We formulate a one-parameter extension of Weyl transformations in first-order gravity and show that it defines a conformally coupled scalar sector with dynamical torsion. The construction reduces to the standard torsionless conformal coupling in the limit $λ\to 1$. In the corresponding Einstein-Cartan-Maxwell theory, we derive exact static solutions in asymptotically flat and asymptotically locally AdS spacetimes. These solutions describe scalar-dressed black holes, regular black holes, and traversable wormholes, depending on the values of the integration constants and of the deformation parameter. We show that torsion can regularize the scalar field and, for suitable branches, also improve the geometric singularity structure. In the AdS sector, the existence of topological black holes requires a nonvanishing electric charge. These results provide new exact examples of regular and torsional configurations in four-dimensional gravity.

We introduce a perturbative framework for anomalous scaling in turbulent transport based on multiplier statistics, rather than zero-mode calculations. We illustrate the approach using a shell model combining deterministic and Kraichnan-like stochastic components. The problem is reduced to the analysis of a stationary Fokker--Planck equation for Kolmogorov multipliers, defined as ratios of successive scalar amplitudes. Its solution yields the invariant measure through a perturbative expansion around a Gaussian distribution. Using the resulting multiplier statistics, we compute explicit anomalous scaling exponents for structure functions of arbitrary order, including odd, even, and non-integer moments. More broadly, the results suggest that multiplier statistics provide a viable route for computing anomalous exponents in turbulent transport, complementing recent hidden-symmetry approaches while circumventing the limitations of zero-mode methods based on a closed Hopf hierarchy.

Let $k$ be an $F$-finite and infinite field of characteristic $p>2$. We show, there exist infinitely many $F$-finite local domains $(R,\mathfrak{m})$ which are not $\mathbb{Q}$-Gorenstein and $τ_{\mathrm{b}}(R;\mathfrak{m}^t)$ has all but finitely many \emph{irrational} $F$-jumping numbers.

Metric Differential Privacy (mDP) generalizes differential privacy by allowing privacy guarantees to be expressed with respect to an arbitrary distance metric over secrets. While mDP has been adopted in geo-location protection, most existing mechanisms perturb each location record in isolation and do not model how contextual information (e.g., recent mobility history) affects the utility of the released data. This mismatch is particularly pronounced for vehicle mobility traces, where service quality often depends on temporally correlated locations. In this paper, we propose Context-aware mDP (C-mDP), a framework for vehicle location privacy that incorporates contextual dependencies into both the utility model and the privacy notion. C-mDP treats the protected secret as a context-augmented record and enforces metric indistinguishability over this augmented domain. We formulate optimal C-mDP mechanism design as a linear program (LP) that minimizes expected utility loss subject to C-mDP constraints. To improve scalability, we exploit conditional-independence structure between the current location and contextual variables to derive a reduced formulation with substantially fewer decision variables and constraints. We evaluate C-mDP on real-world vehicle mobility datasets and compare it with standard mDP baselines. The results show that C-mDP consistently achieves higher utility under the same privacy budget while satisfying the required metric privacy guarantees.

Modern image formation algorithms in radio interferometry rely on repeated applications of the operator Φ modelling the measurement process and its adjoint {Phi^\dagger} to enforce consistency with the acquired data, specifically via their composite mapping {Phi^\daggerΦ} encoding the array's point spread function (PSF). The large data volumes produced during wideband observations yield significant computational challenges for image formation. Moreover, for widefield imaging, the baseline components along the line of sight w complicate severely the measurement model beyond the conventional 2-dimensional non-uniform Fourier transform (NUFFT), making the PSF highly position-dependent. We propose a distributed resource-adaptive implementation of the widefield measurement model, enabled by a hybrid w-stacking/w-projection approach, whereby the number of w-bins is set in a fully automated manner to minimise the computational cost under the compute system's memory constraints. The resulting measurement model is naturally decomposed and distributed into low-dimensional operators specific to w-bins. Residual w-offsets are integrated as measurement-specific Fourier kernels augmenting the sparse de-gridding matrix of the basic NUFFT model. An optional data dimensionality reduction is also introduced, jointly encoding the sequential Fourier de-gridding/gridding operations in {Phi^\daggerΦ} into a holographic matrix when required by memory constraints. For further parallelisation, the sparse de-gridding or holographic matrices are decomposed into blocks via memory-controlled Fourier partitioning. The approach has been validated in prior works through real data case studies for both monochromatic and wideband imaging of MeerKAT and ASKAP data. We provide herein a thorough analysis of its computational efficiency using simulated MeerKAT data. A MATLAB implementation is available in BASPLib.

We develop a framework for studying how global spectral structure emerges from interacting local sectors in stratified operadic systems. The central object is the interaction residue, which measures the failure of exact spectral decomposition across interfaces. Under suitable localization assumptions, the global spectrum decomposes into local spectral sectors together with interface-generated residue contributions. The theory introduces a classification of spectral defects based on interface geometry and algebraic structure. Point interfaces produce isolated spectral contributions; line and surface interfaces produce extended spectral regimes. Non-semisimple operator structure generates nilpotent defects associated with Jordan blocks and generalized eigenspaces, yielding a two-dimensional defect taxonomy combining geometric localization with Jordan complexity. Several structural results are established, including interface localization, rigidity and vanishing criteria, refinement functoriality, and deformation stability. Under a local triviality condition, the residue is homotopy invariant, preserving its homology and Betti numbers throughout admissible deformations. The framework is illustrated through explicit operator and block matrix examples demonstrating how localized interactions generate localized spectral defects. The nilpotent sector connects the theory with classical operator theory via generalized eigenvectors, functional calculus, and perturbative Jordan splitting. Overall, the framework provides a unified viewpoint for understanding how interface interactions and non-semisimple structure influence global spectral behavior.

The identification of invariant objects and Lagrangian coherent structures is a cornerstone of dynamical systems. As a consequence, several diagnostic indicators have been established over time, such as the fast Lyapunov indicator, the finite-time Lyapunov exponent, and Lagrangian descriptors, among others. In this work, we introduce the Strong Trajectorial Ontological Differentiation (STOD) as a novel tool to identify phase-space structures. Unlike other indicators, STOD does not rely on the study of the tangent flow; instead, it identifies phase-space structures by comparing trajectories through a component-wise cancellation process inspired on the Ontological Differentiation (OD) that was originally developed for lexical networks [P. García-Cuadrillero, F. Revuelta, J. A. Capitán, Phys. Rev. E 113, 014305 (2026)]. By applying a reversed-time version of STOD (FinSTOD) to five paradigmatic autonomous and non-autonomous systems of increasing complexity, we show the excellent performance of this indicator in the identification of phase-space structures, adding a new useful tool to the chaotic toolbox.

Liquid mixtures with a nematogen can undergo both fluid phase separation and a transition from an isotropic to a nematic state. These phase transitions can couple and lead to phase behavior distinct from simple liquid mixtures or pure liquid crystals. We measured the phase behavior of mixtures of a nematogen (5CB) with simple liquid solvents (squalane and/or squalene). We observed two distinct kinds of binary phase diagrams: with and without a region of isotropic-isotropic coexistence. Varying the ratio of squalene to squalane, we continuously tuned the phase boundaries of the apparent binary system and revealed a region of three-phase coexistence. A mean-field model combining classical models of liquid mixing and nematic ordering quantitatively describes both binary and ternary phase behavior. This simple model predicts a range of topologically complex ternary phase diagrams and extends naturally to systems with more components.

We show that, given $d \geq 4$ and two closed connected oriented PL $4$-manifolds $M$ and $N$ such that $N$ has a handle decomposition with no $1$- and $3$-handles, there exists a $d$-fold simple branched covering $p \colon M \darrow{d} N$ if and only if there is an isometric embedding of intersection lattices $d \cdot I_N \hookrightarrow I_M$. Moreover, if such $p$ exists, one can build it in such a way that its branch set $B_p \subset N$ is locally flat PL embedded if $d \geq 5$ and has at most nodal singularities if $d=4$.

The unitary Fermi gas serves as a tunable realization of a strongly coupled CFT, making it a powerful system for probing universal quantum many-body phenomena. Precise measurement of its properties remains experimentally challenging: finite-temperature effects and spatial inhomogeneity introduced by external trapping potentials can significantly distort observables. Cylindrical trap geometries are commonly used in experiments. This note extends an existing theoretical framework to this geometry, deriving how the cylindrical confinement modifies the dynamic structure factor at zero temperature. These results provide a necessary correction for the interpretation of experimental spectra in trapped unitary gases.

Analyses of recurrent hypoglycemia are critical for effective treatment management in diabetic patients. Typically, within-subject dependency in such analyses is captured through subject-level frailty. Recent research has modeled recurrent hypoglycemia using the first hitting times of a reflected Brownian motion. A close examination of this approach reveals that it does not adequately account for varying frailties among individuals, which indicate notable heterogeneity. To address this gap, we propose a finite mixture model of the first hitting time distribution of the reflected Brownian motion. This model allows for component-specific regression coefficients and frailty parameters, providing nuanced insights into how risk factors differently affect patient subgroups. We employ a Bayesian framework for inference, utilizing Markov chain Monte Carlo for estimation. Model selection is conducted using the Deviance Information Criterion and the Logarithm of the Pseudo-Marginal Likelihood. The effectiveness of these criteria is assessed through simulation studies. Application to recurrent hypoglycemia modeling revealed two subgroups with different risk profiles, as reflected in their volatilities. Bayesian model comparison criteria favor the model with component specific regression coefficients for volatilities. The subgroup with lower volatility exhibits a larger variance and, hence, a greater level of heterogeneity.

We determine the $RO(C_2)$-graded Hurewicz images of the $C_2$-equivariant Eilenberg--MacLane spectra $H\underline{\mathbb F_2}$, $H\underline{\mathbb Z}$ and $H\underline{A}$, where $\underline{\mathbb F_2}$ and $\underline{\mathbb Z}$ denote the constant Mackey functors with values in $\mathbb F_2$ and $\mathbb Z$, respectively, and $\underline A$ denotes the Burnside Mackey functor. Surprisingly, the answer is closely tied to the problem of vector fields on spheres: the element $\fracθ{ρ^kτ^n}$ in the negative cone of the homotopy groups of $H\underline{\mathbb F_2}$ lies in the Hurewicz image if and only if $S^n$ admits $k$ linearly independent vector fields. Moreover, using the Generalized Leibniz Rule and the Generalized Mahowald Trick introduced by arXiv:2412.10879, we show that there are nonzero Adams differentials of arbitrary length supported by filtration-$0$ elements in the genuine $C_2$-equivariant Adams spectral sequence.

Uncertainty relations are usually formulated as trade-off relations between two or more observables. Here we show that the uncertainty of a single observable already has a nontrivial lower bound originating from the noncommutativity between the observable and the quantum state. We prove sharp lower bounds on the variance of a single observable and then sharpen them further by introducing the classical uncertainty of the observable under a fixed state. The optimal coefficient is determined solely by the smallest and largest eigenvalues of the state. Our results include an optimal state-dependent improvement of Luo's Wigner--Yanase-type relation and a direct bound showing that coherence or asymmetry of the state with respect to the observable gives an unavoidable contribution to its uncertainty. For qubits, the sharpened bounds become exact identities, giving a complete decomposition of the variance into classical and noncommutative parts. These single-observable relations also yield improved product-form uncertainty relations for pairs of observables.

Most generalized fractional operators rely on prescribed memory kernels, restricting hereditary behavior to predefined forms and limiting flexibility in modeling diverse memory effects. Motivated by these limitations, this paper develops a generator-based framework for fractional calculus in which memory laws are systematically generated through a dynamic memory generator in the Laplace domain. The resulting construction produces dynamic-memory kernels via inverse Laplace transforms, leading to generalized dynamic-memory fractional integrals together with Riemann--Liouville and Caputo dynamic-memory fractional derivatives. Fundamental analytical properties are established, including inverse relations, composition formulas, admissibility conditions, semigroup structures, and consistency principles. In addition, a unified convolution-symbol operational calculus and generalized dynamic-memory Mittag--Leffler functions are developed. Unlike fixed-kernel formulations, the proposed framework can generate singular, nonsingular, tempered, logarithmic, oscillatory, and multiscale memory behaviors within a single analytical setting. Numerous classical and modern fractional operators are recovered as special cases, demonstrating the unifying capability and flexibility of the developed theory.

Tele-ultrasound through teleoperation allows experts to perform examinations remotely in communities, but limited connectivity can lead to communication delays that reduce usability and diagnostic performance. Visual-haptic model mediated teleoperation reslices a pre-acquired ultrasound volume in real time to provide an accurate, delay-independent preview image for the sonographer. This enables fast and robust exploration before using the live image for fine tuning. However, existing reslicing techniques do not account for the directional nature of ultrasound - the fact that a structure looks different when imaged from different directions. This paper presents Directionality-Aware Reslicing (DARE), an ultrasound volume reconstruction and reslicing framework that takes directionality into account. The presented GPU-accelerated algorithm allows real-time reslicing from arbitrary viewpoints to generate accurate preview images. The method is evaluated quantitatively through image similarity metrics and qualitatively through a user study, and significantly outperforms existing reslicing methods in image similarity and realism compared to a ground truth. This can improve the effectiveness and robustness of tele-ultrasound in low-resource areas.

Looking at physical systems as computers allows us to regard physical properties, such as thermal noise, symmetry or topology, as unconventional resources for computation. However, harnessing these resources requires programming computational functionality through strong, controllable nonlinearities in the system. Here, we show that cavity optomechanical interactions allow laser-controlled computation with nanomechanical degrees of freedom. We demonstrate a set of basic digital logic gates with level restoration and controlled mechanical couplings as essential ingredients for arbitrary computing networks. Owing to the strong optomechanical nonlinearity and precise readout, the system operates close to thermal amplitudes, in the regime where thermodynamic stochasticity governs its behavior. This opens a new path for the realization of physical computing with controlled nonlinear resonators.

Generalized inverses play a fundamental role in numerical linear algebra, particularly when matrices are rectangular, singular, or rank deficient. Even when the input matrix is sparse, generalized inverses such as the M-P pseudoinverse are typically dense, leading to high storage requirements, expensive matrix-vector multiplications, and reduced efficiency. We investigate computing sparse symmetric generalized inverses for sparse symmetric matrices, extending previous work on sparse generalized inverses for rectangular rank-deficient matrices. We consider minimizing the vector 1-norm over the set of symmetric generalized inverses, using vector 1-norm minimization as a surrogate for sparsity promotion. We give a new characterization of symmetric generalized inverses of symmetric matrices, which yields a compact affine reformulation of the problem. From this, we develop a Douglas-Rachford splitting (DRS) algorithm equipped with a closed-form projection onto the feasible affine space. Computational experiments compare the proposed DRS approach with exact linear-optimization formulations solved by a commercial optimizer, as well as with local-search heuristics. The results demonstrate that the proposed formulation and algorithm produce generalized inverses that are substantially sparser than the Moore-Penrose pseudoinverse while maintaining significantly smaller 1-norms than competing approaches. Moreover, the DRS algorithm exhibits superior scalability relative to exact linear-optimization formulations, successfully solving instances far beyond the reach of commercial solvers. As an application, we investigate the computation of least-squares solutions for problems involving many right-hand-side vectors and sparse rank-deficient design matrices.

We present a fast Jacobi-like algorithm for computing the eigenvalues, and optionally the eigenvectors, of a real normal matrix. The method gains a computational advantage by using Paardekooper's method for skew-symmetric matrices The method is most efficient for matrices where most eigenvalues are complex, such as random orthogonal matrices arising in the context of statistics on manifolds. In this case, the method is faster than the other Jacobi-like algorithms. In the last section of this paper, we also give explicit formulas for the nearest symmetric skew-Hamiltonian and the nearest ortho-symplectic matrix. These problems arise in the design and the analysis of the algorithm.

The business model of surveillance capitalism, premised on the extraction of behavioral data and its predictive potential for profit, relies on extensive material infrastructure. Such profit is typically driven by practices such as telemetry, user tracking, data analytics, secondary data uses, increased user engagement, and AI model training, as well as large-scale data storage systems that retain personal information for sale or reuse. This paper is motivated by the question: how much of the rising carbon impact of ICT can be attributed to this material infrastructure? Such an inquiry provides a foundation for quantifying the environmental costs of surveillance capitalism by proposing a conceptual framework and research direction that link processes of surveillance with their underlying material realities. To demonstrate the applicability of this framework, we examine the proportion of network traffic caused by surveillance capitalism processes through a comparative case study of a corporate social media platform, X/formerly Twitter, and a decentralized, non-commercial alternative, Mastodon. Our findings highlight the existence of corporate overhead: excess resource consumption driven by corporate social media practices, which is used as an initial proxy for the activities of surveillance capitalism. Our findings further demonstrate how the corporate overhead of X can be used to establish a lower bound in CO2e emissions attributable to for-profit activities that do not contribute to the user experience.

This companion paper provides artifacts and instructions on replicating the experiments in the ACM Multimedia 2024 paper entitled "Swarical: An Integrated Hierarchical Approach to Localizing Flying Light Specks." Swarm-based hierarchical, Swarical, is a localization technique that enables miniature drones, Flying Light Specks (FLSs), to accurately and efficiently localize and illuminate complex 2D and 3D shapes. It consists of two components, an offline planner and an online localization technique that executes on an FLS. The offline planner uses the FLS sensor specification for positioning to convert mesh files into swarms of FLSs. Some FLSs are dark and used only for localization. We reported the online localization technique to be fast and highly accurate. We describe how to reproduce this finding using our artifacts.

We propose a Bayesian latent variable model to estimate covariate-assisted dependence structures across multiple modalities of multivariate data that may be observed asynchronously. This setting commonly arises in longitudinal biomedical research, especially in observational and clinical studies of complex diseases, where dynamic and heterogeneous dependence across biomarker modalities can be pathologically and clinically informative. For example, the biological diagnosis and staging of Alzheimer's disease require integrated evaluation of multimodal biomarkers, including imaging and biofluid biomarkers, and the Alzheimer's Disease Neuroimaging Initiative (ADNI) study has collected biomarker data longitudinally for over two decades. However, quantitative analysis is often challenged by asynchronous collection of multimodal profiles due to study design and data collection constraints. Common analytic strategies that restrict inference to complete observations or analyze each modality separately can lose information and introduce bias. Therefore, we aim to jointly model all available data and estimate the population-level cross-modal dependence structure that evolves over time and varies across demographic or clinical groups, where the cross-covariance matrices for modality pairs serve as the primary quantities of interest. The proposed model uses modality-specific low-rank loading structures with shared latent variables to borrow information across modalities, visits, and subjects while accounting for repeated measurements. The application to ADNI data reveals clinically meaningful patterns in longitudinal cross-modal biomarker dependence, and the simulation study shows improved recovery under limited modality synchrony.

Binary neutron star mergers provide a unique laboratory for studying matter under conditions that cannot be reproduced in terrestrial experiments. They probe dense matter at supranuclear density, finite temperature, rapid rotation, strong gravity, and extreme neutron excess, while producing observable signals in gravitational waves, electromagnetic radiation, and, in principle, neutrinos. This review focuses on the nuclear physics of binary neutron star mergers. We discuss the dense-matter equation of state (EoS), the inspiral and merger dynamics, the structure and lifetime of the post-merger remnant, transport and dissipative processes, weak interactions and neutrino transport, and the production of heavy elements through $r$-process nucleosynthesis. Particular emphasis is placed on the connection between microscopic physics and multimessenger observables, including tidal deformability, post-merger gravitational-wave spectra, kilonova light curves, short gamma-ray bursts, and afterglows. We also review how observations of events such as GW170817, together with neutron star mass and radius measurements, laboratory nuclear experiments, and theoretical many-body calculations, constrain the EoS and the composition of dense matter. The goal is to summarize the current understanding of how nuclear physics controls the dynamics and observable signatures of binary neutron star mergers, and to identify the open questions that future multimessenger observations and improved nuclear theory will address.

In this article, we provide the first theoretical framework guaranteeing that computers can, in principle, be used to analyze the parameter space of complex Hémaps. More precisely, we obtain computability results for hyperbolic polynomial diffeomorphisms of $\mathbb{C}^2$, for which Hénon maps are prototypical examples. Specifically, we establish computability of the Julia set for hyperbolic maps, semi-decidability of hyperbolicity, and lower computability of the hyperbolicity locus in the parameter space of generalized Hénon mappings of fixed degree at least two. Our approach builds upon techniques developed in our's recent previous works on polynomial maps of $\mathbb{C}$ and polynomial skew products of $\mathbb{C}^2$. In the setting of polynomial diffeomorphisms of $\mathbb{C}^2$, however, establishing hyperbolicity for the Julia set is considerably more difficult, as it requires identifying unstable (and stable) cone fields that are preserved and expanded by $Df$ (respectively $Df^{-1}$), and also due to the lack of algorithmically detectable quantitative shadowing.

The superfluid-insulator transition in systems of lattice bosons is usually analyzed in the framework of the Bose-Hubbard model, and has been extensively studied by theory and simulations. Less attention has been paid to the remnants of the transition in truncated lattices, with or without periodic boundary conditions. Here we consider the hard-core limit of the extended Bose-Hubbard model on small square and triangular grids -- i.e., sections of the square and triangular lattices containing up to 13 sites. By mapping out the zero-temperature phase diagram through exact diagonalization, we find ground-state characteristics that are markedly different from those emerging in the thermodynamic limit, together with similarities. The dichotomy between superfluid-like and insulating-like behavior is then investigated in two-dimensional systems of a few interacting bosons in the continuum, subject to confining and optical-lattice potentials mimicking the $3\times 3$ square grid. Using path-integral Monte Carlo simulations, we compute kinetic and potential energies, as well as superfluidity and exchange-cycle statistics, finding hints of Bose-Hubbard behavior even in systems of just five particles.

In cell-free massive multiple-input multiple-output systems, downlink power control is essential to ensure uniformly high service quality across users. Existing methods range from centralized iterative approaches requiring global channel knowledge and supervised training, to simpler distributed strategies such as fractional power control that rely on local information but perform poorly in terms of fairness. This letter proposes an unsupervised, physics-informed framework that directly optimizes max-min fairness without requiring optimal labels or user position information. The method is inherently scalable in the number of user equipment, does not require retraining when the user population changes, and can be extended to achieve full scalability with respect to both access points and users. Numerical results show that it nearly doubles the worst-user spectral efficiency compared to existing scalable schemes.

We study a Simpson--Visser regularization of the four-dimensional Schwarzschild--anti--de\,Sitter (SV--AdS) black hole, treated as the bulk dual of a planar conformal field theory (CFT) on the AdS boundary. The bulk lapse $f(r)=1-2M/\sqrt{r^2+a^2}+(r^2+a^2)/\ell^2$ is regular at $r=0$ for any $a>0$, and the holographic dictionary inherits this regularity at the boundary CFT level. We derive in closed form the boundary entropy, energy, temperature, and chemical potentials, and we trace how the SV regularization parameter $a$ deforms each of them as a function of the horizon radius. For $\tila<\tila_c=1/\sqrt{24}\approx 0.204$ the bulk temperature develops a van der Waals--type small/intermediate/large branch structure and the off-shell free energy supports three coexisting equilibria; the topological-vector-field analysis assigns local winding numbers $(+1,-1,+1)$ with total charge $W=+1$, matching the universality class of regular AdS black holes (Bardeen-AdS, Hayward-AdS) and distinguishing the SV-AdS family from Schwarzschild-AdS ($W=0$).

The dynamics of the driven van der Pol oscillator are investigated. We study birth and metamorphoses of $1:1$ and $1:3$ resonances within the formalism of differential properties of amplitude-frequency response implicit functions.

AI agents increasingly run untrusted code on developer machines: shell commands generated by language models, third-party scripts retrieved at runtime, and tool plugins of unknown provenance. Existing isolation mechanisms impose tradeoffs that fit this workload poorly: containers and microVMs add privilege, image-management, and startup costs, while ad-hoc process controls and wrappers (e.g. chroot, ulimit) provide weak guarantees and little syscall-level control. Sandlock is a lightweight Linux process sandbox organized around a simple split: static, input-independent policy is compiled into kernel-enforced rules, while a narrow supervisor handles runtime-dependent decisions and virtualized effects. This split lets Sandlock enforce filesystem, network, IPC, and syscall policies without root, cgroups, images, or mandatory namespaces. It also supports dynamic network decisions, HTTP-level access control, TOCTOU-safe inspection of execve arguments, and reversible filesystem effects. On our workstation, Sandlock adds roughly 5 ms of startup overhead and runs Redis at bare-metal throughput (within measurement noise); its pipeline operator further supports per-stage confinement for separating data, network, and untrusted-content capabilities. Sandlock is available at https://github.com/multikernel/sandlock

Agentic AI shifts LLM serving from isolated prompt-generation requests to stateful, multi-turn executions that repeatedly invoke the model, call tools, and grow context over time. This paper characterizes ReAct-style agents from both the LLM-serving and tool-execution perspectives using an end-to-end tracing infrastructure across reasoning and non-reasoning Gemma and Qwen configurations on five agentic benchmarks. Our study shows that agentic workloads are not simply long-prompt workloads: with effective context caching, most input tokens are reused across turns, making execution decode-dominated while increasing dependence on long-lived KV-cache state. We also find that tool use has a clear temporal structure, with agents shifting from read/explore behavior early in execution to execute/write behavior later. These results show that efficient agentic serving must jointly manage repeated model re-entry, persistent context state, and workload-dependent tool behavior.

Graph pattern mining is important for analyzing graph data. Graph mining systems typically require answering pattern matching queries, which involve solving the NP-complete subgraph isomorphism problem. To address this, domain experts often develop custom optimization strategies based on exploiting substructural similarities across different patterns. While these optimizers can be effective, their development is challenging, limiting the exploration of interactions between different optimization strategies and restricts experts from continuously improving the optimizers -- such as by incorporating additional custom or general pattern-based equivalences over time. We present a programmable pattern matching query optimizer called Geo, which automatically manages the interactions between various equivalences, ensures the optimizations maintain correctness of results, and simplifies the management of substructure equivalences. Geo exposes a simple but flexible language for expressing pattern equivalences as rewrite rules. By maintaining canonical representations of generated patterns during equality saturation, Geo avoids issues arising from syntactic differences in isomorphic patterns. Additionally, we develop embedded reconstructablility (EmRec) that tracks provenance across equivalences to ensure various reconstructability needs of desired outputs. Our evaluation demonstrates that Geo can discover novel query equivalences through complex composition of various rewrite rules, enabling our optimized queries to achieve a cost reduction of up to 99% compared to the queries in prior work. We further test Geo's effectiveness at speeding up practical graph mining problems by using it in two representative case studies -- approximate pattern matching and quasi-clique mining, and find it is highly effective at optimizing these tasks, enabling cost reductions of up to 71%.