We explore the interpretation that the diffuse astrophysical neutrino flux is dominated by a single standard candle-like source class. Since recent observations favor a broken power law with a spectral break around 30 TeV, we postulate that the $pγ$ channel is the dominant neutrino production process creating a peak at these energies. We use a SOPHIA-based photo-pion interaction model with a thermal target including high-energy processes, such as multi-pion production, which turns out to be relevant for the interpretation. We demonstrate that target photon temperatures 0.1 to 1 keV are preferred in a multi-parameter fit, whereas the maximal neutrino energies can be limited by A) soft injection spectra, B) a maximal proton energy in the PeV range, or C) magnetic field effects on the secondary muons, pions, and kaons with B in the few 10 kG range. We predict that future measurements, such as of the neutrino flavor composition or neutrino-antineutrino ratio (Glashow resonance), can discriminate scenarios. We also point out that the parameters obtained in our generic approach, such as in the strong magnetic field values, might be indicative for an AGN core origin as a driver of the diffuse flux.

We propose a deep backward regression-based (DBR) scheme for solving high-dimensional nonlinear parabolic partial differential equations. Building on the DBDP method of Huré, Pham, and Warin~\cite{HCPHWX20}, the proposed method reformulates the local backward losses through conditional expectations and trains the resulting regression problems sequentially in time. This conditional-expectation formulation replaces pathwise Brownian fluctuations in the Euler residual by their averaged effect and therefore provides an intrinsic variance-reduction mechanism before loss evaluation. In practice, the conditional expectations are approximated by local multi-path Monte Carlo averages, which leads to smoother training targets and improved numerical stability. Numerical experiments show that DBR performs competitively on standard high-dimensional benchmarks and is more stable than DBDP1 on the challenging unbounded benchmark considered in Example~2. Under an idealized population-loss minimization setting, we provide an error analysis and establish a half-order convergence result under suitable approximation and integrability assumptions. We also discuss an extension to variational inequalities.

We propose a systematic Gagliardo-type formulation of fractional Sobolev spaces on arbitrary time scales, based on the Lebesgue Delta-measure and the off-diagonal interaction domain induced by the product measure. For fractional orders strictly between zero and one and for finite Lebesgue exponents, we define a nonlocal Gagliardo seminorm and the associated function space. This construction provides a notion of fractional regularity on time scales that is genuinely nonlocal and structurally distinct from the derivative-based approaches developed in the existing literature. We establish the basic functional properties of these spaces: they are Banach spaces in all admissible cases, reflexive in the strict range of exponents, and Hilbert in the quadratic case. On bounded time scales with finitely many connected components, we identify a sharp criterion for the construction to be nontrivial. We then compare the new framework with the derivative-based Riemann--Liouville fractional Sobolev spaces previously studied on time scales. On a continuous interval, in the supercritical regime, we obtain a norm equivalence with the bilateral Riemann--Liouville space on the subspace of functions with vanishing boundary trace. On hybrid time scales, we prove an explicit obstruction that rules out any analogous equivalence, due to the contribution of the mixed continuous--discrete interactions. On bounded hybrid time scales with finitely many connected components separated by a positive distance, we further establish a Poincaré-type inequality, a fractional Sobolev embedding, and fractional Hardy and Caffarelli--Kohn--Nirenberg-type inequalities for subcritical weights. Together, these results provide a complete functional and geometric framework, together with first geometric estimates, for the nonlocal Gagliardo-type approach to fractional Sobolev spaces on time scales.

Corresponding to a hyperbolic system $(V, p, e)$, where $V$ is a real finite-dimensional vector space and $p$ is a hyperbolic polynomial of degree $n$ in the direction $e$, we consider the eigenvalue map $λ: V \to R^n$ and the hyperbolicity cone $Λ_+$. In such a system, a scaled Jordan frame is defined as a finite set of rank-one elements whose sum lies in the interior of $Λ_+$. We show that when the system has a scaled Jordan frame and $n \geq 2$, $p$ and its derivative polynomial $p^\prime$ are minimal polynomials (generating their respective hyperbolicity cones), thereby extending a result of Ito and Louren{\c c}o proved in the setting of a rank-one generated (proper) hyperbolicity cone. When each element of a scaled Jordan frame has trace one and the total sum is $e$ (such a set is called a Jordan frame), we show that the frame is orthonormal relative to the semi-inner product induced by $λ$ with exactly $n$ elements, and $V$ contains a copy of $R^n$ (as a Euclidean Jordan algebra). We also present a Schur-type majorization result corresponding to a Jordan frame and an $e$-doubly stochastic $n$-tuple.

M-dwarf stars are the most favorable hosts for detecting small transiting planets, yet mid-to-late M-dwarfs that acquired sufficient TESS multi-sector coverage only through recent Cycle 6+ observations represent a newly accessible discovery space. This paper presents a systematic transit survey of 121 M3-M6 dwarfs (Teff = 2700-3400 K) selected as "newly enabled" targets -- stars with <=2 archival TESS sectors that only recently crossed the multi-sector detection threshold, covering P = 0.5-100 d. The sample was selected from 498,312 TIC M-dwarfs via a 9-step funnel. The pipeline combines TLS with a signal validation cascade, TRICERATOPS vetting, Gaia DR3 verification, and three empirical signal reliability tests. Pipeline validation achieved 100% recovery (16/16 planets) on 10 known systems with zero false positives. The survey identifies 20 transit-like signals across 16 systems, none with prior TOI designations. The reliability framework classifies 2 as Tier 1 (High Robustness), 7 as Tier 2 (Moderate), and 10 as Tier 3 (Noise-Susceptible); one monotransit is excluded. No candidate SDE significantly exceeds its host star's noise floor. The global false alarm rate is 17.4% (21/121; Wilson 95% CI: [11.6%, 25.1%]).The 2 Tier 1 candidates are priorities for RV confirmation. The 10 Tier 3 candidates require additional TESS sectors to establish signal persistence; 9 systems need high-resolution imaging.

We consider the question of determining whether or not a given system of fractional-order differential equations is (asymptotically) stable. In particular, we admit systems where each constituent equation may have its own order, independent of the order of the other equations in the system, i.e. we discuss the so-called incommensurate case. Exploiting ideas based in numerical linear algebra, we present an algorithm that can be used to answer this question that is much simpler than known methods. We discuss in detail the case of linear problems where the ratios of orders are rational and indicate how known techniques can be used to apply our findings also to general nonlinear problems with arbitrary orders. A MATLAB implementation of the code is provided.

This study demonstrates that the apparent complexity of fracture in phantom-chain polymer networks is fully decoupled into two universal master curves: (i) macroscopic softening governed by the absolute stretch, and (ii) microscopic scission governed solely by the relative stretch. Using the previously proposed network mechanics model, an analytical expression has been derived to quantitatively capture the nonlinear growth of microscopic damage. Combining the softening exponent with polymer-solution scaling yields a simple novel relationship, $σ_{nb} / G \propto (c / c^* )^{(-1/3)}$, where $σ_{nb}$ is the nominal broken strength, $G$ is the initial shear modulus, $c$ is the prepolymer concentration, and $c^*$ is its overlapping threshold.

p-hacking occurs when researchers conduct multiple significance tests (e.g., p1;H0,1 and p2;H0,2) and then selectively report tests that yield desirable (usually significant) results (e.g., p2 < 0.05;H0,2) without correcting for multiple testing (e.g., 0.05/2 = 0.025). In the present article, I consider p-hacking in the context of two philosophies of significance testing - the error statistical approach and the formal inference approach. I argue that although p-hacking inflates Type I error rates in the error statistical approach, it does not inflate them in the formal inference approach. Specifically, in the error statistical approach, the "actual" familywise error rate (e.g., 1 - [1 - 0.05]2 = 0.098 for two independent tests) is relevant because it covers both the reported and unreported tests in the "actual" test procedure (i.e., p1;H0,1 and p2;H0,2). In this approach, Type I error rate inflation occurs because the "actual" error rate (0.098) is higher than the nominal error rate (0.05). In contrast, in the formal inference approach, the "actual" familywise error rate is irrelevant because (a) the researcher does not report a statistical inference about the corresponding intersection null hypothesis (i.e., H0,1 & H0,2), and (b) the "actual" familywise error rate does not license inferences about the reported individual hypotheses (i.e., H0,2). Instead, in the formal inference approach, only the nominal error rate is relevant, and a comparison with the "actual" error rate is inappropriate. Implications for conceptualizing, demonstrating, and reducing p-hacking are discussed.

Let c(K;F) denote the surface crossing number of a knot K with respect to a closed connected surface F in S^3. We relate c(K;F) to the tunnel number t(K) and to the Heegaard deficiency delta(F)=g(M_1;F)+g(M_2;F)-g(F), where S^3=M_1 union_F M_2. The zero-crossing case gives a structural obstruction: if c(K;F)=0, then t(K) <= delta(F). Conversely, if t(K)>delta(F), then c(K;F) >= 2(t(K)-delta(F))+1. Thus the Heegaard deficiency of F measures the amount of tunnel complexity that can be absorbed by F without producing crossings. The proof combines a surface ascending-number estimate, a bridge-number estimate for surface diagrams, and an amalgamation argument for Heegaard splittings relative to F. We also construct connected-sum families showing that the lower bound has the correct linear order.

The performance of quantum annealing for combinatorial optimization is fundamentally limited by the minimum energy gap $Δ$ encountered at quantum phase transitions. We investigate the scaling of $Δ$ with system size $N$ for two paradigmatic quantum spin-glass models: the two-dimensional Edwards-Anderson (2D-EA) and the all-to-all Sherrington-Kirkpatrick (SK) models. Utilizing a newly proposed unbiased energy-gap estimator for continuous-time projection quantum Monte Carlo simulations, complemented by high-performance sparse eigenvalue solvers, we characterize the gap distributions across disorder realizations. It is found that, in the 2D-EA case, the inverse-gap distribution develops a fat tail with infinite variance as $N$ increases. This indicates that the unfavorable super-algebraic scaling of $Δ$, recently reported for binary couplings [Nature 631, 749 (2024)], persists for the Gaussian disorder considered here, pointing to a universal feature of 2D spin glasses. Conversely, the SK model retains a finite-variance distribution, with the disorder-averaged gap following a rather slow power law, close to $Δ\propto N^{-1/3}$. This finding provides a promising outlook for the potential efficiency of quantum annealers for optimization problems with dense connectivity.

Hong-Ou-Mandel (HOM) interference is a fundamental tool for assessing photon indistinguishability in quantum information processing. While the effect of chromatic dispersion on HOM interference has been widely studied, the interplay between dispersion and the finite detection window of realistic measurement devices remains under-explored. In this work, we demonstrate that the rectangular coincidence window inherent to modern time-tagging modules, which effectively acts as a temporal filter, breaks the standard dispersion cancellation condition and restores sensitivity to symmetric group velocity dispersion. We derive an analytical model for type-II SPDC processes that predicts a modification of the HOM dip shape, specifically the emergence of characteristic oscillations and dip broadening. We experimentally validate this theoretical framework using a ppKTP source and transmission through optical fibers of lengths up to 29 km. The experimental data show excellent agreement with the model, confirming the presence of window-induced oscillations and allowing for the precise extraction of the fiber dispersion parameter. These findings underscore the importance of accounting for finite timing resolution in the design and characterization of dispersive quantum communication links.

Neutral gas outflows play a crucial role in the baryon cycle of galaxies, their properties provide key insights into the transition from star formation to quiescence. In this work, we investigate the neutral gas outflow of 23 massive ($M_\star = 10^{10.1-11.6}\,\rm M_\odot$) quiescent galaxies (QGs) at z=2.82--4.61, selected from the JWST NIRSpec (R~1000) and NIRCam program DeepDive. We trace the neutral gas outflows using the NaI Doublet absorption lines and detect excess NaI D in 13/23 (57%) targets, of which 7/23 (30%) show blueshifted absorption with velocity offsets $|Δv|$ >~ 150 km/s. The z ~ 3.5 targets have $Δv$ similar to those of their local counterparts; they are also equivalent when compared in SFR--$Δv$ space. We derive mass outflow rates and identify the most extreme neutral gas outflow rate $\log(\dot M_{\rm out} / \mathrm{M_\odot \, yr}^{-1})=2.68\pm0.27$ beyond the local Universe, coincident with an X-ray AGN. For all NaI D detected systems, the inferred mass outflow rate can, in principle, suppress ongoing star formation; however, the outflows are unlikely to escape their hosts, suggesting recycling on relatively short timescales (~3--180 Myr), depending on the assumed potential and launching radius. All NaI D detected targets occupy the LI(N)ER region of the BPT diagram and/or are X-ray detected, but we find no strong correlation between ongoing AGN and the neutral outflow: 2/4 broad-line/X-ray AGNs are NaI D undetected -- yet, the outflows can be powered by fossil/episodic AGNs, and one broad-line target shows a possible P-Cygni profile that indicates strong outflows. As neutral outflows alone are not able to permanently quench star formation by removing gas in our sample at z ~ 3.5, the presence of gas cycling in and out of massive passive systems may instead be the signature of feedback-regulated quenching-maintenance processes.

Despite the high volume of open-source Cyber Threat Intelligence (CTI), our understanding of long-term threat actor-victim dynamics remains fragmented due to inconsistent reporting standards and the lack of structured datasets containing comprehensive analytic information. In this paper, we present a large-scale automated analysis of open-source CTI reports spanning two decades. We develop a high-precision, LLM-based pipeline to ingest and structure 16,096 reports, extracting key entities such as attributed threat actors, motivations, victims, reporting vendors, and technical indicators (IoCs and TTPs). Our analysis quantifies the evolution of CTI information density and specialization, characterizing patterns that relate specific threat actors to motivations and victim profiles. Furthermore, we perform a meta-analysis of the CTI industry itself. We identify a fragmented ecosystem of distinct silos where vendors demonstrate significant geographic and sectoral reporting biases. Our marginal coverage analysis reveals that intelligence overlap between vendors is typically low: while a few core providers may offer broad situational awareness, additional sources yield diminishing returns. Overall, our findings characterize the structural biases inherent in the CTI ecosystem, enabling practitioners and researchers to better evaluate the completeness of their intelligence sources.

The paper presents a high Reynolds number experimental study of turbulent boundary layer separation control on a convex plate using the wavy-wall method, which was initially proposed for a flat plate by Dróżdż et al. 2021 (Exp Therm Fluid Sci 2021;121:110291). The application of this method increases the friction coefficient by up to 42.3%, resulting in a substantial delay in turbulent separation from the convex wall, while maintaining total momentum, quantified by changes in momentum-loss thickness. Other parameters indicating the high efficiency of the method are the invariant value of the friction Reynolds number along the flow and the thinner boundary layer. The above indicators demonstrate promising aerodynamic improvements in airfoils, similar to those achieved when active suction is applied to the suction side. The new insight into the physical mechanism of the wavy wall suggests that small-scale turbulent activity is the primary determinant of the effectiveness of the wavy wall in enhancing small-scale streamwise convection and the sweeping motion, resulting in superior momentum transport. However, when the wavy wall, due to poorly selected geometry, induces large-scale motions, such as separation in the trough, it counteracts the mechanism. Then this geometry has a detrimental effect on the efficiency of the method.

It is proved that, for a pre-ordered vector space $X$, the quotient space $(X/A,[W])$ is an Archimedeanization of $X$, where $W$ is the closure of the positive wedge $X_+$ in ru-topology, $A=W\cap(-W)$, and $[W]$ is the quotient set of $W$ in $X/A$.

We explore combinations of particle and anti-particle yields which can be used to test thermal models in a parameter free way. We also explore combinations which can be used to extract $μ_B/T$, $μ_S/T$ and $μ_Q/T$. We use experimentally measured particle-antiparticle specific ratios for proton $p$, Lambda $Λ$, and cascade $Ξ$, for $\sqrt{s_{NN}}=$ 7.7-39 GeV from RHIC BES phase-1 to extract the $μ_{B,S,Q}/T$. These compared well with published STAR freeze-out parameters. These combinations are verified to predict a similar combination of $Ω$ yields. We also extend this idea to predict (anti-)nuclei yields at energies where they are not measured. We also update parametrizations for the $\sqrt{s_{NN}}$ dependence of freeze-out parameters $T$ and $μ_B$, and present for the first time a similar parametrization of $μ_S$.

We study preferential attachment (PA) trees with general attachment functions. PA suggests an intuitive monotonicity: if high-degree vertices are rewarded more strongly, then the resulting tree should become shallower. We examine this principle through the constants governing two natural logarithmically growing observables, the insertion depth of the newest vertex and the height of the whole tree. Growth-ratio dominance (GRD) is the natural order on attachment functions, but we provide an explicit counterexample showing that GRD is not sufficient for either depth or height monotonicity at the level of logarithmic constants. The missing input is a dual tail-order condition on certain measures associated with the CMJ/BRW embedding of the PA tree. Under these profile-order assumptions we prove the expected monotonicity results.

A set of curved beams and shells is geometrically implied by level sets of a scalar function over some bulk domain. The mechanical model for each structure is based on the Kirchhoff--Love theory, that is, small displacements without shear deformations are considered. These models for individual geometries are extended to bulk models, simultaneously modeling the whole set of beams/shells on all level sets. A major focus is on the numerical analysis of such models. A mixed-hybrid and higher-order accurate Bulk Trace FEM is proposed that enables the use of standard $C^0$-continuous Lagrange elements with dimensionality of the bulk domain. That is, the higher-order continuity requirements of displacement-based formulations in context of the Kirchhoff--Love theory are successfully alleviated. Several numerical tests confirm the accuracy and higher-order convergence of the proposed methodology, also qualifying as benchmark test cases in future studies.

Magnetic compensation in rare-earth iron garnets (REIGs) offers a unique setting for which competing sublattice moments can give rise to non-collinear (canted) magnetic configurations, in which the sublattice magnetizations are not aligned with each other or with the external magnetic field. We show that this compensation regime can also host non-trivial magnetic textures. To explore this behavior, we investigated (111)-oriented epitaxial Tb$_3$Fe$_5$O$_{12}$/Pt heterostructures across the compensation temperature region using combined transverse magneto-transport and polar Kerr microscopy. Notably, we observe a topological Hall-like signal in the vicinity of the compensation temperature, a feature often interpreted as evidence for skyrmions in the absence of direct imaging. Here, in contrast, complementary Kerr microscopy reveals instead a non-collinear multidomain state which collapses outside the compensation regime, correlating directly with the appearance and disappearance of the spin Hall topological Hall effect (SH-THE) signal. These observations cannot be accounted for by a simple multi-anomalous-Hall-effect model, ruling out common artifacts as the origin, but indicate the presence of a topologically non-trivial contribution to the Hall response. These results establish strained REIG films as a tunable platform for exploring topological responses arising from compensation-driven non-collinear ferrimagnetic phases.

We present a new algorithm for fast matrix multiplication using tensor decompositions which have special features. Thanks to these features we obtain exponents lower than what the rank of the tensor decomposition suggests. In particular for $6\times 6$ matrix multiplication we reduce the exponent of the recent algorithm by Moosbauer and Poole from $2.8075$ to $2.8019$, while retaining a reasonable leading coefficient.

We introduce a random circuit family and show they are robust against current classical simulation techniques, specifically tensor network contraction and Pauli propagation. We also show that local variables do not concentrate, ensuring enough variance to be able to produce a diverse set of data points. We therefore argue that using these circuits as a "random seed" for a larger classical generative model is a way to make large-scale quantum-classical hybrid models amenable towards NISQ devices.

One of the key challenges in the fabrication of superconducting coils using cuprate tapes is the parametrization of the critical currents and their dependence on magnetic field, temperature, and angle. Discussions at the Magnet Technology Conference (MT29) in Boston (2025) highlighted the need for standardized characterization and a better understanding of these tapes. Without a shared understanding of the physical phenomena governing critical currents, progress in this area remains difficult. We propose to analyze existing data using a model that explains most observed features. Although the model proposed by P. Mathieu and Y. Simon was published 20 years ago, it remains relatively unknown and certainly unused among engineers in the field, although many physicists were convinced of its validity, a consensus not reflected in the literature. The Mathieu/Simon (MS) model emphasizes the importance of surface pinning mechanisms, which dominate critical currents across a large part of the phase diagram of YBaCuO. Unlike strong and weak pinning mechanisms, which are commonly assumed to be dominant, the MS model accurately predicts the order of magnitude of experimentally measured values, suggesting it should at least be considered the dominant mechanism. The results of calculations based on this model are presented and compared with experimental data, offering directions for the development of new materials.

The ordering of rod-like particles in soft, deformable containers emerges from the interplay of anisotropic interactions, geometric confinement, and boundary compliance. This competition couples internal particle organization to container morphology, producing behavior distinct from both rigid confinement and bulk systems. Such coupling is also relevant to biological contexts in which filamentous structures are confined by deformable membranes. Using a minimal model combining experiments and simulations of colloidal rods encapsulated in lipid vesicles, we show that soft confinement drives a bidirectional coupling between internal order and vesicle shape. This interplay gives rise to a phase diagram in which elongated vesicles promote nematic alignment at lower packing fractions, whereas higher packing fractions induce smectic-like ordering that reshapes vesicles into plate-like morphologies with increased bending energy. Furthermore, by controlling vesicle volume and membrane area, we demonstrate that boundary conditions enable reversible tuning of both vesicle shape and internal rod organization. These results establish a framework for dynamically controlling colloidal self-assembly in soft containers and provide insight into the organization of anisotropic building blocks in deformable, cell-like, confinements.

This work is concerned with a switching point optimization problem governed by a semilinear parabolic equation in abstract function spaces. It is shown that the switching-point-to-control mapping is continuously Fréchet-differentiable when considered with values in the dual of Hölder continuous functions in time. By treating the state equation in weak form based on the concept of maximal parabolic regularity, one can then show that the reduced objective is continuously differentiable w.r.t. the switching points, which allows to use gradient-based methods like the proximal gradient method for its minimization. Numerical experiments confirm our theoretical findings, but also illustrate that such a method will in general not be able to solve the problem to global optimality due to the non-convex nature of the switching-point-to-control map. We therefore give a precise characterization of the convex hull of set of feasible switching functions in terms of an extended formulation. The latter might be useful for a branch-and-bound approach for the computation of global minimizers, but this is subject to future research.

Quantum algorithms for binary optimization problems have been the subject of extensive study. However, the application of quantum algorithms to integer optimization problems remains comparatively unexplored. In this paper, we study the Quantum Approximate Optimization Algorithm (QAOA) applied to integer problems on graphs, with each integer variable encoded in a qudit. We derive a general iterative formula for depth-$p$ QAOA expectation on high-girth $d$-regular graphs of arbitrary size. The cost of evaluating the formula is exponential in the QAOA depth $p$ but does not depend on the graph size. Evaluating this formula for Max-$k$-Cut problem for $p\leq 4$, we identify parameter regimes ($k=3$ with degree $d \leq 10$ and $k=4$ with $d \leq 40$) in which QAOA outperforms the Frieze-Jerrum semi-definite programming (SDP) algorithm, which provides the best worst-case guarantee on the approximation ratio. To strengthen the classical baseline, we introduce a new heuristic algorithm based on the degree-of-saturation that achieves strong results on the \texttt{GSet} benchmark with quasi-linear runtime in the number of edges. It empirically outperforms both the Frieze-Jerrum algorithm and shallow-depth QAOA on regular graphs. Nevertheless, we provide numerical evidence that QAOA may overtake this heuristic at depth $p\leq 20$. Our results show that moving beyond binary to integer optimization problems can open up new avenues for quantum advantage.

We advocate for a holographic definition of thermodynamic pressure and volume for black holes based on quasi-local gravitational thermodynamics. When a black hole is enclosed by a finite timelike boundary, York's quasi-local first law includes a surface pressure conjugate to the boundary area. Assuming the existence of a holographically dual theory living on this boundary, these geometric quantities correspond to the pressure and volume of the dual thermal system. In this work we focus on static, spherically symmetric black holes, for which these quantities reduce to global thermodynamic variables. The holographic volume provides a notion of system size, allowing extensivity to be defined in standard thermodynamic terms, and it yields a definition of the large-system limit. For the asymptotically flat case, we show that, in the canonical thermodynamic representation, small Schwarzschild black holes are non-extensive, whereas large black holes become extensive in the large-system limit. A similar conclusion applies to Anti-de-Sitter Schwarzschild black holes, with the difference that the quasi-local energy of the large black hole also becomes extensive in the large-system limit. Before this limit, the energy decomposes into subextensive and extensive contributions, and we derive an explicit expression for the extensive part as a function of the finite volume and entropy.

Recent interest has surged in eigenvalue's nonlinearity-based topological transport governed by the equation of auxiliary eigenvalues $HΨ=ωS(ω)Ψ$ [T. Isobe et al., Phys. Rev. Lett. 132, 126601 (2024); C. Bai and Z. Liang, 111, 042201 (2025); Phys. Rev. A 112, 052207 (2025)] rather than the conventional Schrodinger equation $HΨ=EΨ$ in conservative settings, yet non-Hermitian generalizations remain uncharted. In this work, we are motivated to investigate the nonlinear Thouless pumping in a non-Hermitian and nonlinear Rice-Mele model. In particular, we uncover how non-Hermiticity parameters can induce fractional topological phases--even in the presence of quantized topological invariants as predicted by conventional linear approaches. Crucially, these fractional phases are naturally explained within the framework of the equation of auxiliary eigenvalues, directly linking nonlinear spectral characteristics to the bulk-boundary correspondence. Our findings reveal novel emergent phenomena arising from the interplay between nonlinearity and non-Hermiticity, providing key insights for the design of topological insulators and the controlled manipulation of quantum edge states in the real world.

Open quantum systems can be described by unraveling Lindblad master equations into ensembles of quantum trajectories. Here we investigate how the complexity of such trajectories is affected by conservation laws and other dynamical constraints of the underlying Lindblad evolution. We characterize this complexity using a data-driven approach based on the intrinsic dimension, defined as the minimal number of variables required to encode the information contained in a data set. Applying this framework to several systems, including dissipative variants of the quantum top and of the XXZ chain, we find that the intrinsic dimension is sensitive to the structure of their dynamics. The Lindblad evolution in these systems is typically chaotic; in particular, we report new signatures of autonomous chaos in the quantum top. At specific parameter values, however, additional constraints arise: the dynamics becomes integrable, exhibits Hilbert-space fragmentation, or develops a closed BBGKY hierarchy, leading to pronounced minima in the intrinsic dimension. Our approach results in an unsupervised probe of the complexity of dissipative quantum systems that is sensitive to chaos and ergodicity breaking phenomena beyond the initial transient regime.

Large Language Models (LLMs) have shown promising performance in software vulnerability detection, particularly after domain-specific Supervised Fine-Tuning (SFT). However, it remains unclear whether these models genuinely internalize vulnerability root causes or merely exploit surface-level functional patterns. While prior work documented related failures on pre-trained or zero-shot models, the SFT process itself, and how explicit reasoning supervision modulates it, remains under-explored. We study fine-tuned decoder-only LLMs under vanilla SFT and SFT with reasoning supervision, identifying a failure mode we term the Semantic Trap, characterized by three symptoms: pairing-sensitive performance, gap-dictated decisions, and fragility to semantic-preserving changes. To probe this, we propose TrapEval, an evaluation framework comprising two real-world datasets, V2P (vulnerable paired with patched code) and V2N (vulnerable paired with unrelated normal code), alongside semantic perturbations, CodeBLEU-based gap analysis, and an LLM-assisted reasoning failure taxonomy. Evaluating five representative LLMs fine-tuned with and without explicit reasoning (Chain-of-Thought), our results show vanilla SFT yields deceptively high scores on unpaired data (V2N) while failing all three symptoms. Models suffer high false-positive rates on V2P, degrade under perturbations, and exhibit a systematic dependency on the textual gap between vulnerable and patched code. Finetuning with explicit reasoning reduces these symptoms but costs recall; its lack of measurable gap-dependency partly reflects a floor effect rather than escaping the trap. Furthermore, our taxonomy reveals these models still misinterpret control flow and hallucinate API behavior, indicating current fine-tuning mitigates but does not eliminate reliance on surface features.

Standard approaches to quantum error correction (QEC) require active maintenance using measurements and classical processing. Passive QEC, by contrast, has so far been established only in unphysical spatial dimensions. Here, we give an explicit scheme for autonomous quantum error correction and computation in two dimensions, formulated as a dissipative quantum cellular automaton with a fixed, local and translation-invariant update rule. The construction uses hierarchical, self-simulating control elements based on ideas from the seminal classical results of Gács (1986, 1989) together with a measurement-free concatenated quantum code. We prove the existence of a nonzero noise threshold under a local noise model. Below this threshold, logical errors on encoded initial states are suppressed exponentially with increasing system size and the memory lifetime diverges in the thermodynamic limit. We also describe an implementation in continuous time as a time-independent, translation-invariant local Lindbladian using engineered dissipative jump operators. The recursive nature of our protocol allows for the fault-tolerant execution of quantum circuits specified by the initial state, and thus constitutes a self-correcting quantum computer capable of universal computation.