, we performed a comprehensive set of direct \Nbody simulations over a wide range of initial conditions to study the pure effect of the top-heaviness of the IMF on the formation of the DSC phase. In the Galactic tidal field, top-heavy IMFs lead to the fast evaporation of LSs and the formation of DSCs. Therefore, DSCs can be present even in the outer region of the Milky Way (MW). To successfully transition to the DSC phase, the MW Globular Clusters (GCs) must possess an initial BH mass fraction of $\widetilde{\mathit{M}}_\mathrm{BH}(0)>0.05$. For star clusters with $\widetilde{\mathit{M}}_\mathrm{BH}(0)>0.08$, the DSC phase will be created for any given initial density of the cluster and Galactocentric distance. The duration of the cluster's lifetime spent in the DSC phase shows a negative (positive) correlation with the initial density, and Galactocentric distance of the star cluster if $\widetilde{\mathit{M}}_\mathrm{BH}(0)\leq 0.12$ ($\widetilde{\mathit{M}}_\mathrm{BH}(0)\geq 0.15$). Considering the canonical IMF, it is unlikely for any MW GCs to enter the DSC phase. We discuss the BH retention fraction in view of the observed properties of the GCs of the MW., Comment: 16 pages, 13 Figures, 2 Tables, Accepted for publications in MNRAS

Accurately estimating the complex motion of the heart can unlock enormous potential for kinetic energy harvesting. This paper presents a foundational dataset for heart kinetic motion through in-vivo tests and investigates the most influential factors in heart kinetic motion. In-vivo tests on a living pig's heart, with signal processing, were carried out to study the heart movement by heart beating and respiration motions. A network of nine points on the heart was employed for in vivo measurements. These measurements illustrated the kinetic energy signals in displacement, velocity, and acceleration. The results indicated that the motion level varies in distinct locations over epicardium. The statistical features and autocorrelations were reported for these points, illustrating the highest displacement and acceleration. Each heartbeat generated an energy of 14.35 mJ and a power of 1.03 W. However, this available energy is not uniformly distributed. The results illustrated that not only is cardiac movement location-dependent, but the speed of cardiac displacement cycles is also location-dependent. The right atrium has the highest cardiac kinetic movement with an amplitude of 16.19 mm displacement and 16.3 m/s2 acceleration. To evaluate the energy harvesting possibility from the heart's motion, a piezoelectric energy harvester was simulated by the finite element method, implying that the energy harvesting level significantly depends on implant location over epicardium. The results of this study open the potential of designing novel energy harvesters based on accurate heart movements and provide a foundation for future investigations of energy harvesting for leadless pacemaker energy systems.

Autonomous driving presents a complex challenge, which is usually addressed with artificial intelligence models that are end-to-end or modular in nature. Within the landscape of modular approaches, a bio-inspired neural circuit policy model has emerged as an innovative control module, offering a compact and inherently interpretable system to infer a steering wheel command from abstract visual features. Here, we take a leap forward by integrating a variational autoencoder with the neural circuit policy controller, forming a solution that directly generates steering commands from input camera images. By substituting the traditional convolutional neural network approach to feature extraction with a variational autoencoder, we enhance the system's interpretability, enabling a more transparent and understandable decision-making process. In addition to the architectural shift toward a variational autoencoder, this study introduces the automatic latent perturbation tool, a novel contribution designed to probe and elucidate the latent features within the variational autoencoder. The automatic latent perturbation tool automates the interpretability process, offering granular insights into how specific latent variables influence the overall model's behavior. Through a series of numerical experiments, we demonstrate the interpretative power of the variational autoencoder-neural circuit policy model and the utility of the automatic latent perturbation tool in making the inner workings of autonomous driving systems more transparent., Comment: Submitted to 2024 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2024)

In the dynamic landscape of machine learning, where datasets vary widely in size and complexity, selecting the most effective model poses a significant challenge. Rather than fixating on a single model, our research propels the field forward with a novel emphasis on dynamic model switching. This paradigm shift allows us to harness the inherent strengths of different models based on the evolving size of the dataset. Consider the scenario where CatBoost demonstrates exceptional efficacy in handling smaller datasets, providing nuanced insights and accurate predictions. However, as datasets grow in size and intricacy, XGBoost, with its scalability and robustness, becomes the preferred choice. Our approach introduces an adaptive ensemble that intuitively transitions between CatBoost and XGBoost. This seamless switching is not arbitrary; instead, it's guided by a user-defined accuracy threshold, ensuring a meticulous balance between model sophistication and data requirements. The user sets a benchmark, say 80% accuracy, prompting the system to dynamically shift to the new model only if it guarantees improved performance. This dynamic model-switching mechanism aligns with the evolving nature of data in real-world scenarios. It offers practitioners a flexible and efficient solution, catering to diverse dataset sizes and optimising predictive accuracy at every juncture. Our research, therefore, stands at the forefront of innovation, redefining how machine learning models adapt and excel in the face of varying dataset dynamics.

Numerous developments in the recent literature show the promising potential of deep learning in obtaining numerical solutions to partial differential equations (PDEs) beyond the reach of current numerical solvers. However, data-driven neural operators all suffer from a similar problem: the data needed to train a network depends on classical numerical solvers such as finite difference or finite element, among others. In this paper, we propose a different approach to generating synthetic functional training data that does not require solving a PDE numerically. We draw a large number $N$ of independent and identically distributed 'random functions' $u_j$ from the underlying solution space (e.g., $H_0^1(\Omega)$) in which we know the solution lies according to classical theory. We then plug each such random candidate solution into the equation and get a corresponding right-hand side function $f_j$ for the equation, and consider $(f_j, u_j)_{j=1}^N$ as supervised training data for learning the underlying inverse problem $f \rightarrow u$. This `backwards' approach to generating training data only requires derivative computations, in contrast to standard `forward' approaches, which require a numerical PDE solver, enabling us to generate many data points quickly and efficiently. While the idea is simple, we hope this method will expand the potential for developing neural PDE solvers that do not depend on classical numerical solvers.