Let $G$ be a finite simple graph and $B \subseteq V(G)$. We introduce the \emph{bivariate $B$-restricted clique polynomial} \[ C_B(G;x,y) = \sum_{\substack{K \subseteq V \\ K \text{ is a clique}}} x^{|K|} y^{|K \cap B|}, \] where the coefficient of $x^i y^j$ counts cliques of size $i$ with exactly $j$ vertices in $B$. This polynomial simultaneously captures combinatorial structure, local extremal properties, and spectral constraints associated with the subset $B$. \\ First, we develop vertex and edge deletion recurrences, generalizing classical clique polynomial results. These recurrences imply monotonicity for the largest negative root $ζ_G(B;y)$ (viewed as a polynomial in $x$ for fixed $y \in [0,1]$) under induced and spanning subgraphs. From this, we derive bounds on $B$-independence numbers, $B$-girth, and clique densities restricted to $B$. \\ Next, we prove that for any integer $r \ge 1$, any $r$-connected $K_{r+3}$-free chordal graph $G$, and any subset $B \subseteq V(G)$, the bivariate clique polynomial $C_B(G;x,y)$ is real-stable. \\ Then, we connect $C_B(G;x,y)$ with spectral graph theory. For $(n,d,λ)$-graphs, expansion constraints via Tanner's inequality limit clique growth within $B$, yielding explicit bounds on coefficients and $ζ_G(B;y)$. \\ Finally, we analyze weighted vertices and homomorphism obstructions in this framework, giving a general no-homomorphism criterion. We also conclude the paper with a couple of interesting open problems for young and motivated researchers.

Beyond diagonal reconfigurable intelligent surface (BD-RIS)s enhance wave manipulation through inter-element couplings but pose significant channel estimation challenges due to cascaded channels and block-Kronecker structures. This paper proposes a compressive sensing framework exploiting sparse Tucker decomposition of the measurement tensor and the Kronecker rank-one structure of channel components. Two algorithms are developed: Sparse Tensor Orthogonal Recovery Method (STORM), which uses orthogonal matching pursuit (OMP) for greedy support recovery, and Sparse Tensor subspace- Aided Recovery (STAR), which leverages subspace-based projection for enhanced noise robustness. Both perform joint sparse support identification, followed by a Kronecker rank-one factorization via singular value decomposition (SVD) to recover the channel parameters. Simulations show that STAR achieves oracle-assisted least squares (LS) performance at moderate-to-high signal-to-noise ratio (SNR) with significantly fewer measurements than baseline methods, enabling practical BD-RIS deployment in next-generation millimeter wave (mmWave)/sub-terahertz (sub-THz) networks.

We present a neural operator framework for solving inverse scattering problems. A neural operator produces a preliminary indicator function for the scatterer, which, after appropriate rescaling, is used as a regularization parameter within the Linear Sampling Method to validate the initial reconstruction. The neural operator is implemented as a DeepONet with a fixed radial-basis-function trunk, while the noise level required for rescaling is estimated using a dedicated neural network. A neural tangent kernel analysis guides the architectural design, reducing the network tuning to a single discretization parameter, adjustable according to the wavelength. Two-dimensional numerical experiments demonstrate the method's effectiveness, with a Python toolbox provided for reproducibility.

Preterm birth is associated with premature cervical remodeling, yet current clinical assessments cannot detect the underlying microstructural changes in collagen organization. We apply imaging Mueller polarimetry to murine cervical tissue at three gestational stages (early, mid, late) and develop classification methods to predict gestational stage from polarimetric maps. Using Lu-Chipman decomposition, we extract orientation and azimuth local variability maps that capture collagen fiber alignment and disorder. We evaluate two approaches under 20-fold leave-one-out cross-validation: an analytical threshold classifier on mean azimuth local variability, and a lightweight CNN ensemble (approximately 76k parameters) operating on spatially resolved maps. The ensemble achieves 70..0% sample-level accuracy, outperforming the analytical baseline (55.0%), with strong performance on early (71.0%) and late (86.0%) gestation. Spatial prediction maps confirm that classification accuracy is highest in the stroma, where collagen remodeling is most prominent. These results demonstrate that Mueller polarimetry combined with deep learning models can detect gestational collagen remodeling noninvasively, offering a potential pathway toward objective cervical assessment for preterm birth risk.

We consider a Riemann boundary value problem for monogenic functions in a two-dimensional commutative associative Banach algebra. We prove theorems on the existence of a solution to this problem under different assumptions on the coefficient and free term of the problem, and give an explicit formula for the solution.

We propose a general mechanism for the spontaneous emergence of filling-enforced fully compensated ferrimagnetism (fFIM), characterized by zero net magnetization yet ferromagnetic-like spin-split band structures. Using Hartree-Fock mean-field calculations of the Hubbard model, we map out the stability regime of spontaneous fFIM over a broad parameter space of interaction strength and staggered potential. We show the unique quantum-geometry-governed optical selection rules and the abundant valley- and spin-related physics of electronics and optics arising from the emergence of fFIM order, with tunable spin-polarized and valley-contrasting charge and spin currents. Furthermore, based on our theory, we demonstrate that spontaneous fFIM can be realized in nominally nonmagnetic graphene via defect engineering. Our results establish a unified framework for the mechanism, emergent properties, and materials realization of spontaneous fFIM, opening new opportunities for spintronic, valleytronic, and optoelectronic applications.

In the recent Muon g-2 Theory Initiative white paper update, the hadronic vacuum polarization (HVP) contribution -- which dominates the theoretical uncertainty -- is evaluated as an average of different lattice QCD calculations. Since lattice simulations are mostly carried out in isospin symmetric QCD, corrections due to the mass difference of the up and down quarks and the coupling to photons have to be accounted for. These isospin breaking effects are of order 1\% and can be treated as corrections to the result for the HVP contribution in isospin symmetric QCD. In the current estimate of the HVP contribution, these effects are a large source of uncertainty due to the extensive computational cost to compute all occurring Wick contractions and degrading signal-to-noise behaviour especially for quark disconnected diagrams. We present the current status of the calculation of isospin breaking corrections in the HVP contribution for the RBC/UKQCD collaborations. We use a dataset of propagators computed using stochastic coordinate sampling (SCS) to construct all necessary Wick contractions for the electromagnetic and strong isospin breaking effects. We employ different versions of QED on the lattice, such as QED$_L$, QED$_r$ and QED$_\infty$ to improve our estimate of finite-volume uncertainties.

In a typical two-phase design, a random sample is drawn from the target population in phase 1, during which only a subset of variables is collected. In phase 2, a subsample of the phase-1 cohort is selected, and additional variables are measured. This setting induces a coarsened data structure on the data from the second phase. We assume coarsening at random, that is, the phase-2 sampling mechanism depends only on variables fully observed. We review existing estimators, including the generalized raking estimator and the inverse probability of censoring weighted targeted maximum likelihood estimation (IPCW-TMLE) along with its extensions that also target the phase-2 sampling mechanism to improve efficiency. We further introduce a new class of estimators constructed within the TMLE framework that are asymptotically equivalent.

Generative AI (GenAI) tools are transforming critical societal domains, including the legal sector. While these tools create opportunities such as increased efficiency and potential improvements in access to justice, they also present new challenges, such as the risk of inaccurate legal advice and questions about the legitimacy of legal decisions. However, the full impact remains to be seen and ultimately depends on the way GenAI tools are implemented and used by both, legal professionals and citizens. This makes anticipating and managing the positive and negative impacts of GenAI use in the legal domain challenging but also important to guide the digital transformation of the legal sector into a societally desirable direction. In this paper, we set out to explore the spectrum of possible impacts of GenAI in the legal domain, examining how this technology is anticipated being used and the potential implications this might have for the legal sector and society. Using a scenario writing method, we surveyed participants in the EU and US including both citizens and legal professionals about the potential impact of generative AI on legal conflict resolution. Respondents were tasked with writing a narrative drawing on their experience or expertise about a future in which AI is used throughout the legal process. We qualitatively analysed the prevalence of risk and benefit themes, as well as the types of anticipated legal tasks. We then compared these findings based on expertise status (legal experts versus citizens) and regional regulatory background (the EU with the EU AI Act versus the US with an industry self-regulatory approach). Finally, we describe the emerging trade-offs that will affect decision-makers in the legal sector.

Let $B$ be a $p$-block of a finite group $G$ with defect group $D$. The more difficult direction of the recently proven height zero conjecture says that $D$ is abelian if every character in Irr$(B)$ has height zero. We consider a smaller set than Irr$(B)$. In particular, if $φ\in {\rm IBr}_p(B)$, we let Irr$(φ)$ be the set of characters $χ\in {\rm Irr}(G)$ such that $φ$ is a constituent of $χ^o$. Now suppose $G$ is solvable and $φ$ is a height zero Brauer character in some block $B$ of $G$ with defect group $D$. Here we show that if every character in Irr$(φ)$ has height zero, then the defect group $D$ of the block containing $φ$ is abelian for $p \geq 5$ and almost abelian for $p = 2$ or $3$. This has a nice consequence for primitive characters of $p$-complements in solvable groups.

When it is not feasible to conduct randomized controlled trials (RCTs), the use of external control arms based on real-world data (RWD) may be a viable option. However, challenges arising from data heterogeneity must be addressed to ensure the reliability of trial results. We consider the use of Natural Hermite and propensity score indices to facilitate robust comparisons between RCTs and RWD studies. Illustrations are provided on the implementation and performance of the underlying algorithms using simulated data, as well as synthetic data from a clinical trial and RWD.

We compute the periods associated with a special class of hyperplane arrangements. In particular, we exhibit a combinatorial condition on the intersection lattice of a hyperplane arrangement that ensures that its associated periods are linear combinations of special values of multiple polylogarithms. Our method generalizes Brown's approach to the periods of moduli spaces of curves of genus zero. We apply this result to the reflection arrangement of the full monomial group, whose periods are shown to be linear combinations of values of multiple polylogarithms at roots of unity.

Intelligent recommendation systems have clearly increased the revenue of well-known e-commerce firms. Users receive product recommendations from recommendation systems. Cinematic recommendations are made to users by a movie recommendation system. There have been numerous approaches to the problem of recommendation in the literature. It is viewed as a regression task in this research. A regression model was built using novel properties extracted from the dataset and used as features in the model. For experimentation, the Netflix challenge dataset has been used. Video streaming service Netflix is a popular choice for many. Customers' prior viewing habits are taken into account when Netflix makes movie recommendations to them. An exploratory data analysis on the Netflix dataset was conducted to gain insights into user rating behaviour and movie characteristics. Various kinds of features, including aggregating, Matrix Factorization (MF) based, and user and movie similarity based, have been extracted in the subsequent stages. In addition to a feature in the XGBoost regression algorithm, the K-Nearest Neighbors and MF algorithms from Python's Surprise library are used for recommendations. Based on Root Mean Square Error (RMSE), MF-based algorithms have provided the best recommendations.

Let $F$ be a crossing family over ground set $V$, that is, for any two sets $U,W\in{F}$ with nonempty intersection and proper union, both sets $U\cap{W},U\cup{W}$ are in $F$. Let $σ:V\to \{+,-\}$ be a signing. We call $σ$ a "cosigning" if every set includes a positive element and excludes a negative element. It is "$\cap\cup$-closed" if every pairwise nonempty intersection and co-intersection include positive and negative elements, respectively. We characterize the existence of ($\cap\cup$-closed) cosignings $σ$ through necessary and sufficient conditions. Our proofs are algorithmic and lead to elegant `forcing' algorithms for finding $σ$, reminiscent of the Cameron-Edmonds algorithm for bicoloring balanced hypergraphs. We prove that the algorithms run in polynomial time, and further, the cosigning algorithm can be run in oracle polynomial time through an application of submodular function minimization. Cosigned crossing families arise naturally in digraphs with vertex set $V$ comprised of sources and sinks, where every set in $F$ is "covered" by an incoming arc. Under mild and necessary conditions, we build an outer-planar arc covering of $F$ when the vertices are placed around a circle. These gadgets are then used to find disjoint dijoins in $0,1$-weighted planar digraphs when the weight-$1$ arcs form a connected component that is not necessarily spanning.

Bridging the gap between atomistic detail and continuum mechanics is a central challenge in modeling biological membranes, particularly for mesoscopic phenomena spanning large length and time scales. In this work, we introduce a new, solvent-free, one-particle-thick, coarse-grained model for lipid bilayers, governed by an additive potential. Our approach treats orientational elasticity through distinct additive energy terms for tilt and splay, offering an unbiased potential form. The model is implemented in the LAMMPS molecular dynamics engine. Our simulations show spontaneous self-assembly of lamellar structures and stable vesicles from disordered states. We map the dynamical phase diagram of the system, identifying distinct gel-like, fluid, and gas regimes, controlled by temperature and the steepness of the isotropic attraction. The model accurately reproduces the theoretical $1/q^{4}$ fluctuation spectrum for tensionless membranes and exhibits tunable mechanical properties, including biologically relevant bending rigidities and area compressibility moduli. We show how we can include osmotic pressure and spontaneous curvature in our model. Finally, we demonstrate the model's applicability to complex membrane remodeling by simulating the adhesive wrapping of colloidal nanoparticles, recovering the predicted dependency on particle size and adhesion strength.

Across the peak of cosmic star formation at $z\sim1-2$, inflow, processing, and feedback drive rapid changes in the spatial distribution and chemical composition of baryons in galaxies and surrounding reservoirs; this baryon cycle can be tomographically mapped by line intensity mapping (LIM) of atomic hydrogen, ionized carbon, and carbon monoxide. We present a simulation-based forecasting framework for detecting auto- and cross-power spectra between spectroscopic surveys of four such tracers at $z\sim0.5-1.7$ mapping the same deep field - TIM, EoRSpec/FYST, MeerKAT, & Euclid. We forward-model 3-D distributions for these tracers from magnetohydrodynamic simulations, directly capturing the two-halo, one-halo, and shot statistics without relying on analytical decompositions. We further detail a signal-to-noise formalism, tailored to LIM surveys with highly anisotropic geometries and Fourier-space coverage. We demonstrate that galaxy cross-correlations will be the dominant discovery channel for current-generation surveys. These instruments will detect the auto-spectra for CO and HI 21 cm and the CO $\times$ 21 cm cross-spectrum at modest S/N $\sim 1-10$, while placing upper limits on the [CII]-158$μ$m signals. [CII], CO, and HI LIM will be $\sim3-30\times$ ($0.5-1.5$ dex) more sensitive to cross-correlation with the Euclid survey, however, than their respective auto-correlations, constraining all three models of line emission at high significance (S/N $\sim 10-40$) within this decade. Finally, we formulate a staged instrumental trajectory with planned or reasonable improvements, including the as-proposed SKA-Mid. We forecast advancing the per-$k$-mode sensitivities of each auto-, galaxy-line, and line-line spectrum by several orders of magnitude, enabling new percent- and sub-percent level constraints on cosmology and the redshift evolution of star formation and the baryon cycle.

The evolution of the global solar magnetic field directly impacts the interplanetary magnetic field (IMF). During the solar maximum of Cycle 24, the monthly averaged IMF strength doubled over five Carrington rotations in late 2014. To understand the physical origin of this increase, we investigate the temporal evolution of open magnetic flux resulting from the emergence and decay of bipolar magnetic regions (BMRs). Using surface flux transport and potential field source surface models, we simulated how BMR characteristics, spatial distributions, and interaction with background magnetic fields affect open flux evolution. Our simulation confirmed that the relative configuration of BMRs can either inhibit open flux expansion via closed loops or promote it through favorable connections. The increase in open flux is primarily driven by the equatorial dipole component, which is enhanced by differential rotation acting on tilted BMRs. These behaviors suggest that large open field structures develop from equatorial dipole components formed by these stretched BMRs. We attribute the rapid IMF increase in 2014 (Carrington rotations 2152-2157) to the combination of the following three factors: (1) a specific sunspot configuration that facilitated the expansion of the southern coronal hole; (2) the emergence of a giant sunspot group (active region 12192) with high magnetic intensity; and (3) the diffusion of these regions, which reinforced the global magnetic field. These results imply that rapid open flux variations during solar maximum are governed not only by the characteristics of emerging BMRs but also by their interaction with pre-existing large coronal holes.

We theoretically study microwave absorption spectroscopy of fractional quantum Hall droplets in the presence of quasiparticle tunneling across a quantum point contact. This contact-free probe provides access to collective edge dynamics beyond conventional transport measurements. We develop a nonperturbative path-integral Monte Carlo approach that enables computation of the frequency-dependent response at finite temperature and for arbitrary droplet geometries, and benchmark the method against analytical results in the weak-tunneling regime. We find that tunneling produces measurable shifts and broadening of resonance peaks, with systematic dependence on tunneling strength and device geometry. Such shifts and broadenings are not obtained in perturbative treatments acting directly on the response function, but emerge when interaction-kernel effects are properly incorporated. Our results indicate experimentally accessible signatures of edge-mode interference and tunneling-induced renormalization of collective excitations, and support the use of microwave spectroscopy as a quantitative probe of quasiparticle dynamics in mesoscopic quantum Hall structures.

We resolve a phase identification controversy in the Ag-Sn-S material system by unraveling the polymorphic structure of nanocrystals within the argyrodite material family. Argyrodites are a class of superionic materials used in their bulk form for applications in solid-state batteries and thermoelectrics, where their advantageous properties relate to their polymorphism. However, despite their well-studied bulk applications, the limited exploration at the nanoscale has left considerable potential for the discovery of emerging properties due to size effects. Further, phase identification presents a prominent challenge to the study of polymorphs in superionic conductors and related mate-rials. In this work, we synthesize canfieldite-like (Ag8SnS6) nanocrystals to understand their formation and structural behavior at the nanoscale. We observe the emergence of emissive, meta-stable, cluster-like species. Then, high-resolution transmission electron microscopy reveals indistinguishable polymorphs of canfieldite due to identical heavy-atom frameworks. However, using synchrotron X-ray total scattering for pair distribution function analysis, we uncover structural distortions, showing a pseudo-orthorhombic configuration that likely gives rise to the red emission. Further, we investigate the optical properties and structure of Ag8SnS6 nanocrystals upon the addition of Zn2+, the cation of interest in the canfieldite vs. pirquitasite (Ag2ZnSnS4) phase identification controversy. We show that Zn2+ is incorporated in the canfieldite-like structure through the replacement of Ag+, boosting the emission. Our results solve a standing phase identification challenge and uncover fundamental insights for the synthesis and structure of canfieldite nanocrystals, laying the ground for the exploration of other argyrodite materials with emerging properties at the nanoscale.

Polarons are electronic excitations dressed by a self-consistent lattice distortion, yet their formation has not been directly resolved in real time. We develop a microscopic lineshape framework that connects the growth of a collective lattice polarization to the population-time evolution of the anti-diagonal linewidth in coherent multidimensional spectroscopy. Within this formalism, the anti-diagonal linewidth directly tracks the decay of lattice frequency-frequency correlations. Underdamped phonon environments produce oscillatory linewidth modulation, whereas overdamped collective polarization dynamics generate monotonic exponential broadening. Applying this framework to multidimensional measurements on perovskite quantum dots, we show that the observed approximately 150 femtosecond exponential anti-diagonal broadening reflects the decay of a collective polarization order parameter. These results establish anti-diagonal linewidth dynamics as a direct real-time signature of Landau polaron formation.

We report on the experimental detection of shockwave dynamics produced in a spark discharge, using a nonresonant four-wave mixing optical technique. In particular, we observe the spark-induced local density perturbation across a millimeter-range probe volume, centered on the discharge, via single-shot coherent Rayleigh-Brillouin scattering. We detect the emergence of shock-induced flow velocities, which appear as distinct features in the spectrum, and monitor their dynamic evolution from a few hundred nanoseconds to microseconds after the spark. Finally, we benchmark our measurements against simulations based on a one-dimensional compressible flow model. Our results pave the way for quantitative measurements of highly non-uniform transient flows in challenging environments featuring non-equilibrium gas kinetics.

Functional testing is essential for verifying that the business logic of mobile applications aligns with user requirements, serving as the primary methodology for quality assurance in software development. Despite its importance, functional testing remains heavily dependent on manual effort due to two core challenges. First, acquiring and reusing complex business logic from unstructured requirements remains difficult, which hinders the understanding of specific functionalities. Second, a significant semantic gap exists when adapting business logic to the diverse GUI environments, which hinders the generation of test cases for specific mobile applications. To address the preceding challenges, we propose LogiDroid, a two-stage approach that generates individual functional test cases by extracting business logic and adapting it to target applications. First, in the Knowledge Retrieval and Fusion stage, we construct a dataset to retrieve relevant cases and extract business logic for the target functionality. Second, in the Context-Aware Test Generation stage, LogiDroid jointly analyzes the extracted business logic and the real-time GUI environment to generate functional test cases. This design allows LogiDroid to accurately understand application semantics and use domain expertise to generate complete test cases with verification assertions. We assess the effectiveness of LogiDroid using two widely-used datasets that cover 28 real-world applications and 190 functional requirements. Experimental results show that LogiDroid successfully tested 40% of functional requirements on the FrUITeR dataset (an improvement of over 48% compared to the state-of-the-art approaches) and 65% on the Lin dataset (an improvement of over 55% compared to the state-of-the-art approaches). These results demonstrate the significant effectiveness of LogiDroid in functional test generation.

Plasma-based accelerators are compact and provide high gradients, yet their practical use has been limited by energy gain, stability, beam quality, and energy transfer efficiency. Here, we address several of these challenges simultaneously using a hybrid scheme in which an electron bunch from a laser wakefield accelerator (LWFA) drives a subsequent plasma wakefield accelerator (PWFA) stage with internal witness injection. Close to driver depletion in the PWFA stage, we obtain witness bunches with higher electron energy, reduced energy spread and divergence, and higher angular-spectral charge density compared to LWFA alone. We report energy transformer ratios approaching~2, and about 20\% of the initial energy in the drive beam was transferred to the witness bunch, thereby achieving a driver-to-witness energy transfer efficiency that largely surpasses that of all previous PWFA experiments.

In this paper we propose a Moran model that describes the population dynamics of two types: While the first type has a selective advantage during reproduction, the second type can avoid replacement during reproduction with some positive probability by switching temporarily into a dormant state. We investigate the interplay of both evolutionary strategies by studying the invasion dynamics of the dormant type into the resident (selectively advantageous) population in the large population limit of the system. It turns out that the dormancy trait can not only invade and subsequently fixate under suitable parameter assumptions despite its selective disadvantage (a phenomenon that has already been observed in a related context in Blath and Tóbiás (2020)), but that there is also a novel regime of stable coexistence of both types due to a frequency-dependent balancing effect that did not arise in the previous setup with Lotka--Volterra type symmetric competition. The emergence of a coexistence regime here rests in part on specific properties of the Moran modelling framework, in particular its fixed overall population size that enforces instant re-colonization after death events, as well as on the (positive) mortality and resuscitation rates of the dormant state. We provide heuristic explanations for the observed types of behaviour and the corresponding proofs, which involve comparisons to suitable branching processes, approximations by dynamical systems, and an analysis of asymptotic behaviour of the latter.

The work considers the set $Λ_n^k$ of all $n\times n$ binary matrices having the same number of $k$ units in each row and each column. The article specifically focuses on the matrices whose rows and columns are sorted lexicographically. We examine some particular cases and special properties of this matrices. Finally, we demonstrate the relationship between the Fibonacci numbers and the cardinality of two classes of $Λ_n^k$-matrices with lexicographically sorted rows and columns.

We prove well-posedness and higher-order regularity for a linear structurally damped plate equation with inhomogeneous Dirichlet--Neumann boundary conditions on the half-space and on bounded domains. To this end, we study maximal regularity properties of the related first-order system on weighted Sobolev spaces of arbitrarily high smoothness. In particular, we consider Sobolev spaces with power weights that measure the distance to the boundary. This allows us to avoid unnatural compatibility conditions for the data and treat the plate equation with rough inhomogeneous boundary conditions on bounded $C^{1,κ}$-domains, where $κ\in (0,1)$ depends on the exponent of the spatial power weight, but is independent of the smoothness of the data. Our methods can serve as an example to treat more complicated mixed-order systems as well.

Bosonic quantum error-correcting codes encode logical information in a harmonic oscillator, with the Gottesman-Kitaev-Preskill (GKP) and number-phase (NP) codes representing two fundamentally different encoding paradigms. Although both have been extensively studied, it remains unclear under what physical noise conditions (including photon loss and dephasing) one encoding intrinsically outperforms the other. Here we estimate a quantitative performance boundary between GKP and NP codes under general photon loss-dephasing noise. By optimizing code parameters within each encoding family, we identify the noise regimes in which each code exhibits a fundamental advantage. In particular, we find that the crossover occurs when the dephasing strength is approximately two orders of magnitude smaller than the loss strength, revealing a sharp separation between operational regimes. Beyond this specific comparison, our work establishes a practical and extensible methodology for benchmarking bosonic codes and optimizing their parameters, providing concrete guidance for the experimental selection and deployment of bosonic encodings in realistic noise environments.

The impulse response of a flame to acoustic velocity perturbations is a key quantity for predicting thermoacoustic stability, but its identification from sparse, noisy observations requires solving an ill-posed inverse convolution problem. This is typically achieved with system identification methods, which require hand-tuning of regularization, model order, and sampling parameters, and provide no principled mechanism for incorporating prior physical knowledge. In this paper, we reformulate the identification problem within a Bayesian framework. The impulse response is represented as a physically motivated distributed time delay model, whose parameters correspond to convective delays and dispersive broadening. For a given number of pulses, the model parameters are inferred from the data using Bayesian parameter inference. The number of pulses is then selected using Bayesian model comparison, which balances data fit against model complexity to identify the simplest model capable of explaining the data. The framework is demonstrated on broadband-forced large eddy simulation data from a turbulent swirl-stabilized burner. Bayesian model comparison selects a three-Gaussian impulse response for this flame, consistent with physical interpretations in previous work. Compared with system identification, the Bayesian approach produces impulse responses with fewer spurious features and enables straightforward enforcement of a known low-frequency gain. Finally, we show that the Bayesian approach is robust to significant reductions in recording length, making it appealing for impulse response identification from costly simulations, where there is an incentive to minimize computational cost.

Superconducting quantum processors operate at microwave frequencies in millikelvin environments, making it challenging to interconnect distant nodes using conventional microwave wiring. Coherent microwave-to-optical (M2O) transduction enables superconducting quantum networks by interfacing itinerant microwave photons with low-loss optical fiber. However, many state-of-the-art transducers provide efficient conversion only over a narrow frequency span, complicating deployment with heterogeneous superconducting devices that are detuned by gigahertz-scale offsets. Here we demonstrate a frequency-agile microwave-optical interface that overcomes this bandwidth mismatch by cascading an electro-optic M2O transducer with a multimode microwave-to-microwave (M2M) frequency converter, with in situ tunability of the microwave resonances in both stages. Using this architecture, we realize continuous frequency coverage from 5.0 to 8.5 GHz within a single system. As an application relevant to superconducting-qubit networking, we use the cascaded M2M-M2O interface to optically read out a superconducting qubit whose readout resonator is detuned by 1.7 GHz from the native M2O microwave resonance, demonstrating a scalable route toward fiber-linked superconducting quantum nodes.

The asymmetric tropical distance is a distance measure on the tropical torus $\mathbb{R}^n/\mathbb{R}\mathbf{1}$ and in particular on the Bergman fan $B(K_N) \subseteq \mathbb{R}^{\binom{N}{2}}/\mathbb{R}\mathbf{1}$ of the complete graphical matroid. In this paper, we define and analyse a clustering algorithm for equidistant phylogenetic trees based on this distance, using the correspondence between $B(K_N)$ and the space of equidistant trees with $N$ leaves.