In this paper, we introduce new algorithms for Principal Component Analysis (PCA) with outliers. Utilizing techniques from computational geometry, specifically higher-degree Voronoi diagrams, we navigate to the optimal subspace for PCA even in the presence of outliers. This approach achieves an optimal solution with a time complexity of $n^{d+\mathcal{O}(1)}\text{poly}(n,d)$. Additionally, we present a randomized algorithm with a complexity of $2^{\mathcal{O}(r(d-r))} \times \text{poly}(n, d)$. This algorithm samples subspaces characterized in terms of a Grassmannian manifold. By employing such sampling method, we ensure a high likelihood of capturing the optimal subspace, with the success probability $(1 - \delta)^T$. Where $\delta$ represents the probability that a sampled subspace does not contain the optimal solution, and $T$ is the number of subspaces sampled, proportional to $2^{r(d-r)}$. Our use of higher-degree Voronoi diagrams and Grassmannian based sampling offers a clearer conceptual pathway and practical advantages, particularly in handling large datasets or higher-dimensional settings.

The classical and quantum aspects of the Schwinger model on the torus are considered. First we find explicitly all zero modes of the Dirac operator in the topological sectors with nontrivial Chern index and is spectrum. In the second part we determine the regularized effective action and discuss the propagators related to it. Finally we calculate the gauge invariant averages of the fermion bilinears and correlation functions of currents and densities. We show that in the infinite volume limit the well-known result for the chiral condensate can be obtained and the clustering property can be established.

Accurately distinguishing between quiescent and star-forming galaxies is essential for understanding galaxy evolution. Traditional methods, such as spectral energy distribution (SED) fitting, can be computationally expensive and may struggle to capture complex galaxy properties. This study aims to develop a robust and efficient machine learning (ML) classification method to identify quiescent and star-forming galaxies within the Farmer COSMOS2020 catalog. We utilized JWST wide-field light cones from the Santa Cruz semi-analytical modeling framework to train a supervised ML model, the CatBoostClassifier, using 28 color features derived from 8 mutual photometric bands within the COSMOS catalog. The model was validated against a testing set and compared to the SED-fitting method in terms of precision, recall, F1-score, and execution time. Preprocessing steps included addressing missing data, injecting observational noise, and applying a magnitude cut (ch1 < 26 AB) along with a redshift range of 0.2 < z < 3.5 to align the simulated and observational datasets. The ML method achieved an F1-score of 89\% for quiescent galaxies, significantly outperforming the SED-fitting method, which achieved 54%. The ML model demonstrated superior recall (88% vs. 38%) while maintaining comparable precision. When applied to the COSMOS2020 catalog, the ML model predicted a systematically higher fraction of quiescent galaxies across all redshift bins within 0.2 < z < 3.5 compared to traditional methods like NUVrJ and SED-fitting. This study shows that ML, combined with multi-wavelength data, can effectively identify quiescent and star-forming galaxies, providing valuable insights into galaxy evolution. The trained classifier and full classification catalog are publicly available.

The Closest String Problem is an NP-hard problem that aims to find a string that has the minimum distance from all sequences that belong to the given set of strings. Its applications can be found in coding theory, computational biology, and designing degenerated primers, among others. There are efficient exact algorithms that have reached high-quality solutions for binary sequences. However, there is still room for improvement concerning the quality of solutions over DNA and protein sequences. In this paper, we introduce a three-stage algorithm that comprises the following process: first, we apply a novel alphabet pruning method to reduce the search space for effectively finding promising search regions. Second, a variant of beam search to find a heuristic solution is employed. This method utilizes a newly developed guiding function based on an expected distance heuristic score of partial solutions. Last, we introduce a local search to improve the quality of the solution obtained from the beam search. Furthermore, due to the lack of real-world benchmarks, two real-world datasets are introduced to verify the robustness of the method. The extensive experimental results show that the proposed method outperforms the previous approaches from the literature.

We study the ground-state phase diagram of the spin-$1/2$ Kitaev-Heisenberg model on the bilayer honeycomb lattice with large-scale tensor network calculations based on the infinite projected entangled pair state technique as well as high-order series expansions. We find that beyond various magnetically ordered phases, including ferromagnetic, zigzag, antiferromagnetic (AFM) and stripy states, two extended quantum spin liquid phases arise in the proximity of the Kitaev limit. While these ordered phases also appear in the monolayer Kitaev-Heisenberg model, our results further show that a valence bond solid state emerges in a relatively narrow range of parameter space between the AFM and stripy phases, which can be adiabatically connected to isolated Heisenberg dimers. Our results highlight the importance of considering interlayer interactions on the emergence of novel quantum phases in the bilayer Kitaev materials.

Dust layers have already been reported to have negative impacts on the radiation budget of the atmosphere. But the questions are: How does the atmospheric surface temperature change during a dust outbreak, and what is its temporal correlation with variations of the dust outbreak strength? We investigated these at selected AERONET sites, including Bahrain, IASBS, Karachi, KAUST Campus, Kuwait University, Lahore, Mezaira, Solar Village, in Southwest Asia, and Dushanbe in Central Asia, using available data from 1998 to 2024. The aerosol optical depth at 870 nm and the temperature recorded at each site are taken as measures of dust outbreak strength and atmospheric surface temperature, respectively. The Hybrid Single-Particle Lagrangian Integrated Trajectory (HYSPLIT) model and the aerosol optical depths recorded by the Moderate Resolution Imaging Spectroradiometers (MODIS) on board the Aqua and Terra satellites are used to specify the sources of the dust outbreaks. Our investigations show that in most cases, the temperature decreases during a dust outbreak, but in a considerable number of cases, the temperature rises. Temperature changes are mostly less than 5 °C. We found that a dust outbreak may affect the temperature even up to two days after its highest intensity time. This effect is more profound at sites far from large dust sources, such as IASBS in northwest Iran. For sites that are located on either a dust source or very close to it, the temperature and dust optical depth vary almost synchronously.

The dislocation skin effect exhibits the capacity of topological defects to trap an extensive number of modes in two-dimensional non-Hermitian systems. Similar to the corresponding skin effects caused by system boundaries, this phenomenon also originates from nontrivial topology. However, finding the relationship between the dislocation skin effect and nonzero topological invariants, especially in disordered systems, can be obscure and challenging. Here, we introduce a real-space topological invariant based on the spectral localizer to characterize the skin effect on two-dimensional lattices. We demonstrate that this invariant consistently predicts the occurrence and location of both boundary and dislocation skin effects, offering a unified approach applicable to both ordered and disordered systems. Our work demonstrates a general approach that can be utilized to diagnose the topological nature of various types of skin effects, particularly in the absence of translational symmetry when momentum-space descriptions are inapplicable.

Convolutional neural networks (CNNs) are one of the most widely used neural network architectures, showcasing state-of-the-art performance in computer vision tasks. Although larger CNNs generally exhibit higher accuracy, their size can be effectively reduced by ``tensorization'' while maintaining accuracy, namely, replacing the convolution kernels with compact decompositions such as Tucker, Canonical Polyadic decompositions, or quantum-inspired decompositions such as matrix product states, and directly training the factors in the decompositions to bias the learning towards low-rank decompositions. But why doesn't tensorization seem to impact the accuracy adversely? We explore this by assessing how \textit{truncating} the convolution kernels of \textit{dense} (untensorized) CNNs impact their accuracy. Specifically, we truncated the kernels of (i) a vanilla four-layer CNN and (ii) ResNet-50 pre-trained for image classification on CIFAR-10 and CIFAR-100 datasets. We found that kernels (especially those inside deeper layers) could often be truncated along several cuts resulting in significant loss in kernel norm but not in classification accuracy. This suggests that such ``correlation compression'' (underlying tensorization) is an intrinsic feature of how information is encoded in dense CNNs. We also found that aggressively truncated models could often recover the pre-truncation accuracy after only a few epochs of re-training, suggesting that compressing the internal correlations of convolution layers does not often transport the model to a worse minimum. Our results can be applied to tensorize and compress CNN models more effectively.

The notion of `quantum family of maps' (QFM) has been defined by Piotr Soltan as a noncommutative analogue of `parameterized family of continuous maps' between locally compact spaces. A QFM between C*-algebras $B,A$, is given by a pair $(C,\phi)$ where $C$ is a C*-algebra and $\phi:B\rightarrow A\check{\otimes}C$ is a $*$-morphism. The main goal of this note, is to introduce the notion of `random quantum map' (RQM), which is a noncommutative analogue of `random continuous map' between compact spaces. We define a RQM between $B,A$, to be given by a triple $(C,\phi,\nu)$ where $(C,\phi)$ is a QFM and $\nu$ a state (normalized positive linear functional) on $C$. Our first application of RQMs takes place in theory of completely positive maps (CPM): RQMs give rise canonically to a class of CPMs which we call implemented CPMs. We consider some partial results about the natural and important problem of characterization of implemented CPMs. For instance, using Stinespring's Theorem, we show that any CPM from $B$ to $A$ is implemented if $A$ is finite-dimensional. Our second application of RQMs takes place in theory of quantum stochastic processes: We show that iterations of any RQM with $B=A$, gives rise to a quantum Markov chain in a sense introduced by Luigi Accardi.

The Kennicutt-Schmidt law is an empirical relation between the star formation rate surface density ($\Sigma_{SFR}$) and the gas surface density ($\Sigma_{gas}$) in disc galaxies. The relation has a power-law form $\Sigma_{SFR} \propto \Sigma_{gas}^n$. Assuming that star formation results from gravitational collapse of the interstellar medium, $\Sigma_{SFR}$ can be determined by dividing $\Sigma_{gas}$ by the local free-fall time $t_{ff}$. The formulation of $t_{ff}$ yields the relation between $\Sigma_{SFR}$ and $\Sigma_{gas}$, assuming that a constant fraction ($\varepsilon_{SFE}$) of gas is converted into stars every $t_{ff}$. This is done here for the first time using Milgromian dynamics (MOND). Using linear stability analysis of a uniformly rotating thin disc, it is possible to determine the size of a collapsing perturbation within it. This lets us evaluate the sizes and masses of clouds (and their $t_{ff}$) as a function of $\Sigma_{gas}$ and the rotation curve. We analytically derive the relation $\Sigma_{SFR} \propto \Sigma_{gas}^{n}$ both in Newtonian and Milgromian dynamics, finding that $n=1.4$. The difference between the two cases is a change only to the constant pre-factor, resulting in increased $\Sigma_{SFR}$ of up to 25\% using MOND in the central regions of dwarf galaxies. Due to the enhanced role of disk self-gravity, star formation extends out to larger galactocentric radii than in Newtonian gravity, with the clouds being larger. In MOND, a nearly exact representation of the present-day main sequence of galaxies is obtained if $\epsilon_{SFE} = \text{constant} \approx 1.1\%$. We also show that empirically found correction terms to the Kennicutt-Schmidt law are included in the here presented relations. Furthermore, we determine that if star formation is possible, then the temperature only affects $\Sigma_{SFR}$ by at most a factor of $\sqrt{2}$.

In this work, we report on an $ab-initio$ computational study of the electronic and magnetic properties of transition metal adatoms on a monolayer of NbSe$_2$. We demonstrate that Cr, Mn, Fe and Co prefer all to sit above the Nb atom, where the $d$ states experience a substantial hybridization. The inter-atomic exchange coupling is shown to have an oscillatory nature accompanied by an exponential decay, in accordance with what theory predicts for a damped Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction. Our results indicate that the qualitative features of the magnetic coupling for the four investigated adatoms can be connected to the fine details of their Fermi surface. In particular, the oscillations of the exchange in Fe and Co are found to be related to a single nesting vector, connecting large electrons and hole pockets. Most interestingly, this behavior is found to be unaffected by changes induced on the height of the impurity, which makes the magnetism robust to external perturbations. Considering that NbSe$_2$ is a superconductor down to a single layer, our research might open the path for further research into the interplay between magnetic and superconducting characteristics, which could lead to novel superconductivity engineering.

We develop the framework that reveals the intrinsic conserved stress tensor and current associated with the null infinity of a three-dimensional ($3d$) asymptotically flat spacetime. These are, respectively, canonical conjugates of degenerate metric and Ehresmann connection of the boundary Carrollian geometry. Their conservation reproduces the Bondi-mass and angular momentum conservation equations if the asymptotic boundary is endowed with a torsional affine connection that we specify. Our analysis and results shed further light on the $3d$ flat holography; the stress tensor and current give rise to an asymptotically flat fluid/gravity correspondence. The requirement of a well-defined $3d$ action principle yields Schwarzian action at null infinity governing the dynamics induced by reparametrizations over the celestial circle, in accord with the codimension $2$ holography of $3d$ flat spacetimes.

The COSMOS-Web survey, with its unparalleled combination of multiband data, notably, near-infrared imaging from JWST's NIRCam (F115W, F150W, F277W, and F444W), provides a transformative dataset down to $\sim28$ mag (F444W) for studying galaxy evolution. In this work, we employ Self-Organizing Maps (SOMs), an unsupervised machine learning method, to estimate key physical parameters of galaxies -- redshift, stellar mass, star formation rate (SFR), specific SFR (sSFR), and age -- directly from photometric data out to $z=3.5$. SOMs efficiently project high-dimensional galaxy color information onto 2D maps, showing how physical properties vary among galaxies with similar spectral energy distributions. We first validate our approach using mock galaxy catalogs from the HORIZON-AGN simulation, where the SOM accurately recovers the true parameters, demonstrating its robustness. Applying the method to COSMOS-Web observations, we find that the SOM delivers robust estimates despite the increased complexity of real galaxy populations. Performance metrics ($\sigma_{\mathrm{NMAD}}$ typically between $0.1$--$0.3$, and Pearson correlation between $0.7$ and $0.9$) confirm the precision of the method, with $\sim$ $70\%$ of predictions within 1$\sigma$ dex of reference values. Although redshift estimation in COSMOS-Web remains challenging (median $\sigma_{\mathrm{NMAD}} = 0.04$), the overall success of the highlights its potential as a powerful and interpretable tool for galaxy parameter estimation.

Recent developments have extended the concept of global symmetries in several directions, offering new perspectives across a wide range of physical systems. This work shows that generalized global symmetries naturally emerge in shallow water systems. In particular, we demonstrate that both global and gauge subsystem symmetries-previously studied primarily in exotic field theories-arise intrinsically in the dynamics of shallow water flows. A central result is that the local conservation of potential vorticity follows directly from the underlying gauge subsystem symmetries, revealing that the classic Kelvin circulation theorem is rooted in these symmetries. Notably, the associated charge algebra forms a Kac-Moody current algebra, with the level determined by the spatial variation of the Coriolis parameter. Beyond gauge symmetries, we also identify global subsystem symmetries, construct the corresponding Noether charges, and explore their potential applications.

With the widespread adoption of digital devices equipped with cameras and the rapid development of Internet technology, numerous content-based image retrieval systems and novel image feature extraction techniques have emerged in recent years. This paper introduces a saliency map-based image retrieval approach using invariant Krawtchouk moments (SM-IKM) to enhance retrieval speed and accuracy. The proposed method applies a global contrast-based salient region detection algorithm to create a saliency map that effectively isolates the foreground from the background. It then combines multiple orders of invariant Krawtchouk moments (IKM) with local binary patterns (LBPs) and color histograms to comprehensively represent the foreground and background. Additionally, it incorporates LBPs derived from the saliency map to improve discriminative power, facilitating more precise image differentiation. A bag-of-visual-words (BoVW) model is employed to generate a codebook for classification and discrimination. By using compact IKMs in the BoVW framework and integrating a range of region-based feature-including color histograms, LBPs, and saliency map-enhanced LBPs, our proposed SM-IKM achieves efficient and accurate image retrieval. Extensive experiments on publicly available datasets, such as Caltech 101 and Wang, demonstrate that SM-IKM outperforms recent state-of-the-art retrieval methods. The source code for SM-IKM is available at this http URL.

Reliable diagnosis of brain tumors remains challenging due to low clinical incidence rates of such cases. However, this low rate is neglected in most of proposed methods. We propose a clinically inspired framework for anomaly-resilient tumor detection and classification. Detection leverages YOLOv8n fine-tuned on a realistically imbalanced dataset (1:9 tumor-to-normal ratio; 30,000 MRI slices from 81 patients). In addition, we propose a novel Patient-to-Patient (PTP) metric that evaluates diagnostic reliability at the patient level. Classification employs knowledge distillation: a Data Efficient Image Transformer (DeiT) student model is distilled from a ResNet152 teacher. The distilled ViT achieves an F1-score of 0.92 within 20 epochs, matching near teacher performance (F1=0.97) with significantly reduced computational resources. This end-to-end framework demonstrates high robustness in clinically representative anomaly-distributed data, offering a viable tool that adheres to realistic situations in clinics.

We generalize the theory of k-core percolation on complex networks to k-core percolation on multiplex networks, where k=(k_a, k_b, ...). Multiplex networks can be defined as networks with a set of vertices but different types of edges, a, b, ..., representing different types of interactions. For such networks, the k-core is defined as the largest sub-graph in which each vertex has at least k_i edges of each type, i = a, b, ... . We derive self-consistency equations to obtain the birth points of the k-cores and their relative sizes for uncorrelated multiplex networks with an arbitrary degree distribution. To clarify our general results, we consider in detail multiplex networks with edges of two types, a and b, and solve the equations in the particular case of ER and scale-free multiplex networks. We find hybrid phase transitions at the emergence points of k-cores except the (1,1)-core for which the transition is continuous. We apply the k-core decomposition algorithm to air-transportation multiplex networks, composed of two layers, and obtain the size of (k_a, k_b)-cores.

We aim to discern scenarios of structural evolution of intermediate to high-mass star-forming galaxies (SFGs) since cosmic noon by comparing their stellar mass profiles with present-day stellar masses of $\log(M_{\ast,0}/M_{\odot})=10.3-11$. We addressed discrepancies in the size evolution rates of SFGs, which may be caused by variations in sample selection and methods for size measurements. To check these factors, we traced the evolution of individual galaxies by identifying their progenitors using stellar mass growth histories (SMGHs), integrating along the star-forming main sequence and from the IllustrisTNG simulations. Comparison between the structural parameters estimated from the mass- and light-based profiles shows that mass-weighted size evolves at a slower pace compared to light-based ones, highlighting the need to consider the mass-to-light ratio ($M/L$) gradients. Additionally, we observed mass-dependent growth in stellar mass profiles: massive galaxies ($\log(M_{\ast,0}/M_{\odot})\gtrsim10.8$) formed central regions at $z\gtrsim1.5$ and grew faster in outer regions, suggesting inside-out growth, while intermediate and less massive SFGs followed a relatively self-similar mass buildup since $z\sim2$. Moreover, slopes of observed size evolution conflict with the predictions of TNG50 for samples selected using the same SMGHs across our redshift range. To explore the origin of this deviation, we examined changes in angular momentum (AM) retention fraction using the half-mass size evolution and employing a simple disk formation model. Assuming similar dark matter halo parameters, our calculations indicate that the AM inferred from observations halved in the last 10 Gyr while it remained relatively constant in TNG50. This higher AM in simulations may be due to the accretion of high-AM gases into disks.