Synthetic data has become a prominent solution for preserving privacy while sharing data, but current empirical risk assessment frameworks fundamentally assume a sample-based context that fails to translate for the evaluation of synthetic population level datasets. This commentary explores the implications when synthesizing entire populations in order to do population-level data science, arguing that traditional metrics, such as Membership Inference Attacks (MIA) and Attribute Inference Attacks (AIA), require re-examination. First, MIA may be rendered irrelevant in contexts where population membership is public knowledge or not considered sensitive information. Second, the risk of singling out is heightened because the confidential data contain full population information. Additionally, the absence of an "out-of-sample" comparison group for attribute inference means we need to define other policies when defining acceptable inferences. Finally, we cannot rely on simply returning to subsampling prior to generating synthetic data if the use case is truly to enable population-level data science. This commentary highlights the necessity for considering context when generating and evaluating synthetic population data.

Autonomous synthesis platforms integrating machine learning with in situ diagnostics have the potential to revolutionize thin-film growth by enabling real-time process optimization and reducing the need for manual tuning. However, their application to molecular beam epitaxy (MBE) remains underdeveloped. Here, we present a machine learning-guided framework for MBE growth of GaSe films, leveraging reflection high-energy electron diffraction (RHEED) as an in situ diagnostic alongside ex situ characterization via X-ray diffraction and atomic force microscopy. Unsupervised learning on RHEED patterns reveals a well-defined boundary between high- and low-quality samples, capturing physically meaningful features. Mutual information analysis shows a strong correlation between RHEED embeddings and rocking curve full-width at half-maximum (fwhm), while the correlation with AFM root-mean-square (RMS) roughness is weak. Among key growth conditions, growth rate most strongly influences fwhm, whereas the Se/Ga flux ratio primarily affects RMS roughness and the RHEED embeddings. Supervised learning models trained to predict fwhm and RMS roughness demonstrate moderate accuracy, with significant improvement achieved by incorporating RHEED embeddings. Furthermore, anomaly detection via residual analysis in supervised learning aligns well with unsupervised classification from RHEED, reinforcing the reliability of the predictive models. This study establishes a data-driven framework for machine learning-assisted MBE, paving the way for real-time process control and accelerated optimization of thin-film synthesis.

Autonomous real-time systems (ARTS), such as self-driving vehicles and robotic assembly lines, are increasingly deployed to improve efficiency, accuracy, and responsiveness with reduced human intervention. In ARTS networks, self-triggered (ST) traffic-initiated by internal decision-making rather than fixed schedules or external events-is becoming prevalent and plays a critical role in enabling timely autonomous actions. However, existing network schedulers do not adequately support ST traffic due to two inherent challenges: volatility, where bounded processing jitter leads to uncertain arrival times, and absence, where reserved network resources remain underutilized when ST traffic does not materialize. To address these challenges, we propose ARTSN, an ST-tailored scheduling paradigm built upon time-sensitive networking (TSN). ARTSN introduces two key techniques: (1) an exact offline scheduling method that leverages the inferable arrival information of ST traffic for precise time-slot reservation, and (2) an adaptive online slot-release mechanism that dynamically reclaims unused reservations when ST traffic is absent. Extensive experiments on both a TSN simulator and a real-world testbed show that ARTSN significantly improves schedulability, scalability, and efficiency over state-of-the-art methods while maintaining reliable transmission guarantees.

We study delay-dependent and independent passivity properties of linear port-Hamiltonian systems with delay terms. We derive passivity conditions using a particular storage function and Wirtinger-based inequalities. Furthermore, we recall several conditions for delay-dependent and independent exponential stability. Finally, we present an application of our passivity and stability results to delay equations arising in the modeling of district heating networks and oscillators with delayed damping and stiffness.

Sensors with fast timing capabilities (on the order of tens of picoseconds) are a critical component of future HEP tracking detectors, providing the ability to disentangle high multiplicity events. Silicon 3D sensors are capable of delivering this temporal resolution and additionally display an excellent radiation hardness, suitable for the harsh environments expected in future hadron colliders (e.g. FCC-hh). In the course of the RD50 project "3D detectors optimized for timing applications", double-sided 3D sensors with two different column layouts, hexagonal and orthogonal, and different column counts were designed and produced by CNM. In this study, results of IV, top-TCT and source timing measurements of unirradiated as well as proton irradiated sensor structures are presented. The IV characterisation shows a strong decrease of the overall high leakage current of the sensors after irradiation. Top-TCT measurements with both an infrared and red laser reveal a mostly homogenous charge collection in the sensor bulk, while higher signals are observed in the outermost columns for surface charge injection. The time resolution of sensors irradiated up to a $1 \, \mathrm{MeV}$ neutron equivalent fluence of $3\times10^{15} \, \mathrm{cm^{-2}}$ reaches down to ca. $65\,\mathrm{ps}$, showing only a slight degradation compared to unirradiated sensors.

We develop a geometric model for the spreading of shallow, viscous puddles of arbitrary shape, building on the recent 'capillary current' model for axisymmetric droplets. In short, we assume that a spreading puddle remains close to instantaneous mechanical equilibrium as it spreads, with hydrostatic pressure balanced by surface curvature. In turn, its contact line advances so as to maximize the rate of energy loss subject to viscous dissipation. The resulting system yields a natural geometric evolution equation for both the two-dimensional footprint and the three-dimensional depth profile of a spreading puddle. In appropriate limits, it recovers the classical spreading laws for axisymmetric droplets, a local version of the Hoffman-Voinov-Tanner law for small non-axisymmetric puddles, and a nonlocal Hele-Shaw-like description for large, relatively regular puddles. We show that the model rationalizes new observations of silicone oil spreading over smooth borosilicate glass.

Autonomous robotic systems, including autonomous vehicles, drones, and mobile robots, increasingly rely on on-device Deep Reinforcement Learning (DRL) to adapt to dynamic environments. Unlike cloud-based solutions, embedded DRL must perform training and inference directly on resource-constrained hardware while maintaining timely decision-making. This creates a fundamental challenge: balancing four tightly coupled objectives, real-time performance, task reward, memory utilization, and energy consumption. Optimizing these objectives independently often leads to suboptimal behavior, while conventional multi-objective methods may violate resource constraints and compromise reliability. This paper presents TetraRL, a self-adaptive runtime framework for tetra-objective on-device DRL. TetraRL formulates embedded DRL as a unified optimization problem over real-time, reward, RAM, and reserve (energy) objectives, and employs a preference-conditioned reinforcement learning controller to dynamically navigate the resulting trade-off space. The framework integrates a unified resource-management abstraction, hardware-aware DVFS control, and a runtime Override Layer for robust constraint enforcement. We implement TetraRL on NVIDIA Jetson AGX Orin and Orin Nano platforms and evaluate it across diverse DRL environments. Results show that TetraRL effectively balances all four objectives, achieves competitive trade-offs under varying runtime preferences, and incurs negligible overhead. Moreover, a single trained policy can support runtime-switchable optimization goals, providing a practical foundation for resource-aware and self-adaptive on-device DRL.

We study the mean first-passage time of a random walker to a small absorbing target at the center of a two-dimensional annulus with a specularly reflecting outer boundary. The problem is motivated by natural killer cell migration toward a target cancer cell, where the goal is to quantify how long it takes immune cells to reach the target and how search efficiency depends on directional persistence and chemotactic bias. Cell motion is modeled as a velocity-jump process. We first consider a correlated random walk with a von Mises turning kernel, with a concentration parameter controlling directional persistence. We then extend the model to a biased correlated random walk using a phase-shifted turning kernel that represents preferential motion, for example following a concentration gradient. Our analysis combines closed-form benchmarks for simple and biased random walks, Fourier-mode reductions of the transport equations for the correlated and biased correlated models, and a fast-turning perturbation expansion that gives an analytical correction to the diffusion-limit mean first-passage time for the random walker. Our analytical results are supported by numerical methods that include a semi-Lagrangian solver in radial and angular coordinates, a stationary discretisation designed to handle biased transport, and an event-driven Monte Carlo simulator for cross-validation. Together, our results provide a framework relating persistent and biased immune-cell motion to target-search times in confined two-dimensional domains.

We study holographic entanglement entropy in Coulomb-branch solutions describing spherical shells of D$p$-branes. The corresponding throat geometries contain a flat-space bubble in the infrared region, providing a concrete top-down framework for exploring holographic entanglement of flat space. We find that the flat-space region is associated with a reduction of entanglement and of the effective infrared degrees of freedom in the dual boundary state relative to the standard vacuum. We also examine internal RT surfaces and holographic complexity, and show that they exhibit similar qualitative behavior. Finally, we comment on the broader implications of our results for flat space holography.

Xylem transport relies on a hierarchy of vessels, pits, and porous membranes that redistribute the flow across several length scales. Directly resolving this nested architecture is computationally prohibitive for network-scale studies, while existing reduced models often require prescribed inter-vessel hydraulic resistances. Here, we develop a nested homogenization framework for rigid porous membranes under single-phase viscous flow. The approach first replaces the pore-scale structure of a membrane by an effective stress-jump interface law, and then embeds this effective interface inside a second characteristic problem to obtain a conduit-scale closure for pit-mediated exchange. In this way, pore-scale geometry is systematically propagated to network-scale hydraulic response through effective tensors. The reduced model is compared against fully resolved simulations in simplified xylem-inspired vessel connections, showing that the homogenized description captures the pressure drop and flow redistribution. Finally, the resulting interface law is embedded within a xylem-like network with randomly disabled conducting elements, demonstrating that the model is suitable to describe the emergent hydraulic response from the coupling between local membrane-mediated transfer and network topology. The framework provides a tractable route for studying multiscale porous fluidic networks and forms a basis for extensions involving deformable structures and multiphase flows.

We prove a finite-scale supply--tax reduction for suitable weak solutions of the three-dimensional incompressible Navier--Stokes equations near the local regularity threshold. Along an admissible chain of parabolic windows, let B_k = A_k + C_k + D_k denote the scale-critical reservoir badness. The main PDE theorem says that if B_k stays outside a decay basin for many consecutive scales, then either cutoff/window leakage accumulates or the solution generates a positive cumulative amount of untaxed critical supply. The supply terms come from nonlinear flux, pressure transport, interpolation amplification, and pressure regeneration; the tax terms come from viscous dissipation, expected decay of old reservoir coordinates, and harmonic pressure decay. The theorem is deliberately finite-scale. It is not a proof of global regularity and it is not a construction of a singular solution. Its role is to turn persistent scale-critical badness into an explicit accounting alternative: badness can survive only by paying through untaxed supply or through non-negligible leakage. The second part of the paper interprets the ledger coordinates as a PDE-realizable finite-scale defect package. This leads to a dynamic obstruction language in which a dangerous mechanism must be profitable, reproducible, Navier--Stokes-realizable, and visible or invisible through specified pressure, flux, energy, and trace channels. The final part records finite-window quotient tests, a clean positive-cone anti-phantom theorem, and a conditional localized transfer framework. These results are finite-window or conditional tools built around the main ledger theorem, not an unconditional Navier--Stokes regularity theorem.

Learning graph topology of complex networks is challenging due to limited data availability and imprecise data models. Different from prior works that focus on structural priors with explicit control on macroscopic properties such as sparsity, this paper proposes a novel functional prior approach for graph topology learning. We postulate that complex networks are inherently optimized to perform a certain task (e.g., social networks specialize at optimizing a welfare function, biological networks are resilient towards node/edge deletion), which can be incorporated as a regularizer to assist in graph learning. Mathematically, we formulate a bilevel optimization problem where the lower-level problem solves the associated task on a candidate graph topology and the upper-level problem trades off between data fitting and task performance. We design a two-timescale gradient descent (TTGD) algorithm and show that under verifiable conditions, it finds a stationary point to the bilevel graph learning problem with a sublinear convergence rate. We provide theoretical insights on the graph topology learned from the functional priors and show that the resulting regularizers subsume a broad class of graph filter regularizers, including polynomial graph regularizers as special cases. We show via extensive experiments on synthetic and real datasets that the proposed formulation gives rise to reliable estimates of graph topology, even with insufficient data.

Background: AID algorithms require ongoing software updates and bug fixes. In co-adapted systems, where users tune settings around existing algorithmic behavior, bug fixes can paradoxically disrupt glycemic control. No principled framework evaluates the safety of AID algorithm updates. Methods: Our two-part framework classifies bugs and evaluates the clinical equivalence of AID system software updates. Bugs are classified as factual, heuristic, or computational, each with distinct management strategies. Classifications were validated from porting Trio's oref algorithm from Javascript to a bug-fixed Swift implementation. We compared implementations using shadow execution on 736,480 invocations from eight Trio users. The second component assesses clinical equivalence with error analysis on paired glucose values, applied to both Trio implementations using mechanistic in silico and data-driven replay simulation. Results: In mechanistic in silico simulation, the Swift and Javascript implementations produced nearly identical Time in Range (84.9% vs. 84.9%) and Glycemia Risk Index (23.5% vs. 23.9%), with more than 99% of paired glucose in Parkes Error Grid Zones A and B, meeting our clinical equivalence threshold. Shadow execution showed low mismatch rates in oref components (iob 0.43%, autosens 1.22%, determineBasal 0.07%, meal 0.01%), with clinically meaningful differences in 0.03% of iob invocations. Data-driven replay simulations of bugs revealed more than 99% of downstream paired glucose in Parkes Error Grid Zones A and B, also meeting our clinical equivalence threshold. Conclusions: Our framework integrates bug-fixing principles with multi-method clinical evaluation to assess AID algorithm update safety. It is system-agnostic and applicable to all widely used OS-AID systems, with case studies highlighting the need for systematic remediation of factual and computational bugs.

We show that, under constant-coefficient assumptions, the Ivancevic option-pricing nonlinear Schrödinger equation admits a Betchov-type hydrodynamic formulation analogous to the one appearing in the context of the vortex filament equation. We identify the corresponding continuity equation and momentum-type conservation law satisfied by the density--velocity pair and illustrate the formulation on known Ivancevic-type soliton solutions. The resulting interpretation is structural and model-dependent, and is intended as a bridge between nonlinear wave formulations in mathematical finance and geometric fluid mechanics.

We prove an almost everywhere divergence theorem for Cesàro means of subsequences of partial sums of Walsh--Fourier series. More precisely, we show that there exists a strictly increasing sequence of positive integers $(a_n)$ and a function $f\in L^1(G)$, where $G$ denotes the dyadic group, such that \[ \left( \frac1N\sum_{n=1}^N S_{a_n}f(x) \right)_{N=1}^{\infty} \] does not converge for almost every $x\in G$. The result is motivated by the corresponding trigonometric problem. A problem going back to Zalcwasser (1936) and remaining open for almost ninety years was recently solved in the trigonometric setting by Gát, who proved almost everywhere divergence for suitable subsequential arithmetic means of partial sums. In the Walsh--Paley setting the situation is more delicate. The dyadic structure gives positive convergence results; for instance, the partial sums $S_{2^m}f$ converge almost everywhere to $f$ for every $f\in L^1(G)$. Our theorem shows that, despite this stabilizing dyadic structure, suitably chosen arithmetic means of Walsh--Fourier partial sums may still diverge almost everywhere.

Enabled by inverted-mode scanning tunneling microscopy (IM-STM) and the use of functionalized molecular tools, we demonstrate positionally-controlled mechanosynthetic addition (donation) of carbon and subtraction (abstraction) of silicon atoms on a model build site: atomically clean and crystalline Si(100). The resulting structures represent the first demonstrations of an emerging ability to manipulate radical chemistry with positional control of specific atoms and moieties in 3D. Furthermore, by comparing the behavior of molecular tools designed for atomic donation versus abstraction, we highlight general principles governing molecular tool design for selective and reliable mechanosynthetic functionality.

This article gives an explicit local stable resolution of cusps on GIT-stable plane quartic models. More generally, we consider a smoothing of an ordinary plane cusp over a complete discretely valued field. We show that, after a finite separable extension and a suitable choice of coordinates, a single weighted blow-up with weights ((1,2,3)) gives the stable resolution. The exceptional component is an explicit semistable Weierstrass cubic. The construction is effective and is implemented in the Sage package "StabilityFunction".

Dynamical multiferroicity, which describes the magnetic fields generated by circularly polarized phonons in materials, is an established mechanism for optical control of magnetism. Here we perform ab initio calculations of dynamical multiferroicity in inorganic and organic framework materials, with the goal of identifying materials which enable the generation of large magnetic fields by light. We find the metal--organic framework material Zn(NH$_4$)(formate)$_3$ to have modes with magnetic moments almost twice that of SrTiO$_3$; these modes involve circular motions of NH$_4^+$ hydrogen ions with high gyromagnetic ratios. The complex structure and flexibility of framework materials can allow such angular momentum localization, and also increase the maximum light-induced magnetization permitted by the Lindemann melting criterion.

We report the structural, electronic, and transport properties of the goldene 2D material using the density functional tight-binding (DFTB) method. Electronic transport calculations were conducted in conjunction with the non-equilibrium Green's functions (NEGF) technique. Our study reveals that the Au 2D material is dynamically and thermally stable, and it possesses good elastic properties. On the other hand, goldene has a linear relationship between current and voltage at low potentials, indicating its metallic character. The calculated current-potential curve correlates well with transmission functions and the electronic density of states around the Fermi level. We also investigated the electronic structure and magnetic properties of silicon (Si)-doped Au 2D material. Our results show that the Si atom can induce a local magnetic state in the goldene monolayer. The resulting magnetic moment is 0.63 $\mu_B$.

This paper establishes the AKSZ theorem for shifted contact structures and its applications. In brief, to resolve certain obstructions, we first define the quotient mapping stack as the quotient of the symplectified mapping space by the constant multiplicative group action. We then prove that if $X$ is an $n$-shifted contact derived Artin stack and $Y$ is an $\mathcal{O}$-compact, $d$-oriented derived stack, the quotient mapping stack $$[\mathrm{Map}(Y, \widetilde{X})/\mathbb{G}_m]$$ admits an $(n-d)$-shifted contact structure. In addition, by formalizing the derived analogue of the graded contact AKSZ formalism, we also introduce the notion of weak shifted contact structures in derived algebraic geometry and prove that under global trivialization of the contact line bundle, the unmodified mapping stack inherits a weak contact structure. Extending this setup to spaces with boundary, we demonstrate that derived fillings naturally induce Legendrian morphisms between quotient mapping stacks, and that topological gluing of cobordisms evaluates to derived Legendrian intersections. Furthermore, we trace the transgression of the canonical shifted $1$-form to prove that our quotient mapping stacks satisfy the derived Classical Master Equation (CME). As applications of our quotient mapping stack formalism, we define the derived analogues of specific topological field theories, including the Jacobi, Courant-Jacobi, and Loop Space Sigma Models. Finally, by composing this geometric construction with the perverse linearization developed in a companion paper, we elevate these moduli spaces to generate Cohomological Contact Extended Topological Field Theories.

Hardware Security at Willamette is a Willamette University affiliated research group studying the hardware-software interface of security critical services. Within our program, we noticed many researchers spent considerable development time learning to understand and manually parse traces-of-execution of hardware designs which are used to identifying whether vulnerabilities or weaknesses arise at the hardware, software, or interface level. We propose the "RTL-Arrow" framework, a framework to compile performant binaries which bridge the hardware/data divide. We translate the outputs of simulated hardware execution, as "value change dumps" into modern data science workflows as cloud-ready "dataframes", to standardize program verification across the hardware and software levels. We describe our approach, its benefits, and lessons learned from the process of packaging and distributing these libraries for our security research program.

We study the finite-sample behavior of the Generalized Fisher Transformation (GFT), the parametrization of a correlation matrix $C$ by $\gamma(C)=\operatorname{vecl}\log C$. The GFT coordinates extend Fisher's transformation to dimension $n>2$: for elliptical data their finite-sample distributions are close to Gaussian. More strikingly, the coordinates are nearly uncorrelated and their covariance is largely invariant to $C$. This approximate orthogonality and invariance make GFT-based inference far better behaved in finite samples than inference based on sample correlations or element-wise Fisher transformed correlations, yielding estimation errors that are approximately Gaussian, weakly dependent, and nearly pivotal.

We study semistable reduction of smooth plane quartic curves over discretely valued fields, including residue characteristic (p=2). Using Geometric Invariant Theory, together with a stability-function method on the Bruhat--Tits building, we compute plane models whose special fibers are close to stable. This provides a practical route from an explicit equation to stable reduction in the non-hyperelliptic case. We prove that a smooth plane quartic admits a unique GIT-stable plane model if and only if its stable reduction is non-hyperelliptic. When this holds, the stable model is obtained from the GIT-stable plane model by a canonical local modification supported at the cusps of the special fiber. This description isolates the geometric mechanism behind the hyperelliptic/non-hyperelliptic dichotomy. The explicit cusp-resolution step is treated separately and is part of the accompanying implementation.

Security validation is an important yet challenging part of the hardware design process, yet, by convention, validation engineers are tasked with defining the threat model, specifying the relevant security properties, detecting any violations of those properties, and assessing the consequences to system security, each of which is manually intensive and may introduce errors. The combined technologies of information flow tracking and specification mining represent an automated approach to property generation and validation, but prior work on information flow tracking on RTL trace data was limited to find cases under which information flowed between registers, without reproducing full paths to capture how sensitive information propagates through a design. With the introduction of new technologies accelerating hardware analysis, we develop a novel approach for constructing information flow paths from register transfer level (RTL) trace data.

Many-body Floquet models with exact space--time symmetry, such as the kicked Ising spin chain (KIC), provide natural examples of systems with dual-unitary dynamics. The requirement of exact space--time symmetry is, however, highly restrictive, as it permits only nearest-neighbor interactions. Based on a pair of Hadamard matrices, we construct a wide family of dual-unitary kicked spin chains with long-range interactions. We show that local two-point correlations in such models propagate along the light-cone edges \( |n| = r|t| \), where \(r\) is the interaction range, and can be derived analytically for operators with local support. This approach is illustrated using the example of a kicked Ising spin chain with next-to-next-neighbor interactions.

Linear logic admits a wide range of semantic presentations reflecting its resource-sensitive notion of consequence. One well-known example is phase semantics: an algebraic semantics in which formulas are interpreted in phase spaces, consisting of a commutative monoid and a fixed subset, with respect to which an orthogonality relation is defined. A rather different and much more recent approach is given by base-extension semantics, which defines validity by inductively extending a provability relation on a base -- a set of inference rules over atomic propositions. We establish an equivalence between the two semantics by first defining bidirectional maps between bases and phase spaces, and then constructing an isomorphism between a phase space (resp. base) and its image under the composition of these maps. As a further contribution, we define the base-extension semantics clauses for the exponentials of linear logic.

The proliferation of large-scale data centers introduces spatially correlated demand profiles that challenge the long-standing assumption of statistical independence of loads in power system analysis. This paper examines the emergence of such load correlations and evaluates their impact on data-center-dominated grids. Analytical derivations reveal that correlated load fluctuations amplify aggregate stochastic disturbances, reduce voltage stability margins through weakened reactive power stiffness, and degrade frequency stability margin by erosion of natural load diversity effects. Real-time digital simulation studies confirm that moderate spatial correlation in distributed data centers produces simultaneous frequency deviations and voltage fluctuations across multiple buses. The findings offer transmission system operators a physics-based perspective to interpret emerging oscillatory phenomena and establish stability planning criteria grounded in measurable load-correlation structures rather than traditional diversity assumptions.

The ringdown phase of a binary black hole merger encodes fundamental information about the remnant through its quasinormal mode (QNM) spectrum. Extracting multiple modes from gravitational-wave data is essential for black-hole spectroscopy but remains challenging due to the short duration of the signal, limited signal-to-noise ratio (SNR), and interference between modes. In this work, we investigate the applicability of Empirical Mode Decomposition (EMD) and Variational Mode Decomposition (VMD) to the analysis of post-merger gravitational-wave signals. Using Monte Carlo simulations of noisy ringdown signals composed of pairs of QNMs, we assessed the ability of these methods to separate the two modes and estimate their frequencies. The instantaneous frequency is obtained via the Hilbert transform (HT) and our new proposed method, named instantaneous frequency and amplitude determination (IFAD). We analyze performance over a wide range of SNR values relevant to current and future gravitational-wave detectors. Our results show that both EMD and VMD can resolve multiple modes, and VMD provides significantly more accurate frequency estimates. We also introduce a modified instantaneous frequency estimator that improves accuracy over the Hilbert transform. The study quantifies the conditions under which two-mode resolution is feasible and highlights the limitations imposed by closely spaced mode frequencies and short signal duration. These results are relevant for current observations and for future high-SNR detections expected from space-based and next-generation ground detectors.

Hidden Markov models are foundational for sequential inference, but their Markovian assumption fails under pathwise constraints such as precedence requirements, visitation cardinalities, or monotonic state progression, which induce long-range dependencies that invalidate standard dynamic programming algorithms. To deal with this, we present Controller-Augmented Hidden Markov Models (CHMMs), a framework that compiles each constraint into a finite-state controller tracking the minimal sufficient history, after which standard forward--backward and Viterbi recursions on the augmented chain compute exact constrained posteriors and maximum a posteriori paths in both discrete and continuous time, the latter through uniformization. We establish four theoretical guarantees: exactness of constrained inference, monotone ascent of constrained EM, inference complexity linear in the controller cardinality, and a total-variation bound under constraint misspecification. A catalog of controller encodings covering 11 constraint families across the ordering, visitation, path, and temporal categories operationalizes the framework. Empirically, we evaluate CHMMs against 6 alternative decoders on 3 real-world sequence-labeling tasks of substantively different character: gene-structure decoding in \emph{Drosophila melanogaster}, free-living activity recognition in CASAS smart-home environments, and protocol-defined human activity recognition from wearable sensors. The results reveal a clean local-versus-cumulative dichotomy in which controller augmentation is uniquely able to recover globally feasible trajectories on cumulative-constraint regimes, whilst simpler decoders are matched in validity on locally-dominated regimes. Together, theory and experiment characterize when exact controller augmentation is necessary and when simpler approaches suffice.

In this work, we derive the working equations for the transition density matrices within the equation-of-motion frozen-pair coupled-cluster framework. We focus specifically on the recently developed EOM-fpCCSD and EOM-ptCCSD models and present the corresponding transition dipole moments and oscillator strengths obtained via approximate expressions. This formulation avoids the computational overhead of solving the coupled-cluster $\Lambda$ equations. Furthermore, we employ a matrix inverse approximation to eliminate the need for explicit calculation of the left EOM eigenvectors. The accuracy of the resulting EOM-fpCCD and EOM-ptCCSD excited-state properties is benchmarked against the linear-response (LR)-CCSD method. Our results demonstrate that the description of excited state properties is improved when using EOM-fpCCSD and EOM-ptCCSD models compared to the standard EOM-CCSD variant.