We extend the classical construction of solvable Lie algebras from a nilradical to compatible Lie algebras. Since the sum of nilpotent ideals may fail to be nilpotent, we replace the usual nilradical by a \emph{special nilradical} that behaves well with the mixed Jacobi identity. We use the maximal tori of diagonal derivations to build solvable extensions. The method is applied to the pairs $(\mathrm L_n,\mathrm R_n)$ and $(\mathrm L_n,\mathrm W_n)$, yielding explicit one-dimensional solvable extensions and proving nonexistence of higher-dimensional ones in these cases. We also study filiform compatible Lie algebras. We introduce the model family $\mathcal L_s$ and show that each $\mathcal L_s$ is a linear deformation of the model filiform Lie algebra $\mathcal L_k$. Finally, we study the existence of solvable extensions of this family, within the framework developed above.

Let $u$ be the first Dirichlet Laplacian eigenfunction of a bounded convex set $Ω$ in $\mathbb{R}^n$. We strengthen the classical result by Brascamp-Lieb which asserts that $u$ is logconcave in $Ω$: we prove that, if $u$ is normalized so that its $L^\infty$-norm does not exceed a threshold $\overlineκ (Ω)<1$ depending explicitly on the diameter of the domain and on its principal frequency, the function $- ( - \log u ) ^{1/2}$ is concave in $Ω$.

Artificial Intelligence (AI) is changing the world, but its impacts on the environment and human well-being remain uncertain. We conducted a systematic literature review of 1,291 studies selected from 6,655 records, identifying the main impacts of AI and how they are assessed. The evidence reveals an uneven landscape: 72% of environmental studies focus narrowly on energy use and CO2 emissions, while only 11% consider systemic effects. Well-being research is largely conceptual and overlooks subjective dimensions. Strikingly, 83% of environmental studies portray AI's impacts as positive, while well-being analyses show a near-even split overall (44% positive; 46% negative). However, this split masks differences across well-being dimensions. While the impacts of AI on income and health are expected to be positive, its impacts on inequality, social cohesion, and employment are expected to be negative. Based on our findings, we suggest several areas for future research. Environmental assessments should incorporate water, material, and biodiversity impacts, and apply a full life-cycle perspective, while well-being research should prioritise empirical analyses. Evaluating AI's overall impact requires accounting for computing-related, application-level, and systemic impacts, while integrating both environmental and social dimensions. Bridging these gaps is essential to understand the full scope of AI's impacts and to steer its development towards environmental sustainability and human flourishing.

Entanglement between solid-state quantum emitters (QEs) is a key resource for photonic quantum technologies. Achieving such entanglement requires strong and controllable long-range interactions between QEs. However, engineering such coupling remains challenging, particularly for on-chip distant solid-state QEs. Here, we introduce a forward-designed platform that enables ultracompact nanophotonic architectures to mediate enhanced long-range QE-QE interactions via engineered surface plasmon polariton interference. Using this strategy, we realize two distinct configurations: a phase-conjugated elliptic design for energy funneling, and a co-radiating hyperbolic design for its suppression. We experimentally demonstrate large enhancement and suppression of energy transfer rates compared to bare substrates. Furthermore, we predict transient entanglement between spatially separated QEs with concurrence peaking at 0.493, approaching the theoretical bound in the transient regime. Extending to the multi-QE case, we observe enhanced energy funneling and predict QE-QE entanglement in three-QE configurations. These results establish a compact and scalable framework for on-chip entanglement engineering in integrated quantum nanophotonic systems.

Based on $e^+e^-$ annihilation data collected with the BESIII detector at center-of-mass energies from 4.600 to 4.699 GeV, corresponding to an integrated luminosity of 4.5 fb$^{-1}$, we present the first measurement of the longitudinal polarization of $Λ$ hyperons produced in the inclusive decay $Λ_c^+ \to ΛX$, where $X$ denotes any allowed final state. The polarizations are determined to be $\mathcal{P}_Λ = -0.393 \pm 0.055_{\mathrm{sta.}} \pm 0.020_{\mathrm{sys.}}$ and $\mathcal{P}_{\barΛ} = 0.288 \pm 0.056_{\mathrm{sta.}} \pm 0.017_{\mathrm{sys.}}$. We then search for CP violation using an asymmetry constructed from the $Λ$ polarization and the $Λ\to p π^-$ decay asymmetry parameters, and obtain $\mathcal{A}_{\mathrm{CP}}^{\mathrm{pol}} = 0.15 \pm 0.12_{\mathrm{sta.}} \pm 0.04_{\mathrm{sys.}}$. We also perform an updated measurement of the absolute branching fraction, resulted as $\mathcal{B}(Λ_c^+ \to ΛX) = (38.07 \pm 0.38_{\mathrm{sta.}} \pm 0.49_{\mathrm{sys.}})\%$, with precision improved by a factor of four relative to the current world average. A search for direct CP violation yields $\mathcal{A}_{\mathrm{CP}}^{\mathrm{dir}} = (1.5 \pm 1.0_{\mathrm{sta.}} \pm 1.0_{\mathrm{sys.}})\%$. No evidence for CP violation in inclusive charm baryon decays is observed.

Relativistic jets from Active Galactic Nuclei (AGN) are highly energetic and emit radiation across a wide range of frequencies. Despite several observational studies, their particle composition still remains a key open question. The detection of high-energy neutrinos from blazar sources such as TXS 0506+056 has highlighted the plausibility of hadronic/lepto-hadronic models for AGN jets. To understand the origin of high-energy neutrinos from such sources, it is imperative to capture the complex interplay between the jet dynamics, their composition, and the mechanism of particle acceleration and cooling in relativistic jets. In this pilot study, we have coupled a numerical multi-zone framework for lepto-hadronic modeling, with 3D relativistic magneto-hydrodynamic simulations of AGN jets, including external photon fields. Our framework provides synthetic multi-wavelength and neutrino flux by spatially sampling the simulated jet into multiple zones. We investigate the implications of such a framework in exploring the different intrinsic and extrinsic pathways for proton-enrichment in jets. Essentially, we find that for low proton-to-electron number density ratios, producing a substantial jet neutrino flux, requires the underlying proton energy distribution to have a relatively flat spectrum with a power-law index of $\simeq 2.0$. We further find that while intrinsic shocks triggered by kink-instabilities in the jet can accelerate electrons to high energies, they may not be sufficient to produce such flat particle energy distributions for the chosen set of parsec-scale jet parameters. Finally, to produce a significant jet neutrino emission, our simulations suggest the need to consider particle acceleration mechanisms through alternative pathways, either internal or external.

This workshop report from "Shaping the Digital Future of ErUM Research: Sustainability & Ethics" (Aachen, 2025) reviews progress on sustainability measures in data-intensive ErUM-Data research since the 2023 call-to-action on resource-aware research. It evaluates short-, medium-, and long-term actions around monitoring and reducing CO2 emissions, improving data and software FAIRness, optimizing workflows and computing infrastructures, and aligning operations with low-carbon energy availability, including concepts such as "breathing" computing centers, long-term data storage strategies, and software efficiency certification. The report stresses the need for systematic teaching, training, mentoring, and new support formats to establish sustainable coding and computing practices, particularly among students and early-career researchers, and highlights the importance of dedicated steering and funding instruments to embed sustainability in project planning. Ethical discussions focus on the transformative use of AI in ErUM-Data, addressing autonomy, bias, transparency, explainability, attribution of responsibility, and the risk of deskilling, while reaffirming that accountability for scientific outcomes remains with human researchers. Finally, the report emphasizes that sustainable transformation requires not only technical measures but also targeted awareness-building, communication strategies, incentives, and community-driven initiatives to move from awareness to action and to integrate sustainability and ethics into everyday scientific practice.

The gravitational-wave (GW) detections reported by the LIGO-Virgo-KAGRA (LVK) collaboration have so far been consistent with quasi-circular compact binary coalescences (CBCs). Nevertheless, a small fraction of binaries driven to merge through dynamical interactions in dense stellar environments or in field triples may retain measurable orbital eccentricity when entering the sensitive frequency band of LVK detectors. Confident measurement of eccentricity in the LVK band would provide strong evidence for such dynamically driven mergers; however, eccentric gravitational-waveform models are computationally expensive, and performing production-level inference on all detected signals is not an efficient use of resources when eccentric signals are expected to be rare. An intermediate step between detection and analysis, in which the signal is assessed for the potential presence of eccentricity, could provide quick recommendations for which signals should undergo full eccentric inference. We apply the wavelet scattering transform (WST) to a large set of synthetic waveforms in realistic noise and assess its discriminatory power using simple linear and shallow neural-network classifiers. We find that the WST representation enables effective discrimination between eccentric and quasi-circular binaries and provides a compact multi-scale representation of GW signals. Our approach achieves ~64% percent detection accuracy at a false alarm rate of 10%, with an AUC of 0.844 and an average precision of 0.876. We also examine the ability of our classifiers to distinguish eccentricity from spin-induced precession and find robust performance across a range of spin-precession magnitudes.

We present observations of the classical T Tauri star DO Tau collected with the near-infrared SPIRou spectropolarimeter and precision velocimeter at the Canada-France-Hawaii Telescope from early 2020 to late 2025. Circularly polarized Zeeman signatures were clearly detected at most epochs in the atomic spectral lines of DO Tau, yielding longitudinal magnetic fields of up to 280 G modulated with a period of 5.128+-0.002 d which we identified as the rotation period of DO Tau. Applying Zeeman-Doppler imaging to the SPIRou data recorded in 2021, 2024 and 2025, we found that DO Tau hosts an unusual large-scale magnetic field that is weaker, less poloidal, more inclined to the rotation axis, and varies more rapidly with time than those of previously studied T Tauri stars, possibly as a result of intense accretion between the inner disk and the stellar surface. The dipole component of this large-scale field of about 0.2-0.3 kG even flipped polarity toward the end of our observing campaign, making DO Tau the first T Tauri star for which a magnetic polarity reversal is reported. The magnetospheric gap surrounding the central star was quite compact, extending to ~1.6 Rstar (0.014 au) as a result of the strong accretion rate (log Mdot = -7.7 Msun/yr), with the inner accretion disk being warped by the tilted stellar magnetic field. Radial velocity variations suggest the presence of a close-in planet of a few Mjup or a density structure in the inner accretion disk at an orbital period of 21 d (corresponding to 0.12 au), which might be linked to the wiggle in the jet axis of DO Tau.

We consider potential-based interactions between beams (or fibers) and shells (or membranes) using a coarse-grained approach with focus on van der Waals attraction and steric repulsion. The involved 6D integral over volumes of a beam and a shell is split into a 5D analytical pre-integration over the beam's cross section and a surrogate plate tangential to the closest point on the shell, and the remaining 1D numerical integration along the beam's axis. This general inverse-power interaction potential is added to the potential energies of the Bernoulli-Euler beam and the Kirchhoff-Love shell. The total potential energy is spatially discretized using isogeometric finite elements, and the nonlinear weak form of quasi-static equilibrium is solved using the continuation method. We provide error estimates and convergence analysis, together with two intriguing numerical examples. The developed approach provides excellent balance between accuracy and efficiency for small separations.

Superconducting quantum interference devices (SQUIDs) are state-of-the-art in ultra-sensitive magnetometry; however, conventional SQUID devices are fundamentally limited by the inherently nonlinear and periodic nature of their transfer function. Although flux-locked loop (FLL) configurations can mitigate this issue, they introduce electronic complexity and bandwidth constraints that hinder scalability in quantum circuits. In this work, we present an experimental demonstration of the bi-SQUIPT, a flux transducer that modulates the density of states in a proximitized superconducting weak link. The device employs a dual-loop architecture with differential readout, which enables cancellation of non-linearities typical of individual elements, achieving a voltage swing of approximately 120 $μ$V. Measurements yield a spurious-free dynamic range (SFDR) of up to 60 dB, consistent with theoretical predictions and comparable to that of SQUID arrays, while maintaining power dissipation in the femtowatt range. The results further highlight a remarkable operational stability up to 600 mK, positioning the bi-SQUIPT as an enabling technology for high-density cryogenic quantum electronics.

Modern supply networks are complex interconnected systems. Multi-agent models are increasingly explored to optimise their performance. Most research assumes agents will have full observability of the system by having a single policy represent the agents, which seems unrealistic as this requires companies to share their data. The alternative is to develop a Hidden-Markov Process with separate policies, making the problem challenging to solve. In this paper, we propose a multi-agent system where the factory agent can share information downstream, increasing the observability of the environment. It can choose to share no information, lie, tell the truth or combine these in a mixed strategy. The results show that data sharing can boost the performance, especially when combined with a cooperative reward shaping. In the high demand scenario there is limited ability to change the strategy and therefore no data sharing approach benefits both agents. However, lying benefits the factory enough for an overall system improvement, although only by a relatively small amount compared to the overall reward. In the low demand scenario, the most successful data sharing is telling the truth which benefits all actors significantly.

Microorganisms live in inherently dynamic environments where fluctuations in biotic and abiotic factors shape their behaviour, physiology, and fitness. The concept of ecological memory: the lasting imprint of prior environmental cues, suggests that past exposures can exert prolonged effects on microbial growth, resilience, and phenotypic expressions. For motile microbes in aquatic ecosystems, environmental variability is mediated by fluid motion, which may engender a form of hydrodynamic memory, whereby prior exposure to specific spatio-temporal cues influence future growth and migratory behaviour. Yet, the emergence of such flow-induced memory, or its long-term consequences for trait evolution and population dynamics, remain unexplored. We integrate millifluidic flow control, high-resolution cell tracking, and tunable hydrodynamic cues to quantify growth and migration of Heterosigma akashiwo, a model microbe, across growth stages. Using two complementary perturbation scenarios: standard (flow after static conditions) and reverse (flow before static growth), we test how the temporal structure of forcing shapes multigenerational responses. This combinatorial design disentangles exposure history from its duration, and reveals how prior flow modulates sensitivity, generating legacy effects. Compared with static controls, repeated hydrodynamic exposure alters doubling time, carrying capacity, gravitactic stability, and swimming speed distributions; shifting growth phase progression and tolerance to subsequent perturbations. These results establish a mechanistic framework for flow-induced memory in motile microbes, revealing how past fluidic cues shape future growth and migration. Our study advances predictive understanding of motile microbes in natural and engineered hydrodynamic systems experiencing increasing variability under global environmental changes.

Dynamical control of the nonlinear optical properties of solids -- with light itself -- will be essential for future ultrafast photonic technologies. Previously, methods to modulate nonlinear processes including second-harmonic generation (SHG) have relied primarily on non-resonant light-matter interaction or photo-generation of hot electrons in nanoscale materials. However, these approaches are typically constrained by limited interaction lengths and the initial frequency conversion is relatively weak under equilibrium conditions. Here, an approximately 30\% modulation of efficient phase-matched SHG in bulk beta-barium borate (beta-BaB2O4) is achieved through transient lattice deformation by intense terahertz (THz) pulses that are tuned to resonance with an infrared-active phonon mode. The effect originates from modification of the index of refraction ellipsiod and the corresponding nonlinear phase-matching conditions, rather than from direct modulation of the nonlinear susceptibility through THz-mediated chi^(3) processes. This mechanism, of resonant selective lattice excitation, points toward novel THz-control schemes to tune the nonlinear optical response in materials.

This work devoted to the description of irreducible cuspidal modules over simple $n$-Lie algebras. Since the description of irreducible modules over $n$-Lie algebra $O^n$ are already well understood, we focus here on the irreducible cuspidal modules over $n$-Lie algebras of Wronskians and Jacobians. First, for a given $n$-Lie algebra $\mathcal{L}$, we analyze the possible Lie and Leibniz structures on $\wedge^{n-1} \mathcal{L}$ and $\otimes^{n-1} \mathcal{L}$ by thoroughly examining existing structures. Next, we classify the irreducible cuspidal modules over the $n$-Lie algebra of Wronskians defined on Laurent polynomials with degree-preserving derivations. Furthermore, we prove that these modules remain irreducible over the $n$-Lie algebra of Jacobians.

We present a large-scale automated audit of WCAG 2.1/2.2 Level AA colour contrast compliance across the 500 most frequently crawled registered domains in Common Crawl's CC-MAIN-2026-08 February 2026 crawl archive. Rather than conducting a live crawl, all page content was sourced from Common Crawl's open WARC archives, ensuring reproducibility and eliminating any load on target web servers. Our static CSS analysis of 240 homepages identified 4,327 unique foreground/background colour pairings, of which 1,771 (40.9%) failed to meet the 4.5:1 contrast ratio threshold for normal text. The median per-site pass rate was 62.7%, with 20.4% of sites achieving full compliance across all detected colour pairings. These findings suggest that colour contrast remains a widespread accessibility barrier on the most prominent websites, with significant variation across domain categories.

The speed of a graph class $\cal G$ measures how many labeled graphs on $n$ vertices one can find in $\cal G$. This graph class complexity function is explicitly provided on graphclasses.org. However, for many graph classes, their speed status is classified as \emph{unknown}. In this paper, w}\shortversion{W}e show that any graph class representable by a finite binary language has at most factorial speed, meaning that its speed function behaves like $2^{Θ(n\log n)}$, and we use this criterion to classify many graph classes whose speed was previously unknown as factorial. As a consequence, inclusions between several graph classes can now be seen to be proper. We also prove that $k$-letter graphs have exponential speed, i.e., the speed function lies in $2^{Θ(n)}$.

We study the rough-smooth boundary in the two-periodic Aztec diamond, a random domino tiling model exhibiting three types of macroscopic regions. We show that the height function at this boundary converges to an independent sum of an Airy surface and an i.i.d. noise field with fluctuations governed by the full-plane smooth phase. Going further, we prove convergence of a family of Temperleyan backbone paths to the Airy line ensemble. This gives the first convergence result for a family of undirected paths converging to the Airy line ensemble, as well as Airy convergence at a noisy boundary.

In many practical applications, quantum algorithms require several qubits, significantly more than those available with current noisy intermediate-scale quantum processors. Distributed quantum computing (DQC) is considered a scalable approach to increasing the number of available qubits for computational tasks. In the DQC setting, a quantum compiler must find the best partitioning for the quantum algorithm and then perform smart non-local operations scheduling to optimize the consumption of Einstein-Podolsky-Rosen (EPR) pairs. In this work, the focus is on minimizing the use of EPR pairs when the circuit structure allows for multiple non-local gates to utilize a single TeleGate operation. This is achieved by using a greedy algorithm that explores the circuit and groups together the gates that could share an EPR pair while also changing the order of commutative gates when necessary. With this preliminary pass, the compiled circuits show reduced depth and EPR usage. Since the quality of each EPR pair quickly deteriorates, the number of non-local gates using the same EPR pair should also be bounded. This means that, depending on the features of the target quantum network, the user can achieve different levels of optimization. Here, it is shown that this approach brings benefits even while assuming a low EPR pair lifetime.

Recent high-cadence observations by Subaru-HSC have identified a population of ultrashort-timescale microlensing events, providing a compelling window for planet-mass primordial black holes (PBHs) to constitute the entirety of dark matter. In this Letter, we demonstrate that this PBH population and the nanohertz stochastic gravitational-wave (GW) background reported by pulsar timing arrays (PTAs) can be naturally unified by a single primordial origin: a broad, nearly-flat enhancement of the curvature power spectrum with an amplitude of $O(10^{-2})$. The resulting PBH mass function spans the planet-to-solar mass range, while remaining consistent with all current observational constraints. This unified PBH--induced-GW framework makes concrete multi-messenger predictions, which can be decisively scrutinized by forthcoming microlensing surveys, next-generation PTAs, space-borne interferometers, precision astrometry, and laser ranging experiments.

We investigate several possible generalisations of $T\overline{T}$ deformations to three- and higher-dimensional field theories. Starting from the two-dimensional $T\overline{T}$ flow, we work out its higher-dimensional uplift, which results in a non-local and non-isotropic three-dimensional theory. Starting instead from the relation between the Nambu-Goto action and $T\overline{T}$ in $d=2$, we study the flow equation obeyed by the Dirac-Nambu-Goto actions in $d>2$ dimensions, written in terms of the stress-energy tensor only. Similarly, we derive the stress-tensor flow obeyed by the Born-Infeld actions in $d$ dimensions and by the Dirac-Born-Infeld actions in $d=2$ and $d=3$.

High contact resistance remains a central obstacle to the integration of two-dimensional (2D) semiconductors in electronic devices. Recent advances have demonstrated that contact performance can be dramatically improved through interface engineering, including the use of group-V semimetals and charge-transfer contacts based on strong interfacial doping. Here, we show that controlled interfacial oxidation provides an effective route to convert a semimetal contact into a charge-transfer contact that degenerately $n$-dopes single layer MoS$_2$. Using a combination of angle-resolved photoemission spectroscopy, X-ray photoelectron diffraction, low-energy electron diffraction and scanning tunnelling spectroscopy, we demonstrate that putting single layer MoS$_2$ in contact with a pristine Bi layer merely results in weak doping, whereas oxidation of the Bi layer leads to a pronounced occupation of the MoS$_2$ conduction band with an electron density on the order of $10^{13}$~cm$^{-2}$. The cause of this strong electron doping is the fact that an ultrathin $β$-Bi$_2$O$_3$ layer forms below the MoS$_2$ and that this has a particularly low work function, thereby acting as an efficient electron donor to MoS$_2$. Interfacial oxidation thus emerges as a powerful design knob for engineering charge-transfer contacts to 2D semiconductors.

Spectral density functions quantify how environmental modes couple to quantum systems and govern their open dynamics. Inferring such frequency-dependent functions from time-domain measurements is an ill-conditioned inverse problem. Here, we use exactly solvable spin-boson models with pure-dephasing and amplitude-damping channels to reconstruct spectral density functions from noisy simulated data. First, we introduce a parameter estimation approach based on machine learning regressors to infer Lorentzian and Ohmic-like spectral density parameters, quantifying robustness to noise. Second, we show that a cosine transform inversion yields a physics-consistent spectral prior estimation, which is refined by a constrained neural network enforcing positivity and correct asymptotic behaviour. Our neural network framework robustly reconstructs structured spectral densities by filtering simulated noisy signals and learning general functional dependencies.

Quantum walks provide a versatile framework for probing the structural and dynamical properties of complex systems ranging from biological networks to synthetic materials. However, their realization on current noisy pre-fault-tolerant quantum computers is fundamentally limited by decoherence. Conventional dense encodings of graph structures require prohibitively deep circuits, making them incompatible with existing hardware. Here we introduce an algorithm that leverages symmetry-sector encoding and trades circuit depth for qubits, while integrating symmetry-respecting postselection as an effective noise-mitigation strategy. This combination enables us to execute practical quantum-walk circuits for biological networks on actual quantum hardware. We benchmark the proposed methodology against known state-of-the-art circuit architectures, highlighting significant reduction of circuit depth in our approach at the cost of moderate qubit overhead. Utilizing 40 qubits, we implement quantum walks on complex graphs containing up to 17 nodes and 20 edges -- the largest experiment on superconducting hardware to date, with the Hellinger fidelity exceeding 87% throughout 7 steps. We present a case study that illustrates how experimentally obtained quantum-walk dynamics on a protein-protein-interaction network can be applied to prioritizing disease-associated genes. We discuss the framework scalability in the pre-fault-tolerant era and its potential for studying larger biological networks.

Experimental data on solubilization kinetics found in literature were analyzed by using the model proposed earlier (1). The rates of oil molecular exchange between the micellar core and the surrounding aqueous solution were determined. It was concluded that the solubilization of hydrocarbon molecules by nonionic surfactants of ethylene oxide type is essentially barrier-free, that is, is diffusion controlled. It is quite different for ionic surfactants, where the rate is one-two orders of magnitude slower, indicating the existence of a potential barrier for hydrocarbons to get inside the micelles. A Fickean diffusion model of solubilization has been proposed to explain these trends. For ionic micelles, the hydrocarbons are predicted to be excluded from the micellar double layer region because of their low dielectric constant. The Poisson-Boltzmann model was used to model this effect; the diffusion retardation factors were compared with the experiment and a fair agreement was seen. For nonionic groups, such as oligoethylene oxide, on the other hand, no such barrier was predicted to exist. The analysis of this paper is performed only for the case of the 'slow' solubilization; it does not cover the case of the rapid, 'catastrophic' solubilization observed in the other group of experiments; the distinction between the slow and fast mechanisms is discussed and a possible explanation is suggested.

The emergence of order and geometric limit shapes in a three-dimensional (3D) Coulomb phase subject to domain wall boundary conditions (DWBC) is investigated. While the arctic circle phenomenon -- the spatial segregation of frozen and fluctuating degrees of freedom -- is well-established in the two-dimensional six-vertex model (square ice), its extension to 3D remains largely unexplored. A cubic lattice model with Ising degrees of freedom living on the edges, whose ground state manifold is governed by a divergence-free (3-in/3-out) local constraint, is considered. In the bulk, this model realizes a classical spin liquid characterized by algebraic correlations and pinch-point singularities in reciprocal space. It is demonstrated that applying DWBC partially lifts the extensive ground state degeneracy, inducing long-range magnetic order in the thermodynamic limit. Despite this ordering, it is found that the system retains a fluctuating component that exhibits the signature of a Coulomb phase. Finally, by mapping the local vertex polarization density, compelling numerical support is provided for a 3D generalization of the arctic limit shape, bridging the gap between topological constraints and emergent geometry in higher dimensions.

We prove a Seidel product formula for the torus-equivariant quantum $K$-theory of a generalized flag variety $G/P.$ This is a natural generalization of the corresponding results by Buch, Chaput, and Perrin for the cominuscule flag varieties. Our proof is based on the $K$-theoretic Peterson isomorphism, due to Kato. We also use a version of the $K$-theoretic nil-Hecke algebra associated with the extended affine Weyl group, which was studied by Ikeda, Shimozono, and Yamaguchi.

An automated algorithm to construct island divertors for stellarators is presented and is used to find divertors that meet heat flux requirements determined by engineering and material limits. The algorithm uses just two initial conditions: two starting coordinates on the island separatrix. We leverage the simplicity of the algorithm to explore the divertor parameter space in a fixed magnetic equilibrium. Heat loads are approximated using the field line diffusion model implemented in the FLARE code. Optimal divertor solutions that satisfy engineering requirements are found using a parameter scan and a Bayesian optimization routine. The optimization achieves a 95% reduction in computational cost compared to the parameter scan. The resulting divertors are proven to be robust to varying plasma parameters through simulations with different cross-field heat diffusivities. This work represents a first step towards island divertor optimization for stellarators.

Two dimensional (2D) magnets have emerged as a compelling platform for spin based nanoelectronics, enabling atomic scale control of magnetic order, interfaces, quantum geometry, and symmetry. Here, we highlight recent advances in 2D ferromagnets, antiferromagnets, altermagnets, and related magnetic phases, emphasizing how enhanced Curie temperatures, perpendicular magnetic anisotropy, and unconventional magnetic orders translate into device relevant functionality. Spin dependent transport in vertical magnetic tunnel junctions and lateral spin valves based on 2D heterostructures are discussed, where atomically sharp interfaces enable highly tunable spin injection, propagation, and detection. We further focused on field free energy efficient spin orbit torque magnetization switching in 2D magnetic heterostructures, in which unconventional spin currents originate from an adjacent low symmetry spin orbit layer. Microscopic mechanisms involving symmetry breaking, Berry curvature, and orbital angular momentum transport are discussed, along with key challenges, including switching determinism and torque efficiency. Materials and device design strategies targeting neuromorphic, hybrid quantum spintronic, and multifunctional architectures are outlined. Collectively, these developments position 2D magnets as a promising candidate for tunable, energy efficient integrated spintronic technologies that can harness intertwined spin, charge, orbital, and topological degrees of freedom at the nanoscale.

In the planned or considered upgrades of LHCb, ALICE and Belle II experiments, the Ring imaging Cherenkov (RICH) detectors will have to be improved in order to function at increased beam interaction density. The photodetectors used in future RICH detector will have to provide high granularity, single photon sensitivity and excellent timing, while being exposed to a couple of 10$^{13}$ 1-MeV neutron equivalent/cm$^2$ of background irradiation during total experiment run time. The spadRICH project is developing a CMOS single-photon avalanche diode (SPAD) based photodetector specifically optimized for the application of the planned RICH detectors, which includes neutron radiation hardness and cryogenic operation. In this work we present recent experimental characterization studies of existing SPADs produced in 55 nm BCD and 110 nm CMOS image sensor technologies. Main results include dark count rate (DCR) measurements with SPADs irradiated up to 10$^{12}$ 1-MeV neutron equivalent/cm$^2$ and cooled down to liquid nitrogen temperature.