Understanding how quasiparticles are generated following a rapid quench of superconductivity in high-Tc cuprates is a key unresolved problem in nonequilibrium superconductivity. Here we resolve these processes in optimally doped YBCO [YBa2Cu3Oy(y=6.94, Tc=92 K)] using broadband (0.16 -4.1 eV, ca. 100 fs) and nearly single-cycle (6 fs) transient reflectivity spectroscopy. We show that within a few femtosecond, enhanced electron-electron Umklapp scattering dominates, signaling a transient modulation of long-range Coulomb interactions on the eV scale. This regime is followed by a rapid suppression of the scattering rate of the mid-infrared absorption associated with carriers dressed by spin fluctuations. We attribute this observation to an ultrafast decoupling of quasiparticles from the spin-fluctuation background, occurring on a 90 fs timescale set by the inverse optical gap. These findings reveal the correlated many-body dynamics underlying quasiparticle generation in cuprates and provide further clues for unconventional pairing mechanism.

Run-length decoding is an operation on sequences in which a positive integer $a$ is replaced by a run(sequence of repeated elements) of length $a$. Iterated run-length decodings applied to sequences with alphabets consisting of pairs of positive integers $\{p, q\}$ have attracted attention from mathematicians, most notably in their role defining the well-known Kolakoski sequence. $n$-th-iterated run-length decodings are controlled by naturally associated permutation automata $A^{p,q}_n$. Here we study the transformation groups $\mathcal{K}^{p,q}_n$ of these automata. They are subgroups of the automorphism group of binary trees of depth $n+1$. They are naturally subgroups of(and likely equal to) a certain group $\mathcal{J}_n^{p,q}$ with an intricate recursive structure; their limit group is plausibly weakly regular branch. As an application we determine the number of maximal-length orbits of the automata given an arbitrary input sequence for odd $n$.

JWST has unveiled an abundant population of compact broad-line emitters largely at $z\gtrsim4$, the Little Red Dots (LRDs), which might represent a previously unprobed supermassive black hole evolution channel predominant at high redshift. However, the LRDs have remained mostly elusive at lower redshift ($z\lesssim2$) where detailed studies are possible from ground-based observatories. We searched for low-redshift LRDs in the Dark Energy Spectroscopic Instrument (DESI) survey. Our search is primarily based on emission line properties, as opposed to earlier approaches that searched for compact sources with specific photometric spectral energy distributions. We report the discovery of eight LRDs at $z=0.2-0.45$, which show spectral features akin to the high-redshift LRDs in the rest-frame optical. The sources are characterized by broad Balmer lines, steep Balmer decrements, compact morphologies, Balmer absorption features and/or strong He I emission, but weak or absent He II, [Ne V] or other high excitation lines typical of Type I AGN. For 7 out of 8 sources, we retrieve dense-cadence light curves from time-domain surveys and for most sources we find weak to no intrinsic variability ($0.0-0.1$ mag) over $4-17$ years in the rest-frame. We also highlight the identification of a quasar with similar Balmer line profiles as LRDs, but shows differences in Balmer decrement, significant variability, and high-ionisation lines. Given the effective volume $4.9{\rm Gpc^3}$ covered by DESI DR1 at $z<0.45$, our sample corresponds to a number density of $1.6\times10^{-9}$Mpc$^{-3}$, indicating a number density $\sim$10,000 times lower than in the first billion years of cosmic time. We find a dearth of luminous and red LRDs at $z<1$ compared to higher-redshift, which could suggest lower gas feeding rates of LRD activity due to higher metallicities at later cosmic epochs.

Elliptic curves over $\Q$ with $j$-invariant 0 or 1728 have additive reduction at all primes of bad reduction. In addition, all elliptic curves with $j$-invariant 0 have bad reduction at $p=3$ and all elliptic curves with $j$-invariant 1728 have bad reduction at $p=2$. In this paper we count elliptic curves with $j$-invariant 0 and 1728 by height and determine asymptotics for the various Kodaira-Néron types at 3 and 2, respectively. We also give related statistics by holding the torsion subgoup and isogeny-torsion graph constant.

The quest for efficient devices has fueled research in thermoelectric materials. In these materials, the goal is to maximize the Figure of Merit $ZT$. One of the components of this quantity is the Seebeck coefficient, which measures the voltage generated in response to a temperature gradient. Recent studies have revealed that strong electronic correlations can enhance the Seebeck coefficient, leading to anomalous behavior near half-filling. However, the impact of interactions beyond the on-site Hubbard remains mostly unexplored. In this work, we investigate the Seebeck coefficient considering attractive interactions, nearest-neighbor interactions, sublattice potentials and electron-phonon coupling. We find that additional interaction scales can enhance the Seebeck coefficient, while also leading to multiple anomalous changes of sign as a function of doping. We also show that the anomalous behavior is connected to a gap opening in the ground state. Moreover, electron-phonon coupling also lead to a Seebeck anomaly, even without on-site repulsion. We connect these changes of sign in the Seebeck coefficient with a restructuring of the Fermi surface and a change in its topology, an effect commonly seen in cuprates.

We present a study of the $τ^- \to ωπ^-ν_τ$ decay in the framework of low-energy effective field theory. By analyzing the $J^{PG}$ quantum numbers of the quark currents and the $ωπ$ final state, we find that only the Standard Model (SM) vector interaction and the non-standard tensor interaction can contribute to this decay. We construct the resonance chiral theory Lagrangian with external tensor sources and calculate both the vector and tensor form factors, with resonance couplings determined through QCD short-distance constraints, spectral function fitting, and chiral perturbation theory matching. The new physics (NP) effect is investigated in the spectral function and forward-backward asymmetry distributions. Our results show that the spectral function is dominated by the SM, while the forward-backward asymmetry, which can only arise from a non-zero tensor interaction, provides a sensitive probe of this NP effect. Future measurements at Belle II, Tera-Z, and STCF facilities are therefore strongly motivated.

A platform trial is an innovative clinical trial design that enables simultaneous and continuous evaluation of multiple treatments within a single master protocol. Existing robust methods restrict analyses to concurrently randomized participants due to concerns that including nonconcurrent data may introduce bias from temporal trends. However, this exclusion represents a missed opportunity to improve efficiency. We propose a Gaussian process framework for incorporating nonconcurrent data that exploits temporal smoothness, a key feature of platform trials. The framework includes single-task and multi-task formulations and provides data-adaptive integration of nonconcurrent data with uncertainty quantification. The connection to kernel ridge regression yields a transparent frequentist interpretation of how nonconcurrent data are integrated. We establish two theoretical guarantees: incorporating nonconcurrent controls reduces the posterior variance of the treatment effect, and the resulting bias is controlled by a non-increasing bound. We extend the framework to discrete outcomes and to covariate adjustment, illustrate it on a hypothetical platform trial constructed from SURMOUNT-1, and provide an implementation in the R package RobinCID.

Hybrid quantum-classical (HQC) algorithms, such as the Variational Quantum Eigensolver (VQE) and the Quantum Approximate Optimization Algorithm (QAOA), are central to near-term quantum computing but remain challenging to test. Sampling-based fuzzing can expose faulty or non-convergent configurations, but under realistic execution budgets, it may miss failure-prone regions in the joint space of classical optimizer settings and quantum circuit parameters. This paper studies failure-guided fuzzing for HQC programs. It models a hybrid input as a pair of classical optimizer hyperparameters and quantum circuit parameters, and evaluates a two-phase strategy that first searches for non-convergent seeds and then locally fuzzes circuit parameters around those seeds. To understand where the gains come from, five budgeted strategies are compared: random hybrid testing, classical enumeration without fuzzing, random-seed local fuzzing, enumeration-seed local fuzzing, and concolic-seed local fuzzing. The study is implemented on a VQE instance and a QAOA MaxCut instance in Qiskit. The results show that failure-guided local fuzzing is the main driver of improvement over random testing, while concolic seed discovery provides additional benefits on VQE but is less stable on QAOA. These findings suggest that reusing failure information is a promising direction for HQC testing, but that the value of concolic seed discovery is workload-dependent.

We investigate localization effects in zigzag graphene nanoribbons with quasiperiodic Fibonacci-type edge extensions, accounting for electron-electron interactions. We employ a tight-binding model that includes first- and third-nearest-neighbor hoppings, in which electronic interactions are treated within a self-consistent mean-field Hubbard approximation. Charge transport properties are calculated using the Landauer-Büttiker formalism. Our results reveal that the combination of quasiperiodic geometry and electronic interactions gives rise to nontrivial transport phenomena. Specifically, the system exhibits three transport regimes: in the non-interacting case, we observe geometric localization. For weak interactions, the system shows a conductive regime with transmission oscillations, whose multiplicity increases with the Fibonacci generation order. In this regime, delocalization emerges from the interplay between geometry and interaction-induced correlations. Finally, for strong interactions, repulsion dominates, and the system returns to a localized state. Our results demonstrate that quasiperiodic edge engineering, combined with electronic interaction control, offers a promising path to modulate transport in graphene nanoribbons.

In spintronics, both electronic charge and spin are used to process and store information. Generation, manipulation, and detection of spin currents are essential for the development of next-generation spintronic technologies. Here, we investigate the spin Hall effect in electronic Lévy glasses composed of graphene ribbons with randomly distributed circular regions of high spin-orbit coupling. These systems exhibit two transport regimes that can be tuned by adjusting the Fermi energy. The superdiffusive regime is characterized by low Fermi energy, low resistivity, and low magnetoresistivity, resulting in a long spin diffusion length, in contrast to the diffusive regime. Employing the Landauer-Büttiker approach in conjunction with numerically exact tight-binding simulations, we compute spin-resolved transmission coefficients to assess the spin Hall current and the spin Hall angle as functions of Fermi energy, spin-orbit coupling strength, and on-site electrostatic potential. Our findings reveal that, in the superdiffusive regime, a low charge current can be converted into a large spin Hall current, whereas in the diffusive regime, the same charge current generates a modest spin Hall current. Moreover, we observe that the spin Hall angle can reach 30% in the superdiffusive regime, whereas in the diffusive regime it is only 5%. These results demonstrate that electronic Lévy glasses provide a versatile platform for controlling spin transport and optimizing the spin Hall effect for spintronic applications.

For the OEIS sequence A032123, the number of length-$2n$ black-and-white strings with $n$ black beads, considered up to reversal, R. J. Mathar contributed in November 2013 the conjectured order-5 P-recursive recurrence \[ \begin{aligned} &n(n-1)\,a(n) - 2(n-1)(3n-4)\,a(n-1) + 4(2n^{2}-14n+19)\,a(n-2) &\qquad + 8(n^{2}+5n-19)\,a(n-3) - 16(n-3)(3n-10)\,a(n-4) &\qquad + 32(n-4)(2n-9)\,a(n-5) \;=\; 0, \qquad n \ge 6. \end{aligned} \] We give a short proof. Burnside's lemma applied to the reversal action gives the closed form $a(n) = \tfrac{1}{2}\bigl(\binom{2n}{n} + [n \text{ even}]\binom{n}{n/2}\bigr)$; the two summands satisfy elementary recurrences of order $1$ and $2$ respectively; and Mathar's order-5 operator, applied to each summand separately, reduces to a polynomial identity that simplifies to zero after a brief calculation. The supplementary archive includes a SymPy script which verifies the polynomial identities symbolically and checks Mathar's recurrence numerically for $n = 6, \ldots, 5000$.

The rise of automated scanning tools and AI assisted reconnaissance agents has significantly altered internet background traffic patterns, threatening the baseline assumptions underlying intrusion detection systems (IDS) deployed in critical infrastructure networks. This paper characterizes the evolution of automated bot traffic by analyzing a longitudinal dataset of 192 million passive darknet packets captured across 2021 and 2025 from the Merit ORION Network Telescope. A modular analysis pipeline was developed to compute metrics including average packet rate, global Shannon entropy, inter-arrival time (IAT) burstiness, geographic attribution, and destination port targeting across key industrial protocols. Results reveal a highly distributed yet focused reconnaissance landscape, with traffic targeting ICS-relevant ports nearly doubling from 0.82% to 1.51% over the four-year period. Furthermore, burstiness analysis exposes intentional micro-pacing behaviors (1ms to 100ms delays) that allow modern botnets to artificially smooth their overall volume. Our simulated anomaly-based IDS demonstrates that these evasion techniques enable 97.47% of modern bot traffic to bypass standard volumetric thresholds undetected. Compensatory sensitivity tuning triggers a 68.10% false-positive rate, highlighting fundamental visibility and alerting gaps in operational technology (OT) environments.

The hitherto neglected close binary V486 Car is studied with the aid of newly applied satellite photometry (HIPPARCOS and TESS), high dispersion spectrometry (HERCULES) and ground-based B and V photometry. While the sinusoidal light variations are suggestive of a near-contact system, the stars have only shallow eclipse, so highly confident parametrization becomes challenging. We find: $M_1 = 2.1 \pm 0.1$, $M_2 = 0.4 \pm 0.1$; $R_1 = 3.20 \pm 0.02$, $R_2 = 1.48 \pm 0.01$; (${\odot}$); $T_{e1} = 10000 \pm 500$, $T_{e2} = 6200 \pm 200$ (K); distance = 162 $\pm$ 12 (pc). New times of minima for V486 Car have been examined, including recent observations from TESS. The role of the relatively significant O'Connell effect is examined. As well as the conspicuous asymmetry from the main effect of about 0.036 mag (V), a jitter, with amplitude of about 0.005 V mag and quasi-period of order $\sim$ 10 d is noticed. There is a tendency for such photometric excursions at one maximum to precede those at the other. As well, the O -- C data indicate the presence of a low mass star $\sim$0.3 M$_{\odot}$ in an orbit separated by a few AU from the close binary. More accurate and plentiful spectroscopic data would be requisite for further investigations. A brief discussion reviews possible approaches to understanding the system in the context of near-contact binary scenarios.

Which categories of explanation content are relevant for users of industrial AI systems, and how can those categories be organized for local, post-hoc explanations? To address these questions, a hybrid inductive-deductive qualitative content analysis was applied to 325 meaning units drawn from six user studies in building technology, manufacturing, AI software development, and hospital cybersecurity. The inductive phase produced an initial twelve-code structure. A theory-informed coverage assessment and expert review then added two further codes, Rule base and What-if backward, that were not instantiated in the corpus but correspond to system architectures documented in the XAI literature. The resulting fourteen-code model is organized into four groups: rule-based, causal, epistemic (actual), and epistemic (similar), with twelve codes grounded in the corpus and two as theoretical extensions. An eleven-member expert panel supported the content adequacy of all codes (I-CVI $\geq$ 0.82; scale-level agreement of 0.93 for relevance, 0.92 for boundary clarity, and 0.94 for understandability). A stratified subsample of 82 units (25\% of the corpus), coded independently by two researchers using the finalized codebook, yielded Krippendorff's $α= 0.920$ and Cohen's $κ= 0.920$. The paper therefore establishes content adequacy and coding reproducibility for a content-level explanation model intended to support elicitation, specification, and later evaluation of explanation content in industrial AI systems. Behavioral validation of downstream effects remains future work.

We consider a generalisation of the classical coupon collector's problem, in which at each time step a collector either receives a new copy of a randomly chosen coupon, or loses all their previously collected copies of that coupon. We consider the amount of time it takes this clumsy coupon collector to obtain the full set of $m$ coupons. We establish limit theorems as $m\to\infty$ for the clumsy coupon collection time, and describe the large $m$ asymptotics of its mean and variance. We identify three regimes, depending on how the probability of a clumsy update, $p$, scales with $m$. If $p=o(1/m)$, we obtain a Gumbel limit theorem, as is the case for the classical coupon collector. If $p=ω(1/m)$, we instead show weak convergence to an exponential random variable. In the critical case, $p=c/m$, we give a full characterisation of the limiting distribution in terms of a birth-death process.

Connected and autonomous vehicles and smart mobility services increasingly use digital route guidance as an operational input to traffic network management. When this information becomes unreliable or adversarial, day-to-day traffic models must represent not only flow adaptation but also the evolution of user trust in the information source. This paper develops a coupled day-to-day traffic assignment and trust-evolution framework for route-guidance misinformation. Within-day congestion is represented by Lighthill-Whitham-Richards network loading, while day-to-day route choice follows bounded-rationality logit learning with trust-dependent reliance on external guidance. Trust is modeled as an aggregate class-level behavioral reliance state encoded by a Beta evidence model and updated from repeated guidance errors. Theoretical analysis establishes stationary equilibria, a conservative stability guide, a weighted compliance index for population-level vulnerability, and an asymmetric recovery law that explains post-attack trust hysteresis. Numerical experiments on Sioux Falls, with an Anaheim robustness check, show that endogenous trust creates a threshold-based resilience mechanism. Below the trust-activation threshold, the attack remains behaviorally stealthy and dynamic trust provides almost no attenuation. Above the threshold, trust erosion reduces the impact of the fixed-trust attack by about 91 percent in Sioux Falls and 85 percent in Anaheim. The experiments also show that CAV penetration increases fixed-trust vulnerability while preserving dynamic attenuation, and that traffic performance can recover before trust, resulting in a 77-day hidden vulnerability window. The results provide a trust-aware modeling basis for resilience analysis in CAV-enabled traffic networks.

In this paper we construct {\em adic}, {\em saturated} and $\varepsilon$-density functions for a torsion-free module in a graded setup. Then we give some simple criteria for checking the integral dependence of two graded modules $N\subseteq M$ in terms of various well-studied invariants.

Collective critical behavior is often identified with thermodynamic nonanalyticities and divergences emerging only in the infinite-size limit. Here we adopt a complementary viewpoint: criticality is a structural property due to the rearrangement of the interactions among system's constituents that already exists at finite size and becomes singular only asymptotically. We show that the microcanonical entropy derivatives provide a natural finite-$N$ arena where such structure is encoded in intrinsic extremal/inflection morphologies, and that microcanonical inflection-point analysis (MIPA) turns these morphologies into a unique finite-size critical marker and a well-defined critical trajectory. Using the mean-field $ϕ^4$ model as a stringent benchmark, we reconstruct $β_N(\varepsilon)$ and $γ_N(\varepsilon)$ from microcanonical simulations, validate them against analytic results, and demonstrate that the MIPA trajectory converges to the exact thermodynamic critical point while simultaneously organizing the approach of other observables to their asymptotic behavior. Our results elevate finite-size criticality from a rounded remnant of the thermodynamic limit to a measurable and predictive object in its own right, with direct relevance to modern finite-system platforms and numerical studies.

I introduce modal group theory, in which we study the category of all groups, considering embeddability as providing a notion of modal possibility. Using HNN extensions and Britton's lemma, I demonstrate that the modal language of groups is more expressive than the first-order language of groups. I interpret the theory of true arithmetic in modal group theory, and show that, as sets of Goedel numbers, it is computably isomorphic to the modal theory of finitely presented groups. I answer an open question of Berger, Block, and Loewe by showing that the formulaic propositional modal validities of groups under embeddings are precisely S4.2. I also analyze sentential validities and worlds validating S5.

We study optimal monopoly pricing over consumer networks governed by general nonlinear utilities. In our framework, a consumer's utility is jointly determined by an individualized price and the consumption choices of their peers, propagated through a directed and signed social graph. This formulation encapsulates a broad class of utility functions; it strictly generalizes the traditional linear-quadratic framework to include logit-type discrete choice, isoelastic, and Stone-Geary utilities under a single theoretical umbrella. We first establish the existence and uniqueness of the consumer-side equilibrium under general contraction and variational conditions, explicitly accommodating asymmetric and signed network externalities. Leveraging this equilibrium characterization, we analyze targeted price discrimination within community-structured and influencer-driven markets. To this end, we introduce a generalized measure of network influence that extends classical Katz-Bonacich centrality beyond the Euclidean domain. Finally, addressing the challenge of unknown consumer utility functions, we develop a shape-constrained, tuning-parameter-free learning approach utilizing isotonic regression, for which we establish strict no-regret convergence guarantees. Supported by extensive simulations, our results seamlessly integrate equilibrium analysis and nonparametric learning into a cohesive monopoly pricing framework.

We describe a general method for constructing representations of finite integral symmetric relation algebras from distance-regular graphs. Given a distance-regular graph of diameter $d$, the distances between vertices induces a coloring of the complete graph with $d$ colors, and we show that this coloring yields a representation of finite integral symmetric relation algebra on $d+1$ atoms. We then introduce a necessary and sufficient condition for when such a representation is algebraic, proving that this occurs if and only if the distance-regular graph is also distance-transitive. We study the diameter-3 case of this method in detail, and we express a condition for the representation's mandatory cycles in terms of the distance-regular graph's intersection array. We apply this result to give a positive answer to an open question of Roger Maddux; namely, whether the relation algebra $30_{65}$ has a representation on a finite set. The representation is given on 42 points, and arises from the second subconstituent of the Hoffman-Singleton graph. We further use this method to describe an infinite class of finite representations of $26_{65}$ and the smallest possible representation of $31_{65}$.

We introduce KnotMosaics, a SageMath package for constructing, visualizing, and analyzing knot mosaic diagrams. The package represents an n-mosaic as a matrix of standard tile labels and implements the local connectivity rules needed to validate mosaics, trace strands and components, compute planar diagram codes, generate random examples, and construct rational tangle mosaics. The planar diagram interface connects the mosaic representation to existing knot and link software, enabling computations such as Jones polynomials and knot Floer homology checks. We describe the package design, its main algorithms, and representative examples that illustrate how KnotMosaics can support computational exploration in knot mosaic theory.

We analyze the radiative decays of the the 1$P$, 1$D$, 2$S$, and 2$P$ $Λ_c$ and 1$D$, 2$S$, and 2$P$ $Ξ_c$ charmed baryons, which belong to the flavor anti-triplet ($\bf {\bar 3}_{\rm F}$), using the constituent quark model. We compute electromagnetic transitions from ground and $P$-wave states to ground states, as well as from second-shell states to both ground and $P$-wave final states. Electromagnetic decay widths are especially valuable for identifying resonances when multiple states share the same mass and total decay width. We give branching ratios which can confirm the assignment of the $Ξ_c(3055)$ reported by LHCb. We also give branching ratios that can support the assignment of the $Ξ_c(3080)$, and discuss the possibilities for the $Ξ_c(3080)$ to be the 1$D$ state with $J^P=5/2^{+}$ or the 2$S$ with $J^P=1/2^{+}$. For the first time, this work provides calculations of electromagnetic decays for $D_ρ$-wave states, $ρ-λ$ mixed configurations, and $ρ$-mode radially excited states in singly charmed baryons of the flavor anti-triplet. Both experimental and model-dependent uncertainties are taken into account throughout our analysis.

Recently, Stull [18], [17] resolved a long-standing open problem posed by Lutz, on whether the set of effective Hausdorff dimensions of points on a straight line in $\mathbb{R}^2$ -- the effective dimension spectrum of the line -- contains a unit interval. This question is related to problems in classical fractal geometry like the Kakeya conjecture and Furstenberg sets. Stull posed an open question on the dimension spectra of polynomial curves. For the first result, with new techniques which adapt the theory of classical real root-finding of polynomials to the current setting, we show that the dimension spectra of every polynomial curve contains at least two points. This answers an open question posed by Stull [18], [17]. We use the main result to construct a class of polynomials which have width strictly greater than 1, answering a second problem stated in [18],[17]. Stull [18] resolved the dimension spectrum conjecture for planar lines, showing that it contains a unit interval. For the second result, we resolve the conjecture for a subfamily of polynomials whose coefficients form a "low" dimension point in $\mathbb{R}^{d+1}$.

We propose a new point-spread function (PSF) deconvolution algorithm for images of galaxies hosting an active galactic nucleus (AGN), designed to simultaneously enhance the spatial resolution of the host galaxy and remove the bright central point source. In this algorithm, an intrinsic image is reconstructed by decomposing an observed image into two components: an image $I_{\rm sm}$ of an extended component (i.e., a host galaxy) and an image $I_{\rm sp}$ of a point-source component (i.e., an AGN). During image reconstruction, three constraints are imposed: (1) a smooth constraint on the image $I_{\rm sm}$ , which spatially smooths the host-galaxy structures; (2) a sparse constraint on the image $I_{\rm sp}$ , which localizes the point source to a small number of pixels; and (3) a new constraint, the point-source balance constraint, based on the pixel-wise product $I_{\rm sm} \times I_{\rm sp}$ , which removes the point source from the host galaxy without over- or under-subtraction. As a test, we apply this algorithm to images of artificial and $z \sim 0-1$ real AGNs observed with Hyper Suprime-Cam on the Subaru Telescope. We find that the spatial resolution of the host-galaxy images is improved to a level comparable to that of images from the Hubble Space Telescope and that the bright central point sources are removed. This algorithm is expected to enable statistical morphological studies of distant AGN host galaxies when applied to wide-field survey data from the Vera C. Rubin Observatory, the Euclid Space Telescope, and the Roman Space Telescope.

Based on X-ray afterglow observations from the Swift satellite, we construct a sample of 169 long gamma-ray bursts (LGRBs) exhibiting the canonical magnetar plateau signature, i.e., a plateau followed by a $t^{-2}$ decay. We derive the plateau luminosity $L_0$ and break time $t_b$ for each burst by performing Markov Chain Monte Carlo (MCMC) fits to the light curves, and estimate pseudo-redshifts for bursts lacking known redshifts via the Amati relation. The fundamental magnetar parameters are subsequently inferred: the surface polar magnetic field strength $B_p \in [0.39,\ 23.08] \times 10^{15}$G and the initial spin period $P_0 \in [0.95,\ 13.79]$ms. Statistical analysis shows that both the known-redshift subsample and the full sample follow the Dainotti correlation between $L_0$ and $t_b$ with a slope close to $-1$, supporting a constant energy injection rate during the plateau phase. Furthermore, we identify a significant correlation between $B_p$ and $P_0$: $B_p \propto P_0^{0.83 \pm 0.09}$ for the full sample and $B_p \propto P_0^{0.80 \pm 0.16}$ for the known-redshift subsample, with both slopes consistent within uncertainties. Compared to magnetars powering superluminous supernovae (SLSNe), GRB magnetars possess systematically stronger magnetic fields (by approximately one order of magnitude), suggesting fundamental differences in their progenitor systems or collapse conditions; while their magnetic field strengths show no significant difference from those powering fast radio bursts (FRBs), suggesting a possible common evolutionary pathway. This study provides a physics-motivated, model-consistent sample of magnetar-candidate GRBs, offering a robust foundation for statistical investigations within the magnetar central engine model and placing new observational constraints on the birth properties of these extreme compact objects.

We determine the pion parton distribution functions (PDFs) from its light-front wave functions, obtained using the holographic Schrödinger equation of light-front chiral QCD combined with the 't Hooft equation in (1+1)-dimensional QCD at large $N_c$. We analyze the large-$x$ behavior of the valence PDF, $\sim (1-x)^{β^{\rm eff}_v}$, finding overall consistency with global analyses. These pion PDFs, together with nuclear PDFs, are then used to compute the differential cross sections up to next-to-leading order for inclusive $J/ψ$ production in pion--nucleus collisions, which show good agreement with experimental data across different energies and nuclear targets.

Real-valued logics have seen a renewed interest in verification for probabilistic and quantitative systems, in particular machine learning models, where they can be used to directly integrate specifications in the training objective. To do so effectively one has to strike a balance between the logical properties of the connectives and their semantics. A major hurdle in this sense is to give ``soft'' (i.e. differentiable) semantics to additive connectives -- in linear and fuzzy logics, additives are necessarily ``hard'' lattice operations. In this paper, we solve this problem by combining an accurate analysis of the properties of sum and product on the reals with a significant revision of sequent calculus. We introduce `quantitative sequent calculi', which simultaneously generalize hypersequent calculi of fuzzy logics and deep inference, and in which validity of a proof and provability of a sequent are real-valued quantities. We present a family of calculi, pQLL, indexed by a hardness degree $p$, prove cut-elimination theorem for them, and show completeness for enriched residuated `soft' lattices. For $p = \infty$, pQLL reduces to MALL, with provability in pQLL converging to provability in MALL when $p \to \infty$.

Photon loss and dephasing rapidly degrade the sensitivity of quantum sensors, yet systematic methods for designing error-correcting codes whose geometry is simultaneously adapted to the sensing task and the noise channel do not exist. Here we establish that orbital-angular-momentum (OAM) encoding and Gottesman-Kitaev-Preskill (GKP) lattice geometry are structurally coupled: an OAM mode of topological charge $\ell$ induces a phase-space rotation $θ_\ell=\ellπ/\ell_{\max}$, corresponding to a family of twisted GKP stabilizer lattices. Using an end-to-end differentiable Strawberry Fields--TensorFlow circuit, we jointly optimise $\ell$, the lattice aspect ratio $r$, and the finite-energy envelope $ε$ to maximise quantum Fisher information subject to $P_{\rm err}\leq10^{-3}$. The optimum occurs at the fractional charge $\ell=1.5$ ($θ=67.5^\circ$), implementable with a half-integer spiral phase plate, which reduces $P_{\rm err}$ by $23.9\times$ relative to the square-lattice baseline while leaving $\mathcal{F}_Q$ unchanged to within $0.2\%$. This surpasses the best integer value ($\ell=2$, $15.7\times$) and arises from an exact $180^\circ$ periodicity of the $P_{\rm err}(θ)$ landscape, confirmed analytically and numerically. We derive a transcendental balance equation for the optimal angle $θ^*(η,γ,r)$ and prove that it decreases with both $γ$ and $η$. A Shannon-inspired metrological capacity $\mathcal{C}=\mathcal{F}_Q\cdot(-\ln P_{\rm err})$, maximised at $\ell=1.5$ with a $41\%$ gain over the square lattice, quantifies the joint sensitivity--fault-tolerance resource. These results establish a geometric design principle for noise-adaptive quantum sensors and a fully open-source differentiable template extensible to other bosonic code families.

We reveal a previously unknown continuous symmetry and conservation law in the equations of linear isotropic elasticity, which describe the chirality of elastic waves. We show that the integral chirality is determined by the population imbalance between right- and left-handed transverse phonons, whereas the local chirality density generally involves both transverse and longitudinal wave components. We also introduce the related concepts of acoustic helicity and ``false chirality''. The theory is illustrated with simple interference fields exhibiting distinct distributions of chirality, spin angular momentum, and false chirality. Our results establish chirality as a fundamental property of elastic waves and provide a general theoretical framework for chiral acoustic phenomena.