On extensions of representations for compact Lie groups

Let $H$ be a closed normal subgroup of a compact Lie group $G$ such that $G/H$ is connected. This paper provides a necessary and sufficient condition for every complex representation of $H$ to be extendible to $G$, and also for every complex $G$-vector bundle over the homogeneous space $G/H$ to be trivial. In particular, we show that the condition holds when the fundamental group of $G/H$ is torsion free.Comment: 10 pages, AMS-LaTeX v1.

Model-based Offline Reinforcement Learning with Count-based Conservatism

In this paper, we propose a model-based offline reinforcement learning method that integrates count-based conservatism, named $\texttt{Count-MORL}$. Our method utilizes the count estimates of state-action pairs to quantify model estimation error, marking the first algorithm of demonstrating the efficacy of count-based conservatism in model-based offline deep RL to the best of our knowledge. For our proposed method, we first show that the estimation error is inversely proportional to the frequency of state-action pairs. Secondly, we demonstrate that the learned policy under the count-based conservative model offers near-optimality performance guarantees. Through extensive numerical experiments, we validate that $\texttt{Count-MORL}$ with hash code implementation significantly outperforms existing offline RL algorithms on the D4RL benchmark datasets. The code is accessible at $\href{https://github.com/oh-lab/Count-MORL}{https://github.com/oh-lab/Count-MORL}$.Comment: Accepted in ICML 202

Incremental Few-Shot Object Detection via Simple Fine-Tuning Approach

In this paper, we explore incremental few-shot object detection (iFSD), which incrementally learns novel classes using only a few examples without revisiting base classes. Previous iFSD works achieved the desired results by applying meta-learning. However, meta-learning approaches show insufficient performance that is difficult to apply to practical problems. In this light, we propose a simple fine-tuning-based approach, the Incremental Two-stage Fine-tuning Approach (iTFA) for iFSD, which contains three steps: 1) base training using abundant base classes with the class-agnostic box regressor, 2) separation of the RoI feature extractor and classifier into the base and novel class branches for preserving base knowledge, and 3) fine-tuning the novel branch using only a few novel class examples. We evaluate our iTFA on the real-world datasets PASCAL VOC, COCO, and LVIS. iTFA achieves competitive performance in COCO and shows a 30% higher AP accuracy than meta-learning methods in the LVIS dataset. Experimental results show the effectiveness and applicability of our proposed method.Comment: Accepted to ICRA 202

Squeeze All: Novel Estimator and Self-Normalized Bound for Linear Contextual Bandits

We propose a linear contextual bandit algorithm with $O(\sqrt{dT\log T})$ regret bound, where $d$ is the dimension of contexts and $T$ isthe time horizon. Our proposed algorithm is equipped with a novel estimator in which exploration is embedded through explicit randomization. Depending on the randomization, our proposed estimator takes contributions either from contexts of all arms or from selected contexts. We establish a self-normalized bound for our estimator, which allows a novel decomposition of the cumulative regret into \textit{additive} dimension-dependent terms instead of multiplicative terms. We also prove a novel lower bound of $\Omega(\sqrt{dT})$ under our problem setting. Hence, the regret of our proposed algorithm matches the lower bound up to logarithmic factors. The numerical experiments support the theoretical guarantees and show that our proposed method outperforms the existing linear bandit algorithms.Comment: Accepted in Artificial Intelligence and Statistics 202

Ultraviolet photodepletion spectroscopy of dibenzo-18-crown-6-ether complexes with alkali metal cations

Ultraviolet photodepletion spectra of dibenzo-18-crown-6-ether complexes with alkali metal cations (M+-DB18C6, M = Cs, Rb, K, Na, and Li) were obtained in the gas phase using electrospray ionization quadrupole ion-trap reflectron time-of-flight mass spectrometry. The spectra exhibited a few distinct absorption bands in the wavenumber region of 35450−37800 cm^(−1). The lowest-energy band was tentatively assigned to be the origin of the S_0-S_1 transition, and the second band to a vibronic transition arising from the “benzene breathing” mode in conjunction with symmetric or asymmetric stretching vibration of the bonds between the metal cation and the oxygen atoms in DB18C6. The red shifts of the origin bands were observed in the spectra as the size of the metal cation in M^+-DB18C6 increased from Li^+ to Cs^+. We suggested that these red shifts arose mainly from the decrease in the binding energies of larger-sized metal cations to DB18C6 at the electronic ground state. These size effects of the metal cations on the geometric and electronic structures, and the binding properties of the complexes at the S_0 and S_1 states were further elucidated by theoretical calculations using density functional and time-dependent density functional theories

Angle Dependence of Landau Level Spectrum in Twisted Bilayer Graphene

In the context of the low energy effective theory, the exact Landau level spectrum of quasiparticles in twisted bilayer graphene with small twist angle is analytically obtained by spheroidal eigenvalues. We analyze the dependence of the Landau levels on the twist angle to find the points, where the two-fold degeneracy for twist angles is lifted in the nonzero modes and below/above which massive/massless fermion pictures become valid. In the perpendicular magnetic field of 10\,T, the degeneracy is removed at $\theta_{{\rm deg}}\sim 3^\circ$ %angles around 3 degrees for a few low levels, specifically, $\theta_{\rm deg}\simeq 2.56^\circ$ for the first pair of nonzero levels and $\theta_{\rm deg}\simeq 3.50^\circ$ for the next pair. Massive quasiparticle appears at $\theta<\theta_{{\rm c}}\simeq 1.17^\circ$ in 10\,T, %angles less than 1.17 degrees. which match perfectly with the recent experimental results. Since our analysis is applicable to the cases of arbitrary constant magnetic fields, we make predictions for the same experiment performed in arbitrary constant magnetic fields, e.g., for B=40\,T we get $\theta_{\rm c}\simeq 2.34^\circ$ and the sequence of angles $\theta_{\rm deg} = 5.11, 7.01, 8.42,...$ for the pairs of nonzero energy levels. The symmetry restoration mechanism behind the massive/massless transition is conjectured to be a tunneling (instanton) in momentum space.Comment: 8 pages, 7 figures, version to appear in PR

Development and characterization of nine polymorphic microsatellite markers in the seven-spotted lady beetle, Coccinella septempunctata (Coleoptera: Coccinellidae)

In this study, nine microsatellite loci were isolated and characterized from the seven-spotted lady beetle, Coccinella septempunctata (Coleoptera: Coccinellidae). The loci were validated and characterized using 20 samples collected from five Korean localities. These results indicate that some loci were highly variable in terms of number of alleles (2 to 13), heterozygosity (0.10 to 0.40), and polymorphic information content (0.31 to 0.85). These microsatellite markers will be very valuable for population genetic studies of C. septempunctata.Key words: Seven-spotted lady beetle, Coccinella septempunctata, microsatellite Deoxyribonucleic acid (DNA)

Image-Object-Specific Prompt Learning for Few-Shot Class-Incremental Learning

While many FSCIL studies have been undertaken, achieving satisfactory performance, especially during incremental sessions, has remained challenging. One prominent challenge is that the encoder, trained with an ample base session training set, often underperforms in incremental sessions. In this study, we introduce a novel training framework for FSCIL, capitalizing on the generalizability of the Contrastive Language-Image Pre-training (CLIP) model to unseen classes. We achieve this by formulating image-object-specific (IOS) classifiers for the input images. Here, an IOS classifier refers to one that targets specific attributes (like wings or wheels) of class objects rather than the image's background. To create these IOS classifiers, we encode a bias prompt into the classifiers using our specially designed module, which harnesses key-prompt pairs to pinpoint the IOS features of classes in each session. From an FSCIL standpoint, our framework is structured to retain previous knowledge and swiftly adapt to new sessions without forgetting or overfitting. This considers the updatability of modules in each session and some tricks empirically found for fast convergence. Our approach consistently demonstrates superior performance compared to state-of-the-art methods across the miniImageNet, CIFAR100, and CUB200 datasets. Further, we provide additional experiments to validate our learned model's ability to achieve IOS classifiers. We also conduct ablation studies to analyze the impact of each module within the architecture.Comment: 8 pages, 4 figures, 4 table