We present an updated transit ephemeris for the exoplanet WASP-18 b and critically examine the existence of a proposed second planet, WASP-18 c. Using 205 transit light curves from TESS, CHEOPS, Exoplanet Watch, Exoplanet Transit Database and previous literature, we derive a refined mid-transit time of 2460933.096346 +/- 0.000022 BJD_TDB and an orbital period of 0.94145252 +/- 1.1 x 10^-8 days for WASP-18 b. Our forward-propagated ephemeris to January 1, 2030, shows a timing uncertainty of 2.41 seconds. This high-precision refinement serves as a robust baseline to test for Transit Timing Variations (TTVs), ensuring that any reported deviations are not artifacts of an insufficiently constrained orbital period. In addition, we analyze 449 radial velocity (RV) measurements from the CORALIE, HARPS, PFS, HIRES and ESPRESSO spectrographs to search for signatures of WASP-18 c, a previously proposed additional planetary companion, and also estimated the k2 love number as 0.62199 +/- 0.0011. However, we do not find significant variations in either transit timing or RV data that support the presence of WASP-18 c. Moreover, the most significantly identified periodicities are not consistently measured across the transit or RV datasets, strongly arguing against the existence of a dynamically relevant second planet in the system. Our results indicate that the claimed WASP-18 c signal is likely spurious in nature. Overall, this work enhances our understanding of the WASP-18 system and provides a valuable resource for future observational campaigns with the refinement of the b planet orbit and falsified status of the previously defined c planet.

We introduce and study a new model of correlated uniform attachment (UA) trees, where correlation is sprinkled throughout the time evolution of the process. In this model, two UA trees are grown in parallel, and at each time step a new node is added to each tree, with an edge between it and a uniformly chosen existing vertex in the respective tree. The two choices of attachment are correlated: with probability $α$, the edges attach to nodes with the same time label in both trees, and with probability $1-α$, the choices are made independently. We study fundamental detection and estimation questions for this model, given two \emph{unlabeled} trees. In our main result, we construct a consistent estimator of the correlation parameter $α$, as the size of the trees goes to infinity. The construction of our statistic relies on two key ideas. First, we use Jordan centrality to identify subsets of vertices of each tree whose intersection has a sufficient number of common early vertices. The second idea is that, across multiple time scales, it is possible to approximately determine the labels of vertices that have attached to these early vertices, using the sizes of fringe subtrees. Our analysis includes novel quantitative bounds on the fraction of early vertices that remain central, which are of independent interest in the network archaeology literature.

This paper introduces the L-shaped refinement chain cuts method, a novel approach for solving two-stage stochastic programs. The proposed method integrates the refinement chain of scenarios within the classical L-shaped decomposition framework. In the proposed approach, the full scenario set is partitioned into subgroups at each level of the refinement chain, and one subproblem is solved for each subgroup rather than for each individual scenario as in the classical L-shaped method. The proposed framework generalizes both the classical multi-cut and single-cut L-shaped formulations. Theoretical convergence properties to the optimal solution of the original two-stage stochastic program are established for every refinement level. In addition, the relationships between consecutive refinement levels are characterized in terms of Benders cuts, leading to the development of an iterative refinement-based solution algorithm across consecutive levels of the refinement chain. The effectiveness of the proposed method is evaluated on a two-stage stochastic fixed-charge multicommodity network design problem under a mean-risk formulation. Computational experiments on benchmark instances demonstrate the promising performance of the proposed framework and highlight its applicability to large-scale risk-averse stochastic optimization problems.

In this thesis we present the combinatorial game theory of the game Rex+. Rex+ is a variant of the game Hex, played on a four sided board made out of hexagons. Both players take turns placing as many stones of their colour as they would like on the board, with the objective being to force the other player to connect their two sides. We describe a new ordering, and present some preliminary results on it.

Flows with high density ratios, such as wave breaking and air entrainment in maritime applications, remain challenging to simulate due to their energetic and strongly nonlinear nature. In such regimes, maintaining numerical robustness is difficult when using the commonly adopted velocity-based formulation. The Consistent Mass-Momentum (CMOM) transport framework improves numerical robustness by enforcing fundamental physical properties, most notably momentum conservation and semi-discrete energy-conserving. However, CMOM replaces the advection of a continuous velocity field with that of a discontinuous momentum field. When combined with sharp interface methods, this leads to severe momentum shocks, for which conventional shock-capturing schemes are ineffective. To reconcile physical fidelity with numerical robustness, this work proposes a Synchronized Donor-Region of Momentum fluxes (SynDRoM) that enforces monotonicity of the transported velocity field. The resulting algorithm effectively eliminates spurious velocity oscillations without sacrificing physical fidelity, as demonstrated through scalar transport and interfacial shear instability test cases. Beyond difficulties from large density ratio, improper estimation of viscosity in the vicinity of the interface can introduce numerical instabilities at finite time steps, thereby undermining overall robustness. To address this issue, a viscosity limiter based on the bounded kinetic viscosity concept is introduced and validated using a gravity-driven plane shear flow. Finally, a breaking wave simulation is performed to assess the combined performance of the proposed physics-preserving numerical schemes for multiphase flows.

In this report we demonstrate dense polycrystalline calcium hydroxide ceramics fabricated by hydrothermally-assisted sintering - often referred to as cold-sintering - to produce high-purity calcium hydroxide targets for calcium oxide thin film deposition. Calcium hydroxide ceramics exhibit up to 98% theoretical density without thermal dehydration, when sintered at temperatures between 100 °C - 300° C with 400 MPa applied uniaxial pressure for 1 hour. The brucite phase is preserved in calcium hydroxide targets at all temperatures. Small equivalent fractions of calcium carbonate are present in both the calcium hydroxide precursor powder and final targets suggesting minimal additional production during formation and densification. Microstructure evolution during densification is documented by scanning electron microscopy, indicating both mass transport and plastic deformation densification mechanisms. The hydrothermal-assisted sintering process is scaled up to produce 2-inch diameter calcium hydroxide targets suitable for sputter deposition. We also report epitaxial calcium oxide film deposition from these targets on r-plane sapphire substrates. (002) oriented epitaxial films are achieved with a time-stable 1.2 nm per minute deposition rate. We note that energetic bombardment during growth can be substantial at these rates even when 1 mol% oxygen is added to the sputtering process necessitating the low deposition rate conditions.

We study admission control to an unobservable M/M/1 queue. A memoryless controller can only randomly thin arrivals (random routing, RR). We show that a gated admission (GA) policy, blocking arrivals for a fixed period after each admission, stochastically dominates RR at equal throughput, improving social welfare under any sojourn-based cost. We characterize the welfare-maximizing threshold and define the Price of Forgetting as the welfare ratio. This ratio is unbounded even though the absolute welfare gain stays uniformly bounded.

Transport of optically excited carriers in semiconductors is typically described within a quasi-equilibrium picture, where energy is carried by a single thermalized quasiparticle population characterized by well-defined transport coefficients. Here, we demonstrate that in epitaxial CsPbBr3 perovskite single crystals, this picture holds near room temperature - but breaks down dramatically at low temperature. Using transient microscopy, we show that optically measured carrier mobilities match device-scale Hall-effect and field-effect transistor measurements across a broad temperature range, resolving reported discrepancies and validating the equilibrium framework in the free-carrier regime. Below ~60 K, however, when excitonic effects become significant, equilibrium models begin to fail. We observe two coupled populations: a transient (<100 ps) hot-exciton gas with a diffusivity ~25-30 cm²/s - greatly exceeding the diffusivity expected for thermalized excitons - and a quasi-localized state that is fed by the cooling of the hot-exciton gas. These results reveal that in CsPbBr3, transport and thermalization are not separable processes: carriers move while still redistributing among internal degrees of freedom, breaking the timescale separation that underpins equilibrium transport theory in conventional semiconductors. By resolving transport at the population level, we can directly access the competing kinetics of exciton formation, interconversion, and cooling, offering a new space for controlling energy flow in perovskite materials and their photonic applications.

Compact disks of planetary debris orbiting white dwarfs provide a crucial window into our understanding of evolved planetary systems. The formation of these disks has been widely modeled with tidal fragmentation of minor planets that are rubble piles with no internal strength. However, rubble piles do have non-zero cohesive strength from Van der Waals forces, and here we demonstrate the consequences: breakup of these rubble piles sets a maximum fragment size, and we calculate this size \jks{for water ice, iron, and material densities corresponding to the lunar highlands, Vesta and the Earth}. We find that for typical minimum rubble pile strengths of $\sim$10-1000 Pa, the maximum fragment size is as large as small asteroids (0.1-1 km). This limit -- the km-size barrier -- also represents the characteristic sizes of tidal fragments. Most of the debris mass is contained in fragments of this size. Consequently, subsequent disk evolution should first feature a prominent dust-forming process, such as collisional grinding, before Poynting-Robertson drag can significantly shape the final disk. \jks{Further, we find that non-zero internal strength more narrowly radially confines the fragments than in the strengthless case.} This correction to previous assumptions adds to the growing evidence of the importance of collisions in the formation and evolution of white dwarf debris disks, while also helping to bound the size distribution in these disks for modeling efforts.

Elongated spin-$1$ condensates present a highly non-trivial local magnetization dynamics, due to the interplay between nonlinear and quantum effects stemming from the inhomogeneous density profile. This interplay results in different dynamical regimes after an initial global quench. In particular, we show that the system may display the coexistence of markedly different dynamical domains separated by a robust interface that acts as a spatial excited-state quantum phase transition. Furthermore, the local spinor dynamics may enter a chaotic regime characterized by irregular evolution and exponential sensitivity to initial conditions. We map the universal phase diagram distinguishing regular and chaotic regimes, which may be probed in on-going experiments.

A laser-plasma acceleration scheme combining electron extraction from a solid overdense target with wakefield acceleration in an adjacent underdense plasma region is presented. A laser pulse excites a diffracted electromagnetic wave at the overdense plasma interface, extracting and pre-accelerating electrons, which are then injected into laser-driven wakefield cavities in the underdense plasma. A parametric study identifies key conditions enabling efficient electron injection and energy gain in this two stage acceleration configuration. Two-dimensional particle-in-cell simulations performed with the \Smilei code show that the proposed scheme produces high quality electron bunches with high amounts of charge and energy at laser intensity $I_0 λ_0^2 \simeq 3.4 \times 10^{19}$ W$μ$m$^2$/cm$^2$ ($λ_0=0.8 μ$m). According to the parameters used, the electron beam is accelerated to peak energies of $\sim150-250$ MeV with an estimated charge in 3D of $\sim50-400$ pC integrated over the full width at half maximum energy range, and $\sim100-1800$ pC with energies above $50$ MeV.

In this paper, we prove that all normalized symplectic capacities agree for dynamically convex domains in $\mathbb{C}^2$ that are invariant under any Hamiltonian $S^1$-action isotopic to the Hopf diagonal action. We also give necessary and sufficient conditions for $S^1$-invariant domains to be dynamically convex.

Programmable photonic meshes provide a promising platform for analog matrix-vector multiplication, but their scalability is often limited by the large phase-shift ranges required in universal interferometer circuits. We introduce a perturbative programming method that operates the circuit near a fixed reference configuration and realizes the target transformation through interferometric subtraction, thereby reducing the required programmable phase excursion. We develop this approach for photonic matrix-vector multiplication architectures based on universal unitary meshes, and low-depth non-unitary constructions based on sums of unitaries. We identify favorable reference configurations through a local conditioning criterion, analyze the phase statistics obtained for random target matrices, and show that perturbative programming produces phase distribution shrinking as the matrix size increases. We further quantify the trade-off between reduced phase range and the intrinsic overhead introduced by the subtraction architecture, and show that for sufficiently lossy phase shifters the reduced phase range can compensate for this penalty. These results identify perturbative programming as a conditional but potentially useful route toward more scalable programmable photonic matrix processors.

The reliable treatment of highly boosted hadrons is crucial for many lattice QCD applications. For all these cases the kinematically enhanced interpolators promise very significant improvements and are, therefore, ever more often used in recent calculations, especially for highly boosted mesons like the pion. Motivated by, e.g., the physics program of the future Electron-Ion Collider (EIC) in the US and Electron-Ion collider in China (EIcC), we systematically benchmark our code for the unpolarized isovector nucleon quark matrix elements extracted at large source-sink separations, where excited state artifacts are significantly suppressed. We find that the precision of the renormalized nucleon matrix elements is typically improved by an order of magnitude at momentum $P_z\sim2.5$ GeV. By comparing the results from three CLS ensembles with different lattice spacings $a$ but the same pion mass, we observe no statistically significant dependence on $a$ in the renormalized matrix elements at nearly identical values of $P_z$. These encouraging results suggest that the use of kinematically improved operators is highly advantageous for parton physics calculations and can be extended to a broader class of baryon observables, making them a promising candidate for a standard component of modern lattice QCD.

Fluctuations of conserved charges are among the main proposed signatures of the quantum chromodynamics (QCD) critical point, but their interpretation requires a dynamical description of how fluctuation correlators evolve during the finite lifetime of the quark--gluon plasma (QGP) fireball. The standard baseline for this evolution is Fickian diffusion, in which the diffusive current follows the local density gradient instantaneously. This instantaneous-current limit can miss delayed-response effects when the current-relaxation time becomes comparable to the relaxation time of the relevant fluctuation modes. In this work we extend this baseline to Maxwell--Cattaneo diffusion, where the current relaxes on a finite time scale and therefore retains memory. We derive closed evolution equations for multi-point Wigner functions and convert the freezeout correlators into acceptance-dependent cumulants along representative trajectories in the QCD phase diagram. While Fickian diffusion already causes the correlators to lag behind their instantaneous equilibrium values, finite current relaxation introduces an additional memory effect beyond this diffusive lag. As a result, current memory can suppress, shift, and reshape the non-monotonic behavior of the cumulants relative to both instantaneous equilibrium and Fickian diffusion, with the most visible effects appearing in higher-order cumulants and their ratios.

For solar energetic particles (SEPs), it is generally expected that observers magnetically closer to the eruption source region exhibit higher particle intensities than those poorly connected to the eruption site. However, the 2023 February 24 SEP event departs from this simple picture: Earth and STA, near 1 au, are nominally better connected to the source region, whereas Solar Orbiter (SolO), at 0.77 au but less favorably connected, observed SEP fluxes more than an order of magnitude higher. This difference cannot be simply explained by nominal magnetic connectivity or radial scaling of SEP fluxes alone. To investigate this behavior, we perform a global magnetohydrodynamic simulation of the associated coronal mass ejection (CME) using the Alfvén Wave Solar-atmosphere Model-Realtime (AWSoM-R). The simulation reveals that the CME flux rope originates close to a coronal streamer and as it propagates and expands, the CME-driven shock is effectively distorted, developing into two distinct flanks with different strengths. Although the three spacecraft are separated by only $\lesssim$30$^{\circ}$ in heliolongitude, their magnetic footpoints differ by $\gtrsim$50$^{\circ}$ in longitude because of a nearby stream interaction region. Specifically, Earth and STA connect to a weaker shock region, while SolO connects to the shock nose with a higher compression ratio and more efficient particle acceleration. We further simulate SEPs using the Multiple-Field-Line Advection Model for Particle Acceleration (M-FLAMPA) coupled with AWSoM-R, obtaining results that reproduce the observed flux differences among the three spacecraft, demonstrating that this counterintuitive behavior results from their connections to different regions of the inhomogeneous CME-driven shock.

By listing the components included in an application, Software Bills of Materials (SBOMs) are intended to support the timely identification of vulnerable components and ensure the security of the software supply chain. However, we question the underlying assumption that there is agreement on the components to be listed in an SBOM and that current technology is sufficient to secure the software supply chain. First, we propose a ground-up analysis of Component Inclusion Mechanisms (CIM) in the software's development lifecycle. Then we systematically analyze the four popular SBOM generation tools, cdxgen, syft, trivy, ORT, and the Microsoft sbom-tool, to understand how they define and identify relevant components. Finally, we assess these using a ground truth across the programming languages Python, Java, Go, PHP, Rust, and C. While today's tools are a step toward identifying components, our results show that no tool covers all identified CIMs and that common gaps exist across tools. We demonstrate that, under the current vague definitions and tooling, SBOMs exhibit ambiguity and blind spots in component inclusion. Thus, a security-grade SBOM is not achievable with the evaluated tools, necessitating further progress to ensure software supply chain security. We need to go back to the drawing board to clarify which components should be included in an SBOM and revise SBOM generators accordingly. Without a shared understanding of what a component is, any effort to secure software supply chains with SBOMs will fail.

Microwave crosstalk poses a major challenge to scaling superconducting quantum devices as it introduces excess control errors. Although its magnitude and impact have been explored in various experimental settings, quantitative physical models capable of explaining measured crosstalk for a given device geometry remain scarce. Here, we address this gap by investigating microwave crosstalk in planar superconducting devices with crossovers. We identify two structures that can lead to strong crosstalk: a drive line routed in close proximity to another qubit, and a drive line crossing a qubit-qubit coupler using an air bridge. We design and characterize devices involving these structures and develop physical models that quantitatively explain the experimentally observed crosstalk. Based on these models, we discuss the design considerations for reducing microwave crosstalk. Our results provide practical guidance for low-crosstalk device layouts and establish a basis for the systematic investigation of weaker crosstalk mechanisms.

Artificial Colloidal Ice is an ice-like system used to study the effects of frustration in controlled environments where all degrees of freedom can be accessed at a length-scale large enough for optical visualization and in real time. We modify this model system by inducing anisotropic interactions through an in-plane magnetic field. In this new regime, the system has a well-defined ground state consisting of a checkerboard pattern of fully charged vertices. However, Brownian Dynamics simulations are unable to reach this ground state and instead remain frozen in metastable disordered states, even in the absence of quenched disorder in the lattice. This arrest is caused by the local magnetic enhancement of the potential barrier that the particles need to cross to find a lower energy state.

Prediction algorithms are increasingly used to inform decisions about humans, but maximizing accuracy$\rule[0.25em]{1em}{0.4pt}$the standard learning objective$\rule[0.25em]{1em}{0.4pt}$does not necessarily maximize user benefits. Instead, we propose optimizing social welfare, defined as the average gain users receive from correct predictions. Welfare enables to express, and therefore account for, heterogeneity in how much users benefit from accuracy. But since these valuations are private and users can gain from overreporting them, learning must simultaneously elicit truthful values and optimize welfare with respect to them. To this end, we propose a novel learning algorithm that incorporates a truthful auction. We show how to compute allocations and prices efficiently, and bound the number of paying users$\rule[0.25em]{1em}{0.4pt}$ which surprisingly is independent of the sample size. We conclude with experiments on real and synthetic data that demonstrate our algorithm and explore the connections between welfare and accuracy.

The binary black hole (BBH) merger rate is governed by the progenitor formation rate and the distribution of delay-times between formation and merger, but these functions remain poorly constrained. We introduce a framework that maps the parameters of physics-driven models directly onto existing data-driven fits of the BBH merger rate. This ``regression on regression'' approach enables physical interpretation of flexible population models without the computational burden of reanalyzing the underlying gravitational-wave event data. Applying this method to the \textsc{B-Spline} merger-rate posteriors from the Fourth Gravitational-Wave Transient Catalog, we fit the minimum delay time ($τ_{\text{min}}$), delay-time power-law index ($α$), and progenitor formation parameters controlling the normalization ($\mathcal{A}$), early-time growth ($γ$), and late-time decay ($δ$). Increasing the number of anchoring redshift points from two to four reduces the median sum-squared error (SSE) by a factor of $\approx 4.5$. However, residuals reveal that the physical model does not pass through all four anchors, exposing model misspecification and demonstrating a key strength of the framework: unlike standard inference methods, which preferentially weight compatible curves and mask underlying tensions, our approach exposes BBH posteriors irreconcilable with the model. Despite uncertainties at $z\gtrsim1$, the shape of the progenitor formation rate at low-$z$ is robust and evolves more steeply than the global star formation rate (SFR), supporting a preference for low metallicity environments. Specifically, the log-space slope of the progenitor rate is $\approx 5.3$ times steeper than the SFR between $z=0.1$ and $z=1.0$. Ultimately, a more complex phenomenological model is required to match the \textsc{B-Spline} merger rates.

This note gives a simple algorithm for the following effectivity problem: given a genus $2$ curve $X$ together with a nonconstant map $π:X\to E$ to an elliptic curve, determine an elliptic curve $E'$ and a map $π':X\to E'$ independent of $π$. Equivalently, we compute the complementary elliptic factor in the decomposition of $\operatorname{Jac}(X)$ up to isogeny. While the problem has been studied extensively, and more general ones have been solved by deep and powerful techniques, we are not aware of a reference for the simple explicit procedure described here.

We determine the logarithmic growth exponents of the $L^p$ norms, $1\le p\le\infty$, of $L^2$-normalized Laplace eigenfunctions on the unit disk, for both Dirichlet and Neumann boundary conditions. We also prove sharp uniform $L^p$ upper and lower bounds for every $L^2$-normalized Dirichlet eigenfunction and every non-constant Neumann eigenfunction $u_λ$ on the disk. The proof uses stationary phase estimates and integral estimates for Bessel functions.

For the family of Dirichlet stadia $S_t$ whose rectangular part has height $π$ and half-length $πt/2$, $t \in [1,2]$, we show that for Lebesgue almost every $t$ there exist real eigenfunctions $u_j$ and a smooth mean-zero physical observable $Q$ for which $\langle Q u_j,u_j\rangle$ has a non-zero subsequential limit. Consequently, along the same subsequence, the eigenfunction mass fails to equidistribute on a fixed region whose relative boundary in the interior of the stadium is smooth. This proves a physical-space strengthening of Hassell's non-QUE theorem for generic stadia, and thus gives an affirmative answer to Tao's question in Hassell's generic setting. The proof uses the classification of generic stadia in Hassell's argument. In each of the resulting cases, we construct an appropriate physical observable $Q$ that converts Hassell's phase-space obstruction to QUE into physical-space non-equidistribution.

Interest in leveraging emotions in Interactive Digital Narrative (IDN) has been growing, and Virtual Reality (VR) offers rich access to real-time biometric data such as facial expressions; yet this capability remains underexplored in novel IDN design. Existing approaches typically treat emotion input superficially, such as adjusting system difficulty or aesthetics, but rarely influence how players experience the narrative itself. Prior work also lacks a focus on a specific authored narrative. We propose an experimental affective interaction model that uses a VR headset's built-in face-tracking capability to recognize player emotional states, fostering "emotional perspective-taking" between the player and their embodied story character, thereby deepening the player's emotional connection to the character and their narrative engagement with the VR experience.

Density cube theory extends the canonical quantum density matrix $ρ_{ij}$ with the addition of an extra index to $ρ_{ijk}$. The elements of the density cube with two different indices, $ρ_{iij}$ and $ρ_{ijj}$, correspond to the real and imaginary parts of the off-diagonal element $ρ_{ij}$ of the density matrix and describe double-path interference, while those with three different indices describe non-canonical triple-path interference. In this letter, we propose an equation of motion for the density cube, obtained from the quantization of ternary Nambu dynamics, and find that pairs of triple-path interferences oscillate into each other.

Multi-behavior recommendation improves target-behavior prediction by exploiting heterogeneous auxiliary feedback (e.g., view, collect, and cart), yet its robustness is undermined by behavior-dependent noise and inconsistency. We argue that the key bottleneck is a representation-level failure caused by two coupled heterogeneities. First, intra-behavior representation entanglement arises when multi-hop propagation blends incidental signals with true preferences in the embedding space, making coarse spatial denoising unable to suppress noise without sacrificing informative niche signals. Second, inter-behavior reliability heterogeneity complicates cross-behavior fusion because the predictive value of auxiliary behaviors varies across users and contexts. Without reliability calibration, frequent yet unreliable signals may dominate aggregation and cause target-intent drift. To address this bottleneck, we propose Dynamic Spectral Denoising with Global-Context Attention for Multi-Behavior Recommendation (SpectraMB), a target-oriented model that performs representation purification before reliability-aware fusion. SpectraMB introduces Dynamic Feature-Level Spectral Filtering, which re-parameterizes embeddings along the feature dimension into a feature-frequency space and learns view-adaptive spectral modulation under target supervision, enabling component-wise purification without hand-crafted frequency assumptions. It further proposes Global-Context Attention Fusion, which uses a purified global representation as a context anchor to assess view compatibility and perform reliability-aware aggregation, while a residual global backbone preserves collaborative structure. Extensive experiments on three real-world datasets show that SpectraMB achieves the best results in most evaluation settings and exhibits improved robustness under noisy interactions.

Information Causality was introduced as a physical principle for constraining the set of nonlocal correlations. In recent work, we proposed an extension of Information Causality that allows correlations among Alice's inputs. This extended principle yields tighter constraints than the original formulation and recovers part of the quantum boundary in certain Bell scenarios. In this work, we further investigate the implications of extended Information Causality and apply it to scenarios beyond binary inputs and outputs. We derive a family of quantum Bell inequalities that strengthen previously known constraints on quantum correlations. Using these inequalities, we obtain an improved analytical bound for the Collins-Gisin family of Bell inequalities. We also apply Information Causality to entanglement-assisted random access codes and derive new theory-independent analytical bounds on the winning probability. For this latter task, we prove that, despite being stronger in general, the extended principle does not improve the bounds obtained from the original Information Causality principle. This suggests that the existing Information Causality bounds are optimal for this class of random access codes.

In this article, we study rational representations of $G=\operatorname{GL}_2(q)$, where $q$ is a prime power. Let $ρ$ be an irreducible representation of $G$ over $\mathbb{Q}$. Then $ρ$ affords the character \[ Ω(χ)=m_{\mathbb{Q}}(χ)\sum_{σ\in\operatorname{Gal}(\mathbb{Q}(χ)/\mathbb{Q})}χ^σ, \] for some irreducible complex character $χ$ of $G$, where $m_{\mathbb{Q}}(χ)$ denotes the Schur index of $χ$ over $\mathbb{Q}$, with the converse also holding. We obtain a combinatorial description for the counting of inequivalent irreducible $\mathbb{Q}$-representations of $G$ of distinct degrees. Furthermore, we present a method to construct an irreducible rational matrix representation $ρ$ of $G$ affording the character $Ω(χ)$, where $χ$ is an irreducible complex character of $G$ arising from parabolic induction. Finally, using the results from the rational representations of $G$, we derive an explicit combinatorial formula, depending only on $q$, for the Wedderburn decomposition of $\mathbb{Q}G$.

Correlations in the phase-space distribution of partons play an important role in the initial stage of relativistic heavy-ion collisions, where the matter is dense and far from equilibrium. Photons produced in the hot medium, which predominantly originate from two-parton initial states, are sensitive to two-particle correlations in the phase-space distribution. In this work, we study how pair correlations in non-equilibrium QCD matter affect in-medium photon production. We decompose the two-particle distribution as $\mathcal F_{ab}=f_a f_b+g_{ab}$, where $g_{ab}$ is the pair correlation. Focusing on the $2\to2$ quark--antiquark annihilation and Compton channels, we compute the leading-logarithmic photon spectrum by expanding the single-particle distribution and pair correlation in a spectral basis, thereby accommodating a broad class of two-particle distributions. For a rotationally invariant medium, we find that relative-angle modes of the pair correlation generate sign-changing modifications to the photon spectrum, with magnitudes that can be comparable to the factorized contribution. Thus, photon spectra, although single-particle observables, can measure the momentum correlations of the emitting medium and therefore probe the early-time hydrodynamization.