We investigate whether the formally infinite-dimensional supertranslation sector of the Bondi-Metzner-Sachs (BMS) group remains fully physically admissible once classical energy conditions are enforced. Working in a perturbative framework $g_{ab}\rightarrow g_{ab}+h_{ab}$, we first develop a general toolkit by expanding the curvature tensors and the Ricci scalar in powers of the perturbation $h_{ab}$ and recast the strong, weak, null and dominant energy conditions (SEC, WEC, NEC and DEC, respectively) as explicit inequalities on $h_{ab}$ following from the Raychaudhuri equation. The formalism is general, but to obtain concrete constraints we specialize to the standard BMS form on a Schwarzschild background and parametrize $h_{ab}=\mathcal{L}_ηg_{ab} $ by a supertranslation function $f(θ,ϕ)$. We find that the SEC and WEC impose nontrivial angular restrictions on $f$ already at next-to-leading order (NLO) in the perturbation, whereas the NEC and DEC are preserved at linear order and acquire their first nontrivial contributions only at next-to-next-to-leading order (NNLO). Notably, the NNLO NEC reduces to a purely angular condition (independent of the radial coordinate), providing the strongest constraint on admissible supertranslations. Thus, imposing energy conditions substantially reduces the space of physically admissible supertranslations; the allowed sector, although remains infinite-dimensional in principle, is substantially constrained in practice.

It is well-known that shear flows in a strip or in the half plane are unstable for the incompressible Navier-Stokes equations if the viscosity $ν$ is small enough, provided the horizontal wave number $α$ lies in a small interval, between the so called lower and upper marginal stability curves. Moreover, a Hopf bifurcation occurs at the upper marginal stability curve. In this article, for various shear flows, we give numerical evidences that this bifurcation is subcritical.

We characterize the coherence of a triangular exchange-only (EO) spin qubit operated at a leakage-protected idle (LPI) point. The triangular geometry enables independent control of all three pairwise exchange interactions, and the LPI condition occurs when these couplings are turned on simultaneously and tuned to equal strength. In this configuration, the exchange interaction induces an energy gap $E_g = 3J/2$ that suppresses leakage from the computational subspace while leaving the qubit state unaffected. We develop procedures to calibrate the LPI point and measure $E_g$, and use these to characterize the qubit dephasing time over a broad range of gap energies. While operating with large always-on exchange couplings exposes the qubit to charge noise, we find that $\tilde{T}_2^*$ still exceeds that of conventional exchange-only spin qubits for $E_g/h < 60$ MHz. The precise control of simultaneous, all-to-all connected exchange demonstrated here presents a natural path towards improving the performance of EO qubits and also enables novel qubit encodings.

We present the resummed predictions for a vector boson pair production at the LHC. We have performed threshold resummation to next-to-next-to-leading logarithmic (NNLL) accuracy, and then matched them to next-to-next-to-leading order (NNLO) QCD results. After resummation, we observe a reduction in the scale uncertainties arising from unphysical renormalization and factorization scales. We find that the resummed corrections add a few per cent to the fixed order results for both ZZ and WW production.

We present explicit infinite families of twisted torus knots that are not fibered. Our approach relies on an explicit formula for the Alexander polynomial derived in our previous work. We show that the leading coefficients of the Alexander polynomials of twisted torus knots can take arbitrary integer values, which immediately yields infinitely many examples of non-fibered twisted torus knots.

Probabilistic evaluation improves the trade-off between target coverage and OAR sparing in IMPT but remains computationally demanding. This study proposes sparse probabilistic evaluation (SPE), a computationally efficient approach integrated into a clinical TPS. Clinical plans of 20 IMPT HNC patients treated in 2024 were included. SPE used a predefined setup and range error grid with Monte Carlo computed dose distributions. Two grid settings were evaluated: the maximum error Emax (3$σ$ or 4$σ$) and the number of setup error points nsetup (7, 33, 123). Accuracy and duration of SPE with each grid were evaluated in the calibration group (5 patients). 1000 treatments with normally distributed random ($σ$ = 1 mm) and systematic ($σ$ = 0.92 mm) setup and range ($σ$ = 1.5%) errors were simulated. The dose distribution of the nearest error point in the grid was assigned to each fraction. Probability distributions derived from SPE were compared with those from a reference based on 35,000 Monte Carlo calculations. The found optimal grid (Emax = 3$σ$, nsetup = 33) was applied to the validation group (15 patients). Accuracy of SPE in the calibration group increased significantly as the number of error points increased from 7 (tavg = 2 minutes) to 33 (tavg = 9 minutes), with no further improvement between 33 and 123 (tavg = 27 minutes) error points. Increasing Emax only improved accuracy for values above the 98th percentile. Applying SPE to the validation group resulted in median errors of 0.02 Gy RBE (range:-0.11 to 0.07) for the 10th percentile of the D99.8%, CTV distribution and 0.0 Gy RBE (range:-0.14 to 0.23) for the 95th percentile of the D0.03cc,SpinalCord Core distribution. Sparse probabilistic evaluation achieves sufficient accuracy while requiring clinically acceptable computation times, paving the way for probabilistic evaluation in clinical practice.

In this contribution, we present our recent study on the second-order corrections of pseudo-scalar($A$) Higgs decay to three partons, at higher orders in the dimensional regulator. We have studied the one and two-loop amplitudes for processes, $A\to ggg$ and $A\to q\bar{q}g$ in the effective theory framework. Our results, after suitable crossings of the external momenta, are important ingredients for predicting the differential distribution of the pseudo-scalar Higgs boson in association with a jet at hadron colliders.

In this paper, we study quasi-twisted codes and their relationship with additive constacyclic codes through a polynomial-based approach. We first present a polynomial characterization of quasi-twisted codes over finite fields analogous to quasi-cyclic codes and determine Euclidean, Hermitian, and symplectic duals of quasi-twisted codes with index $2$. Additionally, we provide necessary and sufficient conditions for the self-orthogonality of appropriate quasi-twisted codes. Next, we explore a one-to-one correspondence between quasi-twisted codes of length $lm$ with index $l$ over $\mathbb{F}_q$ and additive constacyclic codes of length $m$ over $\mathbb{F}_{q^l}$. We establish relationships between trace inner products in the additive setting and Euclidean, symplectic inner products in the quasi-twisted setting. Using these relations and the correspondence, we determine the dual of additive constacyclic codes with respect to the trace inner products. As a consequence, we conclude that determining the trace Euclidean dual and trace Hermitian dual of an additive constacyclic code is equivalent to determining the Euclidean and symplectic dual of the corresponding quasi-twisted code.

The adoption of Digital Twin technologies is rapidly expanding in diverse industrial, economic, and societal domains. Over the past decade, a multitude of studies, surveys, and investigations have been conducted, examining the nature, applications, and advantages of Digital Twins. However, up until now, no proposal for a comprehensive feature model exists that effectively captures the mandatory and optional features of Digital Twins. To address this shortcoming, in this article, we present a general feature model for Digital Twins. Based on a systematic mapping study of existing literature, we developed a generalized feature model for Digital Models, Shadows, and Twins. To assess the validity of our proposed feature model, we have applied them to three use cases from the emergency, vehicular, and manufacturing domain. We conjecture that our proposed general feature model advances the field around Digital Twins by facilitating informed decision-making during design, enabling improved model-driven development of Digital Twins, and, eventually, fostering verification~\&~validation of Digital Twins by delivering a model-based foundation for test case inference.

The $^{16}$O$(p,α)^{13}$N reaction plays a key role in shaping the $α$-particle abundance during explosive oxygen burning in Type Ia supernovae. By enhancing $α$-production, this reaction directly affects the calcium-to-sulphur (Ca/S) and argon-to-sulphur (Ar/S) ratios, which serves as a tracer of progenitor metallicity. However, recent work suggests that the rate must be enhanced by a factor of up to seven over the standard value to explain observed Ca/S ratios across a range of progenitor metallicities. To explore this impact, available experimental cross-section data for the $^{16}$O$(p,α)^{13}$N reaction have been compiled and critically evaluated. Significant discrepancies are identified in the low-energy region ($E_{\mathrm{cm}}$ = 5.7--7.0 MeV), primarily due to limitations of the activation method. To resolve this, the first direct measurement at astrophysical energies has been performed using the MUSIC active-target detector. The new $^{16}$O$(p,α)^{13}$N thermonuclear reaction rate is found to be approximately 1.5 times higher than the REACLIB rate in the temperature range T = 3--4 GK, with more constrained uncertainties that resolve the previously large spread among existing data. The suggested factor of seven enhancement is excluded and these results indicate that this reaction alone cannot fully explain the variation in the Ca/S and Ar/S ratios observed across different progenitor metallicities. Therefore, future work should focus on reducing the uncertainties in other key oxygen-burning reactions, particularly $^{16}$O+$^{16}$O and $^{12}$C+$^{16}$O. Further reducing the constraints on the $^{16}$O$(p,α)^{13}$N rate is also needed to fully determine to whether a nuclear physics solution to this discrepancy is possible.

We investigate the magnetic signature of oceanic circulation in Ganymede's subsurface ocean using kinematic induction modeling. Our approach couples zonal jet flows from rotating thermal convection simulations with magnetic field models incorporating Ganymede's internal dynamo and external contributions from Jupiter. We solve the induction equation in spherical geometry for deep-ocean (493 km) and shallow-ocean (287 km) scenarios with varying magnetic Reynolds numbers. Ocean flows generate a predominantly toroidal magnetic field through the omega-effect, with a weaker poloidal component pervading beyond the conductive ocean layer. For some, but not all, induction configurations, analysis of the time-averaged Lowes-Mauersberger spectra reveals that ocean-induced signals dominate at spherical harmonic degrees $\ell \geq 4$. Deep ocean scenarios with magnetic Reynolds numbers above unity produce surface magnetic signals up to 9 nT. Our results demonstrate that Ganymede's intrinsic magnetic field creates favorable conditions for detecting subsurface ocean dynamics, thus emphasizing the need for low-altitude orbits for the Juice probe.

Inter-symbol interference (ISI) with heteroscedastic, or state-dependent, noise is a defining feature of molecular communication via diffusion (MCvD). However, such noise variance dependency across ISI states has not been systematically considered in prior detector designs. This letter introduces two decoding mechanisms, Belief-Adaptive Maximum A Posteriori (BA-MAP) and Soft BA-MAP, that explicitly incorporate state-dependent means and variances of the molecular count channel. The BA-MAP method derives per-symbol adaptive MAP thresholds based on the receiver's current state beliefs, whereas the Soft BA-MAP approach computes mixture log-likelihood ratios by weighting all possible ISI states. Simulation and information-theoretic analyses confirm that the proposed detectors outperform conventional equalization and fixed-threshold methods, achieving up to 100% throughput improvement under realistic MCvD settings.

The automotive industry faces increasing challenges in ensuring both functional safety (FuSa) and cybersecurity for complex semiconductor devices. Traditional Failure Mode and Effects Analysis (FMEA) primarily addresses safety-related failure modes, often overlooking synergistic vulnerabilities and shared consequences with cybersecurity threats. This paper introduces an Integrated Failure and Threat Mode and Effect Analysis (FTMEA) framework that systematically co-analyzes FuSa and cybersecurity. A cornerstone of this framework is the introduction of rigorously defined Cross-Domain Correlation Factors (CDCFs), which quantify the interdependencies and mutual influences between safety-related failures and cybersecurity threats. These factors are derived from a combination of structured expert knowledge, static structural analysis metrics (e.g., Controllability/Observability), and validated against empirical data from fault/attack injection campaigns. We propose a modified Risk Priority Number (RPN) calculation that systematically integrates these correlation factors, enabling a more accurate and transparent prioritization of risks that span both domains. A detailed case study involving an automotive ASIC configuration register proves the practical application of the FTMEA. We present explicit mapping tables, quantitative CDCF values, and a comparative analysis against a baseline FMEA/TARA (Threat Analysis and Risk Assessment), illustrating how the integrated approach uncovers previously masked cross-domain risks, improves mitigation strategy effectiveness, and provides a clear quantitative justification for the derived correlation values. This framework offers a unified, traceable, methodology for risk assessment in critical automotive systems, thereby overcoming the limitations of conventional analyses and promoting optimized, cross-disciplinary development.

Axial plugging is a critical challenge for fusion in open-ended magnetic confinement systems. Multi-mirror systems, consisting of a series of axially aligned magnetic mirrors, aim to enhance axial confinement by increasing the effective diffusion coefficient; however, additional plugging is required to meet the Lawson criterion. In [T. Miller et al., Phys. Plasmas 30, 072510 (2023)], it was found that applying a traveling and rotating electric field in multi-mirror machines can significantly suppress axial loss due to a selectivity effect induced by the Doppler shift of the ion cyclotron resonance. However, this method is energetically expensive and vulnerable to plasma screening effects. Here, we propose using a traveling, rotating magnetic field that can achieve comparable plugging effectiveness while offering better penetration and lower energy costs. Two limiting scenarios, with and without an induced electric field, were considered. The confinement enhancement is calculated using a semi-kinetic rate equation model, in which the flux coefficients are determined from single-particle simulations. While both scenarios exhibit significant confinement enhancement, the scenario without an induced electric field is much more energetically efficient, as it relies on phase-space mixing rather than on energy deposition in the escaping particles. The decoupling of confinement from plasma collisionality enables fusion conditions in the central cell while allowing affordable and efficient confinement enhancement in the multi-mirror sections.

The infrared structure of QED and gravity is known to be governed by an infinite-dimensional symmetry group which extends the Poincaré group to include, respectively, large $U(1)$ transformations and BMS supertranslations. We describe how the unitary irreducible representations (UIRs) of these asymptotic symmetry groups encode universal infrared features of a scattering process. Motivated by the goal of defining an infrared-finite $S$-matrix based on these UIRs, we also study supermomentum eigenstates and contrast our construction with the dressed-state approach for infrared-safe amplitudes.

We have investigated the unitarity violation scale of a non-minimally coupled scalar field with quartic self-coupling. This model is widely studied in the literature but the estimation of the unitarity violation scale has not been consistently discussed, especially in the Jordan frame. We have calculated the six-point scattering amplitudes of the scalar particles in both the Jordan frame and the Einstein frame, and explicitly shown the frame-independence of the results. Since the extended target space with the conformal mode is trivial in the single-field case, the dominant contribution comes from the potential of the scalar field. The results in both frames become trivial in the vanishing self-coupling limit as expected.

In the line-based dial-a-ride problem (liDARP), vehicles operate along a predefined bus line, with the possibility of skipping stations and turning when empty. Motivated by the practical observation that tight passenger time windows often limit pooling in on-demand services, we introduce a new variant of this transportation system by removing all temporal constraints, which we call the liDARP without TWs. We introduce a new MILP formulation for the liDARP without TWs, which constructs feasible tours as sequences of stopping patterns; first, we consider a fundamental single-vehicle, single-pass special case. Based on our insights, we develop a branch-and-price algorithm where the pricing problem generates profitable stopping patterns. For practical applications, we additionally propose a root node heuristic, using the stopping patterns generated at the root node. Computational experiments show that our branch-and-price algorithm is competitive, finding solutions with a MIP gap of less than 5% for large instances in 60 minutes. Further, the root node heuristic scales to instances with up to 100 requests, outperforming the state-of-the-art and reaching optimality gaps of less than 5% within 15 minutes. This method is highly effective in generating solutions for practical applications, where solving large problems quickly is more valuable than reaching optimality.

The dynamics and instability of the magnetized jets connected to jet acceleration are complicated and are not yet well understood. Quasi-periodic oscillations (QPOs) as special timing features in black hole systems can directly probe dynamics and structure of accreting and outflow materials. Recently, GHz-band radio polarization oscillations in a stellar-mass black hole are reported, and the physical origin is unclear. We propose that the QPOs in both radio flux and linear polarization will be connected to kink instability in relativistic magnetized jets. The simulations are performed to fit the observed curves of radio flux and linear polarization modulations, in addition, the kink instability model well explains the anti-correlation between flux and linear polarization. These polarized QPOs provide evidence for kink stability in relativistic jets, a phenomenon of significant theoretical importance for understanding the magnetic field configuration near the black hole, as well as for particle acceleration in jets.

Statistical modeling of dependent directional data remains relatively underexplored, particularly in high-dimensional spatial settings. Existing approaches for spatial angular data primarily rely on wrapped Gaussian process (WGP) models, which provide a coherent framework for capturing spatial dependence on the circle. However, WGP-based methods become computationally challenging when the spatial domain is large, and observations are available at high resolution. This limitation is especially relevant in the analysis of large-scale geological and climate phenomena, such as tsunamis and hurricanes, where directional measurements (e.g., wave or wind directions) may be available over an entire ocean basin. To address these challenges, we propose a wrapped Gaussian Markov random field (WGMRF) model for large spatial directional datasets. By exploiting the sparse precision structure inherent in Gaussian Markov random fields, the proposed approach achieves substantial computational gains while preserving flexible spatial dependence on the circular scale. We discuss key properties of the model, including its identifiability and dependence characteristics. The model fitting involves standard Markov chain Monte Carlo techniques. Through extensive simulation studies and an application to the wave direction data across the Indian Ocean during the 2004 Indian Ocean Tsunami, we compare the proposed method with both a non-spatial wrapped Gaussian model and a low-rank WGP alternative. The results demonstrate that the WGMRF offers improved predictive performance and scalability in large-domain applications.

Intrinsically disordered regions of proteins play a crucial role in cell signaling and drug discovery. However, their high structural flexibility makes accurate residue-level prediction challenging. Existing methods often rely on single-view representations or rigid manual fusion strategies, which fail to effectively balance the complex interplay between local amino acid preferences and long-range sequence patterns. To address these limitations, we propose D2MOE, a Dual-View Multiscale Features and Multi-objective Evolutionary Algorithm, which consists of two stages. First, a dual-view multiscale feature extraction method is introduced. This method integrates evolutionary views with deep semantic views and employs multiscale extractors to capture structural information across diverse receptive fields. Second, a multi-objective evolutionary algorithm is designed to adaptively discover optimal fusion architectures. By co-evolving discrete feature selection and continuous fusion weights, the algorithm adaptively explores optimal cross-feature architectures to enhance predictive accuracy while maintaining model compactness. Experimental results across three benchmark datasets demonstrate that D2MOE consistently outperforms state-of-the-art methods. D2MOE combines the feature extraction capabilities of deep learning with the global search advantages of evolutionary algorithms, enabling efficient feature integration without manual design, and providing a robust computational tool for protein disorder prediction.

The first process for the Latin American Strategy Forum for Research Infrastructure for High Energy, Cosmology and Astroparticle Physics (LASF4RI-HECAP) came to a conclusion in October 2020, with a Physics Briefing Book (PBB) presented in (2104.06852). Here we present an updated PBB, the result of the first update of LASF4RI-HECAP. The update process began with a call for White Papers from the HECAP community. The submitted contributions were presented at the III LASF4RI for HECAP Symposium: Update of the Strategic Plan, held at ICTP-SAIFR in São Paulo in August 26-29, 2024, with the participation of the Preparatory Group, High Level Strategy Group, Funding Agencies and representatives of similar efforts from around the globe. This updated PBB was written by the Preparatory Group based mainly on 46 White Papers submitted by the community and is organized around seven working groups: Astronomy, Astrophysics and Astroparticle Physics; Cosmology; Dark Matter; Neutrinos; Electroweak and Strong Interactions, Higgs Physics, CP and Flavour Physics and BSM; Instrumentation and Computing; Advanced Training and Capacity Building. It is intended to provide the essential input for the creation of a long-term HECAP strategy in the region.

Cellular traction forces are conventionally measured by tracking the displacement of beads or micropillars, an approach fundamentally limited by optical diffraction and the classical Euler-Bernoulli beam assumption, which is accurate only when the traction-induced deformation is relatively small while the aspect ratio of micropillars is large. Here we introduce an alternative approach: quantifying force through direct measurement of rotational angle, in addition of displacement of the micropillar, using fluorescent nanodiamonds as embedded 3D orientation markers. Specifically, by integrating optically detected magnetic resonance (ODMR) with laser polarization modulation (LPM), we determine the complete three-dimensional orientation of nanodiamonds attached to PDMS micropillars with sub-degree precision ($\sim$0.5$^\circ$). This angle-based measurement framework bypasses the resolution constraints of displacement tracking and remains valid for stocky beams or when large deformations occur. Finite-element simulations demonstrate that our method reduces force estimation errors by at least 10% compared to conventional displacement-based approaches. Moreover, we successfully capture multidimensional pillar deformations -- including bending and twisting -- that are inaccessible to conventional displacement-only method. Taken together, our work establishes diamond-based angular force microscopy as a high-precision platform for mechanobiology.

The stabilizer ground state is defined is the lowest energy stabilizer state with respect to a given Hamiltonian. In many cases it is highly degenerate and does not give a unique stabilizer state. We define the optimal stabilizer ground state as the stabilizer ground state which has the highest fidelity with the true ground state. This is useful in quantum simulation contexts as it allows for a Clifford circuit approximation of a ground state that can be further refined towards the true ground state. We show how the optimal stabilizer ground state may be evaluated. We show applications of this state in the context of measurement-based deterministic imaginary time evolution (MITE), which converges to the ground state with high efficiency. By classically selecting the optimal stabilizer generator group and employing the stabilizer tableaux formalism, the method prepares the corresponding stabilizer ground state with maximal fidelity. The identification and refinement of this generator group are performed using a genetic algorithm tailored to the structure of the target Hamiltonian. The complexity analysis further demonstrates that algorithm's quantum resource cost scales polynomially with system size, highlighting its high efficiency and potential quantum advantage.

Given a strongly inaccessible cardinal $λ$, we study the Fraïssé class of all Boolean algebras of size $<λ$, together with regular embeddings. We prove that this is indeed a Fraïsséclass, and its limit has the same completion as the Lévy collapse. We also give a direct proof that the collapsing algebra of density $κ$ is not the union of a $κ$-chain of regular sub-algebras of density $<κ$.

Charge-density-wave (CDW) order and superconductivity often compete in low-dimensional materials, yet their interplay in Janus MXenes remains largely unexplored. Here, we present a comprehensive first-principles investigation of the structural, vibrational, and electronic properties of Mo2NF2. Phonon calculations reveal an unstable soft phonon mode at the M point in the high-symmetry structure, signaling a CDW instability. Analysis of phonon linewidths and the real and imaginary parts of the bare electronic susceptibility demonstrates that the CDW is not driven by simple Fermi-surface nesting but instead originates from strong momentum-dependent electron-phonon coupling. Structural relaxation yields a commensurate CDW phase characterized by bond-length modulations involving the Mo, N, and F sublattices. We further show that charge doping alone is insufficient to stabilize the soft phonon, whereas compressive biaxial strain exceeding -3 percent completely suppresses the CDW instability. Electron-phonon coupling calculations indicate that the CDW phase exhibits a reduced coupling constant lambda = 0.40 and logarithmic phonon frequency omega_log = 219 K, leading to a low superconducting transition temperature Tc about 1 K. In contrast, the strain-stabilized high-symmetry phase shows enhanced coupling (lambda = 0.53, omega_log = 272 K) and a higher Tc about 4 K. Our results establish Mo2NF2 as a strain-tunable platform where superconductivity emerges upon suppression of a competing CDW phase, highlighting the crucial role of lattice control in Janus MXenes.

In the face of vast numbers of preventable deaths worldwide and gaping disparities in their distribution, we cannot afford to conduct null and inconclusive effectiveness and implementation trials of evidence-based interventions. The gold standard in biomedical research, the individually randomized clinical trial, is ill-suited as the primary tool for knowledge generation for contextually relevant, scalable, complex public health interventions of multi-component strategies. In this paper, we discuss the new Learn-As-you-GO (LAGO) design. In LAGO trials, the components of a complex intervention package are repeatedly optimized in pre-planned stages, until the package achieves its outcome and power goals with minimized cost and/or other optimization criteria, such as maximizing patient satisfaction. In this paper, the inputs to, and outputs of, LAGO are described, along with its general methodology. The methods are illustrated in the BetterBirth study, a large trial that aimed to reduce maternal and neonatal mortality in Uttar Pradesh, India, using the WHO essential birth practices checklist. Despite its scale, the BetterBirth study failed to demonstrate a significant effect of the intervention package on the primary health endpoint that included maternal mortality. We show how this unfortunate outcome could have been remedied had LAGO been used. LAGO is further illustrated through the discussion of several ongoing LAGO-informed implementation trials of HIV and non-communicable diseases in the United States and Sub-Saharan Africa. The Learn-As-you-GO (LAGO) design optimizes a complex, multi-level intervention for minimum cost, pre-specified power, and a pre-specified effectiveness goal, by adapting the intervention as the study is conducted, reducing risk of trial failure.

We present a methodology that combines Mach-Zehnder interferometry, a custom relative humidity (RH) controlled chamber, and a confined two-dimensional droplet geometry to enable precise investigations of drying of complex fluids and the associated transport mechanisms. This approach is applied to a model binary mixture, water-glycerol, the concentration-dependent thermodynamic and transport properties of which are relatively well documented. High-resolution interferometric imaging (6 $μ$m pixel$^{-1}$, 1 frame s$^{-1}$) allows simultaneous measurement of drying kinetics and internal concentration fields with $\pm 0.5\%$ accuracy, characterized here over a wide range of RH (25-95%), and thus Péclet numbers. The experimental results closely match a quasisteady, isothermal model of vapor-diffusion-controlled evaporation coupled to diffusion within the droplet. These data enable extraction of both the concentration-dependent mutual diffusion coefficient $D(φ)$ and the water chemical activity $a_w(φ)$ over almost the entire range of glycerol volume fraction $φ$, even from a single low-RH experiment. While $a_w(φ)$ agrees well with literature values, our measurements yield a consistent fit for $D(φ)$. Complementary experiments with fluorescence microscopy confirm that buoyancy-driven convection, although present, remains negligible, so that mass diffusion dominates solute transport in this confined geometry. The overall agreement validates the methodology, demonstrating its robustness as a quantitative framework for probing drying dynamics and transport in complex fluids, with broad applicability to controlled evaporation studies.

Recently, Archer et al.\ studied cyclic permutations that avoid the decreasing pattern $δ_k=k(k-1)\cdots21$ in one-line notation and avoid another pattern $τ$ of length $4$ in all their cycle forms. There are three cases in total to consider, namely, $τ=1324, 1342$ and $1432$. They determined two of them, leaving the case $τ=1432$ as an open question. In this paper, we resolve this case by deriving explicit formulas based on an analysis of the structure of cycle forms and an application of Dilworth's theorem.

We study the isotropic six-vertex model on $\mathbb{Z}^2$ with spectral parameter $Δ\in[-1,-1/2]$, that is, with weights $\mathbf{a}=\mathbf{b}=1$ and $\mathbf{c}\in[\sqrt{3},2]$. We show that the associated height function converges, in the scaling limit, to a properly scaled full-plane Gaussian free field. The result extends to anisotropic weights $\mathbf{a}\neq\mathbf{b}$ upon using a suitable embedding of the lattice.

Piezoelectric Micromachined Ultrasonic Transducers (PMUTs) are essential for next-generation ultrasonic sensing and imaging due to their bidirectional electromechanical behavior, compact design, and compatibility with low-voltage electronics. As PMUT arrays grow in size and complexity, efficiently modeling their coupled electromechanical-acoustic behavior becomes increasingly challenging. This work presents a novel computational framework that combines model order reduction with a Discontinuous Galerkin Spectral Element Method (DGSEM) paradigm to simulate large PMUT arrays. Each PMUT's mechanical behavior is represented using a reduced set of vibration modes, which are coupled to an acoustic domain model to describe the full array. To further improve efficiency, a secondary acoustic domain is connected via DG interfaces, enabling non-conforming mesh refinement, with variable approximation order, and accurate wave propagation. The framework is implemented in the SPectral Elements in Elastodynamics with Discontinuous Galerkin (SPEED) software, an open-source, parallelized platform leveraging domain decomposition, high-order polynomials, METIS graph partitioning, and MPI for scalable performance. The proposed methodology addresses key challenges in meshing, supporting high-fidelity simulations for both PMUT transmission and reception phases. Numerical results demonstrate the framework's accuracy, scalability, and efficiency for large PMUT array simulations.