Decoding a quantum error correction code is generally NP-hard, but corrections must be applied at a high frequency to suppress noise successfully. Matchable codes, like the surface code, exhibit a special structure that makes it possible to efficiently, approximately solve the decoding problem through minimum-weight perfect matching (MWPM). However, this efficiency-enabling property can be lost when constructing implementations for fault-tolerant gadgets such as syndrome-extraction circuits or logical operations. In this work, we take a circuit-centric perspective to formalise how the decoding problem changes when applying ZX rewrites to a ZX diagram with a given detector basis. We demonstrate a set of rewrites that preserve MWPM-decodability of circuits and show that these matchability-preserving rewrites can be used to fault-tolerantly extract quantum circuits from phase-free ZX diagrams. In particular, this allows us to build efficiently decodable, fault-tolerant syndrome-extraction circuits for matchable codes.

We use the L-GALAXIES semi-analytic model to investigate the evolution of Brightest Cluster Galaxies (BCGs) found in clusters at $\rm z \sim 0$. BCGs are typically located in the central region of galaxy clusters, near the bottom of the potential well, exposing them to different environmental conditions compared to galaxies in the cluster outskirts or in the field. As a result, BCGs may follow a distinct evolutionary path and exhibit unique properties. We study the physical properties and merger histories of galaxies in 180 simulated clusters at $z \sim 0$, considering all cluster members with present-day stellar masses above $10^9 \ {\rm M_\odot}$ as the starting points for tracing their merger trees. We compare this sample of galaxies to a control sample of field galaxies and highlight their differences in evolution across cosmic time. We find that BCGs have distinct stellar mass formation histories compared to other massive galaxies from our control sample. Surprisingly, (proto)BCGs consistently become the most massive galaxy of their structure only at z $\sim$ 1.3. Despite this late dominance, (proto)BCGs are found to inhabit regions with higher galaxy and stellar mass density than the most massive galaxy in the structure throughout their entire history, indicating that their evolution is tightly linked to the environment from early times. These conditions shape a distinct evolutionary path for BCGs compared to other massive galaxies in clusters and in the field, underscoring the unique nature of BCGs.

Conceptual process design is a crucial aspect of chemical engineering that involves process synthesis. Mixed-integer nonlinear programming is a powerful framework for modeling such design problems by combining discrete and continuous variables; however, the combinatorial complexity of discrete choices, coupled with nonlinearities, presents challenging monolithic problems. Using decomposition, discrete subproblems can potentially benefit from Ising solvers, while simulators and nonlinear solvers offer powerful tools for handling nonlinearities. This work aims to: evaluate use of Ising-based solvers for discrete optimization and holistic process optimization through two case studies: an ionic liquid selection and its process design, and a more complex problem of drug manufacturing process optimization. The discrete subproblem is formulated as an integer program or quadratic unconstrained binary optimization and solved using a commercial classical or Ising solvers such as simulated annealing (SA), quantum annealing (QA), and entropy computing (EC) respectively. The commercial classical solver had the shortest runtime, whereas EC took the longest, followed by QA and SA, in reaching feasible and optimal solutions. The heuristics identified all or most feasible solutions in a single run, demonstrating advantages in solution diversity and efficient and broad exploration of the solution space over the classical solver, while the classical solver provides an optimality guarantee and rapid convergence speed. In process design, where insights of alternative designs and cost comparisons are more valuable than an optimal solution, heuristics offer a better-suited decision-making strategy. The comparative analysis highlights the strengths of each method and underscores the potential of this heterogeneous computing approach that leverages different methods to address practical optimization problems.

We discuss and then resolve a tension between how physicists treat gauge bosons and the celebrated "Wu-Yang dictionary", which identifies particle physics terminology with that of principal bundles and principal connections. We show how this tension leads to an interpretative choice that is not widely discussed in the physics literature. We then show how the same considerations present a dilemma for a recent "particle-first" approach to Yang-Mills theory due to Henrique Gomes. Either the particle-first approach has surplus structure as compared to principal-bundle-based approaches, or gauge bosons are not sections of vector bundles.

This paper focuses on the quantum state transfer in a one-dimensional (1D) high-root topological insulator (HRTI) with an arbitrary number of domains. We present the possibility of having multiple transfer processes in the same model due to the existence of various edge states in distinct energy gaps, which may benefit recent (de)multiplexing technologies. We also derived the relations between transfer times of different root models and different gaps in the same model. We show how the exponential decay in transfer time caused by the fragmentation of a parent chain into domains can be generalized to its higher-root versions while maintaining a high transfer fidelity, and how the increasing number of domain wall states leads to a higher transfer fidelity against a general disorder regime due to the topological protection inherited from the parent model.

In this paper, we examine the properties of spin-polarized interfaces consisting of single-molecule magnet bis(cyclopentadienyl)cobalt(II) (cobaltocene) and two-dimensional magnetic materials, semiconducting CrI$_3$ and metallic Fe$_3$GeTe$_2$, using first-principles density functional theory based calculations. Our calculated adsorption energies indicate the stability of these hetero-interfaces with the observation of hybridization of electronic states across the interface. Magnetic exchange interaction parameters have been obtained from both total energy differences and the Liechtenstein-Katsnelson-Antropov-Gubanov (LKAG) formalism in the basis of maximally localized Wannier functions (MLWFs). Analysis of these parameters shows a strong directional anisotropy in the magnetic substrate-molecule interaction in agreement with the nature of orbital hybridization. Additionally, possible exchange mechanisms are proposed based on orbital-resolved exchange and hopping parameters. We also show that the molecular adsorption may enhance the intralayer exchange interactions, with some exchange parameters reaching up to a 3-fold increase in magnitude compared to the freestanding case. Finally, we observe a 100 % spin polarization at the Fermi level in the cobaltocene/CrI$_3$ interface, which makes it particularly promising for spin-transport applications.

The orthorhombic crystal structure of the MgSnN$_2$ compound with Pna2$_1$ symmetry has been investigated as a low-cost, non-toxic material for photovoltaic (PV) applications using density functional theory (DFT) and spectroscopic limited maximum efficiency (SLME) calculations. A detailed analysis of the electronic and optical properties was performed using the mBJ semilocal exchange functional. The bandgap of MgSnN$_2$ is found to be 2.45 eV. SLME photovoltaic analysis suggests that a thin film of MgSnN$_2$ with a thickness of 2 $μ$m can reach an efficiency of 13.17% at room temperature. This efficiency was further improved through the simulation of a multi-junction device, where the tandem configuration increased the efficiency from 12.80% (single-junction) to 22.42%. Furthermore, introducing cation disorder can further reduce the bandgap, enhancing its suitability for solar cell applications.

Shuffled regression concerns settings in which covariates and responses are observed without their correct pairing. In dependent-data problems, a second form of missing correspondence can arise when responses are also detached from the latent temporal, spatial, or geometric domain that induces their dependence structure. We study regression under this joint loss of correspondence and, to our knowledge, provide the first systematic treatment of this setting. Specifically, we consider a doubly-unlinked regression model in which both the covariate-response link and the response-domain link are unknown, represented by two latent permutation matrices, while dependence is induced by an unobserved stochastic process. This framework unifies shuffled regression and latent-domain permutation models within a common dependent-data setting. We characterize signal-to-noise regimes governing recovery of the regression parameter and the latent permutations, and show that consistent estimation of the regression coefficient can be achieved under strictly weaker conditions than exact permutation recovery. To address the combinatorial difficulty of inference, we develop REPAIR, a variational Bayes method based on a block-structured permutation model that captures localized scrambling while substantially reducing computational complexity. Simulations and an applied example illustrate the empirical behavior of REPAIR and support the theoretical results.

The analysis of nuclear magnetic resonance parameters, such as the indirect nuclear spin-spin coupling constants, in terms of contributions from localised molecular orbitals is a commonly used approach for gaining a deeper understanding of experimentally observed trends in these parameters. In the vast majority of these studies, contributions from pairs of one occupied and one virtual orbital are calculated and analyzed. Analyses in terms of two pairs of an occupied and a virtual orbital, that would allow for the study of coupling pathways, are much more seldom, as they require calculating the coupling constants as a sum over all excited states. Previous studies have shown that, for the often dominating Fermi-contact contribution to the coupling constants, more or less all excited states have to be calculated when employing a Davidson algorithm, because the most high-lying excited states can also make a significant contribution to the Fermi-contact term. In this study we investigated therefore, whether by employing a Lanczos algorithm one can obtain converged values of the Fermi-contact contribution to the indirect nuclear spin-spin coupling constants already with a significantly smaller percentage of the total number of excited states included in the sum-over-states expression. To this purpose we have extended the recent implementation of a Lanczos algorithm for the RPA/TDHF or TDDFT eigenvalue problem in the Dalton program (L. Zamok et al. J. Chem. Phys. 156, 014102 (2022)). The new procedure was tested on 17 molecules containing first, second and third row atoms. We find that, for most coupling constants, less than 50% of the excited pseudo states are necessary for converging the Fermi-contact term with an error of less than 0.5 Hz. For the few exceptions, typically for molecules with third-row atoms, around 60% were necessary.

In 1919, Ramanujan discovered his famous congruences for the partition function. Not too long after, Freeman Dyson conjectured a combinatorial statistic existed that explained the three congruences, which he dubbed the \textit{crank}. A crank generating function for the partition function was discovered in 1988 by George Andrews and Frank Garvan. Since then other crank generating functions have been found for many other kinds of partitions. In this paper, we give a family of crank generating functions which explain some partition congruences for $t$-core partitions.

In this manuscript we lift the theory of r-quasisymmetric functions to the theory of Hopf monoids. We provide a general method of interpolating between two Hopf monoids, one being the free monoid on a positive comonoid and the other being the free commutative monoid on a positive comonoid.

We investigate the behaviour of five classical centrality measures--Jordan, rumor, betweenness, degree, and closeness centralities--in the setting of uniform random recursive trees. Motivated by applications in network archaeology, we focus on two fundamental questions: (i) the birth index (time of arrival) of the most central vertex, and (ii) the relative centrality of the root. We quantify the probability that the root is the most central vertex, analyze its expected rank under each centrality measure, and determine the expected birth index of a central vertex. In addition, we characterize the typical size of the set of top-ranked vertices that contains the root with high probability. Finally, for each centrality notion, we study the persistence properties of the center and the asymptotic behaviour of the root's rank.

This paper presents a process for coordinating stakeholders in their consideration of performance indicators and respective interface requirements for automated vehicles. These performance indicators are obtained and processed based on the system's self-perception and enable the realization of self-aware and self-adaptive vehicles. This is necessary to allow SAE Level 4 vehicles to handle external disturbances as well as internal degradations and failures at runtime. Without such a systematic process for stakeholder coordination, architectural decisions on realizing self-perception become untraceable and effective communication between stakeholders may be compromised. Our process-oriented approach includes necessary ingredients, steps, and artifacts that explicitly address stakeholder communication, traceability, and knowledge transfer through clear documentation. Our approach is based on the experience gained from applying the process in the autotech.agil project, from which we further present lessons learned, identified gaps, and steps for future work.

The study of integer partitions and their congruences dates back to 1919 when Ramanujan discovered his famous congruences for the partition function, $p(n)$. Since then, many other kinds of partition functions have been discovered, as well as their respective congruences. Recently, Hirschorn and Sellers have consider partitions in which the odd parts may appear in $k$ colors and the even parts are restricted to at most one color. It turns out that these partitions exhibit fascinating families of congruences. In this paper, we look at a set of congruences that give rise to infinite families modulo 3. We also give some questions at the end that could aid further research into these partitions.

Determining the randomized (or distributional) communication complexity of disjointness is a central problem in communication complexity, having roots in the foundational work of Babai, Frankl, and Simon in the 1980s and culminating in the famous works of Kalyanasundaram-Schnitger and Razborov in 1992. However, the question of obtaining tight bounds for product distributions persisted until the more recent work of Bottesch, Gavinsky, and Klauck resolved it. In this note we revisit this classical problem and give a short, streamlined proof of the best bounds, with improved quantitative dependence on the error parameter. Our approach is based on a simple combinatorial lemma that may be of independent interest: if two sets drawn independently from two distributions are disjoint with non-negligible probability, then one can extract two subfamilies of reasonably large measure that are fully cross-disjoint (equivalently, a large monochromatic rectangle for disjointness).

A double-heralding technique is presented for producing heralded entangled photon pairs from spontaneous parametric down-conversion (SPDC). Compared to the swap-heralded schemes studied in previous cascaded SPDC and zero-added-loss multiplexing (ZALM) proposals, this double-heralding technique is found to yield the most resource-efficient implementation in terms of minimizing the total number of sources and detectors required to achieve a specified rate and fidelity. This is achieved by reducing the number of modes and mode-sorting optics needed on the heralding path. Specifically, by immediately detecting any two signal photons from an array of down-converters, the corresponding idler photons can be projected onto an anti-correlated pair state which is shown to be unitarily equivalent to the state produced by swap-heralded sources, and hence can be used directly for long-range entanglement distribution in a ZALM architecture. Quasi-deterministic operation through two distinct multiplexing techniques is analyzed. The analysis derives expressions for the heralded pair probability and fidelity assuming realistic detectors with losses, dark counts, and partial photon number resolution (PNR), providing a framework for implementation of the source on a photonic integrated circuit (PIC).

Heat stress has harmful effects that impact communities across the Unitedt States, particularly when high temperatures are accompanied by high humidity. The combined impact of temperature and humidity can be summarized by the heat index (HI). Current state-of-the-art numerical weather prediction models are often biased when forecasting temperature and humidity even within a 24-hour forecast lead time. This study explores the ability of machine learning (ML) models to accurately predict the next-day heat index using Random Forest and single-layer Gated Recurrent Unit (GRU) models in four locations across the United States. We find that Random Forest and GRU models perform reasonably well at all four selected locations. Mean absolute HI error ranges from 4.5 to 6.6 °F. All model versions have an accuracy rate exceeding 80% in three of the four locations in terms of successfully forecasting an extreme heat day, as indicated by a high afternoon HI. The GRU model achieves over 95% accuracy in these three locations. Model performance details vary by location. In Minneapolis and Portland, which have relatively few days with high HI values, models' accuracy is high, but the recall and precision are generally very low. In contrast, Dallas, a location with many high HI days, shows moderately high accuracy, as well as extremely high recall and precision. These differences are likely due to distinct causes of heatwaves in different climatological regions of the United States, as reflected in the feature importance scores output by Random Forest models. The ML models designed in this study can be used to assist with local heat index forecasting and extreme heat warning issuance at minimal computational cost.

In a recent work, a central limit theorem for pattern counts in random planar maps was proven by reducing the problem to a face count problem. We provide a shorter proof by circumventing this reduction through the computation of bivariate coefficient asymptotics from a functional equation with one catalytic variable and extend the result to pattern counts with arbitrary boundary and new map classes.

Discrete differential equations appear most prominently in planar map and lattice path enumeration. In this work we consider discrete differential equations with an additional parameter $x$, where the order of the equation is $1$ for $x=0$ but $k> 1$ for $x\ne 0$. We call such equations singularly perturbed. The main contribution of this work is to show that there is actually a smooth transition under certain natural assumptions. As an application of this result we consider pattern counts in triangular planar maps and derive a central limit theorem for patterns which cannot self-intersect.

Tree-level lepton-flavor-violating decays induced by Lorentz-violating effects within the Yukawa sector of the Standard Model Extension are studied. These new physics effects are parameterized by the $(Y_{f})_{μν}^{AB}$ tensor, with $μ$ and $ν$ denoting Lorentz indices and $A$, $B$ being indices in the flavor space. Since this tensor is antisymmetric under the interchange of Lorentz indices, in analogy with the electromagnetic tensor $F_{μν}$, $(Y_{f})_{μν}^{AB}$ can be expressed in terms of six components associated with two complex three-vectors denoted by $\mathbf{e}_l^{AB}$ and $\mathbf{b}_l^{AB}$. On the assumption that these three-vectors are pure real or pure imaginary and mutually orthogonal, constraints on their magnitudes via experimental bounds on lepton-flavor-violating processes $\mathrm{Br}(l_B\rightarrow γl_A)$ and $\mathrm{Br}(l_B\rightarrow l_A l_C \bar{l}_C)$ are estimated. Thus, the $l_B\rightarrow γl_A$ decay provides the following upper bounds: $\lvert \mathbf{e}_l^{μτ} \lvert < 1.51\times 10^{-11}$ , $\lvert \mathbf{e}_l^{eτ} \lvert < 1.34 \times 10^{-11}$, $\lvert \mathbf{e}_l^{eμ} \lvert < 3.65 \times 10^{-18}$, $\lvert \mathbf{b}_l^{μτ} \lvert < 1.95\times 10^{-11}$, $\lvert \mathbf{b}_l^{eτ} \lvert <1.73\times 10^{-11}$, $\lvert \mathbf{b}_l^{eμ} \lvert < 4.71\times 10^{-18}$. Conversely, by assuming that the Lorentz-violating parameters are purely real, for the $l_B\rightarrow l_A l_C \bar{l}_C$ process it is found that $\lvert \mathbf{e}_l^{μτ}\lvert< 3.05 \times 10^{-12}$ and $\lvert \mathbf{b}_l^{μτ}\lvert< 4.31 \times 10^{-12}$. These results offer more restrictive bounds than those previously reported in the literature.

Multiple randomization designs (MRDs) are a class of experimental designs used to handle interference in two-sided marketplaces. We investigate regression adjustment strategies for estimating total, spillover, and direct effects in MRDs. We derive minimum asymptotic variance estimators among a broad class of linearly adjusted estimators, without assuming a linear model on the potential outcomes. Surprisingly, the optimal regression adjustments are estimable from data and are generally different from regression adjustments in classical randomized experiments. For example, one such optimal estimator for the direct effect corresponds to a weighted regression with interacted two-way fixed effects. We establish model-robustness properties, central limit theorems, and inferential methods for our estimators, relying on improved theoretical results for MRD experiments. Our results provide the analog of classical regression adjustments for marketplace experiments. Numerical simulations demonstrate a considerable increase in efficiency over simpler approaches, enabling better inference when running MRDs.

We develop tools for characterizing vertices of fiber products of polytopes and apply them to simplicial distribution polytopes, a class of probability polytopes arising in quantum foundations and quantum information. In the theory of simplicial distributions, a pair of simplicial sets encoding measurement and outcome spaces determines a convex polytope of compatible probability assignments. Our first results give geometric criteria for detecting vertices of fiber products in terms of support data. These results are obtained in the more general framework of inverse limits of diagrams of polytopes in standard form, and they translate to corresponding criteria for simplicial distributions on arbitrary colimits of measurement spaces. We then focus on one-dimensional measurement spaces, where simplicial distributions recover and generalize local marginal polytopes in graphical models. In this setting, our sharpest results concern dipole graphs, for which we obtain a complete characterization of vertices and refine it to a graph-theoretic criterion. These characterizations are reminiscent of the classical support-graph criteria for transportation polytopes, but they arise in a richer class of polytopes in which vertex structure depends not only on support acyclicity but also on additional geometric compatibility data. Using the collapsing method from simplicial topology, we transfer the dipole characterization to rose graphs and obtain analogous results there. Finally, we apply collapsing to complete bipartite graphs, which encode physically relevant bipartite Bell scenarios, and more generally to arbitrary connected graphs, yielding lower bounds on the number of vertices.

We consider a problem whether bound states are made in a scalar theory with a fourth-order derivative term or not. After rewriting the theory to a standard scalar theory with second-order derivative terms, we calculate a correlation function of the composite operators made out of massive ghosts with negative norm and massive normal fields with positive norm in the ladder approximation. It is shown that there appears a pole of the bound state in the correlation function of the both fields by attraction due to scalar field when the coupling constant is large whereas there does not so in the correlation function of almost massless normal particles corresponding to the graviton. We also point out the relationship between the scalar theory with a fourth-order derivative term and quadratic gravity. Our model may shed some light on the confinement of massive ghost in quadratic gravity, thereby enabling us to solve the problem of unitarity violation associated with the massive ghost.

The no-broadcasting theorem, a fundamental limitation on the communication of quantum information, holds that a physical process cannot broadcast copies of an unknown quantum state to two or more receivers. Recent work has explored ways of circumventing this limitation using "virtual" implementations of non-physical processes using measurement and data-processing on statistical samples of the unknown input. However, the statistical fluctuations of this data degrades the virtual copies so much that the protocol effectively depletes, rather than proliferate, the sample size -- thereby rendering it worse than the "naive" approach of splitting the given sample and sending a subsample to each receiver. In this work, we circumvent this flaw by allowing a small amount of systematic bias in the broadcast data, resulting in approximate virtual copies. We provide efficient semidefinite programs (SDP's) to determine the minimum sample size required to keep the approximation error below a desired threshold and vice versa. For reasonably small error values, we find approximate virtual broadcasting to be viable with sample sizes smaller than naive sample-splitting would demand. Along the way, we prove several symmetry-based simplifications to the problem, allowing optimal approximate broadcasting to be characterized in terms of the simple class of depolarizing channels.

In this letter, we fill a hole in the existing literature about disordered quantum spin systems generated by a random local interaction $\{\mathfrak{h}(Z)\}_{Z\Subset \mathbb{Z}^ν}$ satisfying a statistical version of translation invariance. We show such systems always have disordered ground states in the thermodynamic limit with the same symmetry. A key tool we use is a disordered version of the Lieb-Robinson bounds, which hold almost surely under mild conditions on $\mathfrak{h}$. Along the way, we formalize the notion of a random state on a $C^*$-algebra and prove a weak-$\ast$ version of the Riesz-Markov-Kakutani theorem, which seems not to have been recorded in the vector measures literature. As a consequence of the existence of the aforementioned disordered ground states, we show that the spectrum of the GNS Hamiltonain associated to the bulk dynamics is deterministic with respect to the disorder.

The global majority problem, often referred to as the Density Classification Task, is a classical benchmark in the context of probing the computational capabilities of automata networks. It poses the simple yet challenging problem of determining, by totally local means, whether an arbitrary initial configuration of binary states can evolve to a final, homogeneous global configuration that reflects the initial global majority. Although it is known that in the specific case of cellular automata with periodic boundaries no rule is able to solve the problem, in other formulations solutions are known and, in others, the problem is still open. Aligned with the latter, here we explore the possibility of solving the problem with automata networks, operating only with the local majority rule, with a focus on identifying non-trivial cases where it can be solved and explaining why they do so.

Energy renormalizations of resident carriers and excitons are studied theoretically, and compared with recent experiments of electrostatically-doped WSe$_2$ monolayers. The calculated energy renormalization of resident carriers, subjected to strong out-of-plane magnetic field, reveals the importance of dynamical screening in transition metal dichalcogenides. The energy renormalization of tightly bound excitons is analyzed through the exchange interaction between the electron (or hole) component of the exciton and resident carriers that share the same spin and valley quantum numbers. Our theory explains the weak energy shift of excitonic resonances despite the strong energy renormalization of resident carriers. We identify the dependence of the energy renormalization on the envelope function of a tightly-bound exciton, showing that unlike free electron-hole pairs, this energy renormalization is not the added renormalizations of a resident electron and resident hole.

Considerable observational evidence suggests that the activity of supermassive black holes in galactic nuclei is transient. The term ``active galactic nuclei archaeology'' has even been coined. This implies the possibility of reconstructing the history of activity, such as changes in the nuclear luminosity over time across various regions of the electromagnetic spectrum, by analysing how this activity manifested itself on galactic and extragalactic spatial scales. These phenomena include relic radio structures, gas clouds illuminated by the ``ionising echo'' of past activity, and Fermi/eROSITA bubbles. We provide a review of the results of galactic nucleus activity studies, focusing on its observable impact on the intergalactic medium and circumgalactic environment. Our main focus is on optical observations of ionisation cones and evidence of switching between radiative (ionisation cones) and kinetic (radio jets) modes of nuclear activity.

In this work, we investigate observable signatures of a magnetically charged Anti-de Sitter black hole in string-inspired Euler-Heisenberg theory. We analyze photon trajectories, the photon sphere, and the resulting black hole shadow. We derive the photon sphere and shadow radii and show that both deviate from the Schwarzschild and Schwarzschild-AdS cases. In particular, the radii decrease monotonically as the magnetic charge parameter $Q_m$ increases, indicating that magnetic charge modifies light propagation near the black hole. We also study neutral and charged particle motion and compute the corresponding epicyclic frequencies. Using the effective potential method, we obtain the specific energy and angular momentum for stable circular orbits and determine the innermost stable circular orbit (ISCO). The presence of $Q_m$ shifts the ISCO radius and alters the orbital structure. The radial, vertical, and orbital frequencies show clear deviations from the Schwarzschild case. Finally, we confront the model with twin-peak quasi-periodic oscillation (QPO) data from stellar-mass, intermediate-mass, and supermassive black hole candidates. A two-dimensional Delta chi-square analysis in the ($r$, $Q_m$) space shows that the best fit corresponds to $Q_m=0$, although finite values remain allowed within confidence levels. At the 1 sigma level, we obtain an upper bound $Q_m/M$ less than about 0.2. These results indicate that while magnetic charge produces measurable theoretical deviations, current QPO data place only moderate constraints on its magnitude.

Turbulent separated flows in axisymmetric expansions can sustain fundamentally different transport organization despite nearly identical mean topology. Using stereo-PIV and time-resolved planar PIV, we compare abrupt $90^\circ$ (step) and gradual $45^\circ$ (wedge) axisymmetric expansions at step height Reynolds numbers of 25000 and 35000. Despite similar reattachment lengths, near-separation turbulence differs, with the wedge exhibiting higher turbulent kinetic energy over a broader shear layer, while the step confines production to a thinner region near the corner, where a secondary vortex weakens momentum and fluctuations. The spatial spectra reveal a pronounced spectral hump in the out-of-plane velocity fluctuations near separation. This feature is consistently observed across all cases and reflects the expansion effects on the redistribution of fluctuation energy associated with the interaction between the separating shear layer and the recirculating flow. Temporal spectra show no geometry-specific dominant frequencies, and space-time correlations indicate similar normalized convection velocities across all cases. The primary effect of geometry, therefore, does not lie in the characteristic scales or transport speeds, but in the spatial organization and persistence of coherence. The step cases exhibit stronger spectral concentration, longer local integral time scales, and a broader distribution of space-time correlations in convection velocities associated with momentum-depleted return flow. Finite-time Lyapunov exponent (FTLE) fields confirm that these differences extend to material transport, as the wedge produces larger and less fragmented deformation regions, while the step yields a more segmented pattern that persists downstream of reattachment.