In this paper, we deal with the classification complexity of continuous (Devaney) chaotic systems in dimensions $0,1$ and $\infty$ using the framework of invariant descriptive set theory. We identify the complexity in dimensions $0$ and $\infty$, while in dimension $1$ we get some partial results. More precisely, we prove the topological conjugacy relation of invertible chaotic systems on the Hilbert cube (resp. on all compact metric spaces) has the same complexity as (i.e. is Borel bireducible with) the universal orbit relation induced by a Polish group. As a consequence, this answers a recent question asked by L. Ding. We also prove that the topological conjugacy relation of invertible chaotic systems on the Cantor space has the same complexity as the universal relation induced by the group $S_\infty$. This answers a recent question by M. Foreman. Some non-trivial bounds on the classification complexity of chaotic systems on the interval and on the circle are also obtained. Namely, the lower bound is the Vitali equivalence relation, and the upper bound is the equality of countable sets of reals. This especially implies that the relation is Borel. However, the exact complexity remains unknown.

The diverse nodal spin structures in d/g/i-wave altermagnets (AM) may cause distinct light-induced spin responses yet remain poorly understood. Using time-dependent density functional theory (TDDFT), we reveal that laser induced ultrafast demagnetization dynamics in the g-wave AM CrSb are strongly governed by the laser incidence direction. Under normal incidence along the [0001] axis, two Cr sublattices exhibit symmetric temporal demagnetization but with different amplitudes, preserving the net-zero magnetization, unlike the behavior in d-wave AM. Off-normal incidence, however, induces pronounced asymmetric demagnetization between sublattices, transiently driving the system into a ferrimagnetic-like state with a sizable net magnetization. This direction-dependent response arises from the characteristic nodal structures in bulk g-wave AM electronic structure, which enable anisotropic optical intersite spin transfer (OISTR). By comparing g-wave and d-wave AMs, we propose that light-induced magnetization arises when laser polarization aligns with spin-uncompensated regions in electronic structures. This can be readily determined from the local spin density of states along specific band paths. Our results provide a fundamental understanding for laser-induced ultrafast dynamics in AM.

We report the creation and characterization of a molecular-scale negative differential conductance (NDC) device by assembling a triangular trimer of 4,5,9,10-tetrabromo-1,3,6,8-tetraazapyrene (TBTAP) molecules on a superconducting Pb(111) substrate. Using low-temperature scanning tunneling spectroscopy, we observe robust NDC behavior manifesting as a decrease in current with increasing voltage between 0.7-0.9 V arising from the interplay of Coulomb blockade and strong inter-molecular capacitive coupling within the molecular cluster. Gate-controlled charging and discharging processes are directly visualized via two-dimensional differential conductance mapping, which reveals the emergence of Coulomb rings and spatial regions of NDC. Theoretical modeling using a three-impurity Anderson model and master equation approach quantitatively reproduces the experimental observations and demonstrates that the NDC emerges purely from electron correlations, independent of the underlying superconductivity. By tuning the geometry to a hexamer structure, we further show that cluster topology provides versatile control over electronic properties at the molecular scale. These results establish a functional platform for implementing multifunctional molecular devices and highlight a strategy toward programmable and scalable nanoelectronics.

A new class of exact spacetimes in Einstein's gravity, which are Kerr black holes immersed in an external magnetic (or electric) field that is asymptotically uniform and oriented along the rotational axis, is presented. These are axisymmetric stationary solutions to the Einstein-Maxwell equations such that (unlike in the Plebanski-Demianski spacetime) the null directions of the Faraday tensor are not aligned with neither of the two principal null directions of the Weyl tensor of algebraic type D (unlike the Kerr-Melvin spacetime). Three physical parameters are the black hole mass $m$, its rotation $a$, and the external field value $B$. For vanishing $B$ the metric directly reduces to standard Boyer-Lindquist form of the Kerr black hole, while for zero $m$ we recover conformally flat Bertotti-Robinson universe with a uniform Maxwell field. For zero $a$ the spacetime is contained in the Van den Bergh-Carminati solutions which can be understood as the Schwarzschild black hole in a magnetic field. Our family of black holes with non-aligned Maxwell hair - that can be called the Kerr-Bertotti-Robinson (Kerr-BR) black holes - may find application in various studies ranging from mathematical relativity to relativistic astrophysics.

Automated semantic segmentation of whole-slide images (WSIs) stained with hematoxylin and eosin (H&E) is essential for large-scale artificial intelligence-based biomarker analysis in breast cancer. However, existing public datasets for breast cancer segmentation lack the morphological diversity needed to support model generalizability and robust biomarker validation across heterogeneous patient cohorts. We introduce BrEast cancEr hisTopathoLogy sEgmentation (BEETLE), a dataset for multiclass semantic segmentation of H&E-stained breast cancer WSIs. It consists of 587 biopsies and resections from three collaborating clinical centers and two public datasets, digitized using seven scanners, and covers all molecular subtypes and histological grades. Using diverse annotation strategies, we collected annotations across four classes - invasive epithelium, non-invasive epithelium, necrosis, and other - with particular focus on morphologies underrepresented in existing datasets, such as ductal carcinoma in situ and dispersed lobular tumor cells. The dataset's diversity and relevance to the rapidly growing field of automated biomarker quantification in breast cancer ensure its high potential for reuse. Finally, we provide a well-curated, multicentric external evaluation set to enable standardized benchmarking of breast cancer segmentation models.

Laser pulses are known to induce symmetric demagnetization; equal loss of magnetic moments in the identical sublattices of antiferromagnets and ferromagnets at ultrashort timescale. This is due to their identical local electronic structures guided by the underlying symmetries. Using time-dependent density functional theory, we demonstrate that laser pulses can drive asymmetric demagnetization dynamics of identical sublattices in the d-wave compensated altermagnet RuO2, resulting in a photo-induced ferrimagnetic state with a net moment of ~0.2 {\mu}B per unit cell. This metastable magnetization is highly controllable; depends on the direction of the linear polarized laser. We identify the underlying mechanism as an anisotropic optical-induced intersite spin transfer (a-OISTR) effect, originating from the momentum-dependent spin splitting unique to altermagnets. This a-OISTR effect enables the polarization of light to drive direction-selective transient spin-dependent currents between sublattices, leading to a controllable ultrafast magnetic state transition in AM. These findings uncover novel laser-driven pathways to control magnetic order in altermagnets, enabling a phase transition from AM to ferrimagnetic state.

This Letter reports measurements of muon-neutrino disappearance and electron-neutrino appearance and the corresponding antineutrino processes between the two NOvA detectors in the NuMI neutrino beam. These measurements use a dataset with double the neutrino mode beam exposure that was previously analyzed, along with improved simulation and analysis techniques. A joint fit to these samples in the three-flavor paradigm results in the most precise single-experiment constraint on the atmospheric neutrino mass-splitting, $\Delta m^2_{32}= 2.431^{+0.036}_{-0.034} (-2.479^{+0.036}_{-0.036}) \times 10^{-3}$~eV$^2$ if the mass ordering is Normal (Inverted). In both orderings, a region close to maximal mixing with $\sin^2\theta_{23}=0.55^{+0.06}_{-0.02}$ is preferred. The NOvA data show a mild preference for the Normal mass ordering with a Bayes factor of 2.4 (corresponding to 70\% of the posterior probability), indicating that the Normal ordering is 2.4 times more probable than the Inverted ordering. When incorporating a 2D $\Delta m^2_{32}\textrm{--}\sin^2 2\theta_{13}$ constraint based on Daya Bay data, this preference strengthens to a Bayes factor of 6.6 (87\%).

We present a large family of twisting and expanding solutions to the Einstein-Maxwell equations of algebraic type D, for which the two double principal null directions (PNDs) of the Weyl tensor are not aligned with the null eigendirections of the Faraday tensor. In addition to systematically deriving this new class, we present its various metric forms and convenient parameterizations. We show that in Boyer-Lindquist-type coordinates these solutions depend on 7 parameters, namely the Kerr and NUT (Newman-Unti-Tamburino) twist parameters $a$ and $l$, mass parameter $m$, acceleration $\alpha$, strength of the Maxwell field $|c|$, and angular parameters $\beta, \gamma$ that represent two duality rotations of the Faraday tensor, which include the rotation between the electric and magnetic charges generating the aligned part of the Maxwell field. This coordinate parameterization, analogous to the Griffiths-Podolský form of the Plebański-Demiański solutions, allows us to perform various limits, explicitly identify the subcases, and determine the physical interpretation of the new class. Interestingly, by considering the limit with no acceleration ($\alpha\to 0$), one obtains either the famous Kerr-Newman-NUT black holes (if the parameter $|c|$ remains constant) or the novel Kerr-Bertotti-Robinson black holes, announced recently in our work [Kerr Black Hole in a Uniform Bertotti-Robinson Magnetic Field: An Exact Solution, Phys. Rev. Lett. {\bf 135} (2025) 18, 181401] (if $|c|\rightarrow \infty$ while $\alpha |c|=\mathrm{const.}$). We may thus conclude that this new class of spacetimes represents twisting charged accelerating black holes, immersed in an external magnetic (or electric) field. In the non-twisting subcase, we obtain the previously known solution of Van den Bergh-Carminati.

Seymour's decomposition theorem is a hallmark result in matroid theory presenting a structural characterization of the class of regular matroids. Formalization of matroid theory faces many challenges, most importantly that only a limited number of notions and results have been implemented so far. In this work, we formalize the proof of the forward (composition) direction of Seymour's theorem for regular matroids. To this end, we develop a library in Lean 4 that implements definitions and results about totally unimodular matrices, vector matroids, their standard representations, regular matroids, and 1-, 2-, and 3-sums of matrices and binary matroids given by their standard representations. Using this framework, we formally state Seymour's decomposition theorem and implement a formally verified proof of the composition direction in the setting where the matroids have finite rank and may have infinite ground sets.

We present a theoretical study of the magnetic field generated by a toroidal current loop situated in the equatorial plane of a non-rotating Schwarzschild black hole, based on the dynamics of charged particles. Using the exact general relativistic solution for the magnetic field, we analyze particle motion both analytically and numerically, identifying regions of stable and unstable orbits. In particular, we classify charged particle dynamics into attractive and repulsive Lorentz force configurations and show that in the attractive case, charged particles can accumulate near the current loop, forming collective currents that oppose the original current loop magnetic field. We demonstrate that charged particle accumulation can lead to the formation of toroidal structures analogous to radiation belts in the BH magnetosphere. We compare the curved spacetime solution to flat spacetime analogs and highlight general relativistic effects such as the existence of the innermost stable circular orbit for charged particles, which sets a lower bound for radiation belt formation. The divergence of the vector potential at the loop location in the idealized infinitesimal loop model is addressed, and we argue that a physically realistic model must consider a finite-width current distribution to avoid unphysical divergences in the effective potential.

A transimpedance amplifier has been designed for scanning tunneling microscopy (STM). The amplifier features low noise (limited by the Johnson noise of the 1 G{\Omega} feedback resistor at low input current and low frequencies), sufficient bandwidth for most STM applications (50 kHz at 35 pF input capacitance), a large dynamic range (0.1 pA--50 nA without range switching), and a low input voltage offset. The amplifier is also suited for placing its first stage into the cryostat of a low-temperature STM, minimizing the input capacitance and reducing the Johnson noise of the feedback resistor. The amplifier may also find applications for specimen current imaging and electron-beam-induced current measurements in scanning electron microscopy and as a photodiode amplifier with a large dynamic range. This paper also discusses the sources of noise including the often neglected effect of non-balanced input impedance of operational amplifiers and describes how to accurately measure and adjust the frequency response of low-current transimpedance amplifiers.