This article describes a natural piecewise Euclidean bi-simplicial cell structure for the space of $n$-element multisets in a fixed Euclidean rectangle. In particular, we highlight some connections with spaces of complex polynomials and permutahedra.

The Lindblad (GKLS) master equation, which represents the mathematical form for the general evolution of a density matrix, is a versatile and widely-used tool in open quantum systems. In contrast with the typical approach of imposing additional conditions on the system, such as weak coupling or energy conservation, we explore the structure of the equation with no assumptions. We demonstrate that general quantum dynamics can be expressed through a combination of free evolution, exchanges of some physical quantities (generalised charges), not necessarily commuting with the Hamiltonian, between the system and the bath, and pure dephasing. This result comprises a novel perspective on quantum master equations, employing physical processes as elemental parts. We use it to explore the dynamics and stationary states of a two-level system and show that strong coupling, particle exchange, and non-Abelian effects all share the same physical origin. Moreover, we demonstrate that the generalised Gibbs state for all three cases contains a non-commutation term, which has not been previously considered.

Many combinatorial optimization problems admit a maximin fairness variant, where the aim is to find a distribution over possible solutions which maximizes an expected worst-case outcome. However, the support for an optimal distribution may be exponential, which can be intractable to represent in the worst case. To this end, we propose a quantum based approach to solving distribution optimization problems. Expanding on work analyzing the Dynamical Lie Algebras of the Quantum Approximate Optimization Algorithm (QAOA), we show that with a finite number of layers, a QAOA ansatz can be constructed to capture any distribution over bitstrings. We show that the resulting circuit is able to effectively solve the Fair Cut Cover, a fair interpretation of the classical Fractional Cut Cover Problem. In addition, we show that our algorithm is provably better than classical approximations on certain graph structures and empirically outperforms these classical algorithms on tested instances.

We investigate the thermo solutal transport phenomena and deposition patterns during the evaporation of surfactant laden droplets experimentally and through theoretical scaling based analysis. Experiments were conducted using the sessile droplet configuration in the acrylic chamber for both hydrophilic and hydrophobic substrates. Infrared thermography and particle image velocimetry measurements were conducted during evaporation to illustrate the temperature and velocity distributions, respectively. Sodium dodecyl sulphate SDS surfactant molecules enhanced the evaporation rate with an increase in concentration for the hydrophobic surface. In contrast, the evaporation rate increased up to 0.5 CMC and then decreased for droplets on a hydrophilic substrate. The evaporation rates computed from the shadowgraphy imaging were explained using the average velocities obtained from the PIV analysis. It was found that advection within the droplet is strongly dependent on surfactant concentration and wettability. Further, the theoretically obtained Marangoni velocities were in close agreement with the experimental values. It was found that Marangoni solutal advection dominates other advection mechanisms, such as Marangoni thermal advection and buoyancy driven flow. However, surfactant crowding and viscous resistance with increasing surfactant concentration can dampen the increase in solutal advection. The surface tension and viscosity measurements were also conducted with variation in surfactant concentration to understand the suppression of advection by viscous forces. The computation of contact line velocities showed sudden fluctuations, illustrating stick slip behaviour during droplet drying, complementing microscopic visual observations.

The Klein Paradox -- the anomalous scattering of relativistic fermions off a high potential step -- signals the limit of the single-particle interpretation of the Dirac equation. While Quantum Field Theory (QFT) resolves this via pair production, the microscopic mechanism is often obscured by abstract formalism. In this work, we investigate this phenomenon through the framework of Analog Gravity and Condensed Matter Physics. We utilize a hydrodynamic model wherein a relativistic particle is treated as a localized elastic excitation (defect) within a continuous linear medium. We demonstrate that when the external stress (potential) exceeds the medium's binding energy threshold ($V > 2mc^2$), the system undergoes a mechanical instability analogous to dielectric breakdown. This instability naturally generates modes with inverted topological winding, which we identify as antiparticles. By solving the boundary conditions for this elastic system, we reproduce the transmission coefficients of Hansen and Ravndal and recover the Schwinger limit for pair production rates. This approach provides a clear pedagogical model based on continuum mechanics to visualize vacuum decay processes, suggesting that the "paradox" is simply the elastic response of a medium under supercritical stress. This mechanical analogy serves as a pedagogical bridge for graduate students in condensed matter physics and advanced materials science, offering a concrete visualization of vacuum instability that complements standard abstract QFT derivations.

Here we analyze multiple symmetry-inequivalent atomic configurations across the entire composition range of the isovalent and isostructural Mo$_x$W$_{1-x}$S$_2$ alloy using density-functional theory and Monte Carlo simulations. Our results show that although structural stability and energetics are largely composition-driven, the electronic and optical properties exhibit configuration dependence, with local atomic arrangements critically shaping band-edge splitting, valley structure, effective-mass anisotropy, and optical selection rules. In contrast to the pristine monolayers, even in the absence of spin-orbit coupling (SOC), splitting of the band edges at the $K$ point is observed across the entire composition range. In particular, while the valence-band maximum (VBM) remains largely robust, the conduction-band minimum (CBM) shows strong configuration-dependent splitting from few meV up to hundredths of meV. This behaviour leads to a non-trivial dependence of the valley energetics. Configurations with well-separated conduction bands support additional optically active transitions beyond the conventional A and B excitons in MoS$_2$ and WS$_2$ monolayers, whereas nearly degenerate cases exhibit a reduced number of allowed transitions, observed for specific configurations at $x = 1/3$ and $x = 2/3$. These results demonstrate that the number and character of optically active transitions are governed not only by composition, but also by the microscopic arrangement of atoms. Moreover, we found the hole effective masses at the VBM show configuration-dependent anisotropy, reflecting sensitivity to local symmetry breaking and implying direction-dependent transport.

We report zero-field (ZF) and transverse-field (TF) muon-spin rotation/relaxation ($μ$SR) measurements on superconducting Li$_{0.95}$FeAs ($T_{\rm c}\simeq16.0$ K) grown by a high-pressure self-flux method. The ZF-$μ$SR data show no detectable change of the electronic relaxation rate on cooling through $T_{\rm c}$, providing no evidence for time-reversal-symmetry breaking in the superconducting state. TF-$μ$SR measurements reveal a well-developed vortex response with strong flux pinning and a negligible nonsuperconducting contribution, confirming that superconductivity is a bulk property of the sample. From the second moment of the internal field distribution we determine a low-temperature in-plane magnetic penetration depth $λ_{ab}= 245(15)$ nm. The temperature dependence of the normalized superfluid density is well described by an effective two-gap model with $Δ_1 = 2.0(2)$ meV and $Δ_2 = 0.7(2)$ meV. A quantitative comparison with ARPES-based band weights shows that the $μ$SR response is dominated by the Fermi-surface sheets carrying the intermediate and small superconducting gaps, whereas the band hosting the largest gap contributes only about 3\% to the total superfluid density and is therefore not resolved in the present analysis. Taken together, these results establish Li$_{0.95}$FeAs as a bulk multigap superconductor without detectable time-reversal symmetry breaking and show how $μ$SR reconciles the gap scales reported by bulk and surface-sensitive probes in this multiband system.

Thermal measurements constrain the physical properties of icy satellite surfaces, including grain size, porosity, and regolith structure. On Europa, analyses of the Galileo Photopolarimeter-Radiometer (PPR) dataset revealed thermal inertia heterogeneities, but limited resolution hindered detailed characterization. We reanalyze the PPR dataset to derive maps of Europa's albedo and thermal inertia, and infer the microphysical properties of its icy regolith. Using the KRC thermal model, we fit brightness temperatures and interpret the results with conductivity models of porous ice to constrain grain size, porosity, and sintering processes. We find a mean Bond albedo of 0.64 pm 0.06 and a mean thermal inertia of 56 pm 17 tiu. Thermal inertia varies significantly, with a low-inertia equatorial band (39 pm 7 tiu) and higher values at mid-latitudes and on the trailing hemisphere, likely reflecting compositional differences. These values imply a porous regolith with grain sizes from micrometers to centimeters and an average porosity of 0.61 pm 0.1. Thermal inertia shows little correlation with geological units except for the Pwyll ejecta, which exhibit higher values. Instead, its agreement with sputtering rates suggests sputtering-driven sintering as a key process. Electron-driven sintering appears inefficient, while temperature-gradient metamorphism may enhance grain growth at depth. Modeled surface temperatures range from 67 to 148 K. These results provide a framework for interpreting future observations from Europa Clipper and JUICE.

This paper presents a comparative AC Optimal Power Flow study on a real world city scale islanded microgrid with high solar PV penetration, implemented within a Digital Twin framework. Four objective function cases economic dispatch, voltage stress exposure via PV power factor variation, then optimal load delivery, and capacitor enhanced economic dispatch as recovery options are evaluated over a 47 hour time series horizon on the same network under a shared loading scenario. Optimization sensitivities OSQ and OSV extracted from all cases are combined into a composite placement score used to rank candidate buses for shunt capacitor upgrades. A post processing planning optimization balances capacitor upgrade cost against avoided value-of-lost-load, enabling direct economic comparison of infrastructure investment versus reliability penalties. Results demonstrate that sensitivity guided capacitor placement restores full load service across the horizon and provides targeted reactive support at a quantifiable cost trade off against corrective load shedding.

In high-stakes AI-supported decisions, considerations are not purely technical but involve moral judgments about fairness, responsibility, and harm. While prior research has focused mainly on functional or behavioral alignment, this paper argues that moral alignment may be a more fundamental dimension of human-AI decision-making. Moral alignment is defined as the perceived congruence between the values embedded in an AI system's decision logic and the moral intuitions of stakeholders. Building on Moral Foundations Theory, the paper adopts a multi-stakeholder perspective and highlights why moral (mis)alignment matters for the meaningful integration of AI in sensitive contexts.

Twisted bilayer graphene provides a paradigmatic platform for exploring the interplay between electronic topology and strong correlations. Within the topological heavy fermion model [Song and Bernevig, Phys. Rev. Lett. 129, 047601 (2022)], topology and electron interactions are brought together by including a weak hybridization between the bands of itinerant $c$- and localized $f$-electrons. Hybridization infuses concentrated Berry curvature into the $f$-band, while leaving it flat. These band features have motivated recent proposals of a Mott semimetal phase above the flavor-ordering temperature at charge neutrality. In this work, we develop an analytic theory of the quasiparticle dispersion and lifetime in the Mott semimetal. We reformulate the interacting flat-band Hamiltonian as an on-site Hubbard interaction defined on a set of non-orthogonal orbitals, and compute the electron Green's function using the equation-of-motion method, in close analogy with the Hubbard-III approximation. Unlike the conventional Hubbard model, in our case this approximation is controlled by a well-defined small parameter in the theory. We evaluate the electron self-energy and demonstrate the emergence of well-defined low-energy quasiparticles with the dispersion and relaxation rate proportional to the interaction strength. The quasiparticle spectrum is well-resolved in energy and in momentum down to the very vicinity of the Fermi level. Our results illustrate unconventional spectral properties arising from strong correlations and nontrivial quantum geometry, and have direct relevance for spectroscopic probes such as quantum twisting microscope experiments.

We propose a sequential quadratic programming (SQP) algorithm for inequality constrained optimization that is robust to the presence of bounded noise in function and derivative evaluations. We cover the case where constraint evaluations contain noise as well as the objective. The proposed algorithm is a line search SQP method with relaxations to deal with noise. We study the effect of noise on the global convergence behavior of the algorithm. We implement the algorithm with noise-aware quasi-Newton updates, and numerically observe that the algorithm can achieve accuracy proportional to the noise level and problem-dependent parameters, as suggested by the theory.

We develop a general framework to calculate the many-body density of states (DOS) of isolated and interacting quantum systems. Based on the generalized coherent state formalism and the Simon-Lieb bounds for a quantum partition function, our method provides a general method of calculation for the DOS in high-dimensional irreducible sectors. This framework further provides rigorous bounds for the ground state energy in each sector and enables the calculation of microcanonical observables across the entire spectrum. Using the Lipkin-Meshkov-Glick (LMG) model as a test bed, we validate our framework by successfully identifying quantum phase transitions (QPTs) and excited-state quantum phase transitions (ESQPTs) across spin sectors. Unlike existing model-specific numerical or analytical techniques, our formalism relies on general underlying symmetries, making it broadly applicable. Applying our method to the ferromagnetic transverse field Ising chain with power law interactions, we demonstrate that its highest-spin-sector DOS is qualitatively identical to that of LMG-type Hamiltonians. Our work establishes a versatile and computationally efficient bridge between algebraic structure and many-body thermodynamics.

We study the Ricci-Bourguignon flow on warped product manifolds with noncompact base. This setting leads naturally to a parabolic partial differential equation on the space of smooth warping functions, arising from the necessary and sufficient conditions for a warped metric to evolve under the flow. One of our main results establishes a gradient estimate for this equation, providing the analytic input for the geometric applications developed herein and, in particular, recovering classical gradient estimates for the heat equation under the Ricci flow. Furthermore, we show how to construct explicit warped solutions to the Ricci-Bourguignon flow and present examples that are not only of independent interest but also illustrate and support our results

Streamlines have been widely used to represent and analyze various steady vector fields. To sufficiently represent important features in complex vector fields (like flow), a large number of streamlines are required. Due to the lack of a rigorous definition of features or patterns in streamlines, user interaction and exploration are required to achieve effective interpretation. Existing approaches based on clustering or pattern search, while valuable for specific analysis tasks, often face challenges in supporting interactive and level-of-detail exploration of large-scale curve-based data, particularly when real-time parameter adjustment and iterative refinement are needed. To address this, we design and implement an interactive web-based system. Our system utilizes a Curve Segment Neighborhood Graph (CSNG) to encode the neighboring relationships between curve segments. CSNG enables us to adapt a fast community detection algorithm to identify coherent flow structures and spatial groupings in the streamlines interactively. CSNG also supports a multi-level exploration through an enhanced force-directed layout. Furthermore, our system integrates an adjacency matrix representation to reveal detailed inter-relations among segments. To achieve real-time performance within a web browser, our system employs matrix compression for memory-efficient CSNG storage and parallel processing. We have applied our system to analyze and interpret complex patterns in several streamline datasets. Our experiments show that we achieve real-time performance on datasets with hundreds of thousands of segments.

High-dimensional genetic covariate selection in population pharmacokinetic (PK) models is challenging due to the cohort's restricted size and high correlation among single-nucleotide polymorphisms (SNPs). We propose a fully Bayesian, single-stage framework that jointly infers nonlinear mixed effect model (NLMEM) parameters and SNP effect sizes, providing coherent posterior uncertainty and inclusion summaries within a single model fit. We compare five sparsity-inducing priors -- Spike-and-Slab, Hierarchical Lasso, Regularized Horseshoe, R2--D2, and the $\ell_1$-ball -- calibrated through effect-size and sparsity targets. In simulations, all priors showed low false-discovery rates around $0$--$0.08$ under the null, and recovered the causal signal under the alternative, with peak $F_1$ scores around $0.8$--$0.85$ under reasonable inclusion cutoffs. Spike-and-Slab was especially attractive because it provides analytical posterior inclusion probabilities directly, while among priors requiring tolerance-based proxy inclusion summaries, the $\ell_1$-ball combined similarly strong recovery with the most stable behavior across tolerance values. On genetic and PK data from the ANRS 12154 study in 129 Cambodians living with HIV and receiving nevirapine, posterior predictive checks indicated adequate calibration and PK parameter inference remained stable across priors. While the dominant signal was robust across priors, additional candidate SNPs showed only partial agreement in ranking and more prior-sensitive effect-size estimates. These results support Bayesian variable selection within joint NLMEM as a principled approach for pharmacogenetic analyses when uncertainty quantification and regularization are central.

Nonreciprocal conversion is essential for protecting sources and enabling unidirectional signal routing in photonic, phononic, electronics, and quantum systems, yet conventional implementations rely on magnetic bias that could be challenging to integrate on chip. We propose a magnet-free scheme for frequency-domain nonreciprocity based on sequential, time-gated couplings in a three-mode system. By activating interactions in a fixed temporal order, the forward and reverse frequency conversion pathways acquire unequal dwell times in a lossy intermediate mode, producing strong nonreciprocity without requiring nonlinearities or magnetic materials. Using a harmonic-balance formulation and a Dyson-Born expansion, we derive a compact analytical expression for the isolation ratio that reveals the roles of Floquet sidebands, duty-cycle control, modulation frequency, and dissipation. The results are confirmed by direct time-domain simulations over a wide parameter range. From these results, we extract practical design rules for optimizing isolation through temporal sequencing, loss engineering, and modulation timing. The framework is general and directly applicable to integrated platforms in photonics, phononics, microwave electronics, and superconducting circuits.

Resilience in cyber-physical systems (CPS) is the fundamental ability to maintain safety and critical functionality despite adverse "perturbations," which includes security attacks, environmental disruptions, and hardware or software failures. This survey provides a comprehensive review of CPS resilience, framing the field through five interconnected themes that are required in an integrated whole to achieve real-world resilience. The article first posits that resilience is a system-wide property emerging from interactions between hardware, software, and human users. Second, it addresses the challenges of learning-enabled CPS, which often operate in data-scarce environments characterized by imbalanced or noisy data, requiring innovative solutions like synthetic data generation and foundation model adaptation. Third, the survey examines proactive measures for resilience, which include distinctive aspects of verification, testing, and redundancy. Fourth, it explores recovery mechanisms, moving beyond traditional fault models to design "just good enough" recovery strategies that prioritize safety-critical functions during perturbations. Finally, it highlights the central role of the human, focusing on the different levels of human intervention, the necessity of trust calibration, and the requirement for explainable AI to support human-CPS teaming. These themes are illustrated through representative application domains, primarily Connected and Autonomous Transportation Systems (CATS) and Medical CPS (MCPS). By integrating the five interconnected themes, this survey provides a systematic roadmap for achieving the resilient CPS in increasingly complex and adversarial environments.

Pebble drift plays a central role in modern planet formation models. In this work we carry out planet formation simulations (including pebble accretion and migration) for a range of disc parameters to investigate (a) the impact of the snowline pebble mass flux on final planet orbits and masses, and (b) the back-reaction of growing and migrating planets on the snowline pebble fluxes in their natal discs. We find a strong correlation between the snowline pebble flux (at the time of protoplanet insertion) and the final planet mass. The correlation is continuous in disks with high turbulence levels ($α=10^{-3}$), but exhibits a step function at lower turbulence ($α=10^{-4}$), with giant planet formation requiring (initial) snowline pebble mass fluxes exceeding $100~\mathrm{M_\oplus Myr^{-1}}$. We find qualitative agreement between pebble mass fluxes inferred for discs aged ${\sim}1~\mathrm{Myr}$ and our planet-containing models, especially for larger disks ($\geq$40 au), high $α$ ($10^{-3}$), and low $v_\mathrm{frag}$ ($3\mathrm{~m~s}^{-1}$). Additionally, giant planets in high turbulence disks are found to perturb the snowline pebble flux only temporarily (for ${\approx}10^{5-6}\mathrm{~yr}$) due to them quickly growing and migrating across the snowline. Our simulations show that currently observed pebble fluxes can indeed be used to constrain planet formation simulations, emphasizing that planet formation via pebble accretion is broadly in agreement with the currently available constraints from disc evolution as provided by JWST.

Existing language-based information-flow control (IFC) tools face a fundamental tension: Denning-style systems that track explicit and implicit flows at the variable level typically require compiler modifications, while more coarse-grained approaches, including recent work Cocoon, avoid compiler changes but impose more restrictive programming models. We present Filament, a Denning-style static IFC library for Rust that requires no compiler modifications. Filament addresses three key challenges in building a practical IFC library for Rust. First, it enables fine-grained explicit-flow checking with minimal annotation overhead by leveraging Rust's type inference. Second, it introduces pc_block!, a lightweight construct for enforcing implicit flows via a compile-time program counter label, without requiring compiler support. Third, it provides fcall! and mcall! macros to support seamless and safe interoperability with standard and third-party libraries. Our evaluation shows that Filament incurs negligible compile-time overhead and requires only modest annotations. Moreover, compared to Cocoon, Filament offers a more permissive programming model, reducing the need for frequent escape hatches that bypass security checks.

Chemical reaction networks, or CRNs, are known to stably compute semilinear Boolean-valued predicates and functions, provided that all reactions are irreversible. However, this property does not hold for wet-lab implementations, as all chemical reactions are reversible, even at very slow rates. We study the computational power of CRNs under the reverse-robust computation model, where reactions are permitted to occur either in forward or in reverse up to a cutoff point, after which they may only occur in forward. Our main results show that all semilinear predicates and all semilinear functions can be computed reverse-robustly, and in fact, that existing constructions continue to hold under the reverse-robust computational model. A key tool used to prove correctness under the reverse-robust computation model is invariants: linear (or linear modulo some $m$) combinations of the counts of the species that are preserved by all reactions.

This study investigates whether speech-based depression detection models learn depression-related acoustic biomarkers or instead rely on speaker identity cues. Using the DAIC-WOZ dataset, we propose a data-splitting strategy that controls speaker overlap between training and test sets while keeping the training size constant, and evaluate three models of varying complexity. Results show that speaker overlap significantly boosts performance, whereas accuracy drops sharply on unseen speakers. Even with a Domain-Adversarial Neural Network, a substantial performance gap remains. These findings indicate that depression-related features extracted by current speech models are highly entangled with speaker identity. Conventional evaluation protocols may therefore overestimate generalization and clinical utility, highlighting the need for strictly speaker-independent evaluation.

In this paper, we consider nonlinear optimization problems with a stochastic objective function and deterministic equality constraints. We propose an inexact two-stepsize stochastic sequential quadratic programming (SQP) algorithm and analyze its worst-case complexity under mild assumptions. The method utilizes a step decomposition strategy and handles stochastic gradient estimates by assigning different stepsizes to different components of the search direction. We establish the first known $\mathcal{O}(ε_c^{-2})$ worst-case complexity with respect to the infeasibility measure when no constraint qualification is assumed and a worst-case complexity of $\mathcal{O}(ε_c^{-1})$ when LICQ holds, matching the best known result in the literature. In addition, under mild conditions, our method achieves the optimal $\mathcal{O}(ε_L^{-4})$ complexity with respect to the gradient of the Lagrangian regardless of constraint qualifications. Our results provide the first complexity guarantees for the popular Byrd-Omojukun step decomposition strategy and verify its theoretical efficacy. Numerical experiments show that our algorithm has a superior infeasibility convergence performance and a competitive KKT convergence rate compared to the state-of-the-art stochastic SQP method.

Dynamic Mode Decomposition (DMD) is a data-driven method for approximating the spatiotemporal modes of a system. The eigenvectors and eigenvalues of the system are approximated from a series of time-snapshots of the state variables. The standard formulation of DMD is subject to strict assumptions concerning the time-spacing of the snapshots and is biased by measurement noise. Variations on the method have been developed to address these shortcomings, but the problem is still open. Motivated by the effectiveness of Galerkin methods in the field of model discovery, a weak formulation of DMD is presented, weak-DMD. Weak-DMD precludes timestep considerations and also filters noise. Results for two nuclear engineering applications and the flow of fluid past a cylinder are given and compared with a state of the art DMD algorithm.

Surface-enhanced Raman scattering (SERS) combines analyte-specificity and single-molecule sensitivity, but its potential is limited by slow readout where sophisticated nanosensors are analysed in a serial fashion, one particle at a time. We introduce SERS lock-in sampling to resolve the decades-old trade-off between spectral resolution and widefield imaging. By leveraging the inherent sparsity of Raman spectra, we demonstrate that a simple digital lock-in scheme allows high-quality chemical imaging far beyond the Nyquist-Shannon limit. Our approach integrates an in-situ temporal reference to transform mechanical jitter into an exploitable feature, enabling near-random sampling. We validate SERS lock-in sampling through the multiplexed and simultaneous imaging of thousands of individual SERS-encoded sensors, achieving an orders-of-magnitude throughput-increase over the state-of-the-art. Furthermore, we demonstrate volumetric 3D chemical imaging in biomedically relevant matrices. This robust, computationally simple strategy transforms SERS from a point-observation tool to an imaging modality for clinical diagnostics and real-time chemical observations.

In 1985, Grassmann, Taksar, and Heyman published their celebrated paper, in which they introduced a numerically stable algorithm for computing the stationary probabilities of a finite-state Markov chain, one of the key performance quantities in both theory and applications. This algorithm later became the well-known GTH algorithm (or the state-reduction method) in the literature, becoming one of the standard algorithms in applied probability. Later, this algorithm was extended to deal with the stationary distributions of block-structured Markov chains with repeating rows. In this paper, we focus on the block-form GTH algorithm and organize it into two parts. In the first part, we connect the block-form GTH algorithm to censored Markov chains and the block-form $RG$-factorization. We show that the forward block-elimination and back block-form substitution of the block-form GTH algorithm are equivalent to solving a system formulated using the $RG$-factorization in two steps. We also show that this connection remains valid when the block-form GTH algorithm is extended to infinite-state Markov chains. It is well known that censoring an infinite-state Markov chain to a finite state space yields a stationary distribution that provides a best approximation to the stationary distribution of the original infinite-state Markov chain. In the second part, we first derive an explicit expression for the censored Markov chain from the infinite state space to a finite space for Markov chains of $M/G/1$ type. Based on this expression, we propose a renormalized approximated censored transition matrix (RA-CM). The resulting stationary distribution is shown to be asymptotically optimal in terms of approximation error. We compare the approximation error of the RA-CM with the error arising from the last-block-column augmentation.

We present detailed, multi-wavelength analysis of GRB 210704A: a Fermi Gamma-ray Burst Monitor discovered and Fermi Large Area Telescope (LAT) detected gamma-ray burst (GRB). The burst is dominated by a short ($\approx 2$ s) pulse followed by weaker, softer emission. We line stack our afterglow spectrum and determine the most likely redshift to be $z = 2.34$. This is corroborated by the photometric redshift of the extended source underlying the GRB. The spectral energy distribution fit parameters, late-time imaging, as well as the GRB's energetics, spectral lag, and location point to a collapsar nature. Follow-up observations reveal excess optical/infrared emission with respect to a standard afterglow, peaking around $T_0 + 7$ d ($2$ d in the rest frame). The excess is extremely luminous ($M_{r} = -22.0$ mag) and rapidly evolving. Strikingly, it resembles the emission seen in recently discovered Einstein Probe fast X-ray transients EP241021a and EP240414a, as well as the population of luminous fast blue optical transients (LFBOTs). This provides a link between these sources and GRBs. Fermi/LAT observations imply a high Lorentz factor, making this a case where LFBOT-like emission is also associated with a powerful successfully launched jet. We model the excess as likely coming from an energetic refreshed shock.

Ocean dynamics are often sidelined in exoplanet climate studies due to the high computational cost of fully coupled atmosphere-ocean general circulation models (GCMs). However, ocean heat transport (OHT) can play a critical role in shaping the climate and observables of terrestrial planets. As a compromise, most exoplanet GCMs rely on slab ocean models without OHT. Here, we present an improved compromise - a fast and physically grounded dynamical slab ocean model, implemented in the Generic Planetary Climate Model (Generic-PCM). The model extends previous frameworks by incorporating a Sverdrup balance formulation for wind-driven Ekman transport, the first application of the Gent-McWilliams parameterisation of mesoscale eddies in a slab ocean model, and a spectrally and thickness-dependent treatment of sea ice and snow albedo. In aquaplanet simulations, enabling OHT produces substantial changes in both surface climate and atmospheric circulation, including cooler tropical sea surface temperatures, reduced sea ice, and the emergence of a double-banded equatorial precipitation pattern driven by Ekman-induced upwelling. The resulting OHT profiles show first-order agreement with fully coupled atmosphere-ocean GCMs. Applied to modern Earth, the model reproduces key large-scale climate properties, including a global mean surface temperature of 13°C (within 1°C of observations), planetary albedo of 0.32 (within 0.01), and sea ice extent with significantly reduced seasonal biases relative to simulations without OHT. Due to model parallelisation, these improvements are achieved at almost no additional computation cost compared to OHT-disabled simulations run over the same number of model years. This enables long integrations, making the model particularly well suited for exoplanet and paleoclimate studies where broad parameter exploration is essential.

Extragalactic Fast X-ray Transients (EFXTs) represent an emerging class of high-energy phenomena characterized by X-ray outbursts lasting from tens to hundreds of seconds. However, for more than half of the EFXTs, their physical origins remain elusive. In this Letter, we report the discovery of EP250302a, a luminous EFXT detected by the Einstein Probe (EP) at a redshift of $z = 1.131$. The multi-wavelength light curves of EP250302a reveal remarkable temporal features that distinguish it from the previously known EP-detected EFXT population, most notably a needle-like X-ray flare accompanied by smooth optical rebrightening during the afterglow phase. We suggest that the distinct X-ray and optical behaviors constitute the first observed instance of late-time violent collision of two relativistic shells in an EFXT. Drawing on insights from GRB studies, such a collision process strongly indicates the reactivation of a central engine, making EP250302a-like transients a unique laboratory for probing the late-time activity and jet physics of EFXT central engines.

We present a theoretical analysis of the one-loop effective potential of a self-interacting real scalar field in the presence of two parallel conducting plates with geometric roughness. Using WKB methods to evaluate the spectral density of the modified Laplace-Beltrami operator, together with contour integration within a $ζ$-function regularization scheme, we derive analytical expressions for the quantum corrections to the effective potential induced by perturbative boundary roughness and finite temperature. Furthermore, we compute explicit contributions to the Casimir energy and to the topological mass generation associated with the geometry.