In stochastic evolutionary dynamics, the replacement of an existing genotype or cultural trait by a newly introduced mutant is typically characterized by the quantities of fixation probability and fixation time. But in a structured population, the disappearance of a lineage occurs at a specific place. For evolutionary dynamics on graphs, we define the fixation location as the node occupied by the last wild-type individual immediately before mutant fixation. Conditional on fixation, this location is described by a probability distribution over the nodes of the graph. We study the fixation location for neutral evolution, for the colonization process, and, more generally, for constant selection on small graphs, cycles, tori, random graphs, and island populations. We find that the distribution of the fixation location is often highly nonuniform, depends strongly on the graph structure and the selection strength, and can differ sharply even when classical fixation statistics are similar. For many graphs, some nodes can never be fixation locations. Our results identify fixation location as a fundamental aspect of evolutionary dynamics and suggest new ways to understand, monitor, and potentially mitigate extinction events in biological and social settings.

Federated Learning (FL) is an emerging distributed machine learning (ML) technique that enables in-situ model training and inference on decentralized edge devices. We propose Totoro$^+$, a novel scalable FL system that enables massive FL applications to run simultaneously on edge networks. The key insight is to explore a distributed hash table (DHT)-based peer-to-peer (P2P) model to re-architect the centralized FL system design into a fully decentralized one. In contrast to previous studies where many FL applications shared one centralized parameter server, Totoro$^+$ assigns a dedicated parameter server to each application. Any edge node can act as any application's coordinator, aggregator, client selector, worker (participant device), or any combination of the above, thereby radically improving scalability and adaptivity. Totoro$^+$ introduces three innovations to realize its design: a locality-aware P2P multi-ring structure, a publish/subscribe-based forest abstraction, and a game-theoretic path planning model with a guarantee of an $ε$-approximate Nash equilibrium. Real-world experiments on 500 Amazon EC2 servers show that Totoro$^+$ scales gracefully with the number of FL applications and $N$ edge nodes speeds up the total training time by $1.2\times-14.0\times$, achieves $\mathcal{O}(\log N)$ hops for model dissemination and gradient aggregation with millions of nodes, and efficiently adapts to the practical edge networks and churns.

Relying on the definition of asymptotic conformal Killing horizons, the generators of asymptotic conformal symmetries at future null infinity in Schwarzschild space-time are considered. The algebra they close is an extended version of the BMS one due to the emergence of superdilations. Several features are then studied, such as the related non-trivial charge, ruling out the hypothesis that superdilations are pure gauge transformations. Their effect on a pair of celestial observers can be understood as an angle-dependent redshift, connected to the local non-vanishing flux of the charge.

Recent ground-based microlensing surveys suggest that our Galaxy may abound with small free floating planets, potentially up to $\sim$21 such planets per star. We explore the implication of such possibility on the mass budget for planet formation. When the microlensing planets, both bound and free-floating, are taken into account, along with the short-period planets, T Tauri disks have insufficient mass to source the mass of known planets, even if all the solids convert into planetary bodies. Younger Class 0/I disks can help resolve the problem but generally fall short of the required mass when variable planet formation efficiency from pebble or planetesimal accretion is taken into consideration. If the free-floating planet mass function is as bottom-heavy as reported, heavier Class 0/I disks may be necessary. Alternatively, free-floaters may preferentially form in the most massive disks around massive stars consuming the majority of the mass budget, leading to a decrease in the bound planet occurrence rate for higher mass stars, which is observed. Precise constraints on the bottom of planet mass function are necessary: a peaked mass function may eliminate the missing mass problem; by contrast, verifying a bottom-heavy function could spell a crisis in planet formation.

The most irreplaceable capability of HST in the 2030s is not only its angular resolution or its UV--optical sensitivity, but its accumulated time baseline. We recommend a Hubble Local Group Astrometric Legacy that would obtain matched 2030s ACS/WFC and WFC3/UVIS imaging of selected M31 and M33 star cluster fields, combine those observations with a careful astrometric audit of the existing archive, and deliver public transverse velocity products through MAST. PHAT and PHATTER already provide exceptional first epochs across the nearest large external spirals, resolving tens to hundreds of millions of stars and identifying thousands of star clusters and compact background reference objects. Earlier targeted HST programs, dating back to the mid 90's, can extend the temporal baseline in selected cases, but only after camera, chip, filter, dithering, crowding, and reference-frame triage. A coherent 2030s repeat campaign would turn the best of this archive into bulk cluster motions, enabling the first systematic orbital mapping of star cluster populations beyond the Milky Way. These measurements would constrain disk heating, cluster disruption, accretion histories, stream associations, the M31--M33 interaction, and the mass distributions of Local Group spirals. The same program would also preserve and stress-test the calibration infrastructure needed for high-stability optical/UV astrophysics in the HWO era: geometric-distortion solutions, PSF and CTE modeling, matched-epoch observing strategies, long-term reference frames, and durable public high-level products.

We develop the theory of equivariant, ultra Kolyvagin systems to bypass structural limitations of the Euler system machinery over infinite rings. By utilizing collections of classes living in the exterior powers of patched Selmer groups -- constructed from ultraproducts of classical Selmer groups -- we compute the structure of an Iwasawa Selmer group up to pseudo-isomorphism of Iwasawa modules and prove the absence of finite submodules. We apply this theoretical framework to the fine Selmer group of an elliptic curve and the Bloch-Kato Selmer group of the Rankin-Selberg convolution of modular forms.

The production of single top quarks and top antiquarks via the $t$-channel exchange of a virtual $W$ boson is measured in proton-proton collisions at a centre-of-mass energy of 13 TeV at the Large Hadron Collider. The full Run 2 data sample recorded with the ATLAS detector in the years 2015-2018 is used, corresponding to an integrated luminosity of 140 fb$^{-1}$. The absolute and normalised production cross-sections are measured differentially as a function of the transverse momentum and absolute rapidity of the top quark and top antiquark. In addition, the ratio of top quark to top antiquark production cross-sections is measured. The measured distributions are compared with next-to-leading-order quantum chromodynamics predictions obtained with different combinations of matrix-element generators, parton-shower programs and proton parton distribution functions, as well as to next-to-next-to-leading-order calculations. Overall, good agreement is observed between the measurements and the theoretical predictions. For most measured distributions, the sensitivity to differences between the predictions is limited by the systematic uncertainties in the measurement. The measured differential distributions are also interpreted in an effective field theory approach to constrain the Wilson-Coefficient $C_{Qq}^{3,1}$ associated with a four-quark operator. The interpretation accounts for the effect of the selection efficiency, which is altered significantly by non-zero contributions from $C_{Qq}^{3,1}$.

The application of program transformation and algebraic methods to the development of efficient combinatorial optimization (CO) algorithms relies on an exhaustive combinatorial generator for the problem specification, followed by the fusion of thinning or filtering processes into this specification. However, the effectiveness of such fusion transformations critically depends on the structural compatibility between the objective function and the generator, which is highly problem dependent. In practice, when the majority of candidate solutions remain unfiltered or are not eliminated-as is the case for most intractable CO problems-the overall efficiency of the resulting fused program is largely determined by the intrinsic efficiency of the combinatorial generator. Consequently, if the specification itself exhibits suboptimal performance, the fused program will inherit a correspondingly inferior level of efficiency. We argue that a genuine designed process should also account for hardware compatibility and parallelizability-particularly the ability to support efficient parallel execution on modern hardware architectures, including multi-level cache hierarchies and GPUs. However, does achieving formal correctness necessarily conflict with designing algebraically elegant algorithms that support fusion? Can we obtain both simultaneously? In this paper, we show that techniques from functional programming, provide powerful formal tools for the systematic construction of such hardware-compatible and parallelizable combinatorial generators. This paper investigates generators for two of the most fundamental combinatorial structures-combinations and permutations-together with their natural extension to nested generators (e.g., combinations/permutations of combinations/permutations).

This study analyses the financial resilience of agricultural and food production companies in Spain amid the Ukraine-Russia war using cluster analysis based on financial ratios. This research utilizes centred log-ratios to transform financial ratios for compositional data analysis. The dataset comprises financial information from 1197 firms in Spain's agricultural and food sectors over the period 2021-2023. The analysis reveals distinct clusters of firms with varying financial performance, characterized by metrics of solvency and profitability. The results highlight an increase in resilient firms by 2023, underscoring sectoral adaptation to the conflict's economic challenges. These findings together provide insights for stakeholders and policymakers to improve sectorial stability and strategic planning.

We propose an optical scheme to build an entangled network composed of W state based on polarization encoded qubits (photons). This new setup consists of 2 cNOT gates, 4 V gates, 2 Hadamard gates and basic optical tools such as polarizing beamsplitters (PBSs) and path couplers (PCs). V gate is a specially-designed tool acting as a two-qubit gate which is composed of a cNOT gate, 3 PBSs and a PC. By using this gate, one benefits from the temporarily generated optical degree of freedom, which is the spatial mode of a photon in the proposed scheme. Using an extra degree of freedom allows us to perform more capable processing for W-state creation protocols. We use four photons as input, which means we do not need entanglement as a resource. Also, we show that the proposed scheme can be implemented by operating the quantum optical gates which can be realized via current photonics technology. Additionally, we provide discussions of quantum contextuality and non-locality for W states.

Low-Rank Adaptation (LoRA) has become a widely used mechanism for customizing text-to-image diffusion models, enabling lightweight modules that are shared, reused, and commercialized as independent assets. This LoRA-centric ecosystem shifts copyright protection from foundation models to distributed LoRA modules, which are easy to copy, redistribute, or reuse without authorization. Existing watermarking methods either protect the base diffusion model or require watermark-aware retraining for each target LoRA, limiting their practicality in open community settings. To address this limitation, we propose LoRA-Key, a user-centric LoRA watermarking framework that treats copyright protection as a reusable ownership key. LoRA-Key encapsulates a recoverable secret message into a standalone user-specific Watermark LoRA, which can be attached to different target LoRAs through training-free linear superposition without per-LoRA retraining or structural modification. To train such a reusable key, we first establish a latent watermark prior in the frozen VAE latent space for robust message embedding and recovery, and then optimize the Watermark LoRA with message-conditioned watermark supervision and semantic consistency constraints. We further introduce Gradient Orthogonal Projection (GOP) to suppress watermark updates that conflict with semantic-preserving directions, reducing interference with generation fidelity and downstream style adaptation. Extensive experiments show that LoRA-Key provides lightweight plug-and-play copyright protection while preserving generation quality and style fidelity, and maintains robust ownership verification under image-level distortions, downstream fine-tuning, and multi-LoRA composition.

Let $L$ be the Dunkl Laplacian on the Euclidean space $\mathbb{R}^N$ associated with a normalized root system $R$ and a multiplicity function $k(ν)\geq 0$, $ν\in R$. We establish a Leibniz-type rule for the fractional powers of $L$ on Besov and Triebel--Lizorkin spaces in the Dunkl setting. Our approach exploits the interplay between spectral multipliers and the Dunkl transform, together with the support properties of the distributions associated with Dunkl translations. These results extend the corresponding Leibniz-type estimates previously established on $L^p$ spaces to the broader setting of Besov and Triebel--Lizorkin spaces.

We consider continuous time to treatment initiation. This can commonly occur in preventive medicine, such as disease screening and vaccination; it can also occur with non-fatal health conditions such as HIV infection without the onset of AIDS. While traditional causal inference focused on `when to treat' and its effects, we consider the incremental causal effect when the intensity of time to treatment initiation is intervened upon. We derive the efficient influence function for this estimand and develop an estimation framework that accommodates flexible machine learning methods while achieving fast convergence rates. Valid confidence bands are obtained leveraging empirical process theory. We illustrate our approach via simulation, and apply it to cervical cancer screening data to study the incremental effect of time to subsequent HPV testing on cervical intraepithelial neoplasia detection.

The CMS collaboration has reported a measurement of $Υ$ decays to ditaus using $61.9~{\rm fb}^{-1}$ of scouting data. If interpreted as the decay of $Υ(1S,2S,3S)$, the measured ditau rate is more than ten times that seen in the dimuon final states at the $\sim 3 σ$ level, and is likewise inconsistent with the branching ratios measured at $B$-factories. If confirmed with more data and at higher significance, such a violation of lepton flavor universality would necessitate new physics. In this Letter, we present a simple model with a light pseudoscalar coincidentally near the $Υ(1S)$ mass, which mixes with two Higgs doublets in the alignment limit. Such a particle naturally decays primarily to taus and evades all existing experimental constraints, while implying a number of predictions that can be tested in the near future.

This paper introduces a multifidelity formulation that reduces the computational cost of the proper orthogonal decomposition (POD) of a high-fidelity model by leveraging data from cheaper, lower-fidelity models. POD is a prevalent technique for extracting a low-dimensional basis from training data to achieve subsequent dimension reduction or reduced-order modeling. In scientific and engineering applications, the training data are typically numerical snapshot solutions of a high-fidelity model, and computation of a sufficiently rich snapshot set can be prohibitively expensive, especially when sampling over a high-dimensional parameter space. Insufficient snapshot training data risks overfitting and poor generalizability of the POD basis to outside the training regime. Our multifidelity POD (MFPOD) formulation reallocates computational budget to cheaper, low-fidelity models that can be sampled more extensively. MFPOD then weights high- and low-fidelity snapshot data via a control-variate formulation to guarantee an unbiased estimate of the expected high-fidelity least-squares projection error. The MFPOD subspace is chosen to minimize the estimate of this projection error, and converges in probability to the same subspace as single-fidelity POD in the limit of an arbitrarily large budget. For restrictive computational budgets, the MFPOD cost function has (under some assumptions) lower variance than the POD cost function, which makes the MFPOD subspace more robust against variations in the training data and thus less prone to overfitting. For a numerical example modeling the velocity of the Pine Island glacier, MFPOD achieves the same accuracy as single-fidelity POD with an order of magnitude reduction in the offline computational cost of snapshot generation.

The longest increasing subsequence (LIS) of a random walk has been studied mainly for zero-mean, symmetric step increments. We numerically investigate the LIS of biased Gaussian random walks, with unit-variance increments and positive drift $μ_{p} = Φ^{-1}(p)$, where $p = P(ξ>0)$. In contrast with the symmetric case, we find that for every fixed $p>1/2$ the mean LIS length grows linearly, $\langle L_{n}(p)\rangle \sim a(p)n$, with $a(p)$ increasing from $0$ at $p=1/2$ to $1$ as $p \to 1$. The record count is also linear, with coefficient $λ(p)$ fixed by Spitzer's formula for the ascending ladder epoch, and the LIS becomes increasingly aligned with this record skeleton as $p$ grows. At the symmetric point $p=1/2$, the record skeleton collapses to the Sparre Andersen $\sqrt{n}$ scale, while the LIS returns to the finite-variance $\sqrt{n}\log{n}$ regime. Near this limit the record rate has the closed-form small-drift slope $λ(μ_{p}) \simeq \sqrt{2}\,μ_{p}$, whereas the excess $a(μ_{p})-λ(μ_{p})$ vanishes more slowly than linearly in the drift, although our data do not resolve a single power law. The empirical distribution of $L_{n}$ also changes across this point, from lognormal-like at $p=1/2$ to Gaussian-like for every sampled $p>1/2$.

We give an explicit projectivization algorithm for smooth complete toric varieties in arbitrary dimension $n\ge 2$. After fixing an ordered lattice basis, every smooth complete fan~$\Sig$ admits a basis-canonical refinement~$\wSig=\Gam(\Sig)$ that is smooth, complete, projective, and obtained from~$\Sig$ by star subdivisions of two-dimensional cones. Equivalently, $X_{\wSig}\to X_\Sig$ is a finite sequence of ordinary toric blow-ups along smooth invariant centers of codimension two. The algorithm first constructs a projective wall-arrangement fan by extending the spans of the codimension-one cones of~$\Sig$ to central hyperplanes. It then sign-adapts~$\Sig$ to this arrangement by repeatedly subdividing bad two-cones of maximal weight. A lexicographic badness profile gives termination, while projectivity follows from a wall-bend sandwich argument combining a support function pulled back from the arrangement with a relatively ample perturbation. The construction is canonical relative to the chosen ordered basis and requires no additional projectivizing refinement after wall-adaptation. We illustrate the procedure on Oda's non-projective threefold and compare its deterministic length with a separate threefold whose minimal ordinary invariant projectivization length is exactly two.

The existence of a finite global attractor for polynomial curve system has been known since the work of Belk et al. [5]. However, except in the hyperbolic case, the rate at which the pullback of a curve under a polynomial converges to the attractor remained unclear. In this paper, we introduce the notions of $\textit{quick returns}$ and $\textit{barrier lakes}$ to analyze the combinatorial models of curves. These concepts allow us to show that if a certain number of successive pullbacks do not decrease the complexity of the curve by a definite proportion, then the curve admits a $\textit{thick}$-$\textit{thin}$ $\textit{decomposition}$: most of the curve is organized into finitely many disjoint annuli whose core curves have bounded homotopy type. In this case, we can show that some number of successive pullbacks must decrease the complexity of the curve by a definite factor. This implies that the complexity of a curve $C$ decreases exponentially under iteration of the pullback by a polynomial $f$: \[ N_{\mathcal{F}}(η) \le A \, N_{\mathcal{F}}(C) \, e^{-n δ} + D, \qquad \forall n\ge 1, \] where $\mathcal{F}$ is an admissible family of separation arcs, $N_{\mathcal{F}}(\cdot)$ denotes the minimal intersection number of the curves in its homotopy class and the arcs in $\mathcal{F}$, $δ> 0$ is a constant depending only on $f$, $A, D > 0$ are constants depending only on $\mathcal{F}$ and $f$, and $η$ is any component of $f^{-n}(C)$. Consequently, the pullback of a curve contracts exponentially to the attractor. In particular, this provides a quantitative proof of the finite global attractor conjecture for the polynomial case.

Some near-optimal polynomial root-finders of 2024-25, based on subdivision iterations, approximate all complex roots of a polynomial or all roots lying in a fixed Region of Interest in the complex plane. We combine these iterations with Newton's and/or Schroeder's to yield significant empirical acceleration versus each approach standing alone. Like the cited recent algorithms, our root-finders can be applied not only to a polynomial represented in monomial basis by its coefficients but also to a black box polynomial represented by an oracle (black box subroutine) for its evaluation. Some by-products of our study such as an extension of the Gauss-Lucas theorem and a fast black box estimator for root radius can be of independent interest.

Let $\mathbb{U}$ be the unit disk in the complex plane. Denote by $s_\mathbb{U}(x,y)$ the triangular ratio metric in $\mathbb{U}$; for $x\neq y$ the value of $s_\mathbb{U}(x,y)$ equals the ratio of the Euclidean distance $|x-y|$ between $x$, $y\in \mathbb{U}$ to the value $\inf_{z\in \partial \mathbb{U}}(|x-z|+|z-y|)$. In the monograph by P.~Hariri, R.~Klén, and M.~Vuorinen "Conformally invariant metrics and quasiconformal mappings" (2020) the following problem was stated: for every Moebius automorphism of the unit disk, $w=f(z)=\frac{z+a}{1+za}$, $0\le a<1$, and every points $z_1$, $z_2\in \mathbb{U}$ the sharp inequality $s_\mathbb{U}(f(z_1),f(z_2))\le (1+a)s_\mathbb{U}(z_1,z_2)$ holds. We prove that the conjecture is valid.

We define Seshadri constants for Higgs bundles on smooth projective varieties over algebraically closed fields of characteristic zero. This definition is inspired by and analogous to the notion of Seshadri constants for ordinary vector bundles. We prove a series of properties of Higgs Seshadri constants which are analogous to the corresponding properties in the case of ordinary Seshadri constants. In particular, we prove a Seshadri criterion for Higgs ampleness and prove that Higgs Seshadri constants can be computed by restriction to curves.

We compute the finite-$N$ Witten index of BMN matrix quantum mechanics after summing over all partition-labeled supersymmetric vacuum sectors. Starting from the unitary-matrix integral for each sector, we develop two complementary evaluation methods: a symmetric-group character expansion, which reduces each fixed fugacity order to a finite combinatorial sum, and a residue expansion in which the contributing poles are organized by rooted trees, with a colored-tree generalization for multi-partition sectors. Where practical, direct integration and extraction of the constant term in the expanded integrand give independent coefficient-by-coefficient checks. We evaluate every vacuum sector for $N\leq 9$. In the equal-fugacity expansion, the coefficients near charges $j\sim N^2$ show entropy growth of order $N^2$, and, in this range, the sector sum does not cancel this growth. The finite-$N$ data also reveal a nontrivial sectoral organization: near $j=N^2$, the sector giving the largest contribution changes with $N$, from single-partition sectors at small rank to double-partition sectors starting at $N=5$. We call this phenomenon dominance switching. These results provide quantitative finite-$N$ input for using the BMN index as a diagnostic of protected plane-wave black-hole sectors and suggest a D2 dressed black-hole interpretation in the controlled type-IIA regime, where D0 black-hole sectors are accompanied by macroscopic spherical D2-brane degrees of freedom, analogous to dual dressed black holes in $AdS_5\times S^5$.

The greatest integer that does not belong to a numerical semigroup S is called the Frobenius number of S, and finding the Frobenius number is called the Frobenius problem. In this paper, we solve the Frobenius problem for shifted square sequences starting with a multiple of 4.

Deep reinforcement learning (DRL) has long been a promising solution for sequential resource management in wireless networks. However, conventional DRL methods are fundamentally limited by their reliance on unimodal policy distributions, inefficient exploration in high-dimensional action spaces, and poor adaptability to dynamic and heterogeneous environments. Meanwhile, diffusion models (DMs) as one of the most powerful families of generative AI have demonstrted remarkable capabilities in modeling complex, multi-modal data distributions across diverse domains. The integration of DMs and DRL has opened a new and rapidly growing research direction, in which DM-enabled policies substantially enhance decision quality by capturing the complex, discontinuous, and multimodal action structures inherent in wireless resource management. In this paper, we present a comprehensive survey of DM-enabled DRL algorithms and their applications for various issues in wireless networks. Particularly, we first provide the theoretical background of DM and present different DM-enabled DRL algorithms. We then systematically review applications of DM-enabled DRL for across computation offloading in mobile edge computing, UAV-assisted, vehicular, and AIGC-driven systems, as well as wireless resource allocation, physical-layer security, and robotics and UAV planning. We conclude the paper by higlight future research directions.

The concept of distinguishability lies at the heart of quantum information theory. We introduce \textit{left-right relative entropy} as a quantitative measure of distinguishability within the space of boundary states in two-dimensional conformal field theories (CFTs). By tracing over either the left- or right-moving modes, we derive a universal formula for arbitrary regularized boundary states defined on a circle. Remarkably, the resulting quantity reduces to a Kullback--Leibler divergence, where the associated probability distribution is determined entirely by the modular $\mathcal{S}$-matrix and the boundary data. For diagonal CFTs, we obtain exact expressions for the left-right relative entropy in terms of modular data, and extend the framework to define \textit{Sandwiched Left-Right Rényi relative entropies} and \textit{left-right fidelity}. Applying this formalism to the Ising model, tricritical Ising model, and $\widehat{su}(2)_k$ WZW model, we uncover a striking phenomenon: the left-right relative entropy between certain reduced boundary states vanishes even though the corresponding global boundary states are orthogonal. This observation motivates the introduction of \textit{relative entanglement sectors}, defined as equivalence classes of boundary states that are indistinguishable with respect to left-right relative entropy. These sectors transform as NIM-representations of global symmetries and exhibit level-dependent structures that mirror $\mathbb{Z}_2$ 't Hooft anomalies. Our findings establish an unexpected bridge between quantum information measures, boundary conformal symmetry, and quantum anomaly constraints.

We define a complete metric structure on the family $\text{PL}_q^p(\mathbb{R}^n)$ of probability measures with densities in $L^p(\mathbb{R}^n)$ and finite $q$-moments. We establish the existence of generalized minimizing movements for the isoperimetric ratio and characterize absolutely continuous curves in this space through weak solutions of the continuity equation with velocity fields satisfying a first-order integral condition. We also characterize absolutely continuous curves in the $\infty$-Wasserstein space and prove a Benamou--Brenier formula for $W_\infty$.

We study controlled McKean--Vlasov contagion with state-dependent killing, common noise, loss feedback, and interacting populations. The main result is a comparison principle for the two-population killed-particle HJB on a decomposed state space of alive sub-probability measures and cemetery masses. The proof combines a Wasserstein smooth-gauge comparison argument with a killing-jump absorption estimate for mass transfer into the cemetery state. We also establish a multi-population mean-field limit, an explicit first-order particle convergence rate, conditional propagation of chaos, controlled well-posedness, and a steep-killing bridge to absorbing-boundary default. Finite-particle convergence tests and a two-population HJB feedback experiment illustrate the theory.

This study examines the dynamics of quantumness in two-flavor neutrino oscillations subjected to a dephasing channel, using representative oscillation parameters associated with the KamLAND, MINOS, and Daya Bay experiments. We analyze three complementary quantum-correlation measures -- entanglement of formation (EOF), quantum discord (QD), and local quantum uncertainty (LQU) -- within an effective two-qubit description. In the unitary case, all three measures display oscillatory behavior controlled by flavor mixing, and their amplitudes are strongly shaped by the relevant mixing angle. MINOS exhibits the largest correlations because $θ_{23}$ is close to maximal, KamLAND shows intermediate values associated with the solar sector, and Daya Bay yields smaller correlations due to the relatively small value of $θ_{13}$. Under dephasing, the off-diagonal coherence terms are suppressed and the three quantifiers decrease accordingly, while QD remains non-zero in regimes where entanglement is weak. For pure states, LQU satisfies $\mathcal{U}=\mathcal{C}^2$ and therefore tracks entanglement monotonically, whereas QD provides a broader witness of non-classical correlations. These results provide a compact quantum-information description of two-flavor neutrino oscillations in both coherent and dephased regimes. We also quantify the sensitivity of these observables to oscillation and decoherence parameters, showing that their main added value relative to flavor probabilities is their direct response to off-diagonal coherence loss.

We study a regulation problem for stochastic systems subject to both continuous fluctuations and rare but significant shocks, modeled as a jump-diffusion with uncertainty in both the drift and the jump intensity. Such settings arise in applications including inventory control, cash management, and capacity planning. We formulate the problem as a robust ergodic singular control problem in which a decision maker applies upward and downward interventions while accounting for model ambiguity through entropy-penalized distortions. The resulting max-min problem involves a long-run average performance criterion. We show that the associated Hamilton--Jacobi--Bellman equation reduces to a nonlinear integro-differential free-boundary problem with a tractable structure. The worst-case model exhibits a bang-bang form, and the optimal policy is characterized by reflecting barriers. Under exponentially distributed jumps, the problem further reduces to a system of ordinary differential equations, enabling efficient numerical computation.

We formulate a framework of Floquet algebraic tomography for finite-dimensional non-Hermitian monodromy matrices from observable trace sequences $ζ_n^{(O)}={\rm Tr}(OM^n)$. Since these sequences are constrained by the characteristic polynomial of $M$, the inverse problem is a finite-dimensional algebraic reconstruction problem rather than a generic exponential fit. We organize the reconstruction through the observable resolvent, spectral determinant, and Dirichlet spectral data, separating the common spectral skeleton from observable-dependent dressing. Cayley--Hamilton and Hankel methods recover the similarity-invariant spectral data, while multi-observable and Liouville-space extensions connect the construction to realization theory and tomography reconstruction. We further clarify the limits of identifiability from restricted observable algebras: the data determine a visible representative, micromotion can enlarge the sampled visible operator space, and exact symmetries impose residual invisible sectors. Two examples, a driven transmon qutrit and a finite non-Hermitian Floquet SSH chain, demonstrate leakage-induced visibility expansion, observable-dependent phase response, EP-accessible branch geometry, and disorder/probe-dependent observable-dimension readouts.