We develop a linear vibronic coupling (LVC) model for polyenes described by the extended Hubbard-Peierls Hamiltonian. This model is applied to trans-hexatriene to benchmark quantum-classical dynamics methods against fully quantum simulations. We find that surface-hopping methods describe short times more accurately than multi-trajectory Ehrenfest. None of the quantum-classical methods studied obtain the long-time population oscillations found in fully quantum simulations. Varying the parameters of the LVC Hamiltonian, we find that surface hopping reproduces the correct trends in the long-time dynamics across a wide range of parameters, but generally overestimates the degree of internal conversion. On the other hand, multi-trajectory Ehrenfest gives more accurate long-time populations in proximity to the hexatriene parameter set.

Polymer models are effective in describing quantum gravity effects around the initial singularity, leading to its replacement by bouncing surfaces on which the curvature and densities are finite. Their properties depend on the space-time symmetry and on the particular polymerisation scheme adopted. In this article we investigate anisotropic models under the Gambini-Benítez-Pullin polymerisation, recently used to quantise spherically symmetric black-holes, whose interiors are isometric to Kantowski-Sachs (KS) space-times. Demanding that the minimum area defined by the bouncing surface matches the Loop Quantum Gravity area gap, we can find its radius alongside the curvature and effective density and pressures at the bounce. The density is always positive, while the pressures are negative enough to avoid the singularity. Due to the positive spatial curvature, the solution is oscillatory, reaching a maximum radius where a re-collapse occurs. Therefore, a positive cosmological constant is included in order to have an eternal expansion to a late de Sitter phase. We have also considered a Bianchi III metric, showing that the bounce is still present, but the space-time is asymptotically flat in this case, with no re-collapse. In this hyperbolic space, the minimal area constraint can also be imposed on compact $2$-surfaces. Nevertheless, in contrast to the KS case, it is enough for avoiding the singularity, independently of polymerisation procedures.

We analyze Su-Schrieffer-Heeger (SSH) models using the doubling method for orthogonal polynomial sequences. This approach yields the analytical spectrum and exact eigenstates of the models. We demonstrate that the standard SSH model is associated with the doubling of Chebyshev polynomials. Extending this technique to the doubling of other finite sequences enables the construction of Hamiltonians for inhomogeneous SSH models which are exactly solvable. We detail the specific cases associated with Krawtchouk and $q$-Racah polynomials. This work highlights the utility of polynomial-doubling techniques in obtaining exact solutions for physical models.

We construct a simple holographic model incorporating higher-order coupling terms for electron self-interactions. It can exhibit typical behavior of a Mott insulator, including a metal-insulator transition and a decrease in DC conductivity with the increase of charge density. In the analysis of AC conductivity, a soft gap is generally observed. Notably, when the DC conductivity approaches zero, the AC conductivity reveals a multi-peak structure, which can be attributed to the Mott and charge-transfer gaps observed experimentally in transition metals. With the increase of DC conductivity, the multi-peak structure gradually reverts to soft-gap behavior or even metallic conductivity. The accuracy of the numerical result is guaranteed by $σ(ω\to 0)=σ_{DC}$ and sum rules.

The forthcoming space-based gravitational-wave observatory Laser Interferometer Space Antenna (LISA) should enable the detection of Extreme Mass Ratio Inspirals (EMRIs), in which a stellar-mass compact object gradually inspirals into a supermassive black hole while emitting gravitational waves. Modeling the waveforms of such systems is a challenging task, requiring precise computation of energy and angular momentum fluxes as well as proper treatment of orbital resonances, during which two fundamental orbital frequencies become commensurate. In this work, we perform a systematic comparison of fluxes derived from three approaches: the quadrupole formula, post-Newtonian approximations, and time-domain solutions of the Teukolsky equation. We show that quadrupole-based fluxes remain in good agreement with Teukolsky results across a broad range of orbital configurations, including perturbed orbits. Building on these insights, we explore the dynamical impact of resonance crossings within the adiabatic approximation. By introducing novel numerical methods, we reduce computational costs and uncover diverse resonance-crossing behaviors. These results contribute to the effort to understand theoretically and model adequately resonance crossings during an EMRI.

We prove that the excedance relation on permutations defined by N. Bergeron and L. Gagnon actually extends to a congruence of the lattice on alternating sign matrices. Motivated by this example, we study all lattice congruences of the lattice on alternating sign matrices whose quotient is isomorphic to the Stanley lattice on Dyck paths, which we call catalan congruences. We prove that the maxima of the congruence classes are always covexillary permutations (and all covexillary permutations appear this way), and that the minimal permutations in each class are always precisely the $321$-avoiding permutations. Finally, we show that any choice of representative permutations in each congruence class yield a basis of the Temperley-Lieb algebra with parameter $2$, vastly generalizing the bases arising from the excedance relation.

We identify a sharp geometric threshold governing the infrared spectral behavior of the spatial Lichnerowicz operator on asymptotically flat three-dimensional manifolds. Let $(M,g)$ be asymptotically flat and let $L=Δ_L$ denote the spatial Lichnerowicz operator acting on symmetric $2$-tensors. Assume \[ |{\rm Riem}(x)| \lesssim r(x)^{-p} \quad \text{as } r(x)\to\infty. \] If $p>3$, curvature is spectrally short-range: $L$ exhibits regular low-energy scattering and zero energy is not singular. At the critical decay \[ |{\rm Riem}(x)| \sim r^{-3}, \] dispersion and curvature balance. Zero enters the essential spectrum, and the weighted resolvent develops a threshold singularity. For $s\in(1/2,1)$, \[ \|\langle r\rangle^{-s}(L-i\varepsilon)^{-1}\langle r\rangle^{-s}\| \gtrsim \varepsilon^{-(1-s)} \quad \text{as } \varepsilon \downarrow 0 . \] Thus, the limiting absorption principle fails at zero energy. This singularity provides a spatial spectral mechanism for the infrared sector of linearized gravity. The same inverse-cube scaling governs long-range correlations, irregular low-frequency scattering, and soft gravitational modes. Numerical simulations of a radial model and the full tensor operator confirm that $p=3$ marks a sharp transition between negligible and marginal curvature. The associated branch point at zero energy determines late-time relaxation, yielding the universal tail exponent \[ t^{-(2\ell+3)}, \] a spectral consequence of nonzero ADM mass. More generally, in $d$ spatial dimensions, the critical decay \[ |{\rm Riem}(x)| \sim r^{-d} \] forms a universal boundary for curvature-coupled Laplace-type operators, encoding the infrared structure of gravity in the spectral geometry of a Cauchy slice.

We propose a system-oriented basis-set design based on even-tempered basis functions to variationally encode electronic ground-state information into molecular orbitals. First, we introduce a reduced formalism of concentric even-tempered orbitals that achieves hydrogen energy accuracy on par with the conventional formalism, with lower optimization cost and improved scalability. Second, we propose a symmetry-adapted, even-tempered formalism specifically designed for molecular systems. It requires only primitive S-subshell Gaussian-type orbitals and uses two parameters to characterize all exponent coefficients. In the case of the diatomic hydrogen molecule, the basis set generated by this formalism produces a dissociation curve more consistent with cc-pV5Z than cc-pVTZ at the size of aug-cc-pVDZ. Finally, we test our even-tempered formalism against several types of tetra-atomic hydrogen molecules for ground-state computation and point out its current limitations and potential improvements.

We report direct, simultaneous measurements of the London penetration depth ($λ_L$) and Bardeen-Cooper-Schrieffer (BCS) coherence length ($ξ_0$) in oxygen-doped niobium, with impurity concentrations spanning the "clean" to "dirty" limits. Two depth-resolved techniques - low-energy muon spin spectroscopy (LE-$μ$SR) and secondary-ion mass spectrometry (SIMS) - were used to quantify the element's Meissner screening profiles, analyzed within a framework that accounts for nonlocal electrodynamics. The analysis indicates intrinsic length scales of $λ_L = 29.1(10)$ nm and $ξ_0 = 39.9(25)$ nm, corresponding to a Ginzburg-Landau (GL) parameter of $κ= 0.70(5)$. The obtained $λ_L$ and $κ$ values, accurately quantified at the nanoscale, are smaller than values commonly used in applications and modeling, and indicate that clean niobium lies at the boundary between type-I and type-II superconductivity, supporting the contemporary view that its intrinsic state may be type-I.

We consider the problem of maximizing a convex function over a closed convex set in a real Hilbert space. For linear functions, we show that a single orthogonal projection suffices to obtain an approximate solution. For continuous convex functions over convex sets, we show that projected subgradient ascent converges to a first-order stationary point when using arbitrarily large step sizes. Taking the step sizes to infinity leads to a deterministic variant of the conditional gradient algorithm, and iterated linear optimization as a special case.

This paper develops a general concentration inequality for the suprema of empirical processes with dependent data. The concentration inequality is obtained by combining generic chaining with a coupling-based strategy. Our framework accommodates high-dimensional and heavy-tailed (sub-Weibull) data. We demonstrate the usefulness of our result by deriving non-asymptotic predictive performance guarantees for empirical risk minimization in regression problems with dependent data. In particular, we establish an oracle inequality for a broad class of nonlinear regression models and, as a special case, a single-layer neural network model. Our results show that empirical risk minimzaton with dependent data attains a prediction accuracy comparable to that in the i.i.d. setting for a wide range of nonlinear regression models.

In solving $q$-difference equations, and in the definition of $q$-special functions, we encounter formal power series in which the $n$th coefficient is of size $q^{-\binom{n}{2}}$ with $q\in(0,1)$ fixed. To make sense of these formal series, a $q$-Borel-Laplace resummation is required. There are three candidates for the $q$-Laplace transform, resulting in three different resummations. Surprisingly, the differences between these resummations have hardly been discussed in the literature. Our main result provides explicit formulas for these $q$-exponentially small differences. We also give simple Mellin--Barnes integral representations for all the basic hypergeometric ${}_rϕ_s$ functions and derive a third (discrete) orthogonality condition for the Stieltjes--Wigert polynomials. As the main application, we introduce three resummations for the ${}_2ϕ_0$ functions which can be seen as $q$ versions of the Kummer $U$ functions. We derive many of their properties, including interesting integral and sum representations, connection formulas, and error bounds.

Frequency combs consist of a spectrum of evenly spaced spectral lines. Optical frequency combs enable technologies ranging from timing, LiDAR, and ultra-stable signal sources. Microwave frequency combs are analogous to optical frequency combs, but often leverage electronic nonlinearity for comb generation. Generating microwave frequency combs using piezoelectric mechanical resonators would enable this behavior in a more compact form factor, thanks to the shorter acoustic wavelengths. In this work, we demonstrate a microwave frequency comb leveraging thermal nonlinearity in high quality factor ($Q$) overmoded acoustic resonators in thin film lithium niobate. By providing input power at 257 MHz, which is the sum frequency of two acoustic modes at 86 MHz and 171 MHz, we generate parametric down conversion and comb generation. We explore the nonlinear mixing regimes and the associated conditions for comb generation. Comb spacing is observed to vary significantly with drive frequency and power, and its general behavior is found to rely heavily on initial conditions. This demonstration showcases the potential for further improvement in compact and efficient microwave frequency combs, leveraging nonlinear acoustic resonators.

We discuss the correspondence between highly excited strings and black holes in the presence of angular momentum. At fixed imaginary angular velocity $ν$, we show that free strings exhibit a Hagedorn instability due to a thermal-winding mode turning tachyonic. This allows us to determine the exact Hagedorn temperature $β_H(ν)$ for bosonic, type II, and heterotic strings. Using the effective field theory for the thermal-winding mode around the $ν$-dependent background, we find a novel `rotating string star' saddle (perturbatively in the angular velocity) and study its properties. This configuration describes a self-gravitating bound state of highly excited rotating strings. As in the non-rotating case, the saddle is qualitatively shown to interpolate between the rotating strings phase and a rotating black hole. We also comment on the implications of these results for anti-de Sitter space.

Voice interfaces are increasingly used in high stakes domains such as mobile banking, smart home security, and hands free healthcare. Meanwhile, modern generative models have made high quality voice forgeries inexpensive and easy to create, eroding confidence in voice authentication alone. To strengthen protection against such attacks, we present a second authentication factor that combines acoustic evidence with the unique motion patterns of a speaker's lower face. By placing lightweight inertial sensors around the mouth to capture mouth opening and evolving lower facial geometry, our system records a distinct motion signature with strong discriminative power across individuals. We built a prototype and recruited 43 participants to evaluate the system under four conditions seated, walking on level ground, walking on stairs, and speaking with different language backgrounds (native vs. non native English). Across all scenarios, our approach consistently achieved a median equal error rate (EER) of 0.01 or lower, indicating that mouth movement data remain robust under variations in gait, posture, and spoken language. We discuss specific use cases where this second line of defense could provide tangible security benefits to voice authentication systems.

A weak $c$-colouring of a design is an assignment of colours to its points from a set of $c$ available colours, such that there are no monochromatic blocks. A colouring of a design is block-equitable, if for each block, the number of points coloured with any available pair of colours differ by at most one. Weak and block-equitable colourings of balanced incomplete block designs have been previously considered. In this paper, we extend these concepts to group divisible designs (GDDs) and packing designs. We first determine when a $k$-GDD of type $g^u$ can have a block-equitable $c$-colouring. We then give a direct construction of maximum block-equitable $2$-colourable packings with block size $4$; a recursive construction has previously appeared in the literature. We also generalise a bound given in the literature for the maximum size of block-equitably $2$-colourable packings to $c>2$. Furthermore, we establish the asymptotic existence of uniform $k$-GDDs with arbitrarily many groups and arbitrary chromatic numbers (with the exception of $c=2$ and $k=3$). A structural analysis of $2$- and $3$-uniform $3$-GDDs obtained from 4-chromatic STS$(v)$ where $v\in\{21,25,27,33,37,39\}$ is given. We briefly discuss weak colourings of packings, and finish by considering some further constraints on weak colourings of GDDs, namely requiring all groups to be either monochromatic or equitably coloured.

Ensuring the trustworthiness of data from distributed and resource-constrained environments, such as Wireless Sensor Networks or IoT devices, is critical. Existing Reversible Data Hiding (RDH) methods for scalar data suffer from low embedding capacity and poor intrinsic mixing between host data and watermark. This paper introduces Hiding in the Imaginary Domain with Data Encryption (H[i]dden), a novel framework based on complex number arithmetic for simultaneous information embedding and encryption. The H[i]dden framework offers perfect reversibility, in-principle unlimited watermark size, and intrinsic data-watermark mixing. The paper further introduces two protocols: H[i]dden-EG, for joint reversible data hiding and encryption, and H[i]dden-AggP, for privacy-preserving aggregation of watermarked data, based on partially homomorphic encryption. These protocols provide efficient and resilient solutions for data integrity, provenance and confidentiality, serving as a foundation for new schemes based on the algebraic properties of the complex domain.

We advocate for a new statistical principle that combines the most desirable aspects of both parameter inference and density estimation. This leads us to the predictively oriented (PrO) posterior, which expresses uncertainty as a consequence of predictive ability. Doing so leads to inferences which predictively dominate both classical and generalised Bayes posterior predictive distributions: up to logarithmic factors, PrO posteriors converge to the predictively optimal model average. Whereas classical and generalised Bayes posteriors only achieve this rate if the model can recover the data-generating process, PrO posteriors adapt to the level of model misspecification. This means that they concentrate around the true model in the same way as Bayes and Gibbs posteriors if the model can recover the data-generating distribution, but do not concentrate in the presence of non-trivial forms of model misspecification. Instead, they stabilise towards a predictively optimal posterior whose degree of irreducible uncertainty admits an interpretation as the degree of model misspecification -- a sharp contrast to how Bayesian uncertainty and its existing extensions behave. Lastly, we show that PrO posteriors can be sampled from by evolving particles based on mean field Langevin dynamics, and verify the practical significance of our theoretical developments on a number of numerical examples.

Dependency bloat is a persistent challenge in Python projects, which increases maintenance costs and security risks. While numerous tools exist for detecting unused dependencies in Python, removing these dependencies across the source code and configuration files of a project requires manual effort and expertise. To tackle this challenge we introduce PYTRIM, an end-to-end system to automate this process. PYTRIM eliminates unused imports and package declarations across a variety of file types, including Python source and configuration files such as requirements.txt and setup.py. PYTRIM's modular design makes it agnostic to the source of dependency bloat information, enabling integration with any detection tool. Beyond its contribution when it comes to automation, PYTRIM also incorporates a novel dynamic analysis component that improves dependency detection recall. Our evaluation of PYTRIM's end-to-end effectiveness on a ground-truth dataset of 37 merged pull requests from prior work, shows that PYTRIM achieves 98.3% accuracy in replicating human-made changes. To show its practical impact, we run PYTRIM on 971 open-source packages, identifying and trimming bloated dependencies in 39 of them. For each case, we submit a corresponding pull request, 6 of which have already been accepted and merged. PYTRIM is available as an open-source project, encouraging community contributions and further development. Video demonstration: https://youtu.be/LqTEdOUbJRI Code repository: https://github.com/TrimTeam/PyTrim

We study the application of a quasi-Monte Carlo (QMC) method to a class of semi-linear parabolic reaction-diffusion partial differential equations used to model tumor growth. Mathematical models of tumor growth are largely phenomenological in nature, capturing infiltration of the tumor into surrounding healthy tissue, proliferation of the existing tumor, and patient response to therapies, such as chemotherapy and radiotherapy. Considerable inter-patient variability, inherent heterogeneity of the disease, sparse and noisy data collection, and model inadequacy all contribute to significant uncertainty in the model parameters. It is crucial that these uncertainties can be efficiently propagated through the model to compute quantities of interest (QoIs), which in turn may be used to inform clinical decisions. We show that QMC methods can be successful in computing expectations of meaningful QoIs. Well-posedness results are developed for the model and used to show a theoretical error bound for the case of uniform random fields. The theoretical linear error rate, which is superior to that of standard Monte Carlo, is verified numerically. Encouraging computational results are also provided for lognormal random fields, prompting further theoretical development.

To meet the stringent time calibration requirements for the Belle II experiment upgrade, particularly for its large-size KL and Muon Detector comprising tens of thousands of scintillator channels with time resolutions better than 100 ps, we developed a compact and high-speed time calibration system. The system utilizes a laser diode as its light source, integrated with a fast pulse laser drive circuit that employs high-speed switching GaN FETs and gate drivers. A prototype was constructed and rigorously evaluated using scintillators, achieving timing resolutions of about 13 ps for a single calibration channel. Furthermore, internal deviations among calibration channels were analyzed, with most measurements remaining within 250 ps. These results highlight the system's precision, scalability, and suitability for large-scale particle physics experiments.

We investigate the possibility of a Nicolai map for minimal supergravity in four dimensions. Such a map would allow for the computation of quantum supergravity correlation functions in terms of flat-space correlators in an effective nonlocal bosonic theory with the help of a nonlinear field transformation, the inverse Nicolai map. Such a map is guaranteed for off-shell global supersymmetry, but local supersymmetry presents at least three obstacles for the construction. Their effects are analyzed in detail, in an attempt to set up a Nicolai map to leading order in the gravitational coupling. We find indications that the conformal factor of the metric obstructs the off-shell construction, suggesting that the unimodular variant of supergravity may do better. The on-shell supersymmetry approach, successful for super-Yang-Mills theory in its critical dimensions, also fails, because the graviton self-interaction cannot be written as a supervariation. Nevertheless, by brute force we obtain a four-parameter first-order Nicolai map fulfilling the free-action condition. For the acid test of determinant matching, however, one needs to push the general ansatz and the perturbative expansion to the second order and to the quantum level.

We investigate the symmetry structure of five-dimensional Yang-Mills theories with $\mathfrak{su}(N)$ gauge algebra. These theories feature intertwined 0-, 1-, and 2-form symmetries, depending on the global variant one is considering. In the $SU(N)$ theory, there is a mixed 't Hooft anomaly between the instantonic 0-form symmetry and the electric 1-form symmetry. We show that in the $PSU(N)$ theory this translates into a $\mathbb{Z}_N$ extension of the instantonic symmetry, generated by an invertible condensation defect of the magnetic 2-form symmetry. We identify the charged configurations as linked 't Hooft surfaces, while pointlike instanton operators remain insensitive to the extension. We generalize our analysis to the $SU(N)/\mathbb{Z}_k$ global form and show that similar results hold, embedded now in a 3-group structure for generic $k$. We then apply our findings to $SO(3)$ supersymmetric Yang-Mills theory. We determine the global form of the enhanced instantonic symmetry of its superconformal UV completion, showing that it arises through a similar symmetry extension mechanism from the parent $E_1$ theory, which is the UV completion of $SU(2)$ supersymmetric Yang-Mills theory. Finally, we recast our results in the language of the symmetry topological field theory. As a warm-up, we also analyze Maxwell theory, highlighting analogous features involving continuous symmetries and composite currents.

This paper studies a multiple-input multiple-output (MIMO) free-space optical (FSO) communication system employing continuous-variable quantum key distribution (CV-QKD), with the goal to support secret key transmission between two legitimate users, Alice and Bob. All involved wireless channels are subjected to atmospheric turbulence leading to beam spreading, pointing error, and turbulence-induced fading, which along with the presence of hybrid quantum noise negatively impact secret key exchange. Furthermore, the legitimate MIMO FSO system faces the threat of compromise from an eavesdropper, Eve, employing a collective Gaussian attack to intercept the secret key exchange. Novel one- and two-way protocols for enhancing the security of the transmitted keys are proposed. To this end, the transmissivity of the FSO channels is mathematically formulated and bounds on the mutual information between the transmitted and received coherent states are obtained, which are then used for deriving novel expressions for the secret key rates (SKRs) for both one- and two-way protocols. The presented numerical results corroborate the proposed analytical secrecy framework, quantifying the SKR gains obtained by employing MIMO and the two-way protocol for FSO CV-QKD systems.

Integrated sensing and communications (ISAC) promises new use cases for mobile communication systems by reusing the communication signal for radar-like sensing. However, sensing and communications (S&C) impose conflicting requirements on the modulation format, resulting in a tradeoff between their corresponding performance. This paper investigates constellation shaping as a means to simultaneously improve S&C performance in orthogonal frequency division multiplexing (OFDM)-based ISAC systems. We begin by deriving how the transmit symbols affect detection performance and derive theoretical lower and upper bounds on the maximum achievable information rate under a given sensing constraint. Using an autoencoder-based optimization, we investigate geometric, probabilistic, and joint constellation shaping, where joint shaping combines both approaches, employing both optimal maximum a-posteriori decoding and practical bit-metric decoding. Our results show that constellation shaping enables a flexible trade-off between S&C, can approach the derived upper bound, and significantly outperforms conventional modulation formats. Motivated by its practical implementation feasibility, we review probabilistic amplitude shaping (PAS) and propose a generalization tailored to ISAC. For this generalization, we propose a low-complexity log-likelihood ratio computation with negligible rate loss. We demonstrate that combining conventional and generalized PAS enables a flexible and low-complexity tradeoff between S&C, closely approaching the performance of joint constellation shaping.

Real-time corridor-wide crash-occurrence risk (COR) prediction is challenging because existing near-miss extreme value theory (EVT) models often oversimplify collision geometry, neglect vehicle-infrastructure (V-I) interactions, and inadequately account for spatial heterogeneity in traffic and roadway conditions. This study develops a geometry-aware two-dimensional time-to-collision (2D-TTC) near-miss extraction framework and integrates it with a hierarchical Bayesian grouped random parameter unified generalized extreme value model (HBSGRP-UGEV) to estimate short-term COR in urban corridors. The proposed framework builds on prior grouped EVT formulations while explicitly accommodating both vehicle-vehicle (V-V) and vehicle-infrastructure (V-I) near-miss processes within a unified corridor-wide modeling structure. High-resolution trajectories from the Argoverse-2 dataset were analyzed across 28 sites along Miami's Biscayne Boulevard to extract extreme near-miss events. The model incorporates vehicle dynamics and roadway features as covariates, with partial pooling across segments and intersections to capture corridor-wide heterogeneity. Results indicate that the HBSGRP-UGEV framework outperforms the fixed-parameter HBSFP-UGEV model, reducing the deviance information criterion (DIC) by up to 7.5 percent for V-V interactions and 3.1 percent for V-I interactions. Predictive validation using receiver operating characteristic area under the curve (ROC-AUC) demonstrates strong classification performance, with values of 0.89 for V-V segments, 0.82 for V-V intersections, 0.79 for V-I segments, and 0.75 for V-I intersections.

As a topological generalization of the notion of a multiset, a boolean multispace is a boolean space $X$ with a continuous function $u\colon X\to \mathbb Z_{>0}$, where $\mathbb Z_{>0}=\{1,2,\dots\}$ has the discrete topology. In this paper the category of boolean multispaces and continuous multiplicity-decreasing morphisms with respect to the divisibility order is shown to be dually equivalent to the category of unital Specker $\ell$-groups and unital $\ell$-homomorphisms. This result extends Stone duality, because unital Specker $\ell$-groups whose distinguished unit is singular are equivalent to boolean algebras. Boolean multispaces, in turn, are categorically equivalent to the Priestley duals of the MV-algebras corresponding to unital Specker $\ell$-groups via the $Γ$ functor. Via duality, we show that the category of unital Specker $\ell$-groups has finite colimits and finite products, but lacks some countable copowers and equalizers.

In over-identified models, misspecification -- the norm rather than exception -- fundamentally changes what estimators estimate. Different estimators imply different estimands rather than different efficiency for the same target. A review of recent applications of generalized method of moments in the American Economic Review suggests widespread acceptance of this fact: There is little formal specification testing and widespread use of estimators that would be inefficient were the model correct, including the use of "hand-selected" moments and weighting matrices. Motivated by these observations, we review and synthesize recent results on estimation under model misspecification, providing guidelines for transparent and robust empirical research. We also provide a new theoretical result, showing that Hansen's J-statistic measures, asymptotically, the range of estimates achievable at a given standard error. Given the widespread use of inefficient estimators and the resulting researcher degrees of freedom, we thus particularly recommend the broader reporting of J-statistics.

We define the Kirkwood-Dirac quasiprobability representation of quantum mechanics associated with the Fourier transform over second countable locally compact abelian groups. We discuss its link with the Kohn-Nirenberg quantization of the phase space $G\times \widehat{G}$. We use it to argue that in this abstract setting the Wigner-Weyl quantization, when it exists, can still be interpreted as a symmetric ordering. Then, we identify all generalized (non-normalizable) pure states having a positive Kirkwood-Dirac distribution. They are, up to the natural action of the Weyl-Heisenberg group, Haar measures on closed subgroups. This generalizes a result known for finite abelian groups. We then show that the classical fragment of quantum mechanics associated with the Kirkwood-Dirac distribution is non-trivial if and only if the group has a compact identity component. Finally, we provide for connected compact abelian groups a complete geometric description of this classical fragment.

The canonical-ensemble description of reactive quantum gas mixtures is reformulated by incorporating a single global particle-number-conservation constraint over the combined spectra of inter-converting species. This constraint replaces the conventional equality of chemical potentials. Fermi-Dirac or Bose-Einstein correlations naturally emerge across one-particle energy eigenstates of species sharing identical spin-statistics, which in ergodic single-systems manifest as intrinsic features of the equilibrium state. By embedding all microstates linked by conversion pathways, the framework incorporates concentration fluctuations in the statistical description. The formalism offers fresh insights into quantum chemical equilibrium in reactive mixtures with composition fluctuations and smoothly reduces to the classical ideal gas limit via an extended partition function that generalizes classical chemical-equilibrium treatments.