In this work, we develop a new framework for computing atom-resolved contributions to optical properties based on atoms-in-molecules (AIM) schemes. The formalism is independent of the specific AIM method and is made rigorous by partitioning momentum matrix elements into atomic contributions while exactly satisfying the relevant sum rules. We apply it to second-harmonic generation (SHG) in six representative UV and deep-UV nonlinear-optical crystals, namely $β$-\ce{BaB2O4} (BBO), \ce{LiB3O5} (LBO), \ce{CsB3O5} (CBO), \ce{CsLiB6O10} (CLBO), \ce{KBe2BO3F2} (KBBF), and \ce{LiCs2PO4} (LCPO). The atom-triplet decomposition reveals a clear hierarchy for the largest SHG component of each crystal. In general, two-center terms provide the leading contribution, one-center terms remain comparatively small, and fully three-center terms supply an important secondary contribution. A motif-triplet decomposition further indicates behavior dominated by the anionic framework in KBBF and LBO. In BBO, CBO, and CLBO, contributions from the anionic framework and the cation sublattice act cooperatively, although the cation contribution is crystal dependent. Moreover, cooperative contributions from the phosphate framework and the Cs sublattice are also observed in LCPO, where the O-Cs contribution is particularly significant. These results may provide a new perspective for understanding the microscopic origin of SHG in nonlinear-optical materials.

The sensitivity of continuous gravitational-wave searches is strictly limited by non-Gaussian spectral artefacts that accumulate coherent power over long observation baselines. In this paper, we present an unsupervised mitigation framework based on adaptive network coherence analysis. Unlike traditional veto methods that discard entire frequency bands, our pipeline selectively suppresses local artefacts while preserving global potentially astrophysical signals. We validate the method using Advanced LIGO O3 data, analysing the cleaning performance across integration times of 1, 3, and 5 days. For the 5-day dataset, the pipeline identifies and mitigates 89\% and 77\% of the total spectral lines in the Hanford and Livingston detectors, respectively, while effectively preserving the coherent population consistent with astrophysical morphologies. This is achieved while modifying less than 7\% of the analysis bandwidth spanning 20~Hz to 2000~Hz. Rigorous statistical verification demonstrates that the mitigation effectively suppresses the non-Gaussian tail of the noise distribution while strictly preserving the statistical integrity of coherent signal candidates. By recovering detector sensitivity in parameter spaces previously contaminated by the spectral forest, this framework provides a robust preprocessing strategy for all-sky searches.

Non-Hermitian systems driven along slow parametric loops undergo non-adiabatic transitions whose outcome depends sensitively on the driving speed, yet no explicit formula has been available for the critical timescale $T_{\mathrm{cr}}$ at which these transitions develop. Using a $2\times 2$ Hamiltonian with circular parameter trajectories, we derive $T_{\mathrm{cr}} = \mathcal{G}\,\ln(1/|Δ|)$ in closed form for non-encircling loops, phase-shifted loops, offset loops, and loops encircling exceptional points, where $\mathcal{G}$ is a geometry-dependent growth factor and $Δ$ is the instability seed. This formula sharply separates the regime where the system remains in the averagely dominant eigenstate ($T< T_{\mathrm{cr}}$) from the superadiabatic regime where the instantaneous dominant eigenstate takes over ($T> T_{\mathrm{cr}}$), resolving the apparent tension between the previous literature. We identify two competing seeds: a geometric Stokes multiplier and the finite-precision floor. When the geometric seed vanishes, precision alone governs the transition, yielding $T_{\mathrm{cr}} \propto m\lnβ$, linear in the number of precision bits $m$. This provides a purely forward-evolution manifestation of precision-induced irreversibility (PIR)~\cite{PIR}, demonstrating that the fundamental limit identified through echo protocols also controls the outcome of slow non-Hermitian dynamics without requiring time reversal. For PT-symmetric energy spectra, $T_{\mathrm{cr}}$ additionally determines the onset of chirality: the dynamics is non-chiral for $T< T_{\mathrm{cr}}$ and chiral for $T> T_{\mathrm{cr}}$.

Vergence is widely used as a proxy for depth perception and spatial attention in immersive and real-world eye-tracking studies. In this paper, we investigate how pupil size artefacts affect vergence estimates during real physical depth viewing with a head-mounted eye tracker. Using a beamsplitter setup with physically near and far targets, we elicited controlled convergent and divergent eye movements under static, luminance-modulated, and blockwise fixation conditions. Near and far targets were reliably separable in vergence angle across participants. However, pupil-vergence coupling varied substantially across individuals and conditions. Static illumination produced large inter-participant variability, while luminance modulation reduced this spread, yielding more clustered estimates. Blockwise and audio-cued recordings further showed that pupil-vergence coupling persists even without visual depth onsets. These results suggest that pupil size fluctuations can systematically influence vergence estimates, and that controlled viewing conditions can reduce--but not eliminate--this effect.

Many nonlinear dynamical systems exhibit symmetry, affording substantial benefits for control design, observer architecture, and data-driven control. While the classical notion of group invariance enables a cascade decomposition of the system into highly structured subsystems, it demands very rigid structure in the original system. Conversely, much more general notions (e.g., partial symmetry) have been shown to be sufficient for obtaining less-structured decompositions. In this work, we propose a middle ground termed "weak invariance", studying diffeomorphisms (resp., vector fields) that are group invariant up to a diffeomorphism of (resp., vector field on) the symmetry group. Remarkably, we prove that weak invariance implies that this diffeomorphism of (resp., vector field on) the symmetry group must be an automorphism (resp., group linear). Additionally, we demonstrate that a vector field is weakly invariant if and only if its flow is weakly invariant, where the associated group linear vector field generates the associated automorphisms. Finally, we show that weakly invariant systems admit a cascade decomposition in which the dynamics are group affine along the orbits. Weak invariance thus generalizes both classical invariance and the important class of group affine dynamical systems on Lie groups, laying a foundation for new methods of symmetry-informed control and observer design.

The realization of the Quantum Internet promises transformative capabilities in secure communication, distributed quantum computing, and high-precision metrology. However, transitioning from laboratory experiments to a scalable, multi-tenant network utility introduces deep orchestration challenges. Current development is often siloed within physics communities, prioritizing hardware, while the classical networking community lacks architectural models to manage fragile quantum resources. This tutorial bridges this divide by providing a network-centric view of quantum networking. We dismantle idealized assumptions in current simulators to address the "simulation-reality gap," recasting them as explicit control-plane constraints. To bridge this gap, we establish Software-Defined Quantum Networking (SDQN) as a prerequisite for scale, prioritizing a symbiotic, dual-plane architecture where classical control dictates quantum data flow. Specifically, we synthesize reference models for SDQN and the Quantum Network Operating System (QNOS) for hardware abstraction, and adapt a Quantum Network Utility Maximization (Q-NUM) framework as a unifying mathematical lens for engineers to reason about trade-offs between entanglement routing, scheduling, and fidelity. Furthermore, we analyze Distributed Quantum AI (DQAI) over imperfect networks as a case study, illustrating how physical constraints such as probabilistic stragglers and decoherence dictate application-layer viability. Ultimately, this tutorial equips network engineers with the tools required to transition quantum networking from a bespoke physics experiment into a programmable, multi-tenant global infrastructure.

Inspired by the work of McGlynn and Simenel [Phys. Rev. C {\bf 102}, 064614 (2020)], this study investigates the quantum tunneling of two interacting distinguishable particles in two potential wells. We first benchmark the system by reproducing key established results: the exact quantum solution and the spurious self-trapping effect that arises in the real-time mean-field dynamics for strong interactions. To exactly capture the tunneling dynamics, we apply the time-dependent generator coordinate method (TDGCM) to the model. Numerical simulations demonstrate that the TDGCM, by utilizing the real-time mean-field states as generator states, successfully overcomes the self-trapping effect, yielding tunneling dynamics in excellent agreement with the exact solution. Furthermore, we explore the expectation values of the generator coordinates from the correlated TDGCM many-body wave function. While different methods for calculating expectation values show consistent results in some cases, significant discrepancies are observed in others, providing critical insights into the emergence of collective and single-particle behaviors in interacting systems. This work also verifies the TDGCM as a robust framework for describing collective quantum tunneling and opens avenues for its application to more complex and realistic systems.

The discovery of superconductivity in the Ruddlesden-Popper (RP) nickelates has opened a new chapter in the search for high superconducting transition temperatures ($T_\mathrm{c}$) materials. A central and puzzling feature of this family is the wide variation in $T_\mathrm{c}$ despite their common NiO$_2$ building blocks, as highlighted by the recent observation of superconductivity at $\sim$ 30 K in trilayer $\mathrm{La_4Ni_3O_{10}}$, significantly lower than 80 K reported in bilayer $\mathrm{La_3Ni_2O_7}$. Understanding the factors that control $T_\mathrm{c}$ in this family is therefore of paramount importance. Here, we use resonant inelastic x-ray scattering (RIXS) to investigate the electronic and magnetic excitations of $\mathrm{La_4Ni_3O_{10}}$ in direct comparison with its bilayer counterpart. Our results reveal a markedly different landscape. $\mathrm{La_4Ni_3O_{10}}$ exhibits a more itinerant character, evidenced by broader Ni $dd$ orbital excitations and a strong Ni 3$d$ fluorescence continuum, suggesting weaker electronic correlations than in the bilayer. Despite this, well-defined collective spin excitations persist, including dispersive acoustic and optical magnon branches alongside an incommensurate spin density wave. Using linear spin wave theory, we extract the interlayer superexchange interaction ($J_z$) to be $\sim$ 22 meV, much smaller than that in $\mathrm{La_3Ni_2O_7}$. The weaker correlation and reduced interlayer exchange together provide a consistent explanation for the substantially lower $T_\mathrm{c}$ in the trilayer compound. Our findings establish interlayer magnetic coupling and electronic correlation as key parameters governing superconductivity in layered nickelates and offer critical constraints for understanding the pairing mechanism in this emerging family.

Linking X-ray variability to the underlying magnetohydrodynamic (MHD) dynamics of black hole X-ray binaries remains challenging. We systematically investigate the stochastic and oscillatory variability of the black hole X-ray binary candidate Swift J1727.8$-$1613 during its 2023 outburst using Gaussian process (GP) regression applied to Insight-HXMT multi-band light curves. The variability is modeled with a physically motivated composite kernel comprising one stochastically driven damped simple harmonic oscillator (SHO) and two damped random walk (DRW) components. The SHO term robustly recovers quasi-periodic oscillations (QPOs) with frequencies $ν_0 \sim 0.07$--$5$ Hz, consistent with the fundamental Alfvén mode of a contracting magnetically confined disk--coronal cavity. The quality factor rises from $Q \sim 3$ to $Q \sim 10$, suggesting increasing coherence of the magnetic cavity. We also find an anti-correlation between QPO frequency and the short DRW damping timescale, supporting our proposed stochastic magneto-active dynamics scenario. Associating the short and long DRW timescales with the local turbulent turnover and thermal adjustment timescales, respectively, we infer an effective viscosity parameter of $α\approx 0.1$, supporting a strongly magnetized accretion flow. Strikingly, near the onset of relativistic jet ejection around MJD 60206, both relaxation timescales collapse toward the 0.1 s sampling limit, suggesting a rapid reorganization of the disk internal energy balance immediately before jet launching. Our results establish GP inference as a powerful route to connecting X-ray timing observables with the dynamical state of black hole accretion flows.

The spin and orbital Hall effects convert longitudinal charge currents into transverse flows of electronic angular momentum. Here we develop an atomistic theory of the recently proposed lattice-vibrational analogue, in which a longitudinal heat current driven by a thermal gradient is converted into a transverse current of phonon angular momentum. We derive a microscopic real-space expression for this current and show that it originates from thermally induced mixing of polarized vibrational motion, leading to a characteristic edge accumulation of phonon angular momentum. We demonstrate the effect in minimal square- and honeycomb-lattice models and compute the resulting phonon angular momentum accumulations for a range of example materials using input from first-principles calculations. Our results confirm that the phonon angular momentum Hall effect is a universal response of crystalline solids and our framework is generically applicable to all materials.

We derive a sharp spectral estimate for a superlinear free boundary problem arising in plasma physics. The semilinear equation is coupled with a constraint, which forces the analysis of a non-local eigenvalue equation. Consequently the corresponding first eigenvalue, say $σ_1$, is not a standard one and it is shown that it cannot satisfy a general isoperimetric property of Faber-Krahn type. This motivates a careful analysis of the problem on balls in any dimension $N\geq 2$, where we prove that in fact $σ_1$ is always positive. The implications about the uniqueness problem for the Emden equation are also discussed.

The X-ray brightness delivered by fourth-generation light sources strongly depends on the electron beam current and transverse emittance. Reaching higher brilliance and lower emittances are increasingly limited by intra beam scattering, particularly at low and medium beam energies, where low emittances combined with high beam currents result in large phase-space densities. Increasing the vertical emittance through betatron coupling is commonly employed to mitigate intra beam scattering by relaxing the phase-space density. However, the redistribution of damping partition numbers due to coupling, the presence of vertical dispersion, and consequently their impact on the balance between synchrotron radiation and intra beam scattering are often neglected. In this work, we develop a self-consistent Ordinary Differential Equations-based framework to describe both the steady-state and time evolution of three-dimensional beam emittances in the simultaneous presence of synchrotron radiation, quantum excitation, betatron coupling, vertical dispersion, and intra beam scattering; allowing for realistic damping partition numbers. The model consistently accounts for the modification of synchrotron radiation damping rates and intra beam scattering growth rates arising from betatron coupling. Application to the BESSY III lattice demonstrates that damping partition redistribution and optics modifications significantly influence the equilibrium emittances. A systematic comparison of vertical emittance generation via a transverse feedback-generated excitation, betatron coupling, and vertical dispersion highlights the trade-offs between horizontal emittance reduction and operational constraints.

We present a loop-shaping approach to coherent feedback (CF) control. By formulating the coupling between a quantum system and its environment in terms of the noise power spectrum, our method enables direct manipulation of the effective dissipation coefficients through spectral shaping. A systematic design framework for CF controllers is also developed, in which transfer functions are shaped to realize desired spectral responses. Applying this framework to optomechanical sideband cooling, we demonstrate that suppression of the Stokes process and enhancement of the anti-Stokes process can be simultaneously achieved, enabling ground-state cooling even in the unresolved-sideband regime. This loop-shaping framework provides an intuitive and general foundation for the design of CF controllers and can be extended to a wide class of quantum systems in which interactions with environments are characterized by noise power spectra.

The phenomenon of opinion disagreement has been empirically observed and reported in the literature, which is affected by various factors, such as the structure of social networks. An important discovery in network science is that most real-life networks, including social networks, are scale-free and sparse. In this paper, we study noisy opinion dynamics in sparse scale-free social networks to uncover the influence of power-law topology on opinion disagreement. We adopt the popular discrete-time DeGroot model for opinion dynamics in a graph, where nodes' opinions are subject to white noise. We first study opinion disagreement in many realistic and model networks with a scale-free topology, which approaches a constant, indicating that a scale-free structure is resistant to noise in the opinion dynamics. Moreover, existing algorithms for estimating opinion disagreement are computationally impractical for large-scale networks due to their high computational complexity. To solve this challenge, we introduce a sublinear-time algorithm to approximate this quantity with a theoretically guaranteed error. This algorithm efficiently simulates truncated random walks starting from a subset of nodes while preserving accurate estimation. Extensive experiments demonstrate its efficiency, accuracy, and scalability.

Deep reinforcement learning (DRL) has recently emerged as a promising tool for Dynamic Algorithm Configuration (DAC), enabling evolutionary algorithms to adapt their parameters online rather than relying on static tuned configurations. While DRL can learn effective control policies, training is computationally expensive. This cost may be justified if learned policies generalize, allowing the training effort to transfer across instance types and problem scales. Yet, for real-world optimization problems, it remains unclear whether this promise holds in practice and under which conditions the investment in learning pays off. In this work, we investigate this question in the context of the carbon-aware permutation flow-shop scheduling problem. We develop a DRL-based DAC framework and train it exclusively on small, simple instances. We then deploy the learned policy on both similar and more complex unseen instances and compare its performance against a static tuned baseline, which provides a fair point of comparison. Our findings show that the proposed method provides a strong dynamic algorithm control policy that can be effectively transferred to different unseen problem instances. Notably, on simple and cheap to compute instances, similar to those observed during training and tuning, DRL performs comparably with the statically tuned baseline. However, as instance characteristics diverge and computational complexities increase, the DRL-learned policy continuously outperforms static tuning. These results confirm that DRL can acquire robust and generalizable control policies which are effective beyond the training instance distributions. This ability to generalize across instance types makes the initial computational investment worthwhile, particularly in settings where static tuning struggles to adapt to changing problem scenarios.

In this work, we investigate the worldsheet symmetry of bosonic brane theories and its quantum consistency in the tensionless limit. We find that the residual worldsheet symmetry after specific gauge fixing is generated by a novel algebra, denoted as $g^{(p)}_λ$. To achieve full quantization of the tensionless brane, we introduce a $bc$ ghost system and derive the overall BRST charge. Moreover, we calculate the quantum anomaly of the $g^{(p)}_λ$ algebra for general parameters $p$ and $λ$ in the framework of canonical quantization. After demanding that this quantum anomaly vanishes, we successfully derive the critical dimensions of the bosonic brane theories. Especially, we obtain nontrivial solutions: $p=3$ in $D=4$ spacetime dimensions when $λ=-3$ and $p=6$ in $D=7$ spacetime dimensions when $λ=3$.

We consider Erdős-Rényi-type random hypergraphs that are non-uniform, in the sense that hyperedges of different sizes may coexist, and inhomogeneous, in that connection probabilities may depend on the hyperedge size. All parameters are allowed to scale with the hypergraph size. We study the random adjacency matrix whose $(u,v)$-entry counts the number of hyperedges containing both vertices $u$ and $v$, and characterize its expected limiting spectral distribution in terms of the connection probabilities and the hyperedge sizes. We provide a Pastur-type condition, in the sense of Chatterjee (2005), under which the matrix can be Gaussianized, as well as a more restrictive but simpler sufficient condition in terms of the generalized average degree of the model. As a second main result, based on such a Gaussianization, we characterize the limiting spectral distributions under non-sparse conditions as semicircle laws with an explicit parametric variance. The latter can be expressed as a convex combination of the variances arising in the uniform cases, with coefficients determined by the trade-off between the different sources of inhomogeneity.

While QKD ensures information-theoretic security at the link level, real-world deployments depend on trusted repeaters, creating potential vulnerabilities. In this paper, we thus introduce a topology-hiding connectivity assurance protocol to enhance trust in quantum key distribution (QKD) network infrastructures. Our protocol allows network providers to jointly prove the existence of a secure connection between endpoints without revealing internal topology details. By extending graph-signature techniques to support multi-graphs and hidden endpoints, we enable zero-knowledge proofs of connectivity that ensure both soundness and topology hiding. We further discuss how our approach can certify, e.g., multiple disjoint paths, supporting multi-path QKD scenarios. This work bridges cryptographic assurance methods with the operational requirements of QKD networks, promoting verifiable and privacy-preserving inter-network connectivity.

We prove that the Lipschitz-free space over any uniformly discrete metric space has the 3-Schur property

We exhibit nontrivial transversal logical multi-controlled-$Z$ gates on $[\![N,Θ(N),\tildeΘ(N)]\!]$ quantum low-density parity-check codes and $[\![N,Θ(N),\tildeΘ(N)]\!]$ quantum locally testable codes with soundness $\tildeΘ(1)$, combining nearly optimal code parameters with fault-tolerant non-Clifford gates for the first time. Remarkably, our proofs are almost entirely algebraic-topological, showing that such presumably intricate logical gates naturally arise as a fundamental topological phenomenon. We develop a general framework for constructing a rich new family of homological invariant forms which we call ''cupcap gates'' that induce transversal logical multi-controlled-$Z$ and, building on insights from [Li et al., arXiv:2603.25831], covering space methods to certify their nontriviality. The claimed almost-good code results follow immediately as examples.

Scaled relative graphs (SRGs) enable graphical analysis and design of nonlinear systems. In this paper, we present a systematic approach for computing both soft and hard SRGs of nonlinear systems using dynamic integral quadratic constraints (IQCs). These constraints are exploited via application of the S-procedure to compute tractable SRG overbounds. In particular, we show that the multipliers associated with the IQCs define regions in the complex plane. Soft SRG computations are formulated through frequency-domain conditions, while hard SRGs are obtained via hard factorizations of multipliers and linear matrix inequalities. The overbounds are used to derive an SRG-based feedback stability result for Lur'e-type systems, providing a new graphical interpretation of classical IQC stability results with dynamic multipliers.

The AGN NGC~1566 is known to present dramatic and regular spectral shape changes, associated with the appearance and disappearance of broad emission lines. The underlying mechanism responsible for such changes is yet to be identified, but occultation, eccentric accretion disks, turbulent disk-dominated broad line regions (BLRs) or binary supermassive black holes have been hypothesized. Because the scenarios used to explain the variable spectral shapes of NGC~1566 each have a specific geometric configuration, we used the VLT/FORS2 instrument to obtain nine 3500-10\,000~Å\, polarized spectra of the source between August 2 and September 21, 2025. We caught the AGN in a type-2 state, i.e., without any broad component in total nor polarized fluxes. Its low and wavelength-independent polarization degree (and angle) above 4000~Å\, argues against occultation of the BLR and is consistent with a significant weakening or disappearance of the BLR. The polarized spectrum reveals a strong rise of polarization in the blue band, likely echoing the 2018 outburst of the AGN. The temporal variability of the total flux continuum but the steadiness of the line profiles demonstrate that the object is viewed close to pole-on, irrespective of its spectral type at the time of observation. Relative to archival data, NGC 1566 shows significant variability in polarization degree, angle, and wavelength dependence. Even more surprisingly, NGC~1566 behaves opposite to the basic predictions of the unified model: its polarization angle is perpendicular to the AGN polar axis and its polarization degree is higher when in a brighter, type-1 phase. The results reported above contradict occultation and binary supermassive black hole hypotheses, rather supporting accretion-driven photoionization/structural changes in the internal accretion flow and the BLR.

We investigate the leading-power fragmentation of triply heavy $Ω$ baryons in high-energy hadronic collisions. Extending our previous work on the $Ω_{3c}$ sector, we release the full OMG3Q1.0 family of collinear fragmentation functions by completing the description of the charm channel and delivering the novel $Ω_{3b}$ functions. These hadron-structure-oriented functions are constructed from improved proxy-model calculations for heavy-quark and gluon fragmentation, matched to a flavor-aware DGLAP evolution based on the HF-NRevo scheme. For phenomenological applications, we employ the (sym)JETHAD multimodular interface to compute and analyze NLL/NLO$^+$ semi-inclusive $Ω_{3Q}$ plus jet distributions at the HL-LHC and FCC. This work consolidates the link between hadron structure, rare baryon production, and resummed QCD at the energy frontier.

We present novel self-similar finite-time blowup scenarios for the 1D Hou--Luo model. We numerically demonstrate that solutions that initially satisfy certain derivative degeneracy condition can develop asymptotically self-similar finite-time blowups with singular self-similar profiles that are unbounded at some point. Moreover, this blowup phenomenon exhibits a two-stage feature: the solution first undergoes a local $L^{\infty}$ blowup at some time $\tilde{T}$, then continues in the weak sense beyond $\tilde{T}$ and develops a local $L^p$ blowup at a later time $T>\tilde{T}$ for some $p>0$. A further numerical investigation indicates that both stages are asymptotically self-similar. Finally, we extend our numerical study to the 2D Boussinesq equations and discover similar self-similar finite-time blowups with singular profiles that also exhibit a two-stage feature.

We investigate the core dynamics behind exotic matter formation via the TQ4Q1.1 set of collinear fragmentation functions for fully charmed or bottomed tetraquarks in three quantum configurations: scalar ($0^{++}$), axial vector ($1^{+-}$), and tensor ($2^{++}$). We adopt leading-power single-parton fragmentation within a nonrelativistic QCD framework tailored to tetraquark Fock states. Initial-scale inputs are constructed from updated gluon- and heavy-quark channels, and evolved through threshold-consistent DGLAP within HF-NRevo. We present the first systematic propagation of uncertainties from color-composite long-distance matrix elements governing tetraquark hadronization. This study advances the connection between hadronic structure, precision QCD, and exotic matter.

In optimization-based image restoration models, the correct selection of hyperparameters is crucial for achieving superior performance. However, current research typically involves manual tuning of these hyperparameters, which is highly time-consuming and often lacks accuracy. In this paper, we concentrate on the automated selection of hyperparameters in the context of image restoration and present a bilevel programming approach that can simultaneously select the optimal hyperparameters and achieve high-quality restoration results. For implementation, we reformulate the bilevel programming problem that incorporates an inequality constraint related to the difference-of-convex functions. Following this, we address a sequence of nonsmooth convex programming problems by employing a feasibility penalty function along with a proximal point term. In this context, the nonsmooth convex programming problem uses the solution of the lower-level problem, which is derived through the alternating direction method of multipliers. Theoretically, we prove that the sequence generated by the algorithm converges to a Karush-Kuhn-Tucker stationary point of the inequality-constrained equivalent bilevel programming problem. We conduct a series of tests on both simulations and real images, which demonstrate that the proposed algorithm achieve superior restoration quality while requiring less computing time compared to other hyperparameter selection methods.

We investigate the high-energy production of tetraquark-jet systems at the LHC and its forthcoming High-Luminosity upgrade. In this review, we examine the leading-power fragmentation of fully heavy tetraquarks ($T_{4Q}$) in hadronic collisions, highlighting their relevance as novel probes of multiquark dynamics in QCD. Our analysis relies on the hadron-structure-oriented TQ4Q1.1 fragmentation functions, built within a nonrelativistic QCD framework that incorporates both gluon- and heavy-quark-initiated channels. Threshold-consistent DGLAP evolution is performed through the HF-NRevo scheme, enabling a unified treatment of mass thresholds and scale variations. We also provide a systematic discussion of uncertainties arising from color-composite long-distance matrix elements (LDMEs) and from perturbative hard- and fragmentation-scale inputs (H- and F-MHOUs). Phenomenological predictions are obtained using the (sym)Jethad framework at NLL/NLO$^+$ accuracy for semi-inclusive tetraquark-jet production at the LHC and beyond. This review connects the emerging spectroscopy of fully heavy exotics with modern fragmentation-based approaches to hadron structure and high-energy QCD.

The chromatic redshift philosophy, introduced by Ausoni and Rognes, suggests that algebraic $K$-theory raises chromatic height by $1$. We show that the analogue of this philosophy fails in the case of rigid symmetric monoidal stable $\infty$-categories. More precisely, we construct examples of rigid $T(n)$-local categories $C$ where a refinement $\mathrm{Dim}$ of the dimension morphism induces an equivalence $$K(C)\to \mathrm{End}(\mathbf{1}_C)^{BS^1}$$ and for which $K(C)$ therefore vanishes $T(n+1)$-locally. In fact, we prove that this equivalence always holds for $\aleph_1$-Nullstellensatzian rigid $T(n)$-local categories in the sense of Burklund, Schlank and Yuan. We study more in depth the rational version of these results to find a rigid rational additive $1$-category witnessing the failure of redshift at height $0$. Finally, we use our methods to prove and generalize a conjecture of Levy about categorification of ordinary rings.

Antiferromagnetic (AFM) and ferromagnetic (FM) skyrmions possess unique advantages for spintronic applications. AFM skyrmions eliminate the skyrmion Hall effect and exhibit fast dynamics, whereas FM skyrmions are easier to nucleate and manipulate. However, realizing a transition between AFM and FM skyrmions within the same two-dimensional (2D) material has remained elusive. Here, using first-principles calculations and atomistic spin simulations on the Janus monolayer Cr2Ge2Te3S3, we demonstrate that strain-driven modulation of magnetic interactions enables switching between AFM and FM skyrmion phases. A compressive strain of $-3\%$ induces an AFM ground state hosting AFM skyrmions, while a tensile strain of $+2\%$ drives the system into a FM skyrmion phase. Moreover, under an out-of-plane magnetic field, FM skyrmions are rapidly transformed into a uniform FM phase, while AFM skyrmions transform into AFM bimerons under stronger fields. These findings establish a framework for controllable transitions between topological magnetic states in a single 2D material.

We study the mechanical response of quasi-brittle polymethyl methacrylate (PMMA) specimens containing controlled random distributions of laser-cut holes. Tensile tests combined with digital image correlation reveal a nearly linear decrease of the Young's modulus with porosity, but with a softening rate far exceeding classical effective medium theory and the Hashin-Shtrikman bound. The extrapolated critical porosity at which the modulus vanishes is well below the 2D percolation threshold, indicating that ideal cylindrical void models fail to capture the observed behavior. Microscopy shows irregular pore geometries and frequent coalescence, which effectively act as crack-like defects and strongly enhance compliance. The rupture stress distributions are well described by a Weibull model accounting for both load-bearing area reduction and stress concentration at hole edges. Digital image correlation reveals heterogeneous but non-localized deformation, with strain increasingly correlated with the hole pattern, indicating a growing influence of defect-induced stress concentrations. These results highlight the dominant role of defect morphology in governing stiffness degradation and fracture statistics in porous quasi-brittle materials.