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Control Barrier Functions (CBF) have provided a very versatile framework for the synthesis of safe control architectures for a wide class of nonlinear dynamical systems. Typically, CBF-based synthesis approaches apply to systems that exhibit nonlinear -- but smooth -- relationship in the state of the system and linear relationship in the control input. In contrast, the problem of safe control synthesis using CBF for hybrid dynamical systems, i.e., systems which have a discontinuous relationship in the system state, remains largely unexplored. In this work, we build upon the progress on CBF-based control to formulate a theory for safe control synthesis for hybrid dynamical systems. Under the assumption that local CBFs can be synthesized for each mode of operation of the hybrid system, we show how to construct CBF that can guarantee safe switching between modes. The end result is a switching CBF-based controller which provides global safety guarantees. The effectiveness of our proposed approach is demonstrated on two simulation studies.

Motivated by recent experimental reports of Majorana zero modes (MZMs) in quantum-dot systems at the ``sweet spot'', where the electronic hopping $t_h$ is equal to the superconducting coupling $\Delta$, we study the time-dependent spectroscopy corresponding to the non-trivial fusion of MZMs. The expression non-trivial refers to the fusion of Majoranas from different original pairs of MZMs, each with well-defined parities. For the first time, we employ an experimentally accessible time-dependent real-space local density-of-states (LDOS) method to investigate the non-trivial MZMs fusion outcomes in canonical chains and in a Y-shape array of interacting electrons. In the case of quantum-dot chains where two pairs of MZMs are initially disconnected, after fusion we find equal-height peaks in the electron and hole components of the LDOS, signaling non-trivial fusion into both the vacuum $I$ and fermion $\Psi$ channels with equal weight. For $\pi$-junction quantum-dot chains, where the superconducting phase has opposite signs on the left and right portions of the chain, after the non-trivial fusion, we observed the formation of an exotic two-site MZM near the center of the chain, coexisting with another single-site MZM. Furthermore, we also studied the fusion of three MZMs in the Y-shape geometry. In this case, after the fusion we observed the novel formation of another exotic multi-site MZM, with properties depending on the connection and geometry of the central region of the Y-shape quantum-dot array., Comment: 14 pages, 10 Figures

Matrix factorization (MF) is a simple collaborative filtering technique that achieves superior recommendation accuracy by decomposing the user-item interaction matrix into user and item latent matrices. Because the model typically learns each interaction independently, it may overlook the underlying shared dependencies between users and items, resulting in less stable and interpretable recommendations. Based on these insights, we propose "Hierarchical Matrix Factorization" (HMF), which incorporates clustering concepts to capture the hierarchy, where leaf nodes and other nodes correspond to users/items and clusters, respectively. Central to our approach, called hierarchical embeddings, is the additional decomposition of the latent matrices (embeddings) into probabilistic connection matrices, which link the hierarchy, and a root cluster latent matrix. The embeddings are differentiable, allowing simultaneous learning of interactions and clustering using a single gradient descent method. Furthermore, the obtained cluster-specific interactions naturally summarize user-item interactions and provide interpretability. Experimental results on ratings and ranking predictions show that HMF outperforms existing MF methods, in particular achieving a 1.37 point improvement in RMSE for sparse interactions. Additionally, it was confirmed that the clustering integration of HMF has the potential for faster learning convergence and mitigation of overfitting compared to MF, and also provides interpretability through a cluster-centered case study.

We investigated the optical properties of single crystals of one-dimensional telluride Ta4SiTe4, which shows high thermoelectric performance below room temperature. Optical conductivity estimated from reflectivity spectra indicates the presence of a small energy gap of 0.1-0.15 eV at the Fermi energy. At the lowest energy, optical conductivity along the Ta4SiTe4 chain is an order of magnitude higher than that perpendicular to this direction, reflecting the anisotropic electron conduction in Ta4SiTe4. These results indicate that coexistence of a very small band gap and anisotropic electron conduction is a promising strategy to develop a high-performance thermoelectric material for low temperature applications., Comment: 6 pages, 4 figures

Major depressive disorder (MDD) is a complex psychiatric disorder that affects the lives of hundreds of millions of individuals around the globe. Even today, researchers debate if morphological alterations in the brain are linked to MDD, likely due to the heterogeneity of this disorder. The application of deep learning tools to neuroimaging data, capable of capturing complex non-linear patterns, has the potential to provide diagnostic and predictive biomarkers for MDD. However, previous attempts to demarcate MDD patients and healthy controls (HC) based on segmented cortical features via linear machine learning approaches have reported low accuracies. In this study, we used globally representative data from the ENIGMA-MDD working group containing an extensive sample of people with MDD (N=2,772) and HC (N=4,240), which allows a comprehensive analysis with generalizable results. Based on the hypothesis that integration of vertex-wise cortical features can improve classification performance, we evaluated the classification of a DenseNet and a Support Vector Machine (SVM), with the expectation that the former would outperform the latter. As we analyzed a multi-site sample, we additionally applied the ComBat harmonization tool to remove potential nuisance effects of site. We found that both classifiers exhibited close to chance performance (balanced accuracy DenseNet: 51%; SVM: 53%), when estimated on unseen sites. Slightly higher classification performance (balanced accuracy DenseNet: 58%; SVM: 55%) was found when the cross-validation folds contained subjects from all sites, indicating site effect. In conclusion, the integration of vertex-wise morphometric features and the use of the non-linear classifier did not lead to the differentiability between MDD and HC. Our results support the notion that MDD classification on this combination of features and classifiers is unfeasible.

We investigate the S=1 antiferromagnetic quantum spin chain with the exchange and single-ion anisotropies in a magnetic field, using the numerical exact diagonalization of finite-size clusters, the level spectroscopy analysis, and the density matrix renormalization group (DMRG) method. It is found that a translational symmetry broken magnetization plateau possibly appears at the half of the saturation magnetization, when the anisotropies compete with each other. The level spectroscopy analysis gives the phase diagram at half the saturation magnetization. The DMRG calculation presents the magnetization curves for some typical parameters and clarifies the spin structure in the plateau phase., Comment: 7 pages, 12 figures, to appear in Phys. Rev. B

Decision trees are essential yet NP-complete to train, prompting the widespread use of heuristic methods such as CART, which suffers from sub-optimal performance due to its greedy nature. Recently, breakthroughs in finding optimal decision trees have emerged; however, these methods still face significant computational costs and struggle with continuous features in large-scale datasets and deep trees. To address these limitations, we introduce a moving-horizon differential evolution algorithm for classification trees with continuous features (MH-DEOCT). Our approach consists of a discrete tree decoding method that eliminates duplicated searches between adjacent samples, a GPU-accelerated implementation that significantly reduces running time, and a moving-horizon strategy that iteratively trains shallow subtrees at each node to balance the vision and optimizer capability. Comprehensive studies on 68 UCI datasets demonstrate that our approach outperforms the heuristic method CART on training and testing accuracy by an average of 3.44% and 1.71%, respectively. Moreover, these numerical studies empirically demonstrate that MH-DEOCT achieves near-optimal performance (only 0.38% and 0.06% worse than the global optimal method on training and testing, respectively), while it offers remarkable scalability for deep trees (e.g., depth=8) and large-scale datasets (e.g., ten million samples)., Comment: 36 pages (13 pages for the main body, 23 pages for the appendix), 7 figures

We present the final results of our search for new Milky Way (MW) satellites using the data from the Hyper Suprime-Cam (HSC) Subaru Strategic Program (SSP) survey over $\sim 1,140$ deg$^2$. In addition to three candidates that we already reported, we have identified two new MW satellite candidates in the constellation of Sextans at a heliocentric distance of $D_{\odot} \simeq 126$kpc, and Virgo at $D_{\odot} \simeq 151$kpc, named Sextans II and Virgo III, respectively. Their luminosities (Sext II:$M_V\simeq-3.9$mag; Vir III:$M_V\simeq-2.7$mag) and half-light radii (Sext II:$r_h\simeq154$ pc; Vir III:$r_h\simeq 44$ pc) place them in the region of size-luminosity space of ultra-faint dwarf galaxies (UFDs). Including four previously known satellites, there are a total of nine satellites in the HSC-SSP footprint. This discovery rate of UFDs is much higher than that predicted from the recent models for the expected population of MW satellites in the framework of cold dark matter models, thereby suggesting that we encounter a too many satellites problem. Possible solutions to settle this tension are also discussed., Comment: 20 pages, 17 figures, 4 tables, accepted for publication in PASJ

Cloud-cloud collisions (CCCs) are expected to compress gas and trigger star formation. However, it is not well understood how the collisions and the induced star formation affect galactic-scale properties. By developing an on-the-fly algorithm to identify CCCs at each timestep in a galaxy simulation and a model that relates CCC-triggered star formation to collision speeds, we perform simulations of isolated galaxies to study the evolution of galaxies and giant molecular clouds (GMCs) with prescriptions of self-consistent CCC-driven star formation and stellar feedback. We find that the simulation with the CCC-triggered star formation produces slightly higher star formation rates and a steeper Kennicutt-Schmidt relation than that with a more standard star formation recipe, although collision speeds and frequencies are insensitive to the star formation models. In the simulation with the CCC model, about 70 per cent of the stars are born via CCCs, and colliding GMCs with masses of $\approx 10^{5.5}\,M_{\odot}$ are the main drivers of CCC-driven star formation. In the simulation with the standard star formation recipe, about 50 per cent of stars are born in colliding GMCs even without the CCC-triggered star formation model. These results suggest that CCCs may be one of the most important star formation processes in galaxy evolution. Furthermore, we find that a post-processing analysis of CCCs, as used in previous studies in galaxy simulations, may lead to slightly greater collision speeds and significantly lower collision frequencies than the on-the-fly analysis., Comment: 18 pages, 16 figures, published in MNRAS

In recent years, document processing has flourished and brought numerous benefits. However, there has been a significant rise in reported cases of forged document images. Specifically, recent advancements in deep neural network (DNN) methods for generative tasks may amplify the threat of document forgery. Traditional approaches for forged document images created by prevalent copy-move methods are unsuitable against those created by DNN-based methods, as we have verified. To address this issue, we construct a training dataset of document forgery images, named FD-VIED, by emulating possible attacks, such as text addition, removal, and replacement with recent DNN-methods. Additionally, we introduce an effective pre-training approach through self-supervised learning with both natural images and document images. In our experiments, we demonstrate that our approach enhances detection performance.

Structural fluctuations and dynamic cross-correlations in the mouse eugenol olfactory receptor (Olfr73) were studied by molecular dynamics (MD) simulation to characterize the dynamic response of the protein upon ligand binding. The initial structure was generated by the artificial intelligence tool AlfaFold2 due to the current lack of experimental data. We focused on the hydrogen (H) bond of the odorant eugenol to Ser113, Asn207, and Tyr260 of the receptor protein, the importance of which has been suggested by previous experimental studies. The H-bond was not observed in docking simulations, but in subsequent MD simulations the H-bond to Ser113 was formed in 2--4 ns. The lifetime of the H-bond was in the range of 1--20 ns. On the trajectory with the most stable (20 ns) H-bond, the structural fluctuation of the $\alpha$-carbon atoms of the receptor main chain was studied by calculating the root mean square fluctuations, the dynamic cross-correlation map, and the time-dependent dynamic cross-correlation. The analysis suggested a correlation transfer pathway Ser113 $\to$ Phe182 $\to$ (Leu259 or Tyr260) $\to$ Tyr291 induced by the ligand binding with a time scale of 4--6 ns., Comment: 6 pages, 8 figures

In the presence of sample selection, Lee's (2009) nonparametric bounds are a popular tool for estimating a treatment effect. However, the Lee bounds rely on the monotonicity assumption, whose empirical validity is sometimes unclear. Furthermore, the bounds are often regarded to be wide and less informative even under monotonicity. To address these issues, this study introduces a stochastic version of the monotonicity assumption alongside a nonparametric distributional shape constraint. The former enhances the robustness of the Lee bounds with respect to monotonicity, while the latter helps tighten these bounds. The obtained bounds do not rely on the exclusion restriction and can be root-$n$ consistently estimable, making them practically viable. The potential usefulness of the proposed methods is illustrated by their application on experimental data from the after-school instruction programme studied by Muralidharan, Singh, and Ganimian (2019).