Spontaneous Raman scattering (SpRS) is a weak non-linear effect, particularly relevant to classical-quantum coexistence transmission and sensing applications. In classical transmission, the relevant Raman effect is stimulated Raman scattering (SRS), and recent studies have examined it in space-division multiplexing (SDM) fibers. An intrinsic relation between SpRS and SRS allows previous SRS results to inform SpRS models. In this work, we extend SpRS models derived for single-mode fibers (SMFs) to SDM fibers with multiple mode groups of degenerate modes, covering both Stokes and anti-Stokes bands. The proposed model is a useful, fiber-design-independent tool for evaluating scattered noise in optical links, and it is validated through experimental measurements in field-deployed multi-core fibers (MCFs) and multi-mode fiber (MMF), showing good agreement.

The first measurement of the jet axis decorrelation in events with jets recoiling from an isolated photon is presented for lead-lead (PbPb) and proton-proton (pp) collisions at a nucleon-nucleon center-of-mass energy of 5.02 TeV. The jet axis decorrelation is the angular difference ($Δ{j}$) between two definitions of the jet axis. This quantity is expected to be sensitive to the scattering of jet constituents in the quark-gluon plasma (QGP). Events which have a leading isolated photon with transverse momentum 60 $\lt$ $p_{\mathrm{T}}^γ$ $\lt$ 200 GeV and recoiling jets with 30 $\lt$ $p_{\mathrm{T}}^{\text{jet}}$ $\lt$ 100 GeV are selected for the analysis. The PbPb result is reported as a function of collision centrality and compared to pp reference data. Jets with $p_{\mathrm{T}}^{\text{jet}}$ $\lt$ 60 GeV have consistent $Δ{j}$ shapes for pp and PbPb collisions. However, a narrowing is observed for jets with $p_{\mathrm{T}}^{\text{jet}}$ $\gt$ 60 GeV in central PbPb collisions. The results are compared to predictions from the JEWEL, PYQUEN, and HYBRID theoretical models, which include different descriptions of parton energy loss in the QGP.

The swirling flow in a Francis type hydropower turbine is known to be susceptible to the formation of a large helical structure, commonly referred to as a vortex rope. This vortex rope can be interpreted as an unstable mode associated with vortex breakdown. This perspective is adopted here in a simplified laminar flow setting. The helical vortex rope mode is shown to bifurcate supercritically from an axisymmetric baseflow in a Hopf bifurcation within a turbine draft tube. When wall friction effects are neglected, a large recirculation region at the axis can form and a range of subcritical solutions is identified for a flow regime corresponding to partial load of the turbine. The existence of these subcritical solutions promotes the emergence of a hysteresis loop. We further describe a regular dynamics of a formation of recirculation bubble at the axis and its destruction due to the emergence of a helical vortex rope at its periphery. Increasing the axial flow discharge towards the regime corresponding to nominal turbine load leads to an unfolding of the steady solutions branch in a transcritical bifurcation. This bifurcation takes place at finite Reynolds number and complements existing evidence of transcritical bifurcation of the swirling jet flows, previously reported only in the inviscid limit.

Detecting the global 21 cm signal from the epoch of reionization remains a major observational challenge due to bright foregrounds and instrumental systematics. As part of the Colombian Antarctic Telescopes for 21 cm Absorption during Reionization (CANTAR) initiative, we present a simulation and analysis framework to evaluate antenna chromaticity, optimize instrument design, and assess site suitability for global 21 cm experiments. Using frequency-dependent beam models and Haslam-based sky maps, we compute dynamic spectra for the EDGES blade dipole and a set of dipole and novel monopole antennas optimized via particle swarm optimization. The optimized designs exhibit improved spectral smoothness compared to EDGES, particularly in the 70-120 MHz range. We also evaluate latitude-dependent sky brightness and identify mid-latitude sites (-40° to +5°) as optimal for foreground suppression. We apply Bayesian inference together with posterior predictive model validation to the publicly released EDGES data, assessing statistical consistency rather than hypothesis testing or model comparison. We find that physically motivated foreground and ionospheric models are statistically consistent with the data only when a 21 cm absorption feature is excluded. From the validated posterior, we generate a statistically validated ensemble of foreground corrections for use in beam-sky simulations. These results support a two-phase strategy for CANTAR: Antarctic deployments for calibration and testing, and future science operations at mid-latitude sites. Our framework provides a validated path toward robust foreground modeling, antenna design, and systematics control for global 21 cm signal detection.

We show that the images of the Bethe subalgebras of the Yangians $Y(\mathfrak{gl}_{n})$ and $Y(\mathfrak{gl}_{m})$ under the homomorphisms to $U(\mathfrak{gl}_{n+m})$ given by the Olshanski centralizer construction coincide. We use this result to obtain the $(\mathfrak{gl}_{n},\mathfrak{gl}_{m})$-duality of the trigonometric Gaudin model and the XXX-spin chain. The duality is obtained in an explicit way relating the generating differential operator on one side and the generating difference operator on the other, thus agreeing with the result of Mukhin, Tarasov and Varchenko arXiv:math/0605172.

Entity-Relationship (ER) modeling is commonly taught as a primarily technical activity, despite its central role in shaping how data systems represent people, processes, and institutions. Prior research in participatory design demonstrates that involving diverse stakeholders in modeling can surface tacit knowledge, challenge implicit assumptions, and produce more inclusive data representations. However, database education currently lacks structured pedagogical approaches for teaching participatory ER modeling in practice. We introduce the GARLIC methodology for teaching and learning participatory ER modeling. GARLIC adapts and extends the ONION participatory ER modeling framework of Makovska et al.(HILDA 2025) into a workshop-based learning format that combines role-playing, collaborative synthesis, guided critique, and iterative refinement. GARLIC is designed to develop both technical modeling skills and critical awareness of the social and ethical dimensions of data representation. GARLIC lowers the barrier to participatory ER modeling and equips students with practical skills for collaborative, inclusive data model design.

We study the two-dimensional equations of motion for a charged particle subjected to white, thermal, and active noises in uniform a magnetic field. By deriving the corresponding Fokker Planck equation, analytical solutions for the joint probability density are obtained in different time domains.

In this paper, we present novel methodologies that incorporate auxiliary variables for multiple hypotheses testing related to the main point of interest while effectively controlling the false discovery rate. When dealing with multiple tests concerning the primary variable of interest, researchers can use auxiliary variables to set preconditions for the significance of primary variables, thereby enhancing test efficacy. Depending on the auxiliary variable's role, we propose two approaches: one terminates testing of the primary variable if it does not meet predefined conditions, and the other adjusts the evaluation criteria based on the auxiliary variable. Employing the copula method, we elucidate the dependence between the auxiliary and primary variables by deriving their joint distribution from individual marginal distributions.Our numerical studies, compared with existing methods, demonstrate that the proposed methodologies effectively control the FDR and yield greater statistical power than previous approaches solely based on the primary variable. As an illustrative example, we apply our methods to the Set4$Δ$ mutant dataset. Our findings highlight the distinctions between our methodologies and traditional approaches, emphasising the potential advantages of our methods in introducing the auxiliary variable for selecting more genes.

Static security analysis is a widely used technique for detecting software vulnerabilities across a wide range of weaknesses, application domains, and programming languages. While prior work surveyed static analyzes for specific weaknesses or application domains, no overview of the entire security landscape exists. We present a systematic literature review of 246 static security analyzers concerning their targeted vulnerabilities, application domains, analysis techniques, evaluation methods, and limitations. We observe that most analyzers focus on a limited set of weaknesses, that the vulnerabilities they detect are rarely exploitable, and that evaluations use custom benchmarks that are too small to enable robust assessment.

The steady-state quantum dynamics of three dipole-dipole coupled two-level emitters, fixed at the vertices of an equilateral triangle, and interacting via the environmental thermostat is investigated. We have analytically obtained the populations of the involved three-atom cooperative states as well as of the second- and third-order spatial photon correlation functions of the light scattered by the few-qubit sample. As a consequence, we have demonstrated that this incoherently excited system spontaneously generates streams of single photons possessing sub-Poissonian photon statistics. In analogy to the dipole-dipole blockade, one may expect that at smaller inter particle distances, compared to the photon emission wavelength, the reported phenomenon has the same origin. However, we have shown that the quantum photon features are due to the interaction's nature of the few symmetrically arranged two-level emitters with the surrounding thermal reservoir. Respectively, at larger atomic intervals the effect occurs because of high-order spatial interference phenomena. Sub-wavelength interference fringes can be observed too, via measurements of spatial higher-order photon correlation functions.

Symmetry-lowering structural phase transitions result in multiple degenerate structures whose coexistence is determined by macroscopic strain compatibility. In quantum materials, these structural transformations often couple to electronic degrees of freedom, yet how the structural arrangements influence electronic phase transitions remains poorly understood. By analyzing hundreds of diffraction peaks from X-ray reciprocal space mapping, we determine the lattice basis vectors and mutual orientations of all coexisting phases in epitaxial V2O3 thin films after a symmetry-lowering transformation coincident with a metal-insulator transition. We identify the orientations of interfaces between all coexisting structures using the theory of martensitic phase transformations and find that the low temperature structure comprises finely tuned layered mixtures of alternating twin variants, akin to metal alloys. By comparing films grown on various substrate orientations, we show that the metal-insulator transition temperature increases monotonically with the degree to which these layered mixtures satisfy macroscopic strain compatibility imposed by the substrate.

Ferroelectric membranes transferred onto arbitrary substrates provide reduced mechanical clamping at the interfaces that can diminish the effective polarization-rotation barrier offering a pathway to engineer larger electromechanical and thermally driven responses in oxide electronics. Here, we report integration of single crystalline thin film BaTiO3 (BTO) ferroelectric membrane on Si and demonstrate a 4x at 30C and 34x at 60C enhancement of pyroelectric coefficient compared to clamped films. The BTO membrane is grown epitaxially on a water-soluble Sr3Al2O6 sacrificial layer, released by selective dissolution, and transferred onto Si, yielding a strain-relaxed membrane with robust intrinsic polarization. Temperature dependent piezoresponse force microscopy (PFM) reveals pronounced thermally driven evolution of domain orientation, consistent with reduced barriers for dipolar modulation in the freestanding state. Variable-temperature Kelvin probe force microscopy (KPFM) quantifies an effective pyroelectric coefficient of ~75 uC/m^2K at 30C and 450 uC/m^2K at 60C with a detectivity of 40 m^2K^-1at room temperature. These results establish lead-free freestanding BTO membranes as a promising silicon-integrable platform for cryogen-free infrared detection and waste-heat energy management.

Engineering and materials software is increasingly difficult to track in the scholarly and technical literature because publication volume is growing rapidly and software citation practices remain inconsistent. This is particularly true for the Ansys Granta product family, which is used for materials education, materials and process selection, sustainability-driven design, and enterprise materials information management. We present a structured and reproducible framework to consolidate evidence of \emph{operational} Granta usage and to support quantitative monitoring of adoption patterns, application domains, and technical impact. The framework is implemented as a curated reference database in \textit{Ansys Granta MI Enterprise}: bibliographic metadata are ingested semi-automatically (e.g., via DOI and citation-file parsing) and complemented by expert curation of usage descriptors (product, context, application domain, and technical depth), with relational links to authors and institutions. Downstream analytics are performed with Python, dashboards, and bibliometric/network visualization tools to enable reproducible querying and reporting. As of September~2025, the database contains more than 1{,}100 curated records spanning journals, conferences, theses, books, patents, standards, and reports, and supports rapid retrieval of validated case studies, reproducible literature reviews, and technology scouting. Example analyses highlight dominant domains, key institutions, and recurring integrations with CAD/CAE/FEM environments. Overall, the approach converts heterogeneous software-usage evidence into structured, analyzable knowledge to improve visibility of engineering software impact and to support evidence-based assessment and strategic decision-making.

Deploying multiple beyond diagonal reconfigurable intelligent surfaces (BD-RISs) can potentially improve the communication performance thanks to inter-element connections of each BD-RIS and inter-surface cooperative beamforming gain among BD-RISs. However, a major issue for multi-BD-RISassisted communication lies in the channel estimation overhead - the channel coefficients associated with the off-diagonal elements in each BD-RIS's scattering matrix as well as those associated with the reflection links among BD-RISs have to be estimated. In this paper, we propose an efficient channel estimation framework for double-BD-RIS-assisted multi-user multipleinput multiple-output (MIMO) systems. Specifically, we reveal that high-dimensional cascaded channels are characterized by five low-dimensional matrices by exploiting channel correlation properties. Based on this novel observation, in the ideal noiseless case, we develop a channel estimation scheme to recover these matrices sequentially and characterize the closed-form overhead required for perfect estimation as a function of the numbers of users and each BD-RIS's elements and channel ranks, which is with the same order as that in double-diagonal-RIS-aided communication systems. This exciting result implies the superiority of cooperative BD-RIS-aided communication over the diagonal- RIS counterpart even when channel estimation overhead is considered. We further extend the proposed scheme to practical noisy scenarios and provide extensive numerical simulations to validate its effectiveness.

Accurate state estimation is a crucial requirement for the reliable operation and control of electric power systems. Here, we construct a data-driven, numerical method to infer missing power load values in large-scale power grids. Given partial observations of power demands, the method estimates the operational state using a linear regression algorithm, exploiting statistical correlations within synthetic training datasets. We evaluate the performance of the method on three synthetic transmission grid test systems. Numerical experiments demonstrate the high accuracy achieved by the method in reconstructing missing demand values under various operating conditions. We further apply the method to real data for the transmission power grid of Switzerland. Despite the restricted number of observations in this dataset, the method infers missing power loads rather accurately. Furthermore, Newton-Raphson power flow solutions show that deviations between true and inferred values for power loads result in smaller deviations between true and inferred values for flows on power lines. This ensures that the estimated operational state correctly captures potential line contingencies. Overall, our results indicate that simple data-based regression techniques can provide an efficient and reliable alternative for state estimation in modern power grids.

We consider the two- and three-flavor QMD models as renormalizable low-energy models for QCD at finite quark chemical potentials with quarks, mesons, and diquarks as effective degrees of freedom. Using the on-shell scheme the parameters in the scalar sector can be fixed and expressed in terms of observed meson masses and decay constants. The remaining parameters can be varied. In the QMD models, all the symmetries are global, including the $SU(N_c)$ symmetry. The breaking of the global symmetries gives rise to a number of Goldstone bosons depending on the symmetry-breaking pattern, i.e. whether the system is in the 2SC phase or the color-flavor-locked (CFL) phase. This is in contrast to perturbative QCD, where some of the gauge bosons become massive via the Higgs mechanism. We classify the Goldstone bosons and show that their type and number are in accordance with general counting rules. The thermodynamic potential $Ω$ is calculated in the mean-field approximation, where we include quark loops, while mesons and diquarks are treated at tree level. As important applications, we study the properties of the pion-condensed phase at finite isospin chemical potential, and the 2SC and CFL phases at finite baryon chemical potential. We present a few numerical results focusing on the speed of sound, gaps, and condensates. It is shown that the BCS gaps approaches a constant for large isospin and baryon chemical potentials and that the speed of sound approaches the conformal value from above in the same limit.

Let $ \mathbb F_2[u]/ \langle u^k \rangle= \mathbb F_2+u\mathbb F_2+u^2\mathbb F_2+\cdots+u^{k-1}\mathbb F_2 ,$ where $u^k=0$ for a positive integer $k$, and $\mathcal{R}=M_4 (\mathbb F_2( u)/ \langle u^k \rangle)$ be the finite noncommutative non-chain matrix ring of order $4\times4$. This paper presents the construction of cyclic codes over the finite field $\mathbb F_{16}$ via the considered matrix ring $\mathcal{R}$. In this connection, first, we discuss the structure of the ring $\mathcal{R}$ and show that $\mathcal{R}$ is isomorphic to the ring $( \mathbb F_{16}+ v\mathbb F_{16} + v^2\mathbb F_{16} + v^3\mathbb F_{16}) + u(\mathbb F_{16} + v\mathbb F_{16} + v^2\mathbb F_{16} + v^3\mathbb F_{16}) + u^2(\mathbb F_{16} + v\mathbb F_{16} + v^2\mathbb F_{16}+ v^3\mathbb F_{16}) + \cdots + u^{k-1}(\mathbb F_{16} + v\mathbb F_{16} + v^2\mathbb F_{16} + v^3\mathbb F_{16})$ where $v^4=0, u^k=0, u^iv^j=v^ju^i$ for $i \in \{1,\dots, k-1\}$ and $j \in \{1, 2, 3\}$. Then, we establish the form of ideals of the ring $\mathcal{R}$ and related cyclic codes over $\mathcal{R}$. Further, we show that these cyclic codes can be written as the direct sums of $\mathcal{R}$-submodules of $\frac{\mathcal{R}[x]}{<x^n-1>}$, and derive the formula for the cardinality of cyclic codes over $\mathcal{R}$. Then, we consider the Euclidean and Hermitian duals of the derived cyclic codes over $\mathcal{R}$. Under the module isometry for $\mathcal{R}$, we use the Bachoc map and the Gray map, which takes a derived cyclic code over $\mathcal{R}$ to $\mathbb F_{16}$. Finally, we provide some non-trivial examples of linear codes over $\mathbb F_{16}$ with good parameters that support our derived results and compare a few codes with existing codes in the literature.

This paper considers a millimeter wave (mmWave) integrated sensing and communication (ISAC) system, where a base station (BS) equipped with a large number of antennas but a small number of radio-frequency (RF) chains emits pencillike narrow beams for persistent tracking of multiple moving targets. Under this model, the tracking lost issue arising from the misalignment between the pencil-like beams and the true target positions is inevitable, especially when the trajectories of the targets are complex, and the conventional Kalman filter-based scheme does not work well. To deal with this issue, we propose a Transformer-based mmWave multi-target tracking framework, namely m3TrackFormer, with a novel re-acquisition mechanism, such that even if the echo signals from some targets are too weak to extract sensing information, we are able to re-acquire their locations quickly with small beam sweeping overhead. Specifically, the proposed framework can operate in two modes of normal tracking and target re-acquisition during the tracking procedure, depending on whether the tracking lost occurs. When all targets are hit by the swept beams, the framework works in the Normal Tracking Mode (N-Mode) with a Transformer encoder-based Normal Tracking Network (N-Net) to accurately estimate the positions of these targets and predict the swept beams in the next time block. While the tracking lost happens, the framework will switch to the Re-Acquisition Mode (R-Mode) with a Transformer decoder-based Re-Acquisition Network (RNet) to adjust the beam sweeping strategy for getting back the lost targets and maintaining the tracking of the remaining targets. Thanks to the ability of global trajectory feature extraction, the m3TrackFormer can achieve high beam prediction accuracy and quickly re-acquire the lost targets, compared with other tracking methods.

The invariance properties of Brownian motion are investigated and revisited within a recent Lie symmetry approach to stochastic differential equations. Some notable properties of the process can be recovered by a related integration by parts formula developed in the same research area.

This paper develops a hybrid output-feedback control framework for average dwell-time (ADT) switched linear systems subject to actuator saturation. The considered subsystems may be exponentially unstable, and the saturation nonlinearity is explicitly handled through a deadzone-based representation. The proposed hybrid controller combines mode-dependent full-order dynamic output-feedback controllers with a supervisory reset mechanism that updates controller states at switching instants. By incorporating the reset rule directly into the synthesis conditions, switching boundary constraints and performance requirements are addressed in a unified convex formulation. Sufficient conditions are derived in terms of linear matrix inequalities (LMIs) to guarantee exponential stability under ADT switching and a prescribed weighted ${\cal L}_2$-gain disturbance attenuation level for energy-bounded disturbances. An explicit controller construction algorithm is provided based on feasible LMI solutions. Simulation results demonstrate the effectiveness and computational tractability of the proposed approach and highlight its advantages over existing output-feedback saturation control methods.

Graph colouring is a combinatorial optimisation problem with applications in several important domains, including sports scheduling, cartography, street map navigation, and timetabling. It is also of significant theoretical interest and a standard subject in university-level courses on graph theory, algorithms, and combinatorics. In this paper, we consider the topics of node, edge, and face colouring along with their associated algorithms. Theoretical results are reviewed and brought to life through a collection of detailed, visually engaging figures designed to enhance understanding and appeal.

We compute the value of finitary localizing invariants, including algebraic $K$-theory, on categories of sheaves over stably locally compact spaces $X$. Our formula simultaneously generalizes the cases of locally compact Hausdorff and coherent (spectral) spaces and recovers several smaller $K$-theory calculations as special instances.

A signed graph $(G,σ)$ consists of a graph $G$ and the signature $σ: E(G) \rightarrow \{+1,-1\}$. An incidence of $G$ is a pair $(v,e)$, where $v$ is one of the end vertices of an edge $e \in E(G)$. A proper $q$-edge coloring $γ$ of signed graph $(G,σ)$ is an assignment of colors to incidences satisfying that $γ(v,e) = - σ(e) γ(w,e)$ for every edge $e=vw$ and for any two incidences $(v,e)$ and $(v,f)$, involving the same vertex, $γ(v,e) \neq γ(v,f)$. The chromatic index of a signed graph $(G,σ)$, denoted by $χ'(G,σ)$, is the minimum number $q$ for which $(G,σ)$ has a proper $q$-edge coloring. In this paper, we determine the chromatic index of signed generalized book graphs. We also determine the chromatic index of signed complete graphs of order up to six.

The use of reflection high energy electron diffraction (RHEED) plays a critical role for in-situ characterization in molecular beam epitaxy, pulsed laser deposition and sputtering. While sensitive to crystal symmetries and morphology, it is used ubiquitously to determine the growth modes of thin films. However, analysis of RHEED patterns depends on skilled experts and is therefore difficult to incorporate into the growth strategy in real-time. The development of machine learning (ML) processes, specifically convolutional neural networks (CNNs), presents a unique opportunity towards real-time RHEED pattern recognition. In this study, we develop a CNN model that can accurately classify four common and distinct RHEED patterns present in chalcogenide thin film growth. Its reached accuracy reached 94.9% for single run and 91.2% when averaged over 20 seeds. Our network is able to distinguish the nucleation of three common growth modes encountered in epitaxy, namely Volmer Weber, Stransky-Krastanov and Frank-van der Merwe, potentially enabling future automation of substrate temperature and shutter control informed by RHEED data. The network is material-agnostic and distinguishes the VW process with greater than 98% accuracy but is somewhat more limited in its ability to properly classify roughening and the initiation of Stransky-Krastanov growth. Our findings show that ML techniques can be successfully implemented even in cases where there is no detailed knowledge of growth chemistry providing an avenue towards real-time incorporation of ML to control nanostructure nucleation and thin film morphology.

Keeping pace with rapidly evolving technology is a key challenge in teaching statistics. To equip students with essential skills for the modern workplace, educators must integrate relevant technologies into the statistical curriculum where possible. University-level statistics education has experienced substantial technological change, particularly in the tools and practices that underpin teaching and learning. Statistical programming has become central to many courses, with R widely used and Python increasingly incorporated into statistics and data analytics programmes. Additionally, coding practices, database management, and machine learning now feature within some statistics curricula. Looking ahead, we anticipate a growing emphasis on artificial intelligence (AI), particularly the pedagogical implications of generative AI tools such as ChatGPT. In this article, we explore these technological developments and discuss strategies for their integration into contemporary statistics education.

We present a Rice-like complexity lower bound for any MSO-definable problem on binary structures succinctly encoded by circuits. This work extends the framework recently developed as a counterpoint to Courcelle's theorem for graphs encoded by circuits, in two interplaying directions: (1) by allowing multiple binary relations, and (2) by restricting the interpretation of new symbols. Depending on the pair of an MSO problem $ψ$ and an MSO restriction $χ$, the problem is proven to be NP-hard or coNP-hard or P-hard, as long as $ψ$ is non-trivial on structures satisfying $χ$ with bounded clique-width. Indeed, there are P-complete problems (for logspace reductions) in our extended context. Finally, we strengthen a previous result on the necessity to parameterize the notion of non-triviality, hence supporting the choice of clique-width.

The Laser Interferometer Space Antenna (LISA) mission aims to detect gravitational waves by interferometrically measuring the change of separation between free-falling test masses (TMs). LISA's interferometers must deliver pm/rtHz sensitivity while accommodating beam tilts up to 1 mrad at the photodiodes, which degrade the interferometric amplitude and increase the induced readout noise coupling. This paper uses an analytical framework developed by the authors in a previous work, based on minimal and justified approximations, that relates beam tilt to the resulting heterodyne signal amplitude in a generic two-beam interferometer with circular-area photodiodes (PDs). A set of interferometric topologies is analyzed, all of high relevance for LISA. We derive the exact amplitude response for an infinite detector and a closed-form approximation for finite detectors, and we validate both against numerical simulations and experimental measurements on an ultra-stable LISA-representative testbed. We then use this model to quantify the phase-noise amplification arising from reduced signal-to-noise ratio (SNR) under tilt, showing that curvature mismatches between the interfering beams substantially enhance this effect. Finally, we introduce a compact function that captures the angular dependence of correlated and uncorrelated phase noises in quadrant photodiode (QPD)-based readouts. Here, a new noise feature, caused by wavefront curvature mismatch, is predicted and measured for the first time. These results indicate that controlling wavefront curvature mismatch in the test mass interferometer (TMI) is essential to limit excess phase noise. The models and results derived in this paper, although originating in the context of LISA, are general and can be applied to any interferometric topology undergoing tilts with pivot on the detector plane.

The field of constraint satisfaction problems (CSPs) studies homomorphism problems between relational structures where the target structure is fixed. Classifying the complexity of these problems has been a central quest of the field, notably when both sides are finite structures. In this paper, we study the generalization where the input is an automatic structure -- potentially infinite, but describable by finite automata. We prove a striking dichotomy: homomorphism problems over automatic structures are either decidable in non-deterministic logarithmic space (NL), or undecidable. We show that structures for which the problem is decidable are exactly those with finite duality, which is a classical property of target structures asserting that the existence of a homomorphism into them can be characterized by the absence of a finite set of obstructions in the source structure. Notably, this property precisely characterizes target structures whose homomorphism problem is definable in first-order logic, which is well-known to be decidable over automatic structures. We also consider a natural variant of the problem. While automatic structures are finitely describable, homomorphisms from them into finite structures need not be. This leads to the notion of regular homomorphism, where the homomorphism itself must be describable by finite automata. Remarkably, we prove that this variant exhibits the same dichotomy, with the same characterization for decidability.

In this work, we propose a new three-dimensional nonlocal spinor superfield model. This theory is constructed by introducing form factors in the local spinor superfield action. Then, we couple it minimally to a scalar superfield, for which we calculate the one-loop effective potential as a first constructive example of perturbative calculations in this new theory.

We report an experimental investigation of turbulent Rayleigh-Benard convection in a rectangular cell of large aspect ratio ($Γ= 10$) over the Rayleigh number range $5.4\times10^7 \le Ra \le 7.2\times10^9$ and Prandtl number range $4.3 \le Pr \le 67.3$. Planar particle image velocimetry measurements show that the flow self organises into several horizontally stacked convection rolls, and repeated experiments under identical parameters (both $Ra$ and $Pr$) reveal that the number of rolls varies within the range of 3 to 7 with 6 being the most probable, which demonstrates the presence of multiple flow states. When $Pr$ is increased to 67.3, the number of roll like structures increases significantly, indicating a structural transition from a roll dominated to a plume dominated flow. This transition is reflected in the global momentum transport, for $Pr \leq 18.3$ the Reynolds number scales as $Re \sim Ra^{0.58}Pr^{-0.97}$, whereas the scaling is changed to $Re \sim Ra^{0.72}$ when $Pr$ reaches 67.3. Within individual rolls, we further examine the Reynolds numbers based on horizontal and vertical velocity components, $Re_{u,\text{roll}}$ and $Re_{w,\text{roll}}$, and find that the former increases while the latter decreases with roll size (quantified as the aspect ratio of the roll $Γ_\text{roll}$) due to continuity constraints, with their ratio following $Re_{w,\text{roll}}/Re_{u,\text{roll}} \sim Γ_\text{roll}^{-0.61}$. We impose different initial flow conditions (roll structures) with controlled perturbations, and demonstrate that the initial condition can influence the final turbulent state. We show that the number of horizontally stacked rolls regulates the global transport, larger number of rolls induces greater vertical momentum and heat transfer.