With recent data from the \emph{James Webb Space Telescope} (JWST), it is possible to calculate the mass of the supermassive black holes at the centre of galaxies, and the stellar mass of the host galaxies at $z \gtrsim 5$. In this work, we apply the method of extreme-value statistics to calculate the distributions of extreme black hole and stellar mass for the redshift range $3.5 \lesssim z \lesssim 8.5$. We sample these distributions to obtain a prediction for the black hole to stellar mass ratio of $\sim0.24$ over this redshift range, with the median in each bin varying in the range $0.18-0.35$. Our predictions are consistent with the highest observed values of the ratio from JWST observations of high-redshift galaxies.

In the framework of the $Λ$CDM model, galaxies evolve within dark matter (DM) haloes, where baryonic processes modify the inner structure of the DM distribution. In particular, baryon condensation and feedback can alter the inner density profiles of haloes, motivating studies of their central regions. The aim of this work is to investigate the inner slope of the DM density profiles of galaxies in the TNG50 simulation, its relation to galaxy properties, its evolution with redshift, and the impact of baryonic processes by comparing galaxies to a corresponding dark matter-only (DMO) realisation. Spherically averaged DM density profiles are constructed for galaxies in TNG50 and the DMO run. The inner slope is quantified using an Inner Linear Fit (ILF), defined as a power-law fit to the central region of the density profiles and motivated by the asymptotic behaviour of generalized NFW models. Subhaloes are matched between simulations and tracked across $z=0$, $0.2$, $0.7$, and $1$. The inner DM structure of galaxies in TNG50 shows that high-stellar-mass systems ($M_\star \gtrsim 10^{11}$ M$_\odot$) exhibit shallow inner slopes irrespective of being centrals or satellites, while lower-mass galaxies ($M_\star \lesssim 10^{9}$ M$_\odot$) show a broader diversity of profiles. At fixed stellar mass, low-mass satellites tend to be more cuspy, with the steepest slopes found in redder systems with lower $V_{\max}$ in more massive host haloes. We find a clear cosmic evolution, from shallower slopes at $z \sim 1$ to steeper profiles towards low redshift in both hydrodynamical and DMO runs, with hydrodynamical galaxies steeper. Finally, we verify that the population exhibiting the steepest slopes remains qualitatively robust to variations in the adopted fitting range, as extending the fit to larger radii$-$thereby excluding the innermost regions$-$generally leads to even steeper inferred slopes.

Incels are an online community of men who share a belief in extreme misogyny, the glorification of violence, and biological essentialism. They refer to their core ideology as "The Blackpill", a belief that physical attraction is the only path to romantic success and that women are only attracted to one very specific, hypermasculine archetype. This is not only a belief system; incels believe their ideology grounded in hard science. The research that incels use as evidence of their belief system is collected in an extensive online document, the Scientific Blackpill wiki page. In this research, we analyze the claims made on the wiki against the research cited to assess how the wiki authors are using or misusing science in support of their ideology. We find that the page largely cites legitimate science and describes it partly or mostly accurately. However, in discussing it, the results are often overgeneralized, stripped of context, or otherwise distorted to support the preexisting incel viewpoint. This echoes previous findings about motivated reasoning and borrowing scientific legitimacy in other misinformation and conspiracy-minded ideologies. We discuss the implications this has for understanding online radicalization and information quality.

We study toric orbifolds of real dimension four with vanishing odd-degree cohomology and obtain a basis for its degree-two equivariant cohomology with integral coefficients by identifying it with the intersection of certain lattices. As applications, we provide an alternative construction of the \emph{algebraic cellular basis} for integral ordinary cohomology \cite{FSS2}. In addition, when the toric orbifold is an algebraic variety, we determine its Cartier divisor group and Picard group.

In this paper, we discuss topological aspects of the space of valuations $\mathbb{V}$ and the valuative tree $\mathcal{T}(v,Λ)$. We present a relation between the weak tree topology and the Scott topology in $\mathcal{T}(v,Λ)$ and describe the supremum of an increasing family of valuations in a special subtree. We also view the valuative tree as a subset of the product $(Λ_\infty)^{K[x]}$ and prove that it is closed if we consider the natural product topology.

We establish a variant of Monge--Kantorovich duality for a constrained optimal transport problem with a continuum of agents, a finite set of alternatives, and general linear constraints. As an application, we revisit the large-market model of indivisible goods in Azevedo et al. (2013), identify a flaw in the original equilibrium-existence proof stemming from an incorrect compactness claim, and recover equilibrium existence via our duality approach. We also characterize equilibrium prices as minimizers of a potential function, which yields a method for computing equilibrium prices.

Path queries are crucial for property graphs, and there is growing interest in queries that combine regular expressions over labels with constraints on property values of vertices and edges. Efficient evaluation of such general path queries requires that intermediate results be eliminated early when there is no possible completion to a full result path. Neither state-of-the-art (SOA) graph DBMS nor relational DBMS currently can do this effectively for a large class of queries. We show that this problem can be addressed by giving a relational optimizer ``a little help'' by specifying early filtering opportunities explicitly in the query. To this end, we propose ReCAP, an abstraction that greatly simplifies the implementation of early filtering techniques for any type of property constraint for which such early filtering can be derived. No matter how complex the constraint, one only needs to implement (1) an NFA-style state transition function and (2) a handful of functions that mirror those needed for user-defined aggregates. We show that when using ReCAP, a standard relational DBMS like DuckDB can effectively push property constraints deep into the query plan, beating the SOA graph and relational DBMS by a factor up to 400,000 over a variety of queries and input graphs.

We introduce chaos-controlled Reservoir Computing (cc-RC) for living neural cultures: dynamically rich substrates of unique potential for adaptive computation. To account for intrinsic biological variability, cc-RC combines: (i) pre-training identification of each culture's dynamical signature and phase-portrait attractor; (ii) low-power optical chaos control to stabilize spontaneous and stimulus-evoked activity; (iii) readout training within this controlled regime. Across hundreds of neural samples, cc-RC enables robust learning and pattern classification, improving both accuracy and model longevity by approximately 300% over standard RC. We further propose Knowledge Transplant (KT), for which the reservoir map learned by an expert culture is transplanted to an attractor-equivalent student culture, reducing training time to minutes while improving performance. By enabling cross-substrate, reusable learned models, KT paves the way for knowledge accumulation and sharing across neural populations, transcending biological lifespan limits.

Silicon photo-multipliers (SiPMs) are state-of-the-art sensors capable of detecting a single photoelectron under cryogenic conditions, with potentially lower radioactivity than widely used photomultiplier tubes. The DarkSide-20k experiment, designed to perform direct dark matter searches using liquid argon as the target material, employs SiPM technology to detect interactions in the active detector volumes, including the central dual-phase Time Projection Chamber and the Inner and Outer Veto volumes. The vetoes are designed to discriminate against radiogenic neutron and cosmic muon backgrounds associated with the dark matter search. This paper describes the completed production and test protocols for the "Veto Tiles" (called vTiles, arrays of 24 SiPMs integrated on a printed circuit board providing the power distribution and signal amplification); 16 vTiles are grouped into "Veto Photo-Detector Units" to instrument the Inner Veto volume. Each vTile underwent detailed testing at room and cryogenic temperatures, confirming stable operation, high signal-to-noise ratio, and low radioactive contamination, demonstrating the robustness of the proposed design for cryogenic conditions. The final production yield exceeded 87%, surpassing the 80% requirement and corresponding to 1920 Veto Tiles to populate 120 Veto Photo-Detector Units, plus an additional 6% as spares.

Efficient simulation of strongly correlated electrons has become a routine tool in molecular electronic structure theory due to recent advances in approximate configuration interaction (CI) techniques. Nonetheless, the quantitative and predictive description of molecular electronic states remains a significant challenge due to the difficulty of computing all-electron correlation beyond CI. Here, we describe a new open-source implementation of the anti-Hermitian contracted Schrödinger equation (ACSE) for use in accurate simulation of all-electron correlation in molecules. In contrast to standard approaches via multireference perturbation theory, the scaling of the ACSE does not depend on the complexity of the strongly correlated reference wavefunction. Furthermore, the ACSE employs the exact electronic Hamiltonian, rather than an approximate perturbative Hamiltonian. Our benchmark results demonstrate good accuracy for main group and transition metal systems, in weakly and strongly correlated regimes, with various basis sets, and for ground and excited states. The results suggest that the ACSE has potential as a scalable and robust technique for simulating all-electron correlation in molecular ground and excited states.

Coding agents represent a new paradigm in automated software engineering, combining the reasoning capabilities of Large Language Models (LLMs) with tool-augmented interaction loops. However, coding agents still have severe limitations. Top-ranked LLM-based coding agents still fail on over 20% of benchmarked problems. Yet, we lack a systematic understanding of why (i.e., the causes) agents fail, and how failure unfolds behaviorally. We present a large-scale empirical study analyzing 9,374 trajectories from 19 agents (8 coding agent frameworks, 14 LLMs) on 500 tasks. We organize our analysis around three research questions. First, we investigate why agents fail on specific tasks and find that patch complexity alone does not explain difficulty: 12 never-solved tasks require only simple patches and were considered easy by human annotators, yet all agents fail due to gaps in architectural reasoning and domain knowledge. Second, we examine how behavioral patterns differentiate success from failure. The widely reported correlation between trajectory length and failure reverses direction once task difficulty is controlled, revealing it as a confound. Instead, trajectory structure discriminates consistently: agents that gather context before editing and invest in validation succeed more often, and these strategies are agent-determined rather than task-adaptive. Third, we disentangle LLM capability from framework design and find that the LLM is the primary driver of both outcome and behavior: agents sharing the same LLM agree on far more tasks than agents sharing the same framework, and the framework performance gap shrinks with each generation of LLM improvement. Framework prompts do influence agent tactics, but this influence diminishes with stronger LLMs.

The rapid adoption of AI coding agents and AI assistant web services is fundamentally changing how developers discover, consume, and interact with technical documentation. This paper studies that transformation across three interconnected dimensions: documentation accessibility, content analytics, and feedback systems. We present an empirical study of HTTP request fingerprints from nine AI coding agents (Aider, Antigravity, Claude Code, Cline, Cursor, Junie, OpenCode, VS Code, and Windsurf) and six AI assistant services (ChatGPT, Claude, Google Gemini, Google NotebookLM, MistralAI, and Perplexity) accessing a live developer documentation endpoint, revealing identifiable behavioral signatures in HTTP runtime environments, pre-fetch strategies, User-Agent strings, and header patterns. Our study shows that AI agent access compresses multi-page navigation into a single or two requests, making traditional engagement metrics - session depth, time-on-page, click path, and bounce rate - unreliable indicators of actual documentation consumption. We discuss practical adaptations for developer portal teams, including tokenomics-aware documentation design, adoption of emerging machine-readable standards (AGENTS.md, llms.txt, skill.md, agent-permissions.json), MCP server-based feedback channels, and analytics instrumentation for AI referral traffic.

We show that cascade-free counting from carry theory is a special case of a general transfer matrix construction. For any binary stateful digit-wise operation with GEN/PROP/KILL decomposition, the number of cascade-free sequences of length $L$ depends on only two parameters: the alphabet size $N$ and the product $d = |\text{GEN}| \cdot |\text{PROP}|$. The resulting sequence satisfies $a(L) = N a(L-1) - d a(L-2)$ and equals a scaled Chebyshev polynomial of the second kind with coupling parameter $x = N/(2\sqrt{d}) \geq 1$. We instantiate this for digit-wise addition and doubling in base $p$. For odd primes the exact relation $a_{\text{carry}}(L) = p^L a_{\text{dbl}}(L)$ holds. For $p = 3$ the cascade-free doubling count equals the Fibonacci bisection $F(2L+2)$ via $U_L(3/2) = F(2L+2)$ (OEIS A001906); we are not aware of this interpretation in the existing literature. We analyse the dispersion index $D = \text{Var}(ν)/E[ν]$ of the state count for uniformly distributed inputs. For symmetric chains ($g = k$) the Poisson transition $D_\infty = 1$ occurs at $μ= 1/3$, corresponding to base 3 where the Fibonacci bisection appears. The finite Poisson transition point $μ^*(L)$ decreases strictly to $1/3$ with rate $1/(6L) + O(1/L^2)$. We generalise to state spaces $|S| > 2$ via state avoidance. The restricted transfer matrix has dimension $s-1$; the Chebyshev representation persists for $|S| = 3$.

Coherent control of neutrons via Bragg diffraction forms the foundation of perfect crystal neutron interferometry, facilitating both fundamental tests of quantum mechanics and applications in quantum information science. In cavity geometries, perfect crystals enable neutron confinement and have been employed in precision measurements of spin-orbit interactions and for neutron electric dipole moment (nEDM) searches. However, in these conventional configurations, neutrons undergo a single pass through the crystal geometry, placing a physical constraint on both crystal and in-flight interaction times and measurement sensitivity. In this work, we introduce a neutron loop cavity that coherently recirculates neutrons through repeated Bragg reflections between perfect silicon crystal blades. This structure is predicted to achieve a neutron survival probability of $\sim64~\%$ for 10,000 Bragg reflections, corresponding to confinement times on the order of seconds. We propose a Schwinger interaction measurement that achieves a $π$ spin rotation in 800 Bragg reflections, representing more than a tenfold improvement in sensitivity over recent measurements. Further applications include high-sensitivity nEDM searches targeting the $10^{-27}~$e$\cdot$cm scale, as well as competitive experimental tests of neutron parity violation, the neutron lifetime, and the quantum Zeno effect with neutrons.

In this paper, we propose an efficient algorithm for data clustering based on the Moreau envelope, which approximates nonsmooth and nonconvex components of the generalized multi-source Weber problem. The number of clusters is not fixed in advance and is determined automatically by progressively removing empty or redundant clusters. The smoothing induced by the Moreau envelope transforms the original problem into a structured optimization task that can be efficiently solved using first-order methods and simple matrix vector operations. Numerical experiments on synthetic and real datasets show that the proposed approach is fast, scalable, and competitive with existing methods in both clustering quality and computational efficiency.

Perfect quantum state transfer is achievable in different settings, including linear qubit chains, bi-dimensional arrays, ladders, etc. The most studied case contemplates transferring arbitrary one-qubit pure states in systems with homogeneous interactions. These restrictions allow finding numerous examples of systems that show perfect transfer but in geometries that are not implementable or are very difficult to implement in actual experimental settings. Relaxing the homogeneity of the interactions and inspired by the $XX$ qubit chains that show perfect transmission, we present a simple scheme based on the Givens Transformations to analyse and obtain a class of qubit graphs that possess perfect quantum state transmission. We present some simple examples and show how it is possible to generalize them for longer transmission lengths.

We report a study of the diazabicyclo[2.2.2]octane (DABCO) molecule photoionized using VUV synchrotron radiation in combination with an ion--electron coincidence spectrometer. We determine accurately the adiabatic ionization energy to $7.199\pm0.006$~eV. Two vibrational progressions of DABCO cation ground state are resolved at $847~\text{cm}^{-1}\pm27~\text{cm}^{-1}$ and $1257~\text{cm}^{-1}\pm67~\text{cm}^{-1}$, which we assign to modes of $e'$ symmetry. Analysis of the photoelectron angular distribution shows that the anisotropy parameter depends on the vibrational excitation. This dependence of the $β$ parameter with the vibrational excitation is attributed to the scattering of the outgoing wavefunction mediated by high-lying Rydberg states.

Nonlinear contact dynamics are widely regarded as intrinsically nonlinear systems whose behaviour depends strongly on geometry and impact conditions. Here we show that any one-dimensional conservative contact system satisfying monotone energy-consistent conditions admits two complementary structures: (i) a canonical action-angle representation in physical time, and (ii) an exact harmonic oscillator representation under an energy-based coordinate transformation combined with time reparametrisation. This reveals a hidden linear structure underlying nonlinear contact interactions. Building on this result, we derive a unique universal damping law that preserves linear dissipative dynamics in the transformed harmonic space, and establish a rigorous, closed-form lower bound for the critical timestep in numerical simulations. The framework generalises classical power-law contact models and provides a unified basis for restitution control across arbitrary geometries, recovering known exact solutions as explicit monomial special cases.

We present \texttt{DR-DAQP}, an open-source solver for strongly monotone affine variational inequaliries that combines Douglas-Rachford operator splitting with an active-set acceleration strategy. The key idea is to estimate the active set along the iterations to attempt a Newton-type correction. This step yields the exact AVI solution when the active set is correctly estimated, thus overcoming the asymptotic convergence limitation inherent in first-order methods. Moreover, we exploit warm-starting and pre-factorization of relevant matrices to further accelerate evaluation of the algorithm iterations. We prove convergence and establish conditions under which the algorithm terminates in finite time with the exact solution. Numerical experiments on randomly generated AVIs show that \texttt{DR-DAQP} is up to two orders of magnitude faster than the state-of-the-art solver \texttt{PATH}. On a game-theoretic MPC benchmark, \texttt{DR-DAQP} achieves solve times several orders of magnitude below those of the mixed-integer solver \texttt{NashOpt}. A high-performing C implementation is available at \textt{https://github.com/darnstrom/daqp}, with easily-accessible interfaces to Julia, MATLAB, and Python.

The South Pole Telescope (SPT) collaboration has recently embarked upon a campaign to monitor the brightness of a sample of active galactic nuclei (AGN), both in real time and in archival SPT data. The original design of the SPT was optimized for observations of the cosmic microwave background (CMB) at arc-minute and larger angular scales, and it has been used for this purpose for nearly twenty years, using three generations of CMB cameras. Recently it has been recognized that data from CMB experiments have the potential to be used for AGN monitoring. In this paper, we present the first public release of data from a full sample of SPT-monitored AGN, comprising 158 AGN light curves and associated data from the SPTpol camera, which was operational from 2012-2016. These light curves were created using observations from the SPTpol 500 deg$^{2}$ survey, in which the instrument was used to scan a 500 deg$^2$ patch of the sky several times per day with detectors sensitive to radiation in bands centered at 90 and 150 GHz. We provide a comprehensive description of the observations, the data processing methods, and the resulting light curve catalog. As an example of analyses that these data enable, we searched for a correlation between variability and spectral index, and we looked for ``bluer-when-brighter'' trends in the sample. Our analysis finds $> 10 σ$ correlation between fractional intrinsic variance and mean spectral index in the sample, but no significant evidence for bluer-when-brighter trends. The datasets from this study can be accessed through the SPT Treasury Record of AGN With Historical Activity and Time-Series or STRAWHAT catalog. This initial data release includes SPTpol light curves at 90 and 150 GHz, focusing on total intensity. In later updates, SPTpol polarization data and new observations from the SPT-3G instrument at 90, 150, and 220 GHz will be included.

Statistical methods are indispensable to scientific inference. However, there exists a longstanding tension across a wide range of scientific disciplines about the role that ``context'' should play in the application of statistical methods and the interpretation of statistical results. Though frequently invoked, the notion of ``scientific context'' refers to at least two distinct concepts: a set of foundational nuanced and elusive background assumptions and substantive features of a given area of study that shape the validity and reliability of statistical methods; and more quantifiable contextual issues that affect the performance of statistical methods and interpretation of statistical results. I argue here that the application and interpretation of statistical methods requires careful consideration of foundational contextual issues. To motivate the arguments, I review a recent re-formulation of the $p$-value as a measure of divergence between an observed dataset and a set of assumptions used to construct statistical measures. I use this framework to illustrate the role that context plays in two randomized trials: on low-dose aspirin for pregnancy loss, and a new inhibitor of a key biochemical pathway affecting ankylosing spondylitis. Finally, I note that the adoption of low significance thresholds in genome-wide association studies and high energy particle physics has been successful more so because of extensive validity-checking gauntlets and contextual considerations that have accompanied these low thresholds, not because of the low thresholds themselves. I use these illustrations and arguments to suggest that (i) the adoption of a universal threshold for significance testing should be abandoned as a goal of statistics reform; and (ii) the validity and optimal use of applied statistical tools requires careful consideration of nuanced scientific context.

We present SESCC (Speed-Error Signals Cross-Correlation), a method for dating ancient star catalogues from the cross-correlation between stellar proper-motion speeds and positional residuals. At the true epoch, residuals are independent of proper-motion speed; the epoch estimate is the trial date that minimises this cross-correlation. For ecliptic latitudes, SESCC applies the dot product between speeds and residuals across all catalogue stars without subset selection or linear modelling. For ecliptic longitudes, SESCC-pairs uses pairwise longitude differences between neighbouring stars, making the method immune to any global longitude offset by algebraic construction. Validated against Tycho Brahe (1547 CE, true ~1580 CE) and Ulugh Beg (1452 CE, true 1437 CE), and confirmed invariant under offsets of +-6 deg, the method is applied to the Almagest. Both coordinates yield bootstrap distributions with 74% pre-Christian minima, consistent with a Hipparchan origin and inconsistent with a Ptolemaic one. The near-absence of quarter-degree fractions in the Almagest longitudes, explained as the deterministic consequence of Ptolemy's precession correction, provides independent corroboration.

A recent paper by Lien et al. (2025) introduces the "colored linear inverse model" (colored LIM), in which stochastic forcing is modeled using Ornstein-Uhlenbeck colored noise rather than idealized white noise. In that work, it is shown that the derivative-based identification formulas used to estimate model parameters do not admit a regular white-noise limit due to the loss of differentiability of the lag-correlation function at zero lag. Here we revisit the white-noise limit from the perspective of the underlying stochastic differential equations. Treating the colored LIM as an augmented Ornstein-Uhlenbeck system, we show that as the correlation time tau -> 0 the colored-noise-driven system reduces to the classical LIM, and the corresponding stationary covariance satisfies the standard fluctuation-dissipation relation. Re-examining the same linear system used by Lien et al. (2025), we illustrate this convergence numerically. These results highlight a distinction between the singular behavior of derivative-based identification formulas and the regular limiting behavior of the underlying stochastic model. Taken together with recent results showing convergence of estimated parameters in the white-noise limit, they provide a consistent interpretation in which the colored LIM recovers the classical LIM at the level of stochastic dynamics even though certain estimation procedures become ill-defined in that limit.

Asymmetric sound absorption is essential for advanced acoustic manipulation. However, current frequency modulation and broadbanding highly depend on geometric reconfiguration, leading to inevitable structural complexity that impedes their practical applications. Here, we propose a tunable, highly efficient, asymmetric ventilated acoustic system comprising two heterogeneous resonators. Specifically, it couples a highly dissipative space-coiling resonator (SCR) as a dark mode for energy consumption, alongside a weakly damped Helmholtz resonator as a bright mode acting as a reflective soft boundary. Theoretical and numerical analyses reveal strong asymmetry within the deep-subwavelength region (with a resonator size of approximately λ/9.4), achieving 99% absorption for left-incident waves and 98% reflection for right-incident ones. Furthermore, the SCR introduces an interesting degree of freedom for acoustic tuning. Simply rotating the resonator induces a 92% absorption drop (~11 dB attenuation), functioning as an "Acoustic Switch". Moreover, this rotation significantly shifts the operating band. By parallel-coupling multi-angle isomorphic resonators, we achieve efficient broadband absorption (>0.8) from 325 to 375 Hz, offering an attractive paradigm for tunable acoustic metasurfaces and ventilated absorbers.

In this paper, the problem of maximizing the sum-rate is addressed for a multi-user uplink scenario that is assisted by an active reconfigurable intelligent surface (RIS). The maximization is achieved by optimizing the beamforming at the base station, the users' transmit power, active RIS elements phase shifts, and active gains in presence of imperfect channel state information (CSI). The non-convex maximization problem is decomposed into sub-problems and solved via iterative approaches including the Lagrangian method, the projected gradient descent, multi-variate Taylor expansion and fractional programming. Numerical results show that the active RIS is more sensitive to CSI imperfections than passive one at high error variances.

This paper is concerned with eternal AdS black holes. The quantum cosmological future and past interior states of the black hole may be placed on an equal footing to the left and right AdS boundary data by considering the on-shell bulk action as a function of the left/right/future/past data: $S[ϕ^{(0)L},ϕ^{(0)R},ϕ^{(0)F},ϕ^{(0)P}]$. We call this object a holographic banner, and it obeys the Hamilton-Jacobi equation with respect to all four of its arguments. We compute the holographic banner for a scalar field in an AdS black hole background explicitly and use it to construct the semiclassical state in the future interior obtained from a thermofield double state in the past evolved by arbitrary time- and space-dependent boundary sources. When the spacetime itself is dynamical we explain how the holographic banner gives, in principle, a map from boundary data to near-singularity semiclassical quantum cosmology following chaotic BKL dynamics. We obtain the timescale for the BKL dynamics to ergodically mix the future interior quantum state, given a quantum variance in the past state or a classical ensemble of boundary theories.

We present a broadly applicable structurally flat triangular form for x-flat control-affine systems with three inputs. Building on recent results for the derivative structure of flat outputs, we define the triangular form together with regularity conditions that guarantee structural flatness, and derive necessary and sufficient conditions for a system with a given x-flat output to be static feedback equivalent to this form. Further, we present sufficient conditions under which general x-flat three-input systems can be rendered static feedback equivalent to the proposed triangular form after a finite number of input prolongations.

Performance-barrier event-triggered control (P-ETC) is a methodology implemented to increase the dwell-times between events while still preserving a prescribed performance of the system under event-triggered control (ETC). This is achieved by considering the performance residual of the system, which is a measure of the system performance with respect to the prescribed performance. This allows the Lyapunov function candidate to deviate from decreasing monotonically. In order to determine the performance residual, it is required to know the full-state information, leading to all work related to P-ETC to be under full-state feedback. In this article, we propose a novel dynamic performance-barrier under output feedback with an exponentially convergent observer. We consider event-triggered boundary control of a class of $2\times2$ linear hyperbolic PDEs with anti-collocated measurements with the control input. Under the proposed P-ETC mechanism, we prove the existence of a minimum dwell-time, and show the global exponential stability of the spatial $L^2$ norm of the solution of the system. Simulation results are presented to validate the theoretical claims.

We investigate Nelson--Barr solutions to the strong CP problem in which spontaneous CP violation is transmitted to the Standard Model through mixing with a vector-like partner of the SM quark doublet. We show that these constructions constitute compelling and phenomenologically viable alternatives to the more widely studied singlet-based NB models. A key result of our analysis is that an accidental symmetry of the renormalizable theory delays the leading contributions to \barθ until three loops, naturally suppressing hadronic CP violation. We outline the main phenomenological constraints, including future EDM experiments, as well as the main differences between these scenarios and generic models with doublet vector-like quarks.

This work presents the system identification of a variable-pitch propeller (VPP) powertrain, encompassing the full actuation chain from PWM signals to thrust generation, with the aim of developing compact models suitable for real-time digital twinning and control applications. The identification is grounded in experimental data covering both static and dynamic responses of the system. The proposed model takes the form of a Wiener-like architecture, where the PWM inputs are first processed through linear first-order dynamics describing the motor and pitch actuation, and the resulting states are then mapped via a static nonlinear relation to the generated thrust. This structure naturally arises under the assumptions that the electronic actuation operates on a much faster time scale than the mechanical response, and that the contribution of the aerodynamically induced torque is negligible in the tested regime. The resulting parsimonious representation is shown to reproduce the measured dynamics with good accuracy while remaining interpretable and computationally light, thereby providing a practical basis for integration in control-oriented digital twin frameworks.