The extragalactic background light (EBL), the cumulative radiation from all extragalactic sources, traces galaxy formation and cosmic evolution. High-energy $γ$ rays attenuated via pair production with EBL photons are a powerful probe of the EBL. In this work, we use very-high-energy (VHE; $E_γ> 100\,\mathrm{GeV}$) $γ$ rays to measure the local EBL intensity and test its consistency with galaxy counts and direct measurements. Our analysis employs a sample of 268 spectra from 45 sources observed with Imaging Atmospheric Cherenkov telescopes. A model-dependent study shows seven EBL templates require only $\le 10\%$ rescaling to fit the observed $γ$-ray attenuation. The galaxy-count-anchored model gives the closest match. We then derive template-marginalized TeV optical depths from a representative model subset. We combine them with \textit{Fermi}-LAT GeV measurements to reconstruct the EBL at $z = 0$ using empirical and physically motivated models. The two reconstructions agree and follow the integrated galaxy light to within $2$--$3\,\mathrm{nW\,m^{-2}\,sr^{-1}}$ (typically $<25\%$) over $0.5$--$30\,μ$m. Both are consistent with low-zodiacal-light observations, including outer solar system and dark cloud measurements. In contrast, the near-IR excess reported by IRTS and CIBER exceeds our reconstructed intensity by $3$--$5σ$, implying an additional $\gtrsim 5$--$10\,\mathrm{nW\,m^{-2}\,sr^{-1}}$ incompatible with the $γ$-ray optical depths. Combined with GeV constraints on EBL evolution to $z \simeq 4$, these TeV optical depths provide a VHE-anchored determination of the local EBL intensity. The agreement with galaxy counts and deep-space measurements indicates that known galaxy populations account for most of the optical and near-IR background, leaving limited room for an additional diffuse component.

We study a model of 3d gravity relevant to the open sector of a CFT ensemble. The quantum theory is the open Virasoro TQFT, obtained by restricting the full open-closed Virasoro TQFT to a subclass of admissible manifolds. We show that it computes gravitational path integrals on compact regions with fixed-length boundary conditions for states above the black hole threshold, and fixed-angle boundary conditions for states below the threshold. Focusing on a special class of manifolds involving only boundary Wilson loops, we further show that the relation between Conformal Turaev-Viro theory and the diagonal sector of two copies of Virasoro TQFT arises naturally from an open-closed duality.

Solar irrigation systems are increasingly deployed in rural regions, yet their distributed and remote deployment makes maintenance challenging for farmers. While formal monitoring processes and applications exist, they often fall short in practice. We present insights from grid-connected solar irrigation schemes that incentivize farmers to feed energy to the grid, focusing on how farmers maintain their systems. We found that farmers face multiple challenges but are also devising strategies, including the appropriation of WhatsApp to share daily generation data with peers and compare performance across installations to identify potential system anomalies. Our findings highlight how messaging platforms function as informal digital infrastructures enabling collective sensemaking around distributed energy systems. We discuss implications for designing agricultural energy technologies that support peer comparison, contextual interpretation, and community-driven maintenance, framing these as a socio-technical platform. Finally, we outline directions for future work integrating such practices with formal monitoring tools and explore their potential to support citizen science initiatives in environmental sensing.

We investigate the dynamics of viscous fingering (VF) in miscible slices in homogeneous, isotropic porous media. The fluid flow is governed by incompressible Darcy's law, whereas the solute transport is described using an advection-diffusion equation. The viscosity of the miscible system depends on the solute concentration, creating a viscosity contrast between the displacing fluid and the finite sample. When expressed in terms of stream function, the flow is described by a system of nonlinear, two-way coupled advection-diffusion type equations. We consider three types of boundary conditions: (a) periodic, (b) impermeable (zero normal velocity) and no-flux (solute), and (c) permeable (allowing non-zero normal velocity) and no diffusive flux (solute) transverse boundaries. This initial boundary value problem is solved numerically using a fourth-order compact finite difference method, while the Crank-Nicolson technique is used for time integration. Although the onset of viscous fingering and early time behavior are independent of the choice of boundary types, long-time behavior, solute mixing and spreading depend on the boundary conditions. In particular, it is observed that the permeable boundaries allow solute mass to increase, leading to stronger fingering instabilities, larger mixing lengths and non-trivial evolution of interfacial lengths. The findings of this study have implications in chromatography separation.

We study phonon transport in junctions of two harmonic reservoirs coupled together by a spring. The exact steady-state heat currents and thermal conductance are calculated using nonequilibrium Green's functions. We find that the heat currents follow Fourier's law and the thermal conductance has a peak whenever the phonon spectra match. At lower temperatures, however, the thermal conductance maximum may not coincide with the spectra-matching peak due to the exclusion of higher-frequency phonons, whose spectra may match, from participating in the transport. Furthermore, we find that increasing the coupling spring constant increases the thermal conductance. Lastly, the magnitude of the steady-state heat currents and thermal conductance are the same whether the direction of phonon flow is from left to right or vice versa, even with mass and spring constant asymmetry. The properties of this basic model can serve as a reference for more complicated setups of phonon transport in molecular junctions.

We offer an alternative approach to the asymptotic rigidity of codimension-1 isometric immersions via quantitative rigidity estimates. We show that an immersion between compact manifolds $M$ and $N$ of dimensions $d$ and $d + 1$, respectively, with small stretching plus bending energy is close to an isometric immersion. In this way, we recover the results of Alpern, Kupferman, and Maor. In contrast to their intrinsic approach, we reduce the problem to the equidimensional Euclidean setting and apply the Friesecke-James-Müller rigidity estimate to obtain quantitative results. This yields an elementary proof based on Euclidean techniques. The rigidity estimates are of independent interest.

This chapter reviews the current state of observational and theoretical efforts in the characterization of exoplanet atmospheres, with a focus on developments enabled through the Swiss National Centre for Competence in Research (NCCR) PlanetS. It covers the essential physical and chemical processes that govern atmospheric dynamics, radiative transfer, chemistry, and cloud formation in exoplanets and brown dwarfs. The review discusses the modeling approaches used to simulate these processes, ranging from simplified 1D models to fully coupled 3D general circulation models. Atmospheric retrieval frameworks are presented as tools for inferring atmospheric properties from observational data, highlighting both classical Bayesian techniques and emerging machine learning methods. Observational strategies using instruments like HST, JWST, and ground-based high-resolution spectrographs are also examined. Special emphasis is placed on the interplay between theory and observation, and how developments in modeling, data analysis, and instrumentation collectively advance our understanding of planetary atmospheres beyond the Solar System.

We review the plethora of uncertainty relations that appear in quantum mechanics and their nuances. We present both foundational applications, e.g. in understanding and defining complementarity, and practical applications, e.g. in quantum metrology and cryptography. Both variance- and entropy-based uncertainties are covered here.

Many exoplanetary systems are multiplanet configurations whose long-term dynamics are governed by N-body gravitational interactions. Consequently, their detection signatures cannot be adequately described by Keplerian orbits. Accurately interpreting the observational data of these systems -- including radial velocity (RV), astrometry, and transit timing variations (TTVs) -- requires N-body integration. Motivated by this need, we developed a Bayesian fitting framework that couples N-body integration with Markov chain Monte Carlo (MCMC) to retrieve the system parameters of multiplanet systems. The code, named \texttt{Nii-body}, integrates an adaptive Runge--Kutta--Fehlberg 7(8) (RKF78) solver with an automated parallel tempering MCMC algorithm. Using simplified synthetic astrometric observations, we evaluated the efficiency and robustness of \texttt{Nii-body}'s N-body orbit retrieval on an idealized two-planet model, demonstrating its potential for future application to real observational data. The N-body fitting workflow can be readily extended to RV, TTVs, or combined datasets, providing a versatile engine for high-precision orbital inference in multiplanet systems.

The growth of the Quantum Information Science and Engineering (QISE) industry has increased interest in how undergraduate programs prepare students for careers in this field. Prior research emphasizes the value of experiential learning as preparation for the quantum industry, but lacks specificity regarding the experimental skills needed for positions available to bachelor's degree graduates. In this study, we investigate the experimental skills associated with bachelor's-level quantum industry positions through 44 semi-structured interviews with quantum industry professionals. Guided by the American Association of Physics Teachers recommendations for the undergraduate physics laboratory curriculum, we characterize the experimental skills associated with positions described as requiring bachelor's-level preparation and thematically synthesize them into four categories: instrumentation, computation and data analysis, experimental and project design, and communication and collaboration. We further examine how these skills cluster across role types and articulate them as learning goals to provide guidance for educators interested in aligning undergraduate instruction with the needs of students wanting to pursue a career in the quantum industry. Our findings suggest the need to emphasize the discussion of hardware in QISE theory courses, expand experimental training through instructional laboratories, and intentionally integrate professional skills in undergraduate QISE education.

We investigate the fermionic Casimir effect for a Dirac field confined between two parallel plates with MIT bag boundary conditions in the presence of CPT-odd Lorentz-symmetry violation described by a constant axial background vector $b_μ$. The exact mode quantization is derived from the modified Dirac equation in the planar geometry, and the vacuum energy is formulated through a phase-shift representation. For spacelike backgrounds we show that the components parallel to the plates can be absorbed into a shift of the transverse momenta and therefore do not affect the renormalized Casimir energy, while the component normal to the plates modifies the longitudinal spectrum and produces a genuine Lorentz-violating correction. Both the timelike component $b_{0}$ and the normal spacelike component $b_{z}$ can thus be treated within a unified framework characterized by a single effective spectral parameter. A closed logarithmic integral representation for the Casimir energy is obtained and its behavior is analyzed in the Lorentz-symmetric, weak-background, and strong-background regimes.

We extend the notion of representability dimension to partial actions and introduce a notion of dual representability dimension for global actions by finite abelian groups. We show that the Rokhlin dimension of a partial action by a finite abelian group agrees with the dual representability dimension of the dual action on the partial crossed product, while the representability dimension of a partial action agrees with the Rokhlin dimension of its dual.

In optical communications, the Raman effect is exploited for its lasing properties in distributed Raman amplification (DRA) and leads to spectral distortions through inter-channel stimulated Raman scattering (ISRS). In single-mode fibers, these effects are well understood and modeled, but equivalent closed-form expressions for arbitrarily coupled space-division multiplexing (SDM) links are lacking. In this work, we expand upon previous literature by providing closed-form expressions modelling DRA and ISRS in common SDM fiber designs that support arbitrarily-coupled degenerate mode-groups, incorporate mode coupling, and accounting for inter-modal non-linear effects, showing excellent agreement with simulations. The derived formulas are then applied to representative scenarios, illustrating how distinct pump and fiber configurations influence gain and mode-dependent gain (MDG). Finally, we describe suggested routines for experimentally estimating the Raman response profiles of SDM fibers.

Comparing $K$-sample distributions is a fundamental problem in data science that arises in a wide variety of fields and applications. In this article, we introduce a maximum-of-differences approach to make such comparisons. Specifically, we first calculate the pairwise distances from the pooled observations of the $K$ samples. We then define the two observations as connected if their distance is less than a pre-specified threshold value. For each observation, we next calculate the ``within" and the ``between" probabilities associated with these two types of connections for the given observation, i.e., with other observations within the same sample and between the given observation and the observations in other samples. Subsequently, we propose a maximum-of-differences (MOD) test that finds the maximum value among the standardized squared differences between the ``within" and the ``between" probabilities of all observations. Accordingly, the proposed test is not only applicable to multivariate data with $K$ samples, but can also be extended to multivariate regression models. Furthermore, we obtain the covariance-adjusted (CA) version of the MOD (CA-MOD) test, which converges to the Type I extreme value distribution under some conditions. Moreover, we demonstrate the asymptotic properties of the two tests under both the null and alternative hypotheses. The performance and usefulness of the tests are illustrated via simulation studies and real examples.

Accurate representation of non-Gaussian distributions of quantities of interest in nonlinear dynamical systems is critical for estimation, control, and decision-making, but can be challenging when forward propagations are expensive to carry out. This paper presents an approach for estimating probability density functions of states evolving under nonlinear dynamics using Seminonparametric (SNP), or Gallant-Nychka, densities. SNP densities employ a probabilists' Hermite polynomial basis to model non-Gaussian behavior and are positive everywhere on the support by construction. We use Monte Carlo to approximate the expectation integrals that arise in the maximum likelihood estimation of SNP coefficients, and introduce a convex relaxation to generate effective initial estimates. The method is demonstrated on density and quantile estimation for the chaotic Lorenz system. The results demonstrate that the proposed method can accurately capture non-Gaussian density structure and compute quantiles using significantly fewer samples than raw Monte Carlo sampling.

The role of macromolecular crowding in living systems is widely appreciated, but artificial crowders used to model these effects in vitro are often inadequately characterized. In this work, we examine density, viscosity, polymer self-diffusion and water diffusion in crowded dextran systems. Dextran viscosity and self-diffusion follow size-dependent trends, collectively described by universal functions of the overlap concentration corresponding to a Flory exponent of 0.44, characteristic of branched polymers. Viscosity increases with concentration as a power law, with a crossover from dilute to semi-dilute behaviors. Dextran self-diffusion decays exponentially: this can be interpreted in light of Rosenfeld's excess entropy scaling hypothesis. Water self-diffusivity and specific volume decrease with concentration, but show no dependence on polymer size. We show how these results can be used to construct the true volume fraction of crowders, which takes into account bound water. Overall, our findings showcase the power of polymer physics concepts in macromolecular crowding studies in vitro.

As silver nanowire (AgNW) networks reach increasing technological maturity, research efforts are progressively shifting toward their integration into functional devices. In this context, it is essential to assess how thin film coating processes affect the structural and functional integrity of these transparent conducting networks. Radio Frequency (RF) magnetron sputtering is among the most widely used and industrially scalable deposition techniques, making a detailed understanding of its impact on AgNW networks particularly critical. In this work, we experimentally investigate the degradation of AgNW networks observed under specific RF magnetron sputtering regimes. By varying deposition time, oxygen partial pressure, target material, buffer layers and plasma power, we analyze how sputtering conditions influence the electrical, morphological, and structural properties of the networks. Based on these observations, we identify viable strategies to mitigate or suppress network degradation, thereby enabling safer and more reliable coating protocols. These results provide practical guidelines for the integration of AgNW networks into multilayer device architectures.

The "magical" identity discovered by M.~Cotlar in 1955 for the Hilbert transform is established here in the setting of martingale transforms and, in particular, for conformal martingales. This, together with the probabilistic representation of the Riesz transforms, shows that, at the level of martingale transforms and in odd dimensions, they exhibit the same analytic-type structure as the Hilbert transform on the real line. Consequently, Cotlar's proof of the sharp $L^p$ inequality for powers of $2$ applies. The significance of the martingale Cotlar identity, whose proof is entirely elementary, does not lie in providing an alternative proof of this well-known and relatively simple estimate, but rather in the structural viewpoint it reveals. This structure is explored further. Independent of Cotlar's identity, asymptotic bounds for the $L^p$ norm of the vector of Riesz transforms are investigated. It is shown that, in the limit as $p\to\infty$, this norm coincides asymptotically with that of the Hilbert transform on the real line. The study of the Cotlar identity in the martingale setting is motivated by the desire to gain new insight into two longstanding open problems: T.~Iwaniec's 1983 conjecture on the norm of the Beurling-Ahlfors operator and the problem of determining the sharp constant in E.~M.~Stein's 1984 inequality for the vector of Riesz transforms. Related problems are also discussed. The paper contains both a survey of known results and new contributions. An effort has been made to keep the exposition as self-contained as possible and to present the material in an accessible, largely expository style.

Soil moisture is a critical variable for managing irrigation, improving crop yield, and understanding field-scale hydrology. Radars mounted on unmanned aerial vehicles (UAVs) offer a promising means to monitor soil moisture over large fields with flexible, high-resolution coverage. However, during the growing season, canopy scattering and soil reflections become strongly coupled in the radar measurement. These coupled effects vary with crop structure or flight altitude, complicating the retrieval of soil moisture. To overcome this challenge, we present GreenScatter, a physics-based soil moisture retrieval framework for nadir-looking wideband UAV radars. GreenScatter introduces a microwave radiative transfer model that explicitly captures the dominant electromagnetic interactions between vegetation and soil, enabling accurate modeling of coherent ground backscatter through canopy. In parallel, it develops a radar cross-section (RCS) estimation method that transforms time-domain radar signals into calibrated wideband RCS spectra, isolating soil reflections while compensating for hardware and waveform effects. Together, these components enable robust soil moisture estimation through vegetation across varying canopy conditions and UAV configurations. Field experiments across multiple corn and soybean sites demonstrate consistent retrieval with an average volumetric water content (VWC) error of 4.49%.

F$^{19}$ nuclear magnetic resonance free induction decay (FID) data are used to verify the predictions of a universal growth hypothesis for the Lanczos coefficients proposed by Parker et al. Our results strongly support this hypothesis and permit to calculate values of the growth parameter $α$ for three crystal orientations. For the magnetic field parallel the [100] crystal axis, we found $α=3.161 \times 10^{4} sec^{-1}$. The special experimental conditions required for the observability of a singularity in the analytic continuation of the FID, which from the experimental data was found to be of branch-point type, are discussed.

In this work we introduce discrete-time quantum walks in state space, more precisely on Fock-state lattices. Fock-state lattices provide a natural and clean setting for implementing lattice models, particularly in quantum optical systems. Thus, contrary to the common setting where the walker resides in real space or phase space, here the walk takes place in a synthetic space. We present a general formalism based on Lie algebras and their properties. For each Lie algebra one can associate both a phase space and a Fock-state lattice, and by understanding how these spaces are related, together with the action of generalized displacement operators, we construct the discrete unitary operator that generates the walk. In this framework the displacement operators replace the usual nearest-neighbor shifts and lead to state-dependent tunneling on the lattice. By considering several examples we demonstrate ballistic spreading and other characteristic features of discrete-time quantum walks, such as coin-walker entanglement and symmetry-induced interference patterns. We also show that different algebraic structures can give rise to qualitatively different dynamics, including anomalous behavior such as super-ballistic spreading as well as localization effects.

We study the spectral behavior as the sample size $n \to +\infty$ of integral operators defined by convolution of a non-negative symmetric kernel k with respect to empirical measures $μ_n = \frac{1}{n} \sum_{i=1}^n δ_{X_i}$, where $\{X_i\}_{i=1}^n$ are independent uniform samples from a compact probability metric space $(\mathcal{X},d,μ)$. Relaxing the usual positivity and continuity assumptions on k, we prove the convergence of these empirical operators to their continuous counterparts, and provide explicit convergence rates.

The relationship between the star formation rate surface density and the molecular gas surface density in galaxies is key to understanding galaxy evolution. To investigate the molecular Kennicutt-Schmidt (K-S) relation and its dependence on gas density, we analyze a uniform sample of 36 nearby galaxies from the AMISS survey, focusing on the CO(1-0), CO(2-1), and CO(3-2) transitions, which trace progressively denser and warmer molecular gas. Using statistical methods that combine binning with Markov Chain Monte Carlo (MCMC) fitting, we derive the slope, scatter, and intercept of the $Σ_{\mathrm{SFR}}$-$Σ_{\mathrm{CO}}$ relation for each transition. We find power-law slopes of 1.26, 1.14, and 1.07 for CO(1-0), CO(2-1), and CO(3-2), respectively, consistent with a trend toward increasingly linear star formation relations at higher-J transitions. This behavior supports the idea that denser gas is more directly linked to ongoing star formation and is consistent with previous findings of near-linear correlations between HCN or high-J CO luminosities and global SFR. The observed trend suggests an underlying relation between gas and SFR volume densities with a power-law index of $\sim$1.5, indicating enhanced star formation efficiency in denser environments. These findings underscore the critical role of dense gas in regulating star formation and highlight the importance of tracer selection and excitation conditions when interpreting the K-S relation across different environments.

Gravitational-wave memory is a low-frequency, non-oscillatory component of the radiation field that provides a potentially powerful but as yet undetected probe of strong-field gravity. We present the first calculation of gravitational memory from full inspiral--merger--ringdown waveforms in a theory beyond general relativity, focusing on scalar-Gauss-Bonnet gravity as a theoretically well-motivated and numerically accessible extension of GR. Starting from the general memory formulas in Horndeski gravity, we derive explicit spin-weighted spherical-harmonic expressions for the tensor null memory in scalar-Gauss-Bonnet theory and evaluate them on existing numerical-relativity waveforms for both shift-symmetric and dynamically scalarizing binary black hole mergers. We find that the dominant effect is an indirect modification of the tensor memory through changes in the nonlinear merger dynamics, while the direct scalar contribution to the tensor memory remains suppressed by orders of magnitude for the systems considered in this work. For the largest deviations in our dataset, the final memory amplitude differs from the corresponding GR prediction by a few percent and by up to $\sim 4\%$ when compared to the GR template that minimizes the waveform mismatch in a detector-oriented analysis. We further show that including memory increases the mismatch between GR and scalar-Gauss-Bonnet waveforms by more than an order of magnitude, indicating that memory can provide complementary information for testing gravity with third-generation detectors, especially for low-mass binaries.

We investigate ionic fragmentation of CO$_2^{n+}$~\mbox{($2\le n\le 4$)} produced in collisions with Ar$^{q+}$~\mbox{($4\le q\le 16$)} projectiles at a collision velocity of $\approx$~0.3~a.u. For most projectile and fragmentation channel combinations, the shape of the kinetic energy release distribution (KERD) differs with the electron capture mediated charge change (\mbox{$Δq$}) in the scattered projectile: KERD for \mbox{$Δq = 2$} is broader at high KER than for \mbox{$Δq =1$}. The difference generally diminishes with increasing projectile charge. Two deviations in this general trend are seen in the fragmentation of CO$_2^{3+}$, one for Ar$^{4+}$ impact in the high KER region and the other for Ar$^{6+}$ impact in the low KER region. The calculated reaction windows for multielectron capture within the framework of the extended classical over-the-barrier model (ECOBM) indicate that while ionization of the target occurs via multielectron capture, the scattered projectile may subsequently undergo multi-fold autoionization. Interpreting projectile autoionization to be a consequence of capture into highly excited states and high fragment KER to be a consequence of excitation of the ionized target to high-lying states, we find a strong dependence between the target and scattered projectile excitations.

We present ALMA detections (or stringent upper limits) of the [CII] 158 $μm$ emission line and underlying dust continuum from five massive quenched galaxies (QGs) at 2<z<4.7. We find extreme variations in the molecular gas fractions ($\rm{f_g=M_{mol}/M_{\star}}$), spanning 0.1%-25%, if a standard $\rm{α_{[CII]}}$ applies. We attempt a first empirical calibration of $\rm{α_{[CII]}}$ with respect to dust continuum in a $z=2$ lensed QG and with respect to CO(3-2) in a $z=3.1$ QG, finding no evidence of strong deviations from the standard value. Dust continuum measurements, coupled with JWST/MIRI fluxes, suggest higher dust temperatures compared to expectations from $z<2$ QGs, reaching $T_{d}\sim40-50 \,K$ in two galaxies. Coupled with remarkably high total infrared luminosities (LIR) not explained by observed JWST colors not by energy balance based on literature dust extinction measurements, and with [CII] deficits down to $\rm{[CII]/LIR\sim 2\times10^{-4}}$ typical of (Ultra)Luminous Infrared Galaxies, our findings point to additional dust-heating mechanisms other than dust-absorbed stellar radiation. Surprisingly, JWST/NIRCam and ALMA imaging reveal widespread disturbed stellar morphologies and offsets/tails in dust and gas, indicative of ongoing interactions. While larger samples are needed to assess how common these features are in high-z QGs, these findings support a merger-driven origin for the phenomenology observed in these systems, with key similarities with respect to local post-starburst galaxies where low-velocity shocks and turbulence also inject energy into the residual ISM.

Accurate high-resolution vertical profiles of optical turbulence ($C_n^2$), which reflect local meteorology and topography, are crucial for ground-based optical astronomy and free-space optical communication. However, measuring these profiles or generating them with numerical weather models requires substantial operational or computational effort. In this work, we present OTProf, a deep-learning method that estimates high-resolution $C_n^2$ profiles from widely available coarse-resolution ERA5 reanalysis data. We evaluate the approach in the Netherlands and compare it with the commonly used Hufnagel-Valley model. Overall, OTProf reproduces the vertical structure of $C_n^2$ more accurately than Hufnagel-Valley and yields more accurate estimates of the Fried parameter $r_0$ and the scintillation index $σ_I^2$. As typical in machine learning, the $C_n^2$ predictions are slightly smoothed compared to reference data, especially in cases of rare strong turbulence. This smoothing affects the integrated parameters, sometimes leading to overly optimistic $r_0$ and $σ_I^2$ values. Despite this limitation, OTProf offers a more accurate, efficient, and physically consistent alternative to traditional analytical models and computationally expensive mesoscale models.

We formulate a general prescription for spurion analysis in particle-physics models whose selection rules are described by commutative non-invertible fusion algebras. The construction applies to fusion algebras containing non-invertible basis elements that need not be self-conjugate, thereby allowing us to systematically track coupling constants in arbitrary particle scattering processes at tree and loop orders, but without assuming faithful realization of the fusion algebra, or no other quantum numbers for dynamical particles. This unifies and streamlines the previous analysis of near-group fusion algebras and of the $\mathbb{Z}_M/\mathbb{Z}_2$ fusion algebras, and supports the broader viewpoint that the non-invertible selection rules often admit auxiliary descriptions using lifted Abelian groups with a structured set of explicit breaking terms.

We investigate the relationship between product offerings, information dissemination, and consumer decision-making in a monopolistic screening environment in which consumers lack information about their valuation of quality-differentiated products. An intermediary, who is driven by the objective of maximizing consumer surplus but is also biased towards high-quality products, provides recommendations after the monopolist announces the menu of product choices. We characterize the monopolist's profit-maximizing finite-item menu. Our results show that as intermediaries place greater emphasis on consumer surplus over product quality, sellers are prompted to strategically expand their product range. Intriguingly, this augmented product variety decreases economic efficiency compared to scenarios where direct seller-to-consumer information provision is the norm. The role of information intermediaries proves pivotal in shaping consumer welfare, market profitability, and overarching economic efficiency. Our insights underscore the complexities introduced by these intermediaries that policymakers and market designers must consider when designing policies centered on consumer learning and market information transparency.

In this paper, we derive explicit closed-form solutions for the value function and the associated optimal stopping boundaries in an optimal annuitization problem under a mortality shock. We consider an individual whose retirement wealth is invested in a financial fund following the dynamics of a geometric Brownian motion and has the option at any time to irreversibly convert their wealth into a life annuity. The individual faces a sudden, permanent health deterioration occurring at a random, exponentially distributed time, and the annuitization decision is modelled as an optimal stopping problem across two health states. Our analytical expressions characterise both the value function and the optimal timing of annuitization. The results provide clear economic intuition: the optimal strategy is governed by the critical interplay between the relative attractiveness of the annuity (money's worth), the financial returns from the investment fund, and bequest motives across different health states. A numerical analysis compares the optimal annuitization strategy of an individual facing a health shock against a benchmark case with constant mortality, highlighting how the likelihood and severity of a health shock significantly alter optimal annuitization behaviour.