The choice of sample size in the context of co-primary endpoints for a randomised trial is discussed. Current guidance can leave endpoints with unequal marginal power. A method is provided to achieve equal marginal power by using the flexibility provided in multiple testing procedures. A comparison is made to several choices of rule to determine the sample size, in terms of the study design and its operating characteristics.

Bi-conjugate gradient (Bi-CG) and bi-conjugate residual (Bi-CR) methods are underlying iterative solvers for linear systems with nonsymmetric matrices. Residual smoothing is a standard technique for obtaining smooth convergence behavior of residual norms; additionally, it represents the transformation between iterative methods. For example, the residuals of the CR method can be obtained by applying a smoothing scheme to those of the CG method for symmetric linear systems. Based on this relationship, the transformation from Bi-CG residuals to Bi-CR residuals using a smoothing scheme was examined in our previous study [Kawase, A., Aihara, K.: Transformation from Bi-CG into Bi-CR Using a Residual Smoothing-like Scheme. AIP Conference Proceedings (2026)]; however, we only provided heuristic and experimental observations. In the present study, we provide a detailed discussion on the theoretical aspects of these transformations. Specifically, we prove that the resulting algorithm transformed from the Bi-CG method using the residual smoothing technique has the same bi-orthogonal properties as those of the original Bi-CR method. We also present a more concise transformation algorithm and its numerical example. These analyses complement our previous study and provide theoretical validity of the residual transformation between the Bi-CG and Bi-CR methods.

A growing number of critical workflow applications leverage a streamlined edge-hub-cloud architecture, which diverges from the conventional edge computing paradigm. An edge device, in collaboration with a hub device and a cloud server, often suffices for their reliable and efficient execution. However, task allocation in this streamlined architecture is challenging due to device limitations and diverse operating conditions. Given the inherent criticality of such workflow applications, where reliability and latency are vital yet conflicting objectives, an exact task allocation approach is typically required to ensure optimal solutions. As no existing method holistically addresses these issues, we propose an exact multi-objective task allocation framework to jointly optimize the overall reliability and latency of a workflow application in the specific edge-hub-cloud architecture. We present a comprehensive binary integer linear programming formulation that considers the relative importance of each objective. It incorporates time redundancy techniques, while accounting for crucial constraints often overlooked in related studies. We evaluate our approach using a relevant real-world workflow application, as well as synthetic workflows varying in structure, size, and criticality. In the real-world application, our method achieved average improvements of 84.19% in reliability and 49.81% in latency over baseline strategies, across relevant objective trade-offs. Overall, the experimental results demonstrate the effectiveness and scalability of our approach across diverse workflow applications for the considered system architecture, highlighting its practicality with runtimes averaging between 0.03 and 50.94 seconds across all examined workflows.

We study the Merton portfolio management problem within a complete market, non constant time discount rate and general utility framework. The non constant discount rate introduces time inconsistency which can be solved by introducing sub game perfect strategies. Under some asymptotic assumptions on the utility function, we show that the subgame perfect strategy is the same as the optimal strategy, provided the discount rate is replaced by the utility weighted discount rate $ρ(t,x)$ that depends on the time $t$ and wealth level $x$. A fixed point iteration is used to find $ρ$. The consumption to wealth ratio and the investment to wealth ratio are given in feedback form as functions of the value function.

Resonant laser excitation of a two-level system with subsequent single-photon emission can be used to generate single photons with high indistinguishability or Hong-Ou-Mandel (HOM) visibility. However, spectral overlap between excitation laser and emitted photons generally poses significant challenges. Furthermore, emitter re-excitation intrinsically limits achievable single-photon purity. Established solutions mitigate these issues at significant cost to source efficiency and with increased source complexity. This motivates the use of few-level systems with spectral separation of excitation and emission pathways. One option is a three-level cascade. However, without targeted lifetime engineering of emitting states, the cascade naturally limits achievable photon indistinguishability. Here we study a semiconductor quantum dot with resonant and selective cavity-enhancement of biexciton-to-exciton transition. Following resonant two-photon excitation of the biexciton state, we collect the emitted single photon with the cavity. This approach circumvents emitter re-excitation and naturally introduces spectral separation of excitation laser and emitted single photon. Supported by first experimental results, we demonstrate theoretically that with selective Purcell enhancement, the observed quality quantifiers of single-photon emission (purity, equivalently $g^{(2)}(0)$, and HOM visibility $\mathcal{V}$, equivalently indistinguishability) are competitive with respect to high-quality deterministic quantum-dot single-photon sources. This is already achieved without systematic optimization or targeted system engineering, which firmly places the reported approach as a viable route to the next generation of highest-quality quantum-dot based deterministic single-photon sources.

Evaluating the performance of different administrative regions within a country is crucial for its development and policy formulation. The performance evaluators are mostly based on health, education, per capita income, awareness, family planning and so on. Not only evaluating regions, but also ranking them is a crucial step, and various methods have been proposed to date. We aim to provide a ranking system for Indian states that uses a Bayesian approach via the famous Bradley-Terry model for paired comparisons. The ranking method uses indicators from the NFHS-5 dataset with the prior information of per-capita incomes of the states/UTs, thus leading to a holistic ranking, which not only includes human development factors but also take account the economic background of the states. We also carried out various Markov chain Monte Carlo diagnostics required for the reliability of the estimates of merits for these states. These merits thus provide a ranking for the states/UTs and can further be utilised to make informed policy decisions.

We present a general electromagnetic description for dipoles confined to surfaces with oblique dipole moment orientations, extending the conventional in-plane (IP) and out-of-plane (OOP) treatments. This description is useful for describing localized polarization in, \textit{e.g.}, van der Waals heterostructures, thin films of molecular aggregates, and metal-dielectric interfaces. The theory is suitable for any material with vanishingly thin thickness relative to the light wavelength, independent of the geometry of the material and the media interfacing it. We apply the formalism to a uniaxial excitonic sheet, covering a large number of two-dimensional (2D) materials and organic thin films. Our theory reveals pairs of polaritonic resonances originating from the IP and OOP components of the excitonic dipole moment. The formalism suggests experimentally accessible signatures of dipole moment orientation, enhanced by near-field probes. This work proposes a unified language for the description of 2D materials, thin films and interfaces with anisotropic dipolar responses.

Clock synchronization is necessary for communication and distributed computing tasks. Previous schemes based on photon timing correlations use pulsed light or photon pairs for their strong timing correlations. In this work, we demonstrate successful synchronization of crystal clocks using weakly time-correlated photons of 180 ns coherence time from a bunched light source. A synchronization timing jitter of 10 ns is achieved over symmetric -102 dB optical channel loss between two parties, over a span of 25 hours. We also present a model that gives better estimates to the coherence peak finding success probabilities under low signal.

We study verification problems for history-constrained systems (HCS), a model of guarded computation that uses nested systems. An outer system describes the process architecture in which a sequence of actions represents the communication between sub-systems through a global bus. Actions are either permitted or blocked locally by guards; these guards read and decide based on the sequence of actions so far in the global bus. When HCS have both the outer systems and the local guard controllers modelled by finite automata, we show they have the same expressive power as regular languages and finite automata, but they are exponentially more succinct. We also analyse games on this model, representing the interaction between environment and controller, and show that solving such games is EXPTIME-complete, where the lower bound already holds for reachability/safety games and the upper bound holds for any $ω$-regular winning condition. Finally, we consider HCS with guards of greater expressive power, Vector Addition Systems with States (VASS). We show that with deterministic coverability-VASS guards the reachability problem is EXPSPACE-complete, while with reachability-VASS the problem is undecidable.

Automotive software increasingly outpaces hardware availability, forcing late integration and expensive hardware-in-the-loop (HiL) bottlenecks. The InnoRegioChallenge project investigated whether a virtual test and integration environment can reproduce electronic control unit (ECU) behavior early enough to run real software binaries before physical hardware exists. We report a prototype that generates instruction-accurate processor models in SystemC/TLM~2.0 using an agentic, feedback-driven workflow coupled to a reference simulator via the GNU Debugger (GDB). The results indicate that the most critical technical risk -- CPU behavioral fidelity -- can be reduced through automated differential testing and iterative model correction. We summarize the architecture, the agentic modeling loop, and project outcomes, and we extrapolate plausible technical details consistent with the reported qualitative findings. While cloud-scale deployment and full toolchain integration remain future work, the prototype demonstrates a viable shift-left path for virtual ECU twins, enabling reproducible tests, non-intrusive tracing, and fault-injection campaigns aligned with safety standards.

Some have claimed that the future development of powerful AI systems would enable the United States to shift the international balance of power dramatically in its favor. Such a feat may not be technically possible; even so, if American AI development is perceived as a sufficiently severe threat by its nation-state adversaries, then the risk that they take extreme preventive action against the United States may rise. To bolster its security against preventive action, the United States could aim to pursue a strategy of restraint by demonstrating that it would not use powerful AI to threaten the survival of other nations. Drawing from the international relations literature that explores how states can make credible commitments, we sketch a set of options that the United States could employ to implement this strategy. In the most challenging setting, where it is certain that the US will unilaterally obtain powerful new capabilities, it is difficult to credibly commit to restraint, though an approach that layers significant policy effort with technical breakthroughs may make credibility achievable. If an adversary has realistic levels of uncertainty about the capabilities and intentions of the United States, a strategy of restraint becomes more feasible. Though restraint faces difficulties, it deserves to be weighed against alternative strategies that have been proposed for avoiding conflict during the transition to a world with advanced AI.

For a bounded open set $Ω\subset \mathbb{R}^N$ with $N\geq 2$, and for positive continuous functions $w,g$ on $\overlineΩ$, we consider the weighted eigenvalue problem \begin{equation*} \mathcal{L}_{w} u =τgu, \end{equation*} where $\mathcal{L}_{w}$ is the weighted logarithmic potential operator on $L^2(Ω)$ as defined below: \begin{equation*} \mathcal{L}_{w} u(x)=\int_Ω\log\left(\frac{w(x)w(y)}{|x-y|}\right)u(y)dy. \end{equation*} We study the monotonicity and continuity of the largest positive eigenvalue $τ_{w,g}^+(Ω)$ with respect to $Ω$, $w$, and $g$. We also establish that $τ_{w,g}^+(Ω)$ satisfies a reverse Faber Krahn inequality under polarization. We provide a sufficient condition for the existence of a negative eigenvalue in terms of the weighted transfinite diameter of $Ω$, under the assumption that $\log w$ is superharmonic. For $Ω\subset \mathbb{R}^2$, if $Δ\log w $ is a constant $C$, we show that 0 can be an eigenvalue of $\mathcal{L}_{w}$ only when $C=\frac{2π}{|Ω|}$. For such domains, if $\log w$ is a harmonic function on $Ω$, we provide a representation formula for the eigenfunctions. Using this representation, we establish variants of the maximum principles that give some insight into the geometry of these eigenfunctions.

The SIDDHARTA-2 experiment at the DA$Φ$NE collider of INFN-LNF performs high precision light kaonic atoms X-ray spectroscopy to investigate the kaon-nucleon(s) strong interaction in the low-energy (O(10 keV)) regime. A large area Silicon Drift Detectors (SDDs) system has been developed to carry out these measurements. The collaboration aims to extend the measurements campaign to higher mass kaonic atoms, which exhibit transition lines at increased X-ray energies. In this context, the spectroscopic response of the SIDDHARTA-2 SDD system was investigated in terms of linearity and energy resolution up to 50 keV. An accuracy of the energy calibration procedure $ΔE/E < 10^{-3}$ was achieved.

We present a relative forward error analysis of a mixed-precision preconditioned one-sided Jacobi algorithm, analogous to a two-sided version introduced in [N. J. Higham, F. Tisseur, M. Webb and Z. Zhou, SIAM J. Matrix Anal. Appl. 46 (2025), pp. 2423-2448], which uses low precision to compute the preconditioner, applies it in high precision, and computes the singular value decomposition using the one-sided Jacobi algorithm at working precision. Our analysis yields smaller relative forward error bounds for the computed singular values than those of standard SVD algorithms. We present and analyse two approaches for constructing effective preconditioners. Our numerical experiments support the theoretical results and demonstrate that our algorithm achieves smaller relative forward errors than the LAPACK routines $\texttt{DGESVJ}$ and $\texttt{DGEJSV}$, as well as the MATLAB function $\texttt{svd}$, particularly for ill-conditioned matrices. Timing tests show that our approach accelerates the convergence of the Jacobi iterations and that the dominant cost arises from a single high-precision matrix-matrix multiplication. With improved software or hardware support for this bottleneck, our algorithm would be faster than the LAPACK one-sided Jacobi algorithm $\texttt{DGESVJ}$ and comparable in speed to the state-of-the-art preconditioned one-sided Jacobi algorithm $\texttt{DGEJSV}$, but much more accurate.

Quasisymmetry (QS) provides a novel route to understand and control near-degeneracies, Berry curvature, optical selection rules, and symmetry-protected phenomena in quantum materials. Here we give physical interpretations of the emergence of QS operators across multiple material families. Using density functional theory and the $\mathbf{k}\cdot\mathbf{p}$ formalism, we identify QS subspaces and calculate their representation matrices, quantifying the quasisymmetry via a metric $ε$ that measures subspace invariance. For Sn/SiC and transition-metal dichalcogenide monolayers, QS corresponds to an emergent mirror symmetry, whereas in wurtzite crystals it manifests as an emergent spatial inversion. By contrast, for AgLa the QS appearing in avoided crossings is inherited from a nearby high-symmetry point rather than being an emergent lattice symmetry. Combining group-theoretical analysis and $\mathbf{k}\cdot\mathbf{p}$ modeling, our results establish concrete physical pictures for QS and provide practical criteria to diagnose it in first-principles calculations.

The quadrature of cut elements is crucial for all Finite Element Methods that do not apply boundary-fitted meshes. It should be efficient, accurate, and robust. Various approaches balancing these requirements have been published, with some available as open-source implementations. This work reviews these open-sources codes and the methods used. Furthermore, benchmarking examples are developed for 2D and 3D geometries. Implicit and explicit boundary descriptions are available for all models. The different examples test the efficiency, accuracy, versatility, and robustness of the codes. Special focus is set on the influence of the input parameter, which controls the desired quadrature order, on the actual integration error. A detailed comparison of the discussed codes is carried out. The benchmarking allows a conclusive comparison and presents a valuable tool for future code development. All tests are published in an accompanying open-source repository.

A {\it stuck knot} is a knot diagram containing designated crossings, called {\it stuck crossings}, whose incident strands are required to remain locally non-separable. These rigidity constraints restrict the allowable ambient isotopies and introduce new geometric features into the study of knot embeddings. In this paper we develop a topological framework for knots governed by such constraints. We model stuck crossings as locally rigid configurations in spatial embeddings, placing stuck knots in close relation to rigid spatial graph theory while preserving the classical over-under information and orientation of crossings. We formalize the corresponding notion of isotopy and introduce the {\it unstick move}, which releases rigidity and allows classical simplifications to occur. To detect rigid structure algebraically, we construct polynomial invariants for stuck knots, including a HOMFLYPT-type invariant and a state-sum model extending the Kauffman bracket. These invariants show that rigidity contributes independent information even when the underlying classical knot type remains fixed. We further introduce a {\it relaxed isotopy} framework and define the {\it unsticking distance}, a geometric measure quantifying the minimal number of rigidity constraints that must be released in order to relate two stuck knots. This perspective interprets stuck crossings as barriers to isotopy and highlights the role of constraint release in diagrammatic simplification.

Untargeted neutral hydrogen (HI) surveys are well suited to identifying low surface brightness galaxies (LSBGs) that are gas rich, and they offer a complementary view to optically selected populations. We examined the LSBG population as identified via stellar and gaseous content using the MIGHTEE HI XMM-LSS early science data and the publicly available catalogs of optically identified LSBGs. There is currently little overlap between these datasets, with only three galaxies commonly detected. We performed surface brightness photometry of selected MIGHTEE HI detections to find 29 LSBGs, and 26 of these meet the size requirement (R_eff > 1.5 kpc) to be ultra-diffuse galaxies (UDGs). Furthermore, we extracted HI spectra at the location of all optically identified galaxies, placing upper limits on the HI-to-stellar mass ratio in these systems. While the HI-identified population overall tends toward bluer colors, the HI-identified and the optically selected samples mostly overlap in mean effective surface brightness, effective radii, and color. Although it is not straightforward to discern why the HI-identified LSBGs were missed in optical searches, this work highlights the utility of HI surveys in finding these faint systems. The HI-identified LSBGs are gas rich compared to the general HI-selected population. Furthermore, three out of four HI-selected UDGs with available kinematics show no systematic offset from the baryonic Tully-Fisher relation, although we are biased away from sources with low rotational velocities due to the low spectral resolution of the data. This work demonstrates the utility of HI observations for finding and characterizing the low surface brightness Universe.

By cross-matching the eclipsing binary catalog provided by Prsa et al. (2022) with LAMOST medium resolution spectra, we obtained 11 targets. Combining light and radial velocity curves analysis, we have derived accurate physical parameters for these 11 targets. The results indicate that there are 3 deep contact binaries, 3 moderate ones, and 5 shallow ones. Among them, 3 targets exhibit the O'Connell effect, which is attributed to the presence of star-spot on the component's surface. One target is a low-mass ratio deep contact binary and may be contact binary merging candidates. The evolutionary status of these 11 targets was studied using the mass-luminosity and mass-radius relation diagrams. Based on the O-C (Observed minus Calculated) analysis of 10 targets, we found that the orbital periods of 5 contact binaries show a long-term decreasing trend, likely due to the combined effects of mass transfer between the two components and loss of angular momentum. Meanwhile, the orbital periods of the other 4 stars are continuously increasing, which is attributed to mass transfer. Besides, the O-C curves of 3 targets show clear periodic changes, which might result from the Applegate mechanism or the light travel time effect.

Studying Correlations with Ramanujan Expansions, we arrive to present the new class of, say, Two-Seasons Correlations, abbr. T-S, as a natural set expressing some of the features of, say, H-L-like Correlations; these are the ones that mimic the H-L ($=$Hardy-Littlewood) Correlation with shift $2k$, needed to study $2k-$twin primes following Hardy \& Littlewood Conjecture. After introducing the $3-$Hypotheses Correlations in a previous paper, we add two other, very natural, hypotheses: the fifth is a technical one, simplifying calculations; but the fourth is called 'Parity', since it deals with the parity of natural numbers we play with. In particular, we may build (devoting to this 'our mainstream', here) a single Correlation that satisfies these '5 Axioms', thus a T-S one, that 'entangles two different Correlations' (whence Two-Seasons: T-S) depending on $a$ ($=$ the shift) parity. For $a$ even, our 'Artifact' mimics the H-L Correlation, in fact $a=2k$; but, while H-L Correlation is 'negligible', say, on $a$ odd, our Artifact seems to compare at least in the order of magnitude to H-L Correlation on $a$ even, being linked to another additive problem. Namely, on $a$ even, the Artifact 'counts', say, classic solutions to: $p_1+a=p_2$, in odd primes $p_1,p_2$; while, on $a$ odd, it 'counts' solutions to: $p_1+a=2^j p_2$, again with odd primes $p_1,p_2$ and with $j\in \N$ (satisfying the natural arithmetic constraints). More in general, our T-S Correlations 'entangle' two different Diophantine equations.

We propose a computational strategy for NLO+PS simulations in the MC@NLO framework that starts from Born-accurate (LO) events and reweights them to the full MC@NLO S-event weight, while generating H-events separately. We validate the approach on two representative LHC processes and compare to direct NLO event generation for both standard MC@NLO and MC@NLO-Delta matching. Employing large folding values in the radiative variables stabilizes the S-event integral, reduces weight variance, and significantly lowers the fraction of negative weights compared to S-event generation without folding. At fixed precision, this pipeline has comparable wall-clock times relative to standard S-event generation and unweighting, with room for further optimisation.

Previous theoretical studies have shown that attosecond electron dynamics can, in principle, be captured in electron momentum spectroscopy (EMS) using ultrashort electron pulses. By including further analytical considerations on the scattering probability, we here study the effect of the finite transversal extend of the projectile electron wave packet. We find that in wave packet scattering, the target momentum distribution is probed solely in a finite spatial region. This is evident from a spatially filtering Gabor transform appearing in the scattering probability, replacing the full momentum wave function appearing in the conventional plane wave treatment. In addition, by spatially shifting the target with regard to the wave packet focus, we illustrate the influence of vacuum dispersion, i.e., the spatial broadening of the wave packet as it propagates. Our findings are significant for the possibility to correctly interpret future attosecond-EMS results and the considered effects reflect fundamental aspects of wave packet scattering. The EMS setup may, therefore, constitute a useful framework for understanding scattering with finite wave packets.

Borradaile, Le and Sherman-Bennett [Graphs and Combinatorics, 2017] proved that every $n$-vertex $2$-outerplane graph has a set of at least $2n/3$ vertices that induces an outerplane graph. We identify a major flaw in their proof and recover their result with a different, and unfortunately much more complex, proof.

Let $S_n$ be a random walk with i.i.d. increments which have zero mean and finite variance. For every $x\ge0$ we define the stopping time $τ_x:=\inf\{n\ge1:x+S_n\le0\}$ and consider the probabilities $\mathbb{P}(x+S_n\ge y,τ_x>n)$. We study the quality of the normal approximation for these probabilities and derive a Berry-Esseen-type inequality for $\mathbb{P}(x+S_n\ge y|τ_x>n)$. Our Theorem 1 is an extension of the results in our previous paper (arXiv:2412.08502) where we have considered the special case $x=0$. It is also worth mentioning that Theorem 1 complements the results of Siegmund and Yuh (1982) on the corrected diffusion approximation.

The mass composition of ultra-high-energy cosmic rays (UHECRs) is commonly inferred from the first two moments of the depth of shower maximum, $X_{\rm max}$, measured by fluorescence and hybrid detectors. Such analyses require fast and accurate mappings between the moments of $X_{\rm max}$ and those of the logarithmic mass, $\ln A$, based on realistic air-shower simulations. In this work we provide updated parametrizations of the $X_{\rm max}$ moments and distributions for air showers initiated by nuclei from proton to iron, simulated with CONEX for three state-of-the-art hadronic interaction models: Epos LHC-R, Sibyll 2.3e, and QGSJet-III-01. We parametrize the mean depth $\langle X_{\rm max}\rangle$ and the variance $σ^2(X_{\rm max})$ as functions of energy and mass. For the variance we compare a second-order polynomial model with an exponential model. In addition, we model the full $X_{\rm max}$ distributions with a three-parameter generalized Gumbel function. The Gumbel parameters are fitted using an unbinned likelihood and are validated by comparing the implied mean and variance with the raw CONEX samples and with the moment parametrizations. Across the full energy range considered, residuals between the parametrizations (or the Gumbel representation) and the simulations are at the level of a few g cm$^{-2}$ for the mean and a few (g cm$^{-2}$)$^2$ for the variance, making these parametrizations suitable for precision UHECR composition studies and forward-folding analyses of $X_{\rm max}$ distributions.

We study the local statistics of orthogonal polynomial ensembles near a hard edge, subject to a multiplicative deformation of the measure. Probabilistically, this deformation corresponds to a position-dependent conditional thinning of the particles. We prove that, under critical hard edge scaling and for a large class of potentials and deformation symbols, the correlation kernel of the conditional ensemble converges to a universal limit, which we identify as the conditional thinned Bessel point process. We derive an explicit expression for this limiting kernel in terms of the solution to a nonlocal integrable system depending on a parameter. For a special choice of the parameter, this system was recently identified in the study of multiplicative statistics of the Bessel point process. Our results establish that this system governs the full correlation structure of the conditional Bessel point process, extending the classical connection between the standard Bessel kernel and the Painlevé V equation.

Electron-phonon coupling (EPC) governs lattice dynamics, charge transport, and collective electronic phases in quantum materials. In several families of unconventional superconductors, including transition-metal dichalcogenides and kagome metals, growing evidence points to a cooperative role of EPC and dynamic charge-density fluctuations (CDF) in stabilizing superconductivity. However, how the EPC strength evolves across phase diagrams and relates to superconducting properties in strongly correlated systems remains an open question. Here we investigate the interplay between phonons and the CDF recently identified in cuprate superconductors. Using resonant inelastic x-ray scattering, we track the dispersion and intensity of bond-stretching phonons in YBa$_2$Cu$_3$O$_{7-δ}$ over wide ranges of doping, temperature, and momentum. We find that both the phonon softening at the CDF wave vector and the EPC strength, extracted from a pronounced phonon intensity anomaly, are maximized near $p = 0.19$, where superconducting properties are optimal and CDF intensity is strongest. These results identify dynamic charge-density fluctuations, rather than quasi-static charge density waves, as the dominant source of phonon renormalization in cuprates, and establish a direct correlation between EPC strength and the superconducting dome. More broadly, our measurements highlight EPC as a doping-dependent property of correlated materials, shaped by the electronic environment in which lattice vibrations are embedded.

Large main-belt asteroids (diameter $D \gtrsim 120\ \mathrm{km}$) exhibit a surface composition gradient as a function of heliocentric distance, ranging from anhydrous bodies to those rich in hydrated and, possibly, ammoniated materials. Their primordial nature holds key clues to the evolution of the Solar System. It has been suggested that the volatile-rich bodies formed in the outer Solar System and were implanted into the main belt. Alternatively, volatiles may have been delivered via inward-drifting icy pebbles in the protosolar disk. Here, we examine whether in-situ formed rocky embryos can acquire volatiles through pebble accretion as the snowline migrated inward. With the turbulence strength of the disk, radial pebble flux, and the dimensionless stopping time of pebbles (St) as parameters, we calculate the growth of large asteroids. The results are then compared with mass and compositional constraints based on asteroid observations. We find that a moderate pebble flux ($\lesssim18~M_\oplus / \text{Myr}$) is required to enable volatile delivery while preventing the largest asteroids from becoming more massive than Ceres. Water accretion is feasible with $\mathrm{St} \sim 10^{-3}$ ($\sim 1$ mm). However, only the largest asteroids (D > 200 km) can accumulate sufficient ammonia under such conditions. For most asteroids with D between 100 and 200 km, ammonia ice accretion requires $\mathrm{St} \sim 10^{-4}$ ($\sim 100\,μ$m). Such small particle sizes may pose both theoretical and observational challenges. Thus, we propose that the intermediate-sized, potentially ammonia-bearing asteroids serve as a record of the Solar System's dynamic evolution.

Information retrieval evaluation often suffers from fragmented practices -- varying dataset subsets, aggregation methods, and pipeline configurations -- that undermine reproducibility and comparability, especially for foundation embedding models requiring robust out-of-domain performance. We introduce SuiteEval, a unified framework that offers automatic end-to-end evaluation, dynamic indexing that reuses on-disk indices to minimise disk usage, and built-in support for major benchmarks (BEIR, LoTTE, MS MARCO, NanoBEIR, and BRIGHT). Users only need to supply a pipeline generator. SuiteEval handles data loading, indexing, ranking, metric computation, and result aggregation. New benchmark suites can be added in a single line. SuiteEval reduces boilerplate and standardises evaluations to facilitate reproducible IR research, as a broader benchmark set is increasingly required.

The Equation of State (EoS) of dense nuclear matter remains one of the most compelling open questions in high-energy astrophysics. While static EoS models are increasingly well-constrained by observations of binary neutron star (BNS) inspirals, the possibility of a dynamic phase transition occurring during the coalescence has been thus far deferred from standard gravitational-wave (GW) analyses. In this work, we investigate the detectability of such a phase transition, manifesting as a macroscopic shift in the tidal deformability parameter $Λ$, using GWs from Neutron Star-Black Hole (NSBH) coalescences. We argue that NSBH systems serve as a cleaner laboratory for this phenomenology than BNS systems due to the absence of the $\tildeΛ(Λ_1,Λ_2)$ degeneracy, allowing for the isolation of single-body tidal evolution. We introduce a phenomenological waveform model, TROYE (Transitional Representation Of varYing Equation-of-state), which stitches together two waveform approximants in the time domain to simulate a smooth but rapid transition between two equations of state during the late inspiral. We perform a comprehensive Bayesian injection and recovery campaign on 100 simulated events using the bilby inference library. Our results demonstrate that a phase transition corresponding to a tidal shift of $|ΔΛ| \gtrsim 400$ is detectable with Advanced LIGO design sensitivity, yielding decisive statistical evidence ($\ln B > 5$). We further identify a "V-shape" asymmetry in detectability, where "softening" transitions (decreasing $Λ$) are systematically easier to detect than "stiffening" ones due to the specific phase evolution of the tidal sector. Finally, we present "stress tests" showing that the transition remains recoverable even when marginalized over uncertainties in the stitching time and binary mass ratio.