Graph-centric cross-model data integration and analytics (GCDIA) refer to tasks that leverage the graph model as a central paradigm to integrate relevant information across heterogeneous data models, such as relational and document, and subsequently perform complex analytics such as regression and similarity computation. As modern applications generate increasingly diverse data and move beyond simple retrieval toward advanced analytical objectives (e.g., prediction and recommendation), GCDIA has become increasingly important. Existing multi-model databases (MMDBs) struggle to efficiently support both integration (GCDI) and analytics (GCDA) in GCDIA. They typically separate graph processing from other models without global optimization for GCDI, while relying on tuple-at-a-time execution for GCDA, leading to limited performance and scalability. To address these limitations, we propose GredoDB, a unified MMDB that natively supports storing graph, relational, and document models, while efficiently processing GCDIA. Specifically, we design 1) topology- and attribute-aware graph operators for efficient predicate-aware traversal, 2) a unified GCDI optimization framework to exploit cross-model correlations, and 3) a parallel GCDA architecture that materializes intermediate results for operator-level execution. Experiments on the widely adopted multi-model benchmark M2Bench demonstrate that, in terms of response time, GredoDB achieves up to 107.89 times and an average of 10.89 times speedup on GCDI, and up to 356.72 times and an average of 37.79 times on GCDA, compared to state-of-the-art (SOTA) MMDBs.

In recent years, lattice QCD calculations of hadron spectroscopy have concentrated on resonances and shallow bound states detected via poles in two- and three-hadron scattering amplitudes. Hadron interactions have therefore become a key focus. In these proceedings, I review the current state of the art and recent advances in methods for studying hadron interactions via finite-volume spectroscopy and finite-volume quantization conditions. I will also review recent spectroscopy studies and results presented at Lattice 2025, with a focus on charmed mesons, the doubly charmed tetraquark, and the doubly bottom tetraquark.

A thermodynamic framework for asymptotic inference is developed in which sample size and parameter variance define a state space. Within this description, Shannon information plays the role of entropy, and an integrating factor organizes its variation into a first-law-type balance equation. The framework supports a cyclic inequality analogous to a reversed second law, derived for the estimation of the mean. A non-trivial third-law-type result emerges as a lower bound on entropy set by representation noise. Optimal inference paths, global bounds on information gain, and a natural Carnot-like information efficiency follow from this structure, with efficiency fundamentally limited by a noise floor. Finally, de Bruijn's identity and the I-MMSE relation in the Gaussian-limit case appear as coordinate projections of the same underlying thermodynamic structure. This framework suggests that ensemble physics and inferential physics constitute shadow processes evolving in opposite directions within a unified thermodynamic description.

The $L_2$-norm, or collision norm, is a core entity in the analysis of distributions and probabilistic algorithms. Batu and Canonne (FOCS 2017) presented an extensive analysis of algorithmic aspects of the $L_2$-norm and its connection to uniformity testing. However, when it comes to estimating the $L_2$-norm itself, their algorithm is not always optimal compared to the instance-specific second-moment bounds, $O(1/(\varepsilon\|μ\|_2) + t_μ/\varepsilon^2)$, for $t_μ= \|μ\|_3^3 / \|μ\|_2^4 - 1$, as stated by Batu (WoLA 2025, open problem session). In this paper, we present an unbiased $L_2$-estimation algorithm whose sample complexity matches the instance-specific second-moment analysis. Additionally, we show that $Ω(1/(\varepsilon \|μ\|_2) + t_μ/ \varepsilon^2)$ is indeed the per-instance lower bound for estimating the norm of a distribution $μ$ by sampling (even for non-unbiased estimators).

We introduce a novel multi-parameter rating methodology for comparing theoretical models with experimental data in heavy-ion collisions, addressing limitations of the global $χ^2$/ndf criterion. The methodology divides phase space into seven physically motivated kinematic zones. Each zone receives a quality score $Q_i \in [10, 1000]$ via logarithmic transformation of local $χ^2_i/ν_i$ statistics. A composite rating $R$ aggregates weighted average, geometric mean, and minimum scores with a bounded dispersion penalty. The seven-zone division is validated through boundary significance tests on CMS PbPb data at $\sqrt{s_{NN}} = 5.02$ TeV: four of six physical boundaries are confirmed significant ($p < 0.05$) while none of the data-driven $K=9$ candidates carry independent physical significance. Coefficient sensitivity: $\pm 20\%$ variations produce $ΔR < 2\%$ with zero rank changes. Applied to ALICE data for $K^0_S$ mesons and $Λ$ hyperons in p-Pb at $\sqrt{s_{NN}} = 5.02$ TeV, the methodology reveals a hierarchy of model universality: PHSD (microscopic QGP transport + coalescence) achieves near-universal performance ($R=911$ for mesons, $R=893$ for baryons on a synthetic LHCb-kinematics benchmark), while PYTHIA8 ($R=878$) leads in the hard-fragmentation regime via nuclear PDFs. The baryon anomaly peak in zones 3--4 yields $Q_i \sim 950$--$1000$ for coalescence models versus $Q_i \sim 400$--$600$ for fragmentation generators. The near-universal performance of PHSD demonstrates that coalescence mechanisms are critical not only for baryon production but also for a globally consistent description of meson spectra. The methodology is transparent, reproducible, and ready for integration into standard analysis frameworks.

Data cleaning is often framed as a technical preprocessing step, yet in practice it relies heavily on human judgment. We report results from a controlled survey study in which participants performed error detection, data repair and imputation, and entity matching tasks on census-inspired scenarios with known semantic validity. We find systematic evidence for several cognitive bias mechanisms in data cleaning. Framing effects arise when surface-level formatting differences (e.g., capitalization or numeric presentation) increase false-positive error flags despite unchanged semantics. Anchoring and adjustment bias appears when expert cues shift participant decisions beyond parity, consistent with salience and availability effects. We also observe the representativeness heuristic: atypical but valid attribute combinations are frequently flagged as erroneous, and in entity matching tasks, surface similarity produces a substantial false-positive rate with high confidence. In data repair, participants show a robust preference for leaving values missing rather than imputing plausible values, consistent with omission bias. In contrast, automation-aligned switching under strong contradiction does not exceed a conservative rare-error tolerance threshold at the population level, indicating that deference to automated recommendations is limited in this setting. Across scenarios, bias patterns persist among technically experienced participants and across diverse workflow practices, suggesting that bias in data cleaning reflects general cognitive tendencies rather than lack of expertise. These findings motivate human-in-the-loop cleaning systems that clearly separate representation from semantics, present expert or algorithmic recommendations non-prescriptively, and support reflective evaluation of atypical but valid cases.

We prove the local logarithmic Brunn-Minkowski inequality for bodies of revolution. Furthermore, we give a generalization for one origin symmetric body of revolution and one body of revolution that does not need to be symmetric and restrict possible equality cases. The proof uses an operator theoretic approach together with the decomposition of spherical functions into isotypical components with respect to rotations around a fixed axis.

Quantum optimization has gained increasing attention as advances in quantum hardware enable the exploration of problem instances approaching real-world scale. Among existing approaches, variational quantum algorithms and quantum annealing dominate current research; however, both typically rely on one-hot encodings that severely limit scalability. Pauli Correlation Encoding (PCE) was recently introduced as an alternative paradigm that reduces qubit requirements by embedding problem variables into Pauli correlations. Despite its promise, PCE has not yet been studied in the context of constrained optimization. In this work, we extend the PCE framework to constrained combinatorial optimization problems and evaluate its performance across multiple problem sizes. Our results show that the standard PCE formulation struggles to reliably enforce constraints, which motivates the introduction of the Iterative-$α$ PCE. This iterative strategy significantly improves solution quality, achieving consistent constraint satisfaction while yielding better cut sizes across a wide range of instances. These findings highlight both the limitations of current PCE formulations for constrained problems and the effectiveness of iterative strategies for advancing quantum optimization in the NISQ era.

This thesis documents a voyage towards truth and beauty via formal verification of theorems. To this end, we develop libraries in Lean 4 that present definitions and results from diverse areas of MathematiCS (i.e., Mathematics and Computer Science). The aim is to create code that is understandable, believable, useful, and elegant. The code should stand for itself as much as possible without a need for documentation; however, this text redundantly documents our code artifacts and provides additional context that isn't present in the code. This thesis is written for readers who know Lean 4 but are not familiar with any of the topics presented. We manifest truth and beauty in three formalized areas of MathematiCS (optimization theory, matroid theory, and the theory of grammars). In the pursuit of truth, we focus on identifying the trusted code in each project and presenting it faithfully. We emphasize the readability and believability of definitions rather than choosing definitions that are easier to work with. In search for beauty, we focus on the philosophical framework of Roger Scruton, who emphasizes that beauty is not a mere decoration but, most importantly, beauty is the means for shaping our place in the world and a source of redemption, where it can be viewed as a substitute for religion.

Power system security assessments, e.g. via cascading outage models, often use operational set-points based on optimal power flow (OPF) dispatch. However, driven by cost minimization, OPF provides an ideal, albeit unrealistic, clearing of the generating units that disregards the complex interactions among market participants. In addition, existing market modeling tools often utilize economic dispatch and unit commitment to minimize total system costs, often disregarding the profit-driven behavior of market participants. The security of the system, therefore, may be overestimated. To address this gap, we introduce a social-welfare-based day-ahead market-clearing model. The security implications are analyzed using Cascades, a model for cascading failure analysis. We apply this model to the IEEE-118 bus system with three independent control zones. The results show that market dispatch leads to an increase in demand not served (DNS) of up to 80% higher than OPF, highlighting a significant security overestimation. This is especially pronounced in large-scale cascading events with DNS above 100MW. A key driver is the increased dispatch of storage and gas units, which can place the system in critical operating conditions. Operators can use this information to properly estimate the impact of the market on system security and plan efficient expansion strategies.

Thermodynamics is commonly presented as a theory of macroscopic systems in stable equilibrium, built upon assumptions of extensivity and scaling with system size. In this paper, we present a universal formulation of the elementary foundations of thermodynamics, in which entropy and energy are defined and employed beyond equilibrium and without assuming extensivity. The formulation applies to all systems -- large and small, with many or few particles -- and to all states, whether equilibrium or nonequilibrium, by relying on carefully stated operational definitions and existence principles rather than macroscopic idealizations. Key thermodynamic concepts, including adiabatic availability and available energy, are developed and illustrated using the energy-entropy diagram representation of nonequilibrium states, which provides geometric insight into irreversibility and the limits of work extraction for systems of any size. A substantial part of the paper is devoted to the analysis of entropy transfer in non-work interactions, leading to precise definitions of heat interactions and heat-and-diffusion interactions of central importance in mesoscopic continuum theories of nonequilibrium behavior in simple and complex solids and fluids. As a direct consequence of this analysis, Clausius inequalities and the Clausius statement of the second law are derived in forms explicitly extended to nonequilibrium processes. The resulting framework presents thermodynamics as a universal theory whose concepts apply uniformly to all systems, large and small, and provides a coherent foundation for both teaching and modern applications.

We study the implications for $B_s - \bar B_s$ mixing and the neutron electric dipole moment (EDM) in a light dark matter model with sizable invisible rare meson decays to accommodate the recent possible deviations from Standard Model (SM) predictions observed in $B^+\to K^+ν\barν$ by Belle II and $K^+\toπ^+ν\barν$ by NA62. Given that the neutrinos in these decays escape detection, they can be replaced by other invisible final states. Based on effective operator analysis, it has been proposed that branching ratios for $B^+\to K^+ +\mbox{invisible}$ and $K^+\toπ^+ +\mbox{invisible}$ can naturally be larger than the SM predictions due to the emission of light dark matter pairs. We demonstrate that this scenario can be realized within a UV-complete two-Higgs-doublet model (2HDM) where neutral Higgs bosons mediating dark matter interactions induce significant low-energy effects especially for $B_s-\bar B_s$ mixing and neutron EDM. Within the allowed parameter space, we find non-negligible contributions to $B_s - \bar B_s$ mixing. For neutron EDM, there is a cancellation due to the exchange of neutral spin-zero particle, but QCD renormalization group evolution will lift this cancellation which in fact is generally true for any neutral Higgs contribution. However, we demonstrate that such a cancellation does not occur for charged scalar contributions. Ultimately, the allowed CP-violating phases in the Yukawa sector can generate a neutron EDM at a level consistent with current bound.

It is argued that the previously proposed modification of the standard (flat) inflationary $ΛCDM$ model in which cosmological constant is replaced by thermal energy of expanding vacum, characterized by the Gibbons-Hawking temperature, explains the origin of notorious ``Hubble tension''.

We study the excursion decomposition of the two-dimensional critical XOR-Ising model with either $+$ or free boundary conditions. In the first part, we construct the decomposition directly in the continuum. This construction relies on the identification of the XOR-Ising field with the cosine or sine of a Gaussian free field (GFF) $ϕ$ multiplied by $α= 1/\sqrt{2}$, and is obtained by an appropriate exploration of two-valued level sets of the GFF. More generally, the same construction applies to the fields $:\! \cos(αϕ) \!:$ and $:\! \sin(αϕ) \!:$ for any $α\in (0,1)$. In the second part, we show that the continuum excursion decomposition arises as the scaling limit of the double random current decomposition of the critical XOR-Ising model on the square lattice. To this end, we exploit the rich Markovian structure of the discrete decomposition and strengthen the convergence of the double random current height function to the continuum GFF by establishing joint convergence with its cosine and sine. We conjecture that for $α\in [1/2,\sqrt{3}/2)$ the continuum excursion decompositions arise as the scaling limit of those of the Ashkin-Teller polarisation field along its critical line.

We propose a novel computational method for unit commitment UC, which does not require linearized approximation and provides several orders of magnitude performance improvement over current state-of-the-art. The performance improvement is achieved by introducing a heuristic tailored for UC problems. The method can be implemented using existing continuous optimization solvers and adapted for different applications. We demonstrate value of the new method in examples of advanced UC analyses at the scale where use of current state-of-the-art tools is infeasible. We expect that the capability demonstrated in this paper will be critical to address emerging power systems challenges with more volatile large loads, such as data centers, and generation that is composed of larger number of smaller units, including significant behind-the-meter generation.

In soil physics, saturated hydraulic conductivity, K_sat, is among the most important hydraulic properties with broad applications to modeling flow and transport under saturated conditions. Its accurate estimation, however, is challenging and requires precise characterization of pore space. In this study, we applied concepts of critical path analysis (CPA) to estimate K_sat from soil water retention curve. To evaluate the CPA, we used 313 undisturbed soil samples from the Kansas Mesonet database in which the value of K_sat spans over five orders of magnitude in variation. We found that the CPA estimated K_sat reasonably well with root mean square log-transformed error RMSLE = 0.87. For most samples, the predicted values were around the 1:1 line within a factor of 10 of the measurements. We also estimated K_sat using five other methods but none was more accurate than the CPA.

Two-dimensional heterostructures combining sp-sp2 hybridization,blending graphene with graphyne-based allotropes, offer substantial potential for enhancing the tunability of electronic and transport properties while providing significant structural flexibility. These attributes are desirable for next generation nanoscale electronic applications. Despite such potential, their experimental realization remains elusive, as synthesized carbon heterostructures are limited to doped, graphene-based systems exhibiting exclusively sp2 hybridization. Here, we demonstrate the on-surface synthesis of covalently bonded sp-sp2 lateral heterostructures between graphene nanoribbons and graphdiyne networks on Au(111). Atomic-resolution scanning tunnelling microscopy, combined with density functional theory, reveals the formation mechanism of the covalent interfacial bonds between nanoribbons and graphdiynes, also highlighting the key role of surface chemistry. Bromine atoms deriving from the molecules dehalogenation and chemisorbed along the nanoribbon inhibit the junction formation, but bonding efficiency can be boosted up to 71% by controlled removal of these by-products. Electronic structure and transport calculations show that the 2D heterostructure by itself is characterized by disentangled properties for the two subsystems, forming an atomically narrow junction enabling voltage-tunable spatial current separation in two dimensions. There results define a viable strategy for engineering graphene-based sp-sp2 heterostructures, paving the way for the design and synthesis of all-carbon nanoscale electronic architectures.

We develop a simple and general variational method to estimate the solutions of the Gross-Pitaevskii equations and obtain the corresponding density profiles for all spin states of a trapped spin-1 Bose-Einstein condensate. We further employ this approach to obtain the complete phase diagram of the system under quasi-one-dimensional harmonic confinement, with ferromagnetic or antiferromagnetic spin interactions. We identify a suitable scaling that collapses all phase diagrams for different system sizes (i.e., total particle number) into a universal (system size-independent) phase diagram. The complete phase diagram for a confined system shows some significant qualitative differences compared to that of a condensate with homogeneous density distribution. The phase diagrams reported here could help identify the important parameter regimes in which phase transitions in the confined system, in general, occur. This knowledge of the region of phase boundaries can enable a reliable investigation of the instabilities near the boundaries that drive phase transitions.

Large Language Model (LLM) chatbots like ChatGPT have emerged as cognitive scaffolding for autistic users, yet the tension between their utility and risk remains under-articulated. Through an inductive thematic analysis of 3,984 social media posts by self-identified autistic users, we apply a technology affordance lens to examine this duality. We found that while users leveraged ChatGPT to offload executive dysfunction, regulate emotions, translate neurotypical communication, and validate their autistic identity, these affordances coexist with risks to their well-being: reinforcing delusional thinking, erasing authentic identity through automated masking, and triggering conflicts with the autistic sense of justice. As part of our preliminary work, this poster identifies trade-offs in autistic users' interactions with ChatGPT and concludes by outlining our future work on developing neuro-inclusive technologies that address these tensions through beneficial friction, bidirectional translation, and the delineation of emotional validation from reality.

In this paper, we study the timeliness of actions in communication systems where actuation is constrained by control permissions or energy availability. Building on the Age of Actuation (AoA) metric, which quantifies the timeliness of actions independently of data freshness, we introduce a new metric, the \emph{Age of Actuated Information (AoAI)}. AoAI captures the end-to-end timeliness of actions by explicitly accounting for the age of the data packet at the moment it is actuated. We analyze and characterize both AoA and AoAI in discrete-time systems with data storage capabilities under multiple actuation scenarios. The actuator requires both a data packet and an actuation opportunity, which may be provided by a controller or enabled by harvested energy. Data packets may be stored either in a single-packet buffer or an infinite-capacity queue for future actuation. For these settings, we derive closed-form expressions for the average AoA and AoAI and investigate their structural differences. While AoA and AoAI coincide in instantaneous actuation systems, they differentiate when data buffering is present. Our results reveal counterintuitive regimes in which increasing update or actuation rates degrade action timeliness for both AoA and AoAI. Moreover, as part of the analysis, we obtain a novel closed-form characterization of the steady-state distribution of a Geo/Geo/1 queue operating under the FCFS discipline, expressed solely in terms of the queue length and the age of the head-of-line packet. The proposed metrics and analytical results provide new insights into the semantics of timeliness in systems where information ultimately serves the purpose of actuation.

2D materials hold transformative promise for next-generation nanoelectronics. However, successfully integrating these materials from laboratory-scale discoveries into real-world devices depends on precisely controlling their properties, which are fundamentally determined by their composition. Detailed characterisation using atom probe tomography of 2D Ti0.87O2, a candidate high-$κ$ dielectric, reveals deviations from its commonly assumed stoichiometry. Compositional analysis and comparison with the bulk K0.8[Ti1.73Li0.27]O4 precursor evidences an oxygen deficit indicative of oxygen vacancy formation in the 2D material, as well as the retention of low concentrations of alkali metals that were presumed to be removed during synthesis. Such deviations from stoichiometry indicate a reconstruction mechanism that mitigates the effect of the characteristic, negatively charged vacancies on the titanium sublattice, thereby influencing the local electronic structure and, consequently, functional properties. These findings underscore the importance of a detailed compositional analysis in both understanding and optimizing the extraordinary functional properties of 2D materials, opening pathways to tailored functionalities in next-generation nanoelectronics.

AI companions enable deep emotional relationships by engaging a user's sense of identity, but they also pose risks like unhealthy emotional dependence. Mitigating these risks requires first understanding the underlying process of identity construction and negotiation with AI companions. Focusing on Character.AI (C.AI), a popular AI companion, we conducted an LLM-assisted thematic analysis of 22,374 online discussions on its subreddit. Using Identity Negotiation Theory as an analytical lens, we identified a three-stage process: 1) five user motivations; 2) an identity negotiation process involving three communication expectations and four identity co-construction strategies; and 3) three emotional outcomes. Our findings surface the identity work users perform as both performers and directors to co-construct identities in negotiation with C.AI. This process takes place within a socio-emotional sandbox where users can experiment with social roles and express emotions without non-human partners. Finally, we offer design implications for emotionally supporting users while mitigating the risks.

We study how bots contribute to open-source discussions in the Ethereum ecosystem and whether they influence developers' emotional tone. Our dataset covers 36,875 accounts across ten repositories with 105 validated bots (0.28%). Human participation follows a U-shaped pattern, while bots engage in uniform (pull requests) or late-stage (issues) activity. Bots respond faster than humans in pull requests but play slower maintenance roles in issues. Using a model trained on 27 emotion categories, we find bots are more neutral, yet their interventions are followed by reduced neutrality in human comments, with shifts toward gratitude, admiration, and optimism and away from confusion. These findings indicate that even a small number of bots are associated with changes in both timing and emotional dynamics of developer communication.

Coherent multidimensional spectroscopy enables detailed investigations of vibronic effects in molecular and solid-state systems. We present explicit analytical expressions for multidimensional nonlinear response functions in the presence of Herzberg-Teller (non-Condon) coupling, within the displaced harmonic oscillator model. The formulation applies to electronic systems with an arbitrary number N of electronic states and to response functions of arbitrary order M in the light-matter interaction. We show that Herzberg-Teller coupling introduces additional oscillatory factors in the time-domain response functions, leading, upon Fourier transformation, to replicas of the Franck-Condon multidimensional spectra shifted by integer multiples of the vibrational frequencies. The present results provide a general analytical framework for the interpretation of non-Condon effects in coherent multidimensional spectroscopies. A Python code that implements the present approach and simulates multidimensional spectra for N-level systems is available on GitHub.

The Contract Net Protocol (1980) introduced coordination through contracts in multi-agent systems. Modern agent protocols standardize connectivity and interoperability; yet, none provide formal, resource governance-normative mechanisms to bound how much agents may consume or how long they may operate. We introduce Agent Contracts, a formal framework that extends the contract metaphor from task allocation to resource-bounded execution. An Agent Contract unifies input/output specifications, multi-dimensional resource constraints, temporal boundaries, and success criteria into a coherent governance mechanism with explicit lifecycle semantics. For multi-agent coordination, we establish conservation laws ensuring delegated budgets respect parent constraints, enabling hierarchical coordination through contract delegation. Empirical validation across four experiments demonstrates 90% token reduction with 525x lower variance in iterative workflows, zero conservation violations in multi-agent delegation, and measurable quality-resource tradeoffs through contract modes. Agent Contracts provide formal foundations for predictable, auditable, and resource-bounded autonomous AI deployment.

We explore the sum over topologies in AdS$_3$ quantum gravity and its relationship with the statistical interpretation of the boundary theory. We formulate a statistical version of the conformal bootstrap that systematizes the universal statistical properties of high-energy CFT$_2$ data. We identify a series of surgery moves on bulk manifolds that precisely reflect the requirements of typicality and crossing symmetry of the boundary ensemble. These surgery moves generate a large number of bulk manifolds that have to be included in any reasonable definition of the gravitational path integral. We show that this procedure generates only on-shell (hyperbolic) manifolds, although it does not produce all of them. These proofs rely on structure theorems of 3-manifolds, which non-trivially interact with the requirements of the statistical boundary ensemble. We illustrate the application of this procedure with many examples, such as Euclidean wormholes, twisted $I$-bundles and handlebody-knots. Our findings reveal a large space of possible choices of which manifolds can be included in the gravitational path integral, reflecting a wide range of possible statistical ensembles consistent with crossing symmetry and typicality.

Current Large Language Models (LLMs) have advanced automated unit test generation but face a critical limitation: they often neglect to construct the necessary test fixtures, which are the environmental setups required for a test to run. To bridge this gap, this paper proposes Fixturize, a diagnostic framework that proactively identifies fixture-dependent functions and synthesizes test fixtures accordingly through an iterative, feedback-driven process, thereby improving the quality of auto-generated test suites of existing approaches. For rigorous evaluation, the authors introduce FixtureEval, a dedicated benchmark comprising 600 curated functions across two Programming Languages (PLs), i.e., Python and Java, with explicit fixture dependency labels, enabling both the corresponding classification and generation tasks. Empirical results demonstrate that Fixturize is highly effective, achieving 88.38%-97.00% accuracy across benchmarks in identifying the dependence of test fixtures and significantly enhancing the Suite Pass rate (SuitePS) by 18.03%-42.86% on average across both PLs with the auto-generated fixtures. Owing to the maintenance of test fixtures, Fixturize further improves line/branch coverage when integrated with existing testing tools of both LLM-based and Search-based by 16.85%/24.08% and 31.54%/119.66% on average, respectively. The findings establish fixture awareness as an essential, missing component in modern auto-testing pipelines.

Portfolio diversification is a cornerstone of modern finance, while risk aversion is central to decision theory; both concepts are long-standing and foundational. We investigate their connections by studying how different forms of diversification correspond to notions of risk aversion. We focus on the classical distinctions between weak and strong risk aversion, and consider diversification preferences for pairs of risks that are identically distributed, comonotonic, antimonotonic, independent, or exchangeable, as well as their intersections. Under a weak continuity condition and without assuming completeness of preferences, diversification for antimonotonic and identically distributed pairs implies weak risk aversion, and diversification for exchangeable pairs is equivalent to strong risk aversion. The implication from diversification for independent pairs to weak risk aversion requires a stronger continuity. We further provide results and examples that clarify the relationships between various diversification preferences and risk attitudes, in particular justifying the one-directional nature of many implications.

Every surface that is intrinsically polyhedral can be represented by a portalgon: a collection of polygons in the Euclidean plane with some pairs of equally long edges abstractly identified. While this representation is arguably simpler than meshes (flat polygons in R3 forming a surface), it has unbounded happiness: a shortest path in the surface may visit the same polygon arbitrarily many times. This pathological behavior is an obstacle towards efficient algorithms. On the other hand, Löffler, Ophelders, Staals, and Silveira (SoCG 2023) recently proved that the (intrinsic) Delaunay triangulations have bounded happiness. In this paper, given a closed polyhedral surface S, represented by a triangular portalgon T, we provide an algorithm to compute the Delaunay triangulation of S whose vertices are the singularities of S (the points whose surrounding angle is distinct from 2pi). The time complexity of our algorithm is polynomial in the number of triangles and in the logarithm of the aspect ratio r of T. Within our model of computation, we show that the dependency in log(r) is unavoidable. Our algorithm can be used to pre-process a triangular portalgon before computing shortest paths on its surface, and to determine whether the surfaces of two triangular portalgons are isometric.

Quantum advantage is widely understood to rely on key quantum resources beyond entanglement, among which nonstabilizerness (quantum ``magic'') plays a central role in enabling universal quantum computation. However, the exact evaluation of the second-order stabilizer Rényi entropy for generic many-body quantum states remains computationally challenging, with brute-force methods scaling as $\mathcal O(8^N)$ for an $N$-qubit state. Here we develop a deterministic and exact algorithm that reduces this cost to $\mathcal{O}(N4^N)$ while retaining natural parallelism. This advance enables high-precision exact calculations for generic state vectors at medium system sizes, and provides a practical tool for investigating the scaling, phase structure, and nonequilibrium dynamics of quantum magic in many-body systems.