It has recently been shown that the evolution of a state, described by a Partial Differential Equation (PDE), can be more conveniently represented as the evolution of the state's highest spatial derivative (the ``fundamental state''), which lies in $L_2$ and has no boundary conditions (BCs) or continuity constraints. For linear PDEs, this yields a Partial Integral Equation (PIE) parametrized by Partial Integral (PI) operators mapping the fundamental state to the PDE state. In this paper, we show that for polynomial PDEs, the dynamics of the fundamental state can instead be compactly expressed as a distributed polynomial in the fundamental state, parametrized by a new tensor algebra of PI operators acting on the tensor product of the fundamental state. We further define a SOS parametrization of the distributed polynomial and use this to construct a distributed SOS program, for testing local stability of polynomial PDEs.

In this paper, we study modularity in the context of evolution algebras. Although this property has been previously considered, a complete description is still missing in several natural settings. In particular, we obtain a full characterisation of modular evolution algebras in the nilpotent case and in the class of supersolvable regular evolution algebras.

Software engineering students often struggle to appreciate empirical methods and hypothesis-driven inquiry, especially when taught in theoretical terms. This experience report explores whether grounding empirical learning in hype-driven technologies can make these concepts more accessible and engaging. We conducted a one-semester seminar framed around the currently popular topic of AI coding assistants, which attracted unusually high student interest. The course combined hands-on sessions using AI coding assistants with small, student-designed empirical studies. Classroom observations and survey responses suggest that the hype topic sparked curiosity and critical thinking. Students engaged with the AI coding assistants while questioning their limitations -- developing the kind of empirical thinking needed to assess claims about emerging technologies. Key lessons: (1) Hype-driven topics can lower barriers to abstract concepts like empirical research; (2) authentic hands-on development tasks combined with ownership of inquiry foster critical engagement; and (3) a single seminar can effectively teach both technical and research skills.

We study equalizers and fixed points of monomorphisms of free groups at infinity. We show that the action of the equalizer of two monomorphisms on the regular points of the equalizer at infinity has finitely many orbits, showing that the equalizer at infinity is, in some sense, finitely generated and generalizing a previous result of Cooper about fixed points. We additionally show that it is decidable whether an automorphism of a free group has a nontrivial fixed point at infinity. The same result is shown for monomorphisms satisfying the condition of being almost length-increasing. We remark that almost length-increasing monomorphisms are generic among endomorphisms of a free group. We also prove that being almost length-increasing is a decidable condition. We end the paper with several open problems arising from this work.

Hybrid Energy Systems (HES), integrating generation sources, energy storage, and controllable loads, are well-positioned to provide real-time grid flexibility. However, quantifying this maximum flexibility is challenging due to renewable generation uncertainty and the complexity of power allocation across multiple assets in real time. This paper presents a rule-based framework for characterizing HES flexibility and systematically allocating power among its constituent assets. The flexibility envelope defines the dynamic power boundary within which the HES can inject or absorb power without violating operational constraints. Shaped in real time by capacity bids, available solar generation, and power allocation protocol, it enables reliable and predictable HES participation in regulation markets. Depending on the operational objective, the framework supports both symmetric and asymmetric flexibility cases. Further, the proposed power-allocation rule is benchmarked against an optimal dispatch, providing a performance reference under realistic conditions. Finally, state of charge drift correction control is presented to ensure sustained battery operation and system reliability. This work, therefore, offers a rigorous and practical framework for integrating HES into capacity markets through effective flexibility characterization.

In this paper we present a framework for modelling \emph{reward-sensitive bisimulations}, that is, bisimulations that account for quantitative differences such as accumulated rewards. To capture both qualitative and quantitative aspects uniformly, we consider two interacting notions of bisimulation: a graded variant that tracks bounded reward differences, and an ungraded one that abstracts from them. Our characterization of these notions is done in the fibrational and coalgebraic approach to (bi)simulation initiated by Hermida and Jacobs. To formally relate the graded and ungraded notions, we deploy categorical gluing, a standard technique in categorical logic. Furthermore, we show that this construction interacts well with standard coalgebra concepts, such as final coalgebras, and that it yields a unified characterization in terms of combined notions of bisimulations under mild assumptions. In order to demonstrate the versatility of our approach, we show how it encompasses various bisimulation notions for different kinds of systems, including relation-based bisimulations for automata with rewards and metric-based notions of bisimulations for labelled Markov processes.

The energy-energy correlator (EEC) and multiplicity are two fundamental observables probing complementary aspects of QCD jets: the former characterizes the angular structure of energy flows in a scale-dependent manner, while the latter is sensitive to the entire history of particle production. In this \emph{Letter}, we uncover a nontrivial correlation between them by studying the EEC as a function of jet internal multiplicity. We introduce the multiplicity-conditioned EEC jet function (MCJF) and perform a factorization calculation to next-to-leading order accuracy. It is found that, for jet samples selected at a given normalized multiplicity $ν= N_{\rm ch}/\langle N_{\rm ch} \rangle$, the EEC in the angular region $Λ_{\rm QCD}/p_{T,\rm jet}\llχ\ll R$ acquires a $ν$-dependent anomalous dimension. Thus the $ν$-conditioned EEC provides a direct and robust probe to the multiplicity generating function in the perturbative regime. In addition, understanding $ν$ dependence of the EEC is also crucial for isolating possible multiplicity-dependent bias effects in the EEC measurements in nuclear environment.

We present a Bayesian model calibration framework for inferring nonlinear constitutive relationships in heat conduction problems, with a focus on temperature-dependent thermal conductivity. The proposed framework integrates gradient-based optimization and uncertainty quantification (UQ) to address the inverse problem of estimating the conductivity function from transient temperature measurements. A key contribution is an adaptive algorithm that sequentially refines both the numerical discretization for model simulation, and the model complexity used to represent the conductivity curve. The discretization is optimized through the minimization of a loss function, and Morozov's discrepancy principle is used as an uncertainty-motivated stopping criterion. The model complexity is selected using an approach that balances maximizing the likelihood of the data with penalizing excessive model complexity. As a result, the numerical and modeling biases remain of the same order as the uncertainty imposed by the measurement noise, leading to robust and computationally efficient inference. The methodology is demonstrated on both synthetic and experimental data, showing that it enables accurate calibration of nonlinear constitutive models with minimal overfitting and limited computational cost.

Optical atomic clocks have been rapidly developing in recent decades, resulting in major improvements in both precision and accuracy. As a result, they have become instrumental in multiple areas of applied and fundamental research. Despite all atomic frequency references having more than two energy-levels, the commonly used model for evaluating their ultimate limits assumes a two-level atom. This leads to frequency interrogation protocols and theoretical stability bounds that are suboptimal for a true multi-level atom. The most fundamental stability bound assumes two noise sources - quantum projection noise and spontaneous decay from the excited state. In this work, we analyze a model that includes these noise types and is generalized beyond the two-level assumption, where spontaneous decay can branch to more than a single ground state. This model allows for detection and exclusion of atomic frequency interrogations in which the atom decayed, leading to a frequency stability improvement of up to $\approx 4.5 \text{ dB}$ compared with the two-level model. Furthermore, we identify an even greater stability enhancement of $\approx 5.4 \text{ dB}$ for frequency comparisons between atoms in an odd parity Bell state. These enhancements are particularly relevant for the numerous trapped-ion optical clock species that operate close to lifetime-limited stability. We calculate new stability limits for those cases and provide a detailed experimental protocol for frequency interrogation with an $^{27}\text{Al}^{+}$ optical ion clock.

We present an approximate energy-integration method for identifying collisional neutrino flavor instabilities. Direct evaluation of the dispersion relation requires multi-dimensional integrals over neutrino phase space, making systematic searches for unstable modes in numerical models of core-collapse supernovae (CCSNe) and binary neutron star mergers (BNSMs) computationally expensive. In the literature there are some approximate schemes, but they are largely restricted to the homogeneous limit and can exhibit inaccuracies as reported in recent studies. In the current paper, we clarify the origin of the limitations in previous schemes and provide a better approximation method that robustly preserves the key physics of spectral asymmetries and collision rates. It yields a reduced dispersion relation that is inexpensive to evaluate. Comparison with exact solutions demonstrates that our new approximate method shows a good performance in computing both real frequencies and growth rates across a wide range of regimes, including isotropic and anisotropic neutrino distributions for both homogeneous and inhomogeneous modes. This provides a practical, accurate, and scalable framework for identifying collisional flavor instabilities in high-energy astrophysical simulations such as CCSNe and BNSMs.

One hundred years after the creation of quantum theory, there is no consensus on the kind of reality that is described by the theory. Here, I attribute the lack of progress to the prevailing interpretative methodology, which invariably takes the quantum formalism as the starting point for philosophical reflection and analysis. I argue that this methodology is particularly inappropriate, for it invariably marginalizes much of the theory's content, both that implicit in modelling heuristics and experimental practices, and that encapsulated in the mathematical structures of its formalism. In addition, the prevailing methodology offers little protection against undue influence by metaphysically-laden language which invariably accompanies the formalism. Here, I summarize an alternative methodology whose goal is to ensure that an interpretational project take into account all forms of theoretic content. The methodology harnesses the recent results of the quantum reconstruction program. These results distil the mathematical content of the quantum formalism into physical principles and assumptions, which are more readily philosophically digestible than the formalism itself, and bracket much of its metaphysically-laden language. As a case study of reconstruction-based interpretation, I describe the reconstruction of the identical particle formalism, and its step-by-step interpretation, highlighting the key questions that drive the interpretation forwards and the techniques and stances that are employed in each step. The interpretation yields a novel metaphysical profile for systems of identical particles as potential parts of a whole, which can be traced step-by-step to elementary experimental data and the reconstruction's physical postulates and assumptions. I also describe some of the pitfalls that one faces in any attempt to directly interpret the identical particle formalism.

WiFi is inherently vulnerable to eavesdropping because RF signals may penetrate many physical boundaries, such as walls and floors. LiFi, by contrast, is an optical method confined to line-of-sight and blocked by opaque surfaces. We present LightGuard, a dual-link architecture built on this insight: cryptographic key establishment can be offloaded from WiFi to a physically confined LiFi channel to mitigate the risk of key exposure over RF. LightGuard derives session keys over a LiFi link and installs them on the WiFi interface, ensuring cryptographic material never traverses the open RF medium. A prototype with off-the-shelf WiFi NICs and our LiFi transceiver frontend validates the design.

We prove that the Almgren-Pitts and phase-transition half-volume spectra of a closed Riemannian manifold are equal. This confirms a conjecture of Liam Mazurowski and Xin Zhou.

Effective field theories for cosmology offer a powerful framework to investigate the dynamics of space--time and address longstanding open puzzles. In this work, we initiate a programme to analyse the ultraviolet completion of vector--tensor quantum field theories within the asymptotic safety paradigm, focusing on generalised Proca theories with a vector condensate. This enables us to assess whether a consistent fundamental UV completion exists and to constrain the set of viable infrared scenarios. Using the non--perturbative functional renormalisation group, we identify several fixed points, including Proca--type candidates, and, among them, a particularly remarkable one with four relevant directions: two associated with gravity and two induced by matter. This provides evidence for the non--perturbative renormalisability of vector--tensor theories. We further outline how the resulting UV critical surface constrains late--time cosmology.

Deterministic many-body systems governed by simple interactions can self-organize into macroscopic patterns, and the determinants of long-time behavior are assumed to be encoded in the initial configuration. Here we show that predictability can instead be constructed dynamically rather than being accessible in the initial configuration. We study a generalized cellular automaton of secrete-and-sense cells that self-organizes from disorder into static configurations, rectilinear waves, or spiral waves. Although dynamics are deterministic, the final outcome cannot be reliably inferred from the initial state alone. Treating cell states as a discrete phase field, we uncover emergent topological modes - charged vortices connected by strings that form non-contractible loops. Tracking their dynamics reveals that predictive signatures of macroscopic fate appear only late in the trajectory: vortex annihilation becomes readable through loop loss, whereas vortex persistence remains unreadable until spiral waves form abruptly. These results show how predictability can be dynamically constructed in deterministic nonequilibrium systems.

Dynamic Spectrum Sharing (DSS) enables flexible activation of additional spectrum resources but leaves open a key runtime question: once new spectrum becomes available, which steering mechanism should migrate connected devices toward it with minimum service disruption? We present the first PHY-aware characterization of 3GPP-compliant UE steering mechanisms, including Bandwidth Part (BWP) reconfiguration, Carrier Aggregation (CA), E-UTRA-NR Dual Connectivity (EN-DC), Connected-Mode Handover (HO), and Release and Redirection (R&R), using modem-level traces from devices connected to operational networks, collected across 1,600 executions over four months in 12 urban areas. By mapping each mechanism to observable PHY-layer milestones, we decompose steering latency into intrinsic PHY-centric execution and RRC-to-PHY completion components, revealing substantial heterogeneity: NR BWP achieves 6.25 ms mean latency with zero tail exceedance above 50 ms, while CA exceeds 1225 ms; mobility procedures remain largely modem-bound, whereas discovery-driven mechanisms experience significant RRC-to-PHY completion amplification. Guided by these measurements, we design POLARIS, an O-RAN-based system that selects the least disruptive steering mechanism via a two-parameter disruption score. POLARIS reduces mean latency by up to 85.1% and T95 by 89.7% over static or non-adaptive baselines, eliminates tail exceedance above 50 ms, and avoids high-disruption mechanisms, demonstrating that PHY-layer execution profiling enables reliable and context-aware spectrum steering in DSS-enabled networks.

Several photoemission spectroscopies and, in particular, Auger spectroscopy, involve double-ionization processes. For the numerical simulation of these spectroscopies it is convenient to use the particle-particle channel of the two-body Green's functions since its poles correspond to excitation energies in which the final state has two more particles (holes or electrons) than the initial state. In standard approaches it is approximated within the random phase approximation. As a consequence only the quasiparticles of the photoemission spectrum are captured but none of the satellites features. In this work, we go beyond this approximation by employing the multichannel Dyson equation. By coupling the particle-particle two-body Green's function to the 3-hole-1-electron and 3-electron-1-hole channels of the four-body Green's function, the multichannel Dyson equation incorporates correlations beyond the RPA in a straightforward way. We are thus able to describe both quasiparticles and satellites in the photoemission spectra.

This overview of the study arXiv:2407.18845, regarding the possibility of generating gravitational waves from a curvature-induced phase transition of a non-minimally coupled scalar dark matter field with a Higgs-portal, was showcased at the "Workshop on Standard Model and Beyond 2025" of the Corfu Summer Institute 2025. The phase transition dynamics during the transition from inflation to kination were calculated for various inflationary scales, considering both positive and negative values of the non-minimal coupling, while also examining the potential for triggering electroweak symmetry breaking. Notably, kination enhances the GW amplitudes, significantly restricting the viable parameter space. While the GW spectra follow the usual rule for high-frequencies from high inflationary scales, certain regions of the parameter space allow for a potential detection with future experiments.

Motivated by duality phenomena for derived global sections on derived local systems on compact oriented manifolds, we introduce the notion of a $d$-duality context between symmetric monoidal enriched categories. In this setting, the right adjoint of a symmetric monoidal functor carries compatible lax and colax structures twisted by an invertible object $d$. For any enriched dioperad $\mathcal{P}$, we define a $d$-twist $\mathcal{P}\{d\}$ and prove that, in a $d$-duality context, the right adjoint sends $\mathcal{P}$-algebras to $\mathcal{P}\{-d\}$-algebras. To achieve this, the key conceptual result is that Frobenius monoidal functors between symmetric monoidal categories are precisely those functors inducing morphisms between the underlying dioperads. We also develop a dioperadic Day convolution, yielding an alternative proof of the main theorem and suggesting an $\infty$-categorical extension of the theory.

There is a growing need for cybersecurity professionals with practical knowledge and experience to meet societal needs and comply with new standards and regulations. At the same time, the advances in software technology and artificial intelligence point towards a future where software agents will play an important role in protecting the computer systems that are critical for society to function. The training and development of both humans and software agents requires the design and execution of cybersecurity exercises that differ in properties such as size, scope, objectives, difficultly, etc. Cybersecurity scenarios are critical for the operation of cybersecurity exercises as they describe the scope, context, operational environment and storyline of each exercise. In this work, we present an approach to automatically generate cybersecurity scenarios that model enterprise IT systems. Our approach is able to generate a large number of scenarios that differ in multiple criteria including size, scope, difficulty, complexity and diversity. We further release as open source: a simulation and a virtualization environment that can run cybersecurity exercises based on the generated scenarios and a dataset containing 100000 sample scenarios.

3D field-programmable gate arrays (FPGAs) promise higher performance through vertical integration. However, existing placement tools, largely inherited from 2D frameworks, fail to capture the unique delay characteristics and optimization dynamics of 3D fabrics. We introduce a 3D FPGA placement flow that integrates partitioning-based initialization, adaptive cost scheduling, refined delay estimation, and a simulated annealing move set -- all targeted at 3D FPGA architecture. Together, these enhancements improve timing estimates and the exploration of layer assignments during placement. Compared to Verilog-To-Routing (VTR), our experiments show geometric-mean (max) critical-path delay reductions of ~3% (~7%), ~2% (~4%), ~3% (~8%), and ~6% (~18%) for four 3D architectures: 3D CB, 3D CB-O, 3D CB-I, and 3D SB, respectively. We also achieve geometric-mean (max) routed wirelength reductions of ~1% (~3%), ~2% (~8%), < 1% (~5%), and ~5% (~10%), respectively. Our work will be permissively open-sourced on GitHub.

The optimization of over-parameterized deep neural networks represents a large-scale, high-dimensional, and strongly non-convex decision problem that challenges existing optimization frameworks. Current evolutionary and gradient-based pruning methods often struggle to scale to such dimensionalities, as they rely on flat search spaces, scalarized objectives, or repeated retraining, leading to premature convergence and prohibitive computational cost. This paper introduces a hierarchical importance-guided evolutionary framework that reformulates convolutional network pruning as a tractable large-scale multi-objective optimization problem. In the first phase, a continuous evolutionary search performs coarse exploration of weight-wise pruning thresholds to shrink the search space and identify promising regions of the Pareto set. The second phase applies a fine-grained binary evolutionary optimization constrained to the surviving weights, where importance-aware sampling and adaptive variation operators refine local search in the sparse region of the Pareto set. This hierarchical design combines global exploration and localized exploitation to achieve a well-distributed Pareto set of networks balancing compactness and accuracy. Empirical results on CIFAR-10 and CIFAR-100 using ResNet-56 and ResNet-110 confirm the method's effectiveness compared to existing evolutionary approaches: pruning achieves up to 51.9\% and 38.9\% parameter reductions with almost no accuracy loss compared to state-of-the-art evolutionary DNN pruning methods. The proposed method contributes a scalable evolutionary approach for solving very-large-scale multi-objective optimization problems, offering a general paradigm extendable to other domains where the decision space is exponentially large, objective functions are conflicting, and efficient trade-off discovery is essential.

We prove that for almost all symmetric spaces $X$ and for any sequence of compact locally symmetric spaces $Y_n$ which is uniformly discrete, has a uniform spectral gap, and converges in the sense of Benjamini--Schramm to $X$, the joint eigenfunctions of all invariant differential operators on $Y_n$ delocalize on average when their spectral parameters are taken to lie in a fixed spectral window.

We investigate the mechanisms of strangeness production in the $π^- p \to K^{*0} Σ^0$ and $π^- p \to K^{*+} Σ^-$ reactions within a hybrid Regge framework in which effective Lagrangian vertices are combined with Reggeized exchanges. The nonresonant background consists of $t$-channel $K$- and $K^*$-Reggeon exchanges, $s$-channel nucleon and $Δ$ exchanges, and $u$-channel $Σ$- and $Λ$-Reggeon exchanges, whose roles differ markedly between the two isospin channels. We additionally include several $N^*$ and $Δ^*$ resonances in the $s$ channel and find that the $Δ(2150)1/2^-$ resonance provides the dominant near-threshold contribution. The resulting total and differential cross sections and spin-density matrix elements (SDMEs) are in good agreement with the available data. Additional measurements near threshold ($W \lesssim$ 2.5 GeV) would be valuable for clarifying the role of $s$-channel baryon resonances. Within the same framework, with Regge trajectories and energy-scale parameters fixed by a QGSM-motivated prescription, we also predict the cross sections for the charm-production reactions $π^- p \to D^{*-} Σ_c^+$ and $π^- p \to D^{*0} Σ_c^0$. Their total cross sections are suppressed by approximately $4$--$5$ and $7$--$8$ orders of magnitude, respectively, compared with those of the corresponding strangeness-production reactions. These results may serve as useful guidance for future experiments at facilities such as J-PARC.

Computational reproducibility is fundamental to trustworthy science, yet remains difficult to achieve in practice across various research workflows, including Jupyter notebooks published alongside scholarly articles. Environment drift, undocumented dependencies and implicit execution assumptions frequently prevent independent re-execution of published research. Despite existing reproducibility guidelines, scalable and systematic infrastructure for automated assessment remains limited. We present an automated, web-oriented reproducibility engineering pipeline that reconstructs and evaluates repository-level execution environments for scholarly notebooks. The system performs dependency inference, automated container generation, and isolated execution to approximate the notebook's original computational context. We evaluate the approach on 443 notebooks from 116 GitHub repositories referenced by publications in PubMed Central. Execution outcomes are classified into four categories: resolved environment failures, persistent logic or data errors, reproducibility drift, and container-induced regressions. Our results show that containerization resolves 66.7% of prior dependency-related failures and substantially improves execution robustness. However, a significant reproducibility gap remains: 53.7% of notebooks exhibit low output fidelity, largely due to persistent runtime failures and stochastic non-determinism. These findings indicate that standardized containerization is essential for computational stability but insufficient for full bit-wise reproducibility. The framework offers a scalable solution for researchers, editors, and archivists seeking systematic, automated assessment of computational artifacts.

We explore the Mellin space representation for the collinear limit of $N$-point energy correlators in ${\cal N}=4$ super-Yang-Mills theory. We show that these correlators can be written as integro-differential operators acting on star integrals: one-loop $n$-gons in $n$ dimensions. For the three-point energy correlator, we obtain the Mellin representation, use it to relate the correlator to the massive box integral, and show how to solve this relation to match with the expected result. For the four-point energy correlator, we obtain the Mellin representation and use it to write the correlator to a sum of various box and hexagon integrals in special kinematics. Our results provide a systematic method to relate higher-point energy correlators in the collinear limit to star integrals, which are known exactly.

This document presents a self-contained treatment of regularized unfolding based on cubic B-spline representations and eigenmode filtering, following the original formulation by Blobel and direct translation of the original implementation in Fortran into a modern format. The method, which has been called by several names under its various historical representations, is named here as Blobel's Regularised Unfolding (BRU). This method differs from conventional histogram-based unfolding approaches in that the true distribution is represented as a smooth function parametrised by spline coefficients, and the regularization operates through an eigenmode decomposition of the curvature penalty relative to the statistical precision. This document describes the mathematical structure of the method, the mechanism by which the regularisation strength is determined automatically from the data, and provides a detailed comparison with standard methods including Tikhonov regularisation based methods, Richardson-Lucy iteration, and naive matrix inversion.

For a positive integer $k$, a graph property $\mathcal{H}$, and a graph parameter $\mathcal{P}$, let $\operatorname{ex}_{\mathcal{P}}(n, \mathcal{H}; δ\geq k)$ denote the maximum value of $\mathcal{P}$ over all $n$-vertex graphs with minimum degree at least $k$ that do not possess the property $\mathcal{H}$. The corresponding extremal families are denoted by $\operatorname{EX}_{\mathcal{P}}(n, \mathcal{H}; δ\geq k)$. For two disjoint graphs $H_1$ and $H_2$, let $H_1 \cup H_2$ denote their (disjoint) union, i.e., the graph with vertex set $V(H_1) \cup V(H_2)$ and edge set $E(H_1) \cup E(H_2)$; and let $H_1 \vee H_2$ denote their join. In 1962, Erdős established a classical theorem on the maximum number of edges in a non-Hamiltonian graph of given order and minimum degree. Motivated by recent work on feasible graph parameters in \cite{Ai2023}, we prove several extensions of Erdős's 1962 theorem on non-Hamiltonian graphs. The first result gives a common generalization of the extremal theorem due to Erdős and its spectral analogs. As direct applications, we obtain complete solutions to open problems raised in the literature since 2016, thereby improving nearly all related prior results in this direction. Our proof technique differs somewhat from those in \cite{MR3539577,MR3556876}. We also prove an analog theorem for the Hamiltonian-connected property and obtain a result which extends the theorem of Füredi, Kostochka, and Luo \cite{MR3843180} on Hamilton cycles.

We have investigated the results for [Fe/H] and distance for a group of 24 globular clusters in the Galactic bulge, employing recent calibrations of RR Lyrae light curves Fourier decomposition and period-absolute magnitude-metallicity (PMZ) calibrations in the I-band. We have limited our calculations to RR Lyrae stars that have been proven to be very likely cluster members. These results are compared with [Fe/H] and Mv (distance) obtained from well-established Fourier calibrations in the V-band. These calibrations of the I-band were found to produce iron values that can differ from the UVES spectroscopic scale by -0.29 to +0.15 dex. The PMZ distances agree within 0.4 kpc with recent solid critical distance compilations. Adopting the newly derived distances, we conducted a spatial and orbital analysis of the bulge globular clusters in a non-axisymmetric Milky Way potential, and compared their orbital properties with earlier studies, finding broadly consistent trends with small systematic differences driven by the assumed distances and Galactic model. Clusters associated with the in situ bulge component display a narrow range low angular momentum and low orbital energies, consistent with formation in the early inner Milky Way.

This paper proposes a decomposition of human capital into three orthogonal components -- physical-manual (H^P), routine-cognitive (H^C), and augmentable-cognitive (H^A) -- and develops a production function in which AI capital interacts asymmetrically with these components: substituting for routine cognitive work while complementing augmentable cognitive work through an amplification function phi(D). I derive a corrected Mincerian wage equation and show that the standard specification is misspecified in AI-augmented economies. Using LLM-generated measures of occupational augmentability for 18,796 O*NET task statements mapped to 440 Colombian occupations, merged with household survey microdata (N = 105,517 workers), I estimate the augmented Mincer equation. The wage return to H^A increases with AI adoption in the formal sector (beta_2 = +0.051, p < 0.001), while informal workers cannot capture augmentation rents (beta_2 = -0.044). A triple interaction confirms formality as the binding mechanism (beta_{AHC x D x Formal} = +0.272, p < 0.001). The augmentation premium is strongest for experienced workers (ages 46-65) and in health and education sectors. These results provide the first developing-country evidence of cognitive factor decomposition in AI-augmented labor markets and demonstrate that the binding constraint on human-AI complementarity in the Global South is not technology access but labor market institutions.