Dense granular and suspension flows under inhomogeneous shear exhibit persistent particle motion in regions where the local yield criterion is subcritical, an apparent breakdown of locality that has motivated the development of a generation of nonlocal rheological models. Using particle-resolved simulations of frictionless dense suspensions in two-dimensional Kolmogorov flow, we show that two independent considerations together account for this signature. First, replacing the conventional shear stress by a shear-rate-weighted dissipative stress $τ_W=\langle τ\dot γ\rangle/\langle \dot γ\rangle$, which isolates the component of stress that performs irreversible work, restores the homogeneous $μ(J)$ law throughout the bulk of the flow, with the inferred friction remaining strictly above yield. Second, a simple geometric mixing-length construction, applied with conventional stresses and requiring no fluctuation input, accounts for the residual sub-yielding within a sub-diameter layer at flow reversals. Each approach is based on a different philosophy and mechanism, and together they suggest that much of the apparent non-locality in this geometry and frictionless case is an artefact of how stress is measured and averaged rather than an intrinsic breakdown of local rheology.

Tree-based regression models are widely used in supervised learning, with the Classification and Regression Tree (CART) algorithm serving as a standard reference. CART construction involves solving a sequence of split-selection optimization problems. For categorical predictors, this problem can be formulated as a combinatorial fractional optimization problem. This structure makes the exact optimization computationally challenging and leads to standard implementations that rely on greedy heuristics, which may result in suboptimal splits. In this work, we reformulate this fractional problem and apply Dinkelbach (1967) algorithm to convert it into a Quadratic Unconstrained Binary Optimization (QUBO) problem. Using state-of-the-art QUBO solvers, we obtain QUBO-based regression trees with predictive performance comparable to standard CART while yielding higher-quality split solutions. These results highlight the potential of QUBO formulations for improving tree-based learning methods and open perspectives for future hybrid classical--quantum implementations.

We propose a non-intrusive reduced-order modeling framework for parametrized visco-plastic free-surface flows governed by a shallow-water formulation of Herschel--Bulkley fluids. These flows exhibit strong nonlinearities, non-smooth rheology, moving fronts, and yield surfaces, making efficient surrogate modeling particularly challenging. To address this challenge, we employ a tensor-based approach in which the solution manifold is approximated using a low-rank representation obtained via higher-order singular value decomposition of snapshot data over a structured parameter space. The resulting tensorial reduced-order model (TROM) enables rapid online evaluation by directly reconstructing solution trajectories from the compressed representation, thereby avoiding the need to perform time integration of a reduced dynamical system. The proposed non-intrusive framework can be interpreted as an encoder--decoder architecture with a compressed latent representation and efficient multilinear decoding. Numerical experiments demonstrate that the proposed approach accurately captures key flow features, including front propagation, plug and shear regions, and near-stopping dynamics, while achieving substantial computational speedups relative to full-order simulations.

Large language models (LLMs) are increasingly used to provide instructions to many agents who interact with one another. Such shared reliance couples agents who appear to act independently: they may in fact be guided by a common model. This coupling can change the prospects for cooperation among agents with misaligned incentives. We study settings in which multiple LLMs each advise a population of clients who participate in instances of an underlying game, creating strategic interaction at the level of the LLMs themselves. This induces a meta-game among the LLMs, mediated through clients. We first analyze the one-shot setting, where shared instructions can change equilibrium behavior only when an LLM may influence more than one role in the same interaction; in such cases, cooperation may emerge, and the effect of client share can be beneficial, harmful, or non-monotone, depending on the base game. Our main result concerns the repeated setting. We prove a folk theorem for LLMs: despite indirect observation and the clients' inability to identify which LLM advised their opponents, all feasible and individually rational outcomes can be sustained as $\varepsilon$-equilibria. The result does not follow from the standard folk theorem and requires new proof techniques. Together, these results show that shared LLM guidance can sustain cooperation among populations of agents even when the underlying incentives are misaligned.

Anytime-valid tests allow evidence to be checked during data collection: one can either continue testing or stop and reject the null while still controlling type-I error. Yet, in many applications rejection is useful only if it comes soon enough. We introduce a time-sensitive testing-by-betting framework that favours early rejection by assigning rewards to rejection times and maximising their expected value under a given alternative. This encompasses hard deadlines and softer time preferences. The resulting optimal control problem admits a Bellman representation in terms only of time and evidence against the null, rather than the full history. For hard deadlines, the simple-vs-simple case reduces to a finite-horizon Neyman--Pearson problem and identify the corresponding optimal e-process. Furthermore, we show that exponentially decaying rewards admit a stationary approximation, yielding the exponential-decay-optimal (EDO) criterion: a finite-time-scale counterpart to the classical growth-rate-optimal (GRO) viewpoint in anytime-valid statistics, with the GRO criterion recovered in the large-time-scale limit.

Consider a complete Riemannian manifold $(M, g)$ and optimal transport problems on it with cost functions of the form $c(x,y) = h(d_{g}(x,y))$. We study the absolute continuity of the corresponding generalized Wasserstein barycenters of finitely many marginal measures. For general strictly convex profiles $h$ lacking $\mathcal{C}^2$-smoothness, such as $h(d)= d^p / p$ with $1 < p < 2$ that defines the $p$-Wasserstein space, the singularity at $d=0$ prevents the barycenter from inheriting absolute continuity from a single marginal measure as the quadratic case. To overcome this singularity, recent Euclidean results necessitate the absolute continuity of all marginals. Building upon the approximation framework toward absolute continuity in arXiv:2310.13832, we extend the Euclidean advancements to the manifold setting. Stripping away the implicit reliance on flat translational symmetry and local coordinate calculations of their Euclidean proofs, our work handles the singularity in a geometrically transparent way, revealing the precise analytic condition on the cost profile that governs the necessary assumptions.

This work presents the first dedicated optical--mid-infrared time-domain variability and dust-reverberation analysis of the isolated NLSy1 galaxies Mrk 42 and Mrk 493. We combine ZTF optical light curves, WISE mid-infrared monitoring, archival Swift and SDSS data, and high-cadence IAC80 optical observations. Using colour--magnitude relations, flux--flux analysis, and interpolated cross-correlation functions, we trace variable optical continuum and delayed dust response. Both galaxies show positive optical--MIR lags consistent with dust reverberation. For Mrk 493, we measure an observed-frame g--W1 lag of $τ_{\rm obs}=79.4\pm2.2$ d, corresponding to $R_{\rm dust}(W1)\simeq0.0648$ pc. For Mrk 42, the corresponding lag is $τ_{\rm obs}=39.1\pm2.6$ d, giving $R_{\rm dust}(W1)\simeq0.0320$ pc. These lags provide optical--MIR dust-reverberation radii and BLR--dust scale comparisons for both objects; the resulting $R_{\rm dust}/R_{\rm BLR}$ ratios are $\simeq6.8$ for Mrk 493 and $\sim6$--7 for Mrk 42. For Mrk 42, we derive the first host-subtracted AGN continuum luminosity at 5100 Å from SDSS spectral decomposition, giving a self-consistent BLR--dust comparison on an AGN-only luminosity basis. Both galaxies have similar radial hierarchies but different colour behaviour: Mrk 493 shows significant optical and MIR bluer-when-brighter trends, whereas Mrk 42 shows strong optical but weak MIR colour variability. We also identify and analyse a major optical flare in Mrk 42 with four internal maxima spaced by 45--47 d. We interpret this signal as quasi-periodic substructure within a broader accretion-driven flare, rather than as a strictly coherent periodic process. These results indicate that, even in dynamically isolated environments, the variability of low-mass, high-accretion-rate AGNs is governed mainly by the intrinsic state of the accretion flow and its coupling to circumnuclear dust.

The response of ultra-thin superconducting materials under parallel magnetic fields is often leveraged to obtain insight into the nature of the condensate, including features attributable to unconventional forms of pairing. Despite there being multiple competing mechanisms responsible for suppressing superconductivity, it is common for these analyses to overlook certain depairing channels. Here we report an analysis of thickness dependent superconductivity in thin films of \ce{LaBi2} using the multi-mechanism Kharitonov-Feigel'man framework . By resolving field-enhanced superconductivity in the thin-limit, we obtain an estimate the role of spin exchange scattering, in addition to paramagnetic and orbital effects. Our analyses offer insight into how fundamental quantities such as the critical temperature as well as Pauli limit are defined, recasting the landscape for how scattering times in two-dimensional superconductors can be interpreted.

The existence and origin of the ductile to brittle transition in non-Brownian suspensions and pastes is underexplored despite the ubiquity of such materials in practical applications. We demonstrate the phenomenon in candies of sugar crystals in a water-protein-fat matrix prepared by boiling a sugar-cream-butter mixture (known as 'fudge' in some countries). As cooking time or final cooking temperature increases, we observe a transition from a fluid to a ductile solid, then to a brittle solid that abruptly fractures in compression. We propose that this is driven by rising solid sugar crystal volume fraction, and indeed find the same sequence of behaviour in a suspension of non-Brownian calcite particles as the solid fraction moves from frictional jamming to random close packing. Particle-based simulations reveal the sensitivity of the observed phenomenon to boundary conditions.

We study random walks on dynamically evolving graphs, where the environment is given by a time-dependent subset of the edges of an underlying graph. Concretely, following the recently introduced framework of Lelli and Stauffer, we consider a random walk interacting with a dynamical random-cluster environment, in which edges are updated with rate $μ>0$ according to Glauber dynamics with parameters $p$ and $q$, and the walker moves at rate 1 but may only traverse edges that are present at the time of the move. This setting introduces strong dependencies between the walk and the environment, as edge-update probabilities depend on the global connectivity structure. We focus on the case where the underlying graph is a random $d$-regular graph and the parameters lie in the subcritical regime $p < p_{\mathrm{u}}(q, d)$ where it is known that the Glauber dynamics mixes quickly. Our main result is to show that for any $\varepsilon >0$ and all $q \ge 1$, for all $p$ in the subcritical regime, the mixing time of the joint process is $Θ(\log n)$ (in continuous time) whenever $μ\geq \varepsilon \log n$. This matches the mixing time of the simple random walk on a static random regular graph, showing that in this regime the evolving environment does not slow down mixing. Our proof is based on a coupling argument that uses path-count techniques to overcome the dependencies in the edge dynamics by controlling the structure of the environment along typical trajectories.

We prove necessary and sufficient conditions for the Schrödinger operators to have zero-energy bound states at the threshold of the essential spectrum such that they have bounded $k$-th moment. This result is the extension of the results published in D. Hundertmark, M. Jex, and M. Lange [Forum Mathematics, Sigma 11(2023)].

We establish sharp local existence results for the Hirota-Satsuma system in $H^k(\mathbb{R}) \times H^s(\mathbb{R})$, depending on the ratio between the dispersion of the components. These theorems significantly generalize previous works, which were restricted to the diagonal case of equal regularity $s=k$. Furthermore, we extend the known global well-posedness theory to the off-diagonal regime. The argument relies on the Fourier restriction norm method coupled with the concept of integrated-by-parts strong solution - a framework that generalizes the classical notion of strong solution.

We show that an "old dog", the classical discrete Laplace (aka.~geometric) mechanism, can "perform new tricks": 1. It can be post-processed to yield a simple, unbiased estimator of any subexponential function $f$ of the original data, giving a simple, discrete, multivariate version of the recent unbiasing result for the Laplace mechanism by Calmon et al. (FORC '25). 2. It can be post-processed to output the same distribution as the Laplace mechanism or the Staircase mechanism with identical privacy parameters. Thus, the discrete Laplace mechanism is a versatile mechanism that should be preferred over the Laplace and Staircase mechanisms whenever the data is discrete (or can be made discrete while controlling $\ell_1$-sensitivity). We show bounds on the variance of our estimator, compared to the mean square error of the biased estimator that simply evaluates the $f$ on the output of the mechanism. Though our unbiased estimator has exponential running time for worst-case functions, we show that it can often be computed in linear or polynomial time for some common functions exhibiting structure. We showcase the properties of our methods empirically with several use cases including profile and entropy estimation, as well as distributed/federated data analysis applications in which unbiasedness is key to accuracy.

The Hagedorn regime of string theory is usually understood as an equilibrium limiting phenomenon: the exponential growth of the density of states makes the canonical partition function singular at the Hagedorn temperature, while in the microcanonical description additional energy is absorbed predominantly by highly excited long-string configurations. In this work we revisit this regime from a nonequilibrium perspective using Steepest-Entropy-Ascent Quantum Thermodynamics (SEAQT), where thermodynamic evolution is formulated directly on the state manifold and does not require a globally well-defined canonical ensemble. The inverse temperature is treated as an instantaneous, state-dependent quantity, and we derive its exact scalar evolution equation. In the commuting limit, this dynamics is controlled by higher-order fluctuation moments, showing that the Hagedorn regime may act as a dynamical bottleneck for the response of the effective intensive variable. We then extend the construction to an open-system setting through a system--reservoir splitting of the SEAQT metric and show that reservoir coupling can drive the subsystem toward effective Hagedorn slowing-down. A diagonal Hagedorn evaluation further shows that the strength of this bottleneck depends not only on the exponential density of states, but also on its algebraic prefactor. These results provide a nonequilibrium interpretation of Hagedorn behavior and suggest a connection between long-string dominance, thermodynamic slowing-down, and the breakdown of effective descriptions in quantum gravity.

This work has two major parts. First, we extend the recent study of Pham et al. (2025) on point estimation of the association parameter of a bivariate Frank copula. We investigate two Bayes estimators under the generalized flat prior and the Jeffreys prior, and compare them with the maximum likelihood estimator (MLE). Simulation results show that, for small sample sizes (n <= 25), the Bayes estimator under the Jeffreys prior uniformly outperforms both the generalized flat prior estimator and the MLE in terms of mean squared error (MSE). For moderate and large sample sizes, all estimators have very similar performances in terms of bias and MSE. We also discuss computational issues in the R package implementation that may significantly affect the computation of the MLE for very small samples. In the second part, we apply the Frank copula to analyze the association between groundwater arsenic concentration and other hydrochemical variables using a recent dataset from Vietnam. We revisit the goodness-of-fit tests proposed by Genest et al. (2006), investigate several non-intuitive behaviors of the test statistics, and provide extensive simulated critical value tables. Our results complement and refine the computational findings reported in the earlier literature.

This work considers to achieve near-optimal operation for a class of batch processes by employing self-optimizing control (SOC). Comparing with a continuous one, a batch process exhibits stronger nonlinearity with dynamics because of the non-steady operation condition. This necessitates a global version of SOC to achieve satisfactory performance. Meanwhile, it also makes the existing global SOC (gSOC) not directly applicable to batch processes due to the causality amongst variables. Therefore, it is necessary to extend the original gSOC to batch processes. In addition to the nonconvexity challenge of the original gSOC problem, the new extension for batch processes has to face even more challenges. Particularly, the causality due to dynamics of batch processes brings in structural constraints on controlled variables (CVs), making a CV selection problem even more difficult. To address these challenges, the gSOC problem is recast in a vectorized formulation and it is proved that the structural constraints considered are linear in the vectorized formulation. Moreover, a novel shortcut method is proposed to efficiently find sub-optimal but more transparent solutions for this problem. The effectiveness of the new approach is validated through a case study of a fed-batch reactor, where CVs are constructed through a combination matrix with a repetitive structure, resulting in a simple SOC scheme. This simplicity facilitates the implementation of the SOC approach and enhances its practical applicability and robustness.

47 Tucanae is one of the largest, brightest, and closest globular clusters to Earth. It hosts an exotic stellar population with stellar dynamics that indicate a complex evolution history. The cluster contains a large number of X-ray binaries and millisecond pulsars. However, given its large distance relative to the known pulsar population, previous surveys have found only the very brightest sources. Therefore, surveys with increased sensitivity should find many additional pulsars. Increasing the number of pulsars is crucial to investigate the dynamics of this globular cluster and could also lead to the discovery of unusual types of system. With a significantly increased sensitivity compared to earlier telescopes, MeerKAT is the natural choice to perform new surveys. We carried out two campaigns with different observational cadences to account for the high scintillation along the line of sight to this cluster. Here we report the discovery of fifteen new pulsars in 47 Tucanae with MeerKAT. These discoveries bring the total number of known pulsars in this globular cluster to 42, and the MeerKAT discoveries in this cluster to 17. We discuss some of their characteristics, which include preliminary localisations and estimates of orbits for most systems. Highlights include the discovery of 47 Tuc af, a 'black widow' pulsar with a short orbital period that was identified optically in 2002 as a candidate binary pulsar, and 47 Tuc ai, an eccentric binary pulsar with a massive companion, a unique system in 47 Tuc to date. Apart from the new systems, we also re-detect and localise 47 Tuc P and V, two elusive, seldom-detected systems that had no precise localisation from a phase-connected timing solution. The localisation of 47 Tuc V places it in a position consistent with a continuum source detected earlier in MeerKAT imaging data.

We develop a general estimation and inference procedure for the common parameters in linear panel data regression models with nonparametric two-way specification of unobserved heterogeneity. The procedure takes as input any first-step estimators of the nonparametric regression function and the fixed effects and relies on two key ingredients: First, we develop moment conditions for the common parameters that are Neyman orthogonal with respect to the nonparametric regression function. Second, we employ a novel adjustment of the nonparametric regression estimator so the estimated fixed effects do not generate incidental parameter biases. Together, these ensure that the resulting estimator of the common parameters is root-NT -- asymptotically normally distributed under weak conditions on the estimators of fixed effects and regression function. Next, we propose a novel two-step estimator of the nonparametric regression function and the fixed effects and verify that this particular estimator satisfies the conditions of our general theory. A numerical study shows that the proposed estimators perform well in finite samples.

The electronic structure calculations remain a major bottleneck in ab initio nonadiabatic molecular dynamics. We develop an efficient TDDFT-based FSSH implementation in the GPU4PySCF package for medium-sized molecular systems. Our approach combines density fitting, TDDFT with minimal auxiliary basis sets (TDDFT-ris), and an approximate Z-vector solver to reduce the computational cost of TDDFT excited states and derivative coupling calculations. These approximations introduce negligible errors in realistic FSSH workloads while maintaining high computational efficiency. Benchmark results show that, for 73-atom systems with a triple-$ζ$ basis set, individual electronic structure calculations are completed within one minute on a single NVIDIA A100 GPU.

Language Model Agents (LMAs) are emerging as a powerful primitive for augmenting red-team operations. They can support attack planning, adversary emulation, and the orchestration of multi-step activity such as lateral movement, a core enabling capability of advanced persistent threat (APT) campaigns. Using frameworks such as MITRE ATT&CK, we analyze where these agents intersect with core offensive functions and assess current strengths and limitations of LMAs with an emphasis on governance and realistic evaluation. We benchmark LMAs across two lateral-movement scenarios in a controlled adversary-emulation environment, where LMAs interact with instrumented cyber agents, observe execution artifacts, and iteratively adapt based on environmental feedback. Each scenario is formalized as an ordered task chain with explicit validation predicates, leveraging an LLM-as-a-Judge paradigm to ensure deterministic outcome verification. We compare three operational modalities: fully autonomous execution, self-scaffolded planning, and expert-defined action plans. Preliminary findings indicate that expert-defined action plans yield higher task-completion rates relative to other operational modes. However, failure remains frequent across all modalities, largely attributable to brittle command invocation, environmental and deployment instability, and recurring errors in credential management and state handling.

Municipal 311 call centers and complaint intake systems face a structural mismatch between incoming volume and classification capacity. The staff and heuristics available to triage, route, and prioritize complaints cannot scale with demand. This bottleneck produces differential service quality that follows income and racial lines (\cite{liu2024sla}). We develop an equity-centered reinforcement learning (RL) framework that augments call classification capacity across six New York City Department of Buildings (DOB) operational domains: boiler safety, crane and derrick oversight, heat and hot water complaints, housing complaint triage, scaffold safety, and Natural Area District (SNAD) protection. Rather than replacing human classifiers, our agents act as intelligent intake routers: learning to assign incoming complaints to action categories: escalate, batch, defer, inspect now. The proposed technique is designed to maximize throughput, minimize misclassification cost, and actively narrow historical equity gaps in service delivery. We formalize each domain as a Markov Decision Process (MDP) in which equitable classification coverage is a first-class reward objective. Post-hoc SHAP attribution reveals that complaint recurrence and neighborhood-level statistics are stronger predictors of actionable violations than raw complaint volume. This finding has direct implications for complaint routing given the demographic correlates of those features.

Using Schwinger-Keldysh field theory (SKFT), we engineer a dissipative and driven (i.e., out of equilibrium) bosonic bath acting on classical localized spins within a ferromagnetic insulator (FI) layer whose dynamics is governed by the Landau-Lifshitz-Gilbert equation, as is usually assumed in spintronics and magnonics. The bosonic bath is comprised of quantum magnons within a layer of altermagnetic insulator (AMI) that is attached to a conventional FI layer, often one of the key ingredients within spintronic and magnonic multilayers, so that interaction between slow classical (in the FI layer) and fast quantum (in the AMI layer) localized spins ensues. Such a bath, including its driving to produce a nonequilibrium distribution of altermagnetic magnons, generates a rich structure of the SKFT-derived extended LLG equation for classical spins within the FI layer. Our LLG equation contains two damping terms, both of which are spatially nonlocal and anisotropic, while one of them is also intrinsically non-Markovian, i.e., nonlocal in time. We demonstrate how to exploit these terms for tuning spintronic and magnonic effects within the FI layer of AMI/FI bilayers that involve spin wave or domain wall propagation, as well as skyrmion annihilation.

Leap generators have been introduced in [Duchon et al.'04] for exact-size random generation of structures in a class of the form $\mathcal{C}=\mathrm{Seq}(\mathcal{B})$ (sequence construction), in the supercritical case. We extend these generators to supercritical composition schemes $\mathcal{C}=\mathcal{A}\circ\mathcal{B}$. Compared to the sequence construction, the obtained exact-size random generator for $\mathcal{C}$ still has linear time complexity (under conditions on the sampling complexity in $\mathcal{A}$ and $\mathcal{B}$), but perfect uniformity of the distribution is lost in general. However the distribution on $\mathcal{C}_n$, called leap distribution, is asymptotically uniform, the total variation distance from the uniform distribution being $(c+o(1))n^{-1/2}$ for an explicit constant $c$. These generators are simple to implement and can be applied to several classes of walks and trees, in particular Pólya trees. Leap generators can also be given for certain critical composition schemes, those relating planar map families, where this time the total variation distance to the uniform distribution is $\sim c\,n^{-1/3}$ for an explicit constant $c$.

We show that intrinsic and extrinsic area density bounds are equivalent, with matching asymptotic values, for complete, connected, smooth minimal immersions $i:Σ^d\to\mathbb{R}^N$ of any dimension and codimension. Combining our results with a recent breakthrough by Bellettini, we extend the Schoen--Simon--Yau curvature estimates for smoothly immersed, two-sided, stable minimal hypersurfaces $i:Σ^n\to\mathbb{R}^{n+1}$ with bounded intrinsic area density to the missing case $n=6$, which had remained open since.

We calculate the non-planar corrections to the anomalous dimensions of certain quarter BPS states in the symmetric product orbifold $\text{Sym}^N \big({\mathbb{T}^4}\big)$. We find that some of the degeneracies in the spectrum for large twist $w$ and large $N$ are lifted by these contributions. We furthermore find signatures of quantum chaos, namely level repulsion and random matrix statistics. This suggests that integrability is only present in the symmetric orbifold in the planar (i.e. large $N$) limit.

We consider the evolution and interaction of a 2-dimensional nematic liquid crystal of Ericksen-Leslie type within a 1-dimensional flexible viscoelastic structure. This is a fully macroscopic model in which the nematic liquid crystal is modelled by the simplified Ericksen-Leslie system with Ginzburg-Landau approximation. The liquid crystal is contained in a thin viscoelastic shell of arbitrary reference configuration that evolves with respect to the forces exerted by the liquid crystal. Barring any degeneracies in the shell, we construct a global weak solution for the coupled system. We then show that any family of such weak solutions that are parametrized by the Ginzburg-Landau coefficient, converges to a weak solution of the original simplified Ericksen-Leslie system without the Ginzburg-Landau term.

We develop a quantum spin-density-matrix framework for heavy-quark spin dynamics in relativistic heavy-ion collisions. Starting from an initial polarization induced along the magnetic-field direction, we derive the evolution equation for spin polarization within this framework and obtain analytic solutions. The evolved polarization is connected to open heavy-flavor observables via a fragmentation-based hadronization prescription. For vector mesons, the spin-alignment parameter $ρ_{00}$ is constructed by coupling the heavy-quark spin to that of the light antiquark produced during fragmentation. We confront our results with recent ALICE measurements of prompt $D^{*+}$ spin alignment in Pb--Pb collisions at $\sqrt{s_{\rm NN}}=5.02~{\rm TeV}$ and extract an effective depolarization strength that determines the spin-relaxation time scale. Using this fitted parameter, we provide benchmark estimates for $Λ_c^+$ and $\barΛ_c^-$ polarization, up to an overall spin-transfer normalization. We further estimate the recently proposed elliptic polarization harmonic arising from path-length-dependent depolarization in an anisotropic fireball.

Vesicle-mediated secretion of ions or molecules is a central mechanism of cellular communication, for example in processes such as neurotransmission or hormone release. These events are inherently stochastic: vesicle fusions lead to bursts of variable sizes, releasing discrete packets of transmitters that are subsequently cleared or degraded. The dynamics break time-reversal symmetry due to the interplay of spontaneous bursts and continuous degradation. Using generating functions and a recursion relation, we derive an exact solution for the full time-dependent probability distribution of a general batch arrival-degradation model. This framework also enables a full analysis of first-passage times to a concentration threshold representing downstream activation. We show that activation kinetics are not determined by mean dynamics alone, but depend sensitively on the temporal statistics of arrival events, batch-size variability, and degradation. In particular, different arrival processes with identical mean rates can lead to qualitatively distinct first-passage behavior, reflecting the role of time-asymmetric fluctuations. We also discuss extensions incorporating vesicle depletion. Our results provide a transparent link between stochastic release dynamics and activation timing in vesicle-mediated signaling.

We investigate the formal stability of finite-amplitude non-zonal flows bifurcating from the trivial state in the unforced 2D Euler equations on the sphere. To bypass the degeneracy of the spherical Laplacian and filter out the low-frequency Fjørtoft instabilities, we restrict the functional space to the invariant subspace of the tetrahedral symmetry group. Using Arnold's Energy-Casimir method, we prove that the linearized elliptic operator derived via Liapunov-Schmidt reduction acts as the Hessian of the conserved functional. By tracking the critical eigenvalue along the bifurcating branches via the Crandall-Rabinowitz theorem, we establish a relation between the bifurcation topology and formal stability. Applying this framework to four distinct geophysical profile functions, we demonstrate that subcritical polynomial and supercritical sine-Gordon flows achieve a negative-definite second variation, that is, their formal stability. In contrast, subcritical sinh-Gordon and supercritical Liouville exponential flows generate saddle points, making them unstable. This classification identifies the specific nonlinear interactions required for the persistence of large-scale coherent waves in planetary atmospheres.

Data-processing inequalities capture the phenomenon that two probability distributions can only become less distinguishable under any common post-processing. For more fine-grained inequalities, one turns to strong data-processing inequality (SDPI) constants, which give the strongest inequalities for a given channel and reference state for a fixed measure of distinguishability. These quantities have been used to quantify the rate at which time-homogeneous Markov chains contract towards a fixed point both in the classical and quantum setting. In this work, we establish that quantum $f$-divergences satisfy a local reverse Pinsker inequality, which implies the asymptotic contraction rate of a primitive channel to its stationary state is upper bounded by the SDPI constant of any non-commutative $χ^2$-divergence. Using quantum-detailed balance, we establish a sufficient condition for these bounds to be tight. Finally, we apply these results to Petz, Matsumoto, and Hirche-Tomamichel $f$-divergences, establishing new and strengthening previously known results.