Flow matching has recently emerged as a powerful framework for continuous-time generative modeling. However, when applied to long-tailed distributions, standard flow matching suffers from majority bias, producing minority modes with low fidelity and failing to match the true class proportions. In this work, we propose Unbalanced Optimal Transport Reweighted Flow Matching (UOT-RFM), a novel framework for generative modeling under class-imbalanced (long-tailed) distributions that operates without any class label information. Our method constructs the conditional vector field using mini-batch Unbalanced Optimal Transport (UOT) and mitigates majority bias through a principled inverse reweighting strategy. The reweighting relies on a label-free majority score, defined as the density ratio between the target distribution and the UOT marginal. This score quantifies the degree of majority based on the geometric structure of the data, without requiring class labels. By incorporating this score into the training objective, UOT-RFM theoretically recovers the target distribution with first-order correction ($k=1$) and empirically improves tail-class generation through higher-order corrections ($k > 1$). Our model outperforms existing flow matching baselines on long-tailed benchmarks, while maintaining competitive performance on balanced datasets.

We present a novel framework for CBCT-to-MDCT translation, grounded in the Schrodinger Bridge (SB) formulation, which integrates GAN-derived priors with human-guided conditional diffusion. Unlike conventional GANs or diffusion models, our approach explicitly enforces boundary consistency between CBCT inputs and pseudo targets, ensuring both anatomical fidelity and perceptual controllability. Binary human feedback is incorporated via classifier-free guidance (CFG), effectively steering the generative process toward clinically preferred outcomes. Through iterative refinement and tournament-based preference selection, the model internalizes human preferences without relying on a reward model. Subtraction image visualizations reveal that the proposed method selectively attenuates shade artifacts in key anatomical regions while preserving fine structural detail. Quantitative evaluations further demonstrate superior performance across RMSE, SSIM, LPIPS, and Dice metrics on clinical datasets -- outperforming prior GAN- and fine-tuning-based feedback methods -- while requiring only 10 sampling steps. These findings underscore the effectiveness and efficiency of our framework for real-time, preference-aligned medical image translation.

The absorption cross section is studied in the low-frequency region for a propagating scalar field under the warped AdS$_3$ black hole background in the topologically massive gravity. It can be shown that the absorption cross section is significantly deformed by the gravitational Chern-Simons term, which is proportional to the scattering area of black hole with an additional contribution depending on the left-moving and right-moving temperatures. It means that the cross section is larger than the area in spite of the s-wave limit. Finally, we discuss the left-right quasinormal modes for the scalar perturbation in this black hole.

Gravitational waves provide a unique tool for observational astronomy. While the first LIGO--Virgo catalogue of gravitational-wave transients (GWTC-1) contains eleven signals from black hole and neutron star binaries, the number of observations is increasing rapidly as detector sensitivity improves. To extract information from the observed signals, it is imperative to have fast, flexible, and scalable inference techniques. In a previous paper, we introduced BILBY: a modular and user-friendly Bayesian inference library adapted to address the needs of gravitational-wave inference. In this work, we demonstrate that BILBY produces reliable results for simulated gravitational-wave signals from compact binary mergers, and verify that it accurately reproduces results reported for the eleven GWTC-1 signals. Additionally, we provide configuration and output files for all analyses to allow for easy reproduction, modification, and future use. This work establishes that BILBY is primed and ready to analyse the rapidly growing population of compact binary coalescence gravitational-wave signals.

We propose a mesh-free policy iteration framework that combines classical dynamic programming with physics-informed neural networks (PINNs) to solve high-dimensional, nonconvex Hamilton--Jacobi--Isaacs (HJI) equations arising in stochastic differential games and robust control. The method alternates between solving linear second-order PDEs under fixed feedback policies and updating the controls via pointwise minimax optimization using automatic differentiation. Under standard Lipschitz and uniform ellipticity assumptions, we prove that the value function iterates converge locally uniformly to the unique viscosity solution of the HJI equation. The analysis establishes equi-Lipschitz regularity of the iterates, enabling provable stability and convergence without requiring convexity of the Hamiltonian. Numerical experiments demonstrate the accuracy and scalability of the method. In a two-dimensional stochastic path-planning game with a moving obstacle, our method matches finite-difference benchmarks with relative $L^2$-errors below %10^{-2}%. In five- and ten-dimensional publisher-subscriber differential games with anisotropic noise, the proposed approach consistently outperforms direct PINN solvers, yielding smoother value functions and lower residuals. Our results suggest that integrating PINNs with policy iteration is a practical and theoretically grounded method for solving high-dimensional, nonconvex HJI equations, with potential applications in robotics, finance, and multi-agent reinforcement learning.

Variational autoencoders (VAEs), one of the most widely used generative models, are known to suffer from posterior collapse, a phenomenon that reduces the diversity of generated samples. To avoid posterior collapse, many prior works have tried to control the influence of regularization loss. However, the trade-off between reconstruction and regularization is not satisfactory. For this reason, several methods have been proposed to guarantee latent identifiability, which is the key to avoiding posterior collapse. However, they require structural constraints on the network architecture. For further clarification, we define local posterior collapse to reflect the importance of individual sample points in the data space and to relax the network constraint. Then, we propose Latent Reconstruction(LR) loss, which is inspired by mathematical properties of injective and composite functions, to control posterior collapse without restriction to a specific architecture. We experimentally evaluate our approach, which controls posterior collapse on varied datasets such as MNIST, fashionMNIST, Omniglot, CelebA, and FFHQ.

We search for gravitational-wave signals associated with gamma-ray bursts detected by the Fermi and Swift satellites during the second half of the third observing run of Advanced LIGO and Advanced Virgo (1 November 2019 15:00 UTC-27 March 2020 17:00 UTC).We conduct two independent searches: a generic gravitational-wave transients search to analyze 86 gamma-ray bursts and an analysis to target binary mergers with at least one neutron star as short gamma-ray burst progenitors for 17 events. We find no significant evidence for gravitational-wave signals associated with any of these gamma-ray bursts. A weighted binomial test of the combined results finds no evidence for sub-threshold gravitational wave signals associated with this GRB ensemble either. We use several source types and signal morphologies during the searches, resulting in lower bounds on the estimated distance to each gamma-ray burst. Finally, we constrain the population of low luminosity short gamma-ray bursts using results from the first to the third observing runs of Advanced LIGO and Advanced Virgo. The resulting population is in accordance with the local binary neutron star merger rate.

We describe a search for gravitational waves from compact binaries with at least one component with mass 0.2 $M_\odot$ -- $1.0 M_\odot$ and mass ratio $q \geq 0.1$ in Advanced LIGO and Advanced Virgo data collected between 1 November 2019, 15:00 UTC and 27 March 2020, 17:00 UTC. No signals were detected. The most significant candidate has a false alarm rate of 0.2 $\mathrm{yr}^{-1}$. We estimate the sensitivity of our search over the entirety of Advanced LIGO's and Advanced Virgo's third observing run, and present the most stringent limits to date on the merger rate of binary black holes with at least one subsolar-mass component. We use the upper limits to constrain two fiducial scenarios that could produce subsolar-mass black holes: primordial black holes (PBH) and a model of dissipative dark matter. The PBH model uses recent prescriptions for the merger rate of PBH binaries that include a rate suppression factor to effectively account for PBH early binary disruptions. If the PBHs are monochromatically distributed, we can exclude a dark matter fraction in PBHs $f_\mathrm{PBH} \gtrsim 0.6$ (at 90% confidence) in the probed subsolar-mass range. However, if we allow for broad PBH mass distributions we are unable to rule out $f_\mathrm{PBH} = 1$. For the dissipative model, where the dark matter has chemistry that allows a small fraction to cool and collapse into black holes, we find an upper bound f_{\mathrm{DBH}} < 10^{-5} on the fraction of atomic dark matter collapsed into black holes.

We investigate the electroweak phase transition (EWPT) within the inverted Type-I two-Higgs-doublet model, where the observed $125\,\text{GeV}$ Higgs boson is identified as the heavier \textit{CP}-even scalar $H$. Through a comprehensive parameter-space scan consistent with current theoretical and experimental constraints, we identify regions supporting strong first-order EWPTs (SFOEWPTs), including multi-step transitions. We find that two-step SFOEWPTs occur as frequently as one-step transitions, while three-step transitions can occur, albeit rarely. Crucially, the parameter spaces inducing one-step and two-step transitions are partially yet significantly separated: one-step transitions restrict the charged Higgs mass and $\tan\beta$ to $m_{H^\pm}\in[295,441]\,\text{GeV}$ and $\tan\beta\in[4.2,8.8]$, whereas two-step transitions allow $m_{H^\pm}\in[100,350]\,\text{GeV}$ and $\tan\beta\in[2.5,45.4]$. Notably, negative values of $\sin(\beta-\alpha)$ arise almost exclusively in one-step scenarios. We present the calculation of gravitational wave (GW) signal-to-noise ratios (SNRs) at LISA for multi-step EWPTs, finding that detectable GW signals ($\text{SNR}>10$) predominantly emerge from two-step transitions. Furthermore, we demonstrate that the correlation between the vacuum uplifting measure $\Delta F_0$ and $\xi_c$ persists in one-step transitions and breaks down in multi-step cases. Finally, we perform a dedicated collider analysis for representative SFOEWPT parameter points at the $1.5\,\text{TeV}$ CLIC, identifying $e^+ e^- \to H^+ H^- \to W^+ W^- hh$ as a promising discovery channel. Enhanced $h\to\gamma\gamma$ branching ratios for negative $\sin(\beta-\alpha)$ motivate two complementary golden final states, $W^+ W^- b\bar{b} \tau^+ \tau^-$ and $W^+ W^- b\bar{b}\gamma\gamma$, which demonstrate high discovery potential due to negligible Standard Model backgrounds.

We develop the viscosity method for the homogenization of an obstacle problem with highly oscillating obstacles. The associated operator, in non-divergence form, is linear and elliptic with variable coefficients. We first construct a highly oscillating corrector, which captures the singular behavior of solutions near periodically distributed holes of critical size. We then prove the uniqueness of a critical value that encodes the coupled effects of oscillations in both the coefficients and the obstacles.

This paper presents a fully automatic registration method of dental cone-beam computed tomography (CBCT) and face scan data. It can be used for a digital platform of 3D jaw-teeth-face models in a variety of applications, including 3D digital treatment planning and orthognathic surgery. Difficulties in accurately merging facial scans and CBCT images are due to the different image acquisition methods and limited area of correspondence between the two facial surfaces. In addition, it is difficult to use machine learning techniques because they use face-related 3D medical data with radiation exposure, which are difficult to obtain for training. The proposed method addresses these problems by reusing an existing machine-learning-based 2D landmark detection algorithm in an open-source library and developing a novel mathematical algorithm that identifies paired 3D landmarks from knowledge of the corresponding 2D landmarks. A main contribution of this study is that the proposed method does not require annotated training data of facial landmarks because it uses a pre-trained facial landmark detection algorithm that is known to be robust and generalized to various 2D face image models. Note that this reduces a 3D landmark detection problem to a 2D problem of identifying the corresponding landmarks on two 2D projection images generated from two different projection angles. Here, the 3D landmarks for registration were selected from the sub-surfaces with the least geometric change under the CBCT and face scan environments. For the final fine-tuning of the registration, the Iterative Closest Point method was applied, which utilizes geometrical information around the 3D landmarks. The experimental results show that the proposed method achieved an averaged surface distance error of 0.74 mm for three pairs of CBCT and face scan datasets.

This paper proposes a sinogram consistency learning method to deal with beam-hardening related artifacts in polychromatic computerized tomography (CT). The presence of highly attenuating materials in the scan field causes an inconsistent sinogram, that does not match the range space of the Radon transform. When the mismatched data are entered into the range space during CT reconstruction, streaking and shading artifacts are generated owing to the inherent nature of the inverse Radon transform. The proposed learning method aims to repair inconsistent sinograms by removing the primary metal-induced beam-hardening factors along the metal trace in the sinogram. Taking account of the fundamental difficulty in obtaining sufficient training data in a medical environment, the learning method is designed to use simulated training data and a patient-type specific learning model is used to simplify the learning process. The feasibility of the proposed method is investigated using a dataset, consisting of real CT scan of pelvises containing hip prostheses. The anatomical areas in training and test data are different, in order to demonstrate that the proposed method extracts the beam hardening features, selectively. The results show that our method successfully corrects sinogram inconsistency by extracting beam-hardening sources by means of deep learning. This paper proposed a deep learning method of sinogram correction for beam hardening reduction in CT for the first time. Conventional methods for beam hardening reduction are based on regularizations, and have the fundamental drawback of being not easily able to use manifold CT images, while a deep learning approach has the potential to do so.

We provide analysis to determine the effects of gravitational waves on electromagnetic waves, using perturbation theory in general relativity. Our analysis is performed in a completely covariant manner without invoking any coordinates. For a given observer, in the geometrical-optics approximation, we work out the perturbations of the phase, amplitude, frequency and polarization properties--axes of ellipse and ellipticity of light, due to gravitational waves. With regard to the observation of gravitational waves, we discuss the measurement of Stokes parameters, through which the antenna patterns are presented to show the detectability of the gravitational wave signals.

This paper investigates geometric properties and well-posedness of a mean curvature flow with volume-dependent forcing. With the class of forcing which bounds the volume of the evolving set away from zero and infinity, we show that a strong version of star-shapedness is preserved over time. More precisely, it is shown that the flow preserves the $\rho$-reflection property, which corresponds to a quantitative Lipschitz property of the set with respect to the nearest ball. Based on this property we show that the problem is well-posed and its solutions starting with $\rho$-reflection property become instantly smooth. Lastly, for a model problem, we will discuss the flow's exponential convergence to the unique equilibrium in Hausdorff topology. For the analysis, we adopt the approach developed in [Kim-Feldman, 2014] to combine viscosity solutions approach and variational method. The main challenge lies in the lack of comparison principle, which accompanies forcing terms that penalize small volume.

In dental cone-beam computed tomography (CBCT), compact and cost-effective system designs often use small detectors, resulting in a truncated field of view (FOV) that does not fully encompass the patient's head. In iterative reconstruction approaches, the discrepancy between the actual projection and the forward projection within the truncated FOV accumulates over iterations, leading to significant degradation in the reconstructed image quality. In this study, we propose a two-stage approach to mitigate truncation artifacts in dental CBCT. In the first stage, we employ Implicit Neural Representation (INR), leveraging its superior representation power, to generate a prior image over an extended region so that its forward projection fully covers the patient's head. To reduce computational and memory burdens, INR reconstruction is performed with a coarse voxel size. The forward projection of this prior image is then used to estimate the discrepancy due to truncated FOV in the measured projection data. In the second stage, the discrepancy-corrected projection data is utilized in a conventional iterative reconstruction process within the truncated region. Our numerical results demonstrate that the proposed two-grid approach effectively suppresses truncation artifacts, leading to improved CBCT image quality.

We consider Gromov's homological higher convexity for complements of tropical varieties, establishing it for complements of tropical hypersurfaces and curves, and for nonarchimedean amoebas of varieties that are complete intersections over the field of complex Puiseaux series. Based on these results, we conjecture that the complement of a tropical variety has this higher convexity, and we prove a weak form of our conjecture for the nonarchimedean amoeba of a variety over the complex Puiseaux field. One of our main tools is Jonsson's limit theorem for tropical varieties.

In the data obtained by laser interferometric gravitational wave detectors, transient noise with non-stationary and non-Gaussian features occurs at a high rate. This often results in problems such as detector instability and the hiding and/or imitation of gravitational-wave signals. This transient noise has various characteristics in the time--frequency representation, which is considered to be associated with environmental and instrumental origins. Classification of transient noise can offer clues for exploring its origin and improving the performance of the detector. One approach for accomplishing this is supervised learning. However, in general, supervised learning requires annotation of the training data, and there are issues with ensuring objectivity in the classification and its corresponding new classes. By contrast, unsupervised learning can reduce the annotation work for the training data and ensure objectivity in the classification and its corresponding new classes. In this study, we propose an unsupervised learning architecture for the classification of transient noise that combines a variational autoencoder and invariant information clustering. To evaluate the effectiveness of the proposed architecture, we used the dataset (time--frequency two-dimensional spectrogram images and labels) of the Laser Interferometer Gravitational-wave Observatory (LIGO) first observation run prepared by the Gravity Spy project. The classes provided by our proposed unsupervised learning architecture were consistent with the labels annotated by the Gravity Spy project, which manifests the potential for the existence of unrevealed classes.

In the absence of a unique, gauge-independent definition of eccentricity in General Relativity, there have been efforts to standardize the definition for Gravitational-Wave astronomy. Recently, Shaikh et al. proposed a model-independent measurement of eccentricity $e_{\mathrm{gw}}$ from the phase evolution of the dominant mode. Many works use loss functions (LFs) to assign eccentricity to a reference waveform, for instance by fitting a Post-Newtonian expression to assign eccentricity to Numerical Relativity (NR) simulations. Therefore, we ask whether minimizing common LFs on gauge-dependent model parameters, such as the mismatch $\mathcal{M}$ or the $L_2$-norm of the dominant mode $h_{22}$ residuals, for non-precessing binaries, ensures a sufficient $e_{\mathrm{gw}}$ agreement. We use $10$ eccentric NR simulations and the eccentric waveform TEOBResumS-Dali as the parametric model to fit on eccentricity $e_0$ and reference frequency $f_0$. We first show that a minimized mismatch, the $\mathcal{M} \sim 10^{-3}- 10^{-2}$ results in better $e_{\mathrm{gw}}$ fractional differences ($\sim 1\%$) than with the minimized $h_{22}$ residuals. Nonetheless, for small eccentricity NR simulations $(e_{\mathrm{gw}} \lesssim 10^{-2}$), the mismatch can favor quasi-circular ($e_0=0$) best-fit models. Thus, with sufficiently long NR simulations, we can include $e_{\mathrm{gw}}$ in the LF. We explain why solely fitting with $e_{\mathrm{gw}}$ constitutes a degenerate problem. To circumvent these limitations, we propose to minimize a convex sum of $\mathcal{M}$ and the $e_{\mathrm{gw}}$ difference to both assign non-zero eccentric values to NR strains and to control the mismatch threshold.

Graph Neural Networks (GNNs) and Transformer-based models have been increasingly adopted to learn the complex vector representations of spatio-temporal graphs, capturing intricate spatio-temporal dependencies crucial for applications such as traffic datasets. Although many existing methods utilize multi-head attention mechanisms and message-passing neural networks (MPNNs) to capture both spatial and temporal relations, these approaches encode temporal and spatial relations independently, and reflect the graph's topological characteristics in a limited manner. In this work, we introduce the Cycle to Mixer (Cy2Mixer), a novel spatio-temporal GNN based on topological non-trivial invariants of spatio-temporal graphs with gated multi-layer perceptrons (gMLP). The Cy2Mixer is composed of three blocks based on MLPs: A temporal block for capturing temporal properties, a message-passing block for encapsulating spatial information, and a cycle message-passing block for enriching topological information through cyclic subgraphs. We bolster the effectiveness of Cy2Mixer with mathematical evidence emphasizing that our cycle message-passing block is capable of offering differentiated information to the deep learning model compared to the message-passing block. Furthermore, empirical evaluations substantiate the efficacy of the Cy2Mixer, demonstrating state-of-the-art performances across various spatio-temporal benchmark datasets. The source code is available at \url{this https URL}.