We prove that every oriented tree on $n$ vertices with bounded maximum degree appears as a spanning subdigraph of every directed graph on $n$ vertices with minimum semidegree at least $n/2+{\mathrm{o}}(n)$. This can be seen as a directed graph analogue of a well-known theorem of Komlós, Sárközy, and Szemerédi. Our result for trees follows from a more general result, allowing the embedding of arbitrary orientations of a much wider class of spanning ‘tree-like’ structures, such as collections of at most $O(n^{0.99})$ pairwise vertex-disjoint cycles and subdivisions of graphs $H$ with $|H|\lt \exp \bigl (\sqrt {\textrm {O}(\log n)}\,\bigr )$ in which each edge is subdivided at least once.

This paper addresses a class of value-maximization problems in storage-type optimal control involving operational scale and withdrawals with absorption. Moving beyond the drifted Brownian motion model, we develop a unified methodological approach under a general linear diffusion framework. We demonstrate the solvability of a broad class of problems by deriving semi-explicit optimal strategies. We further establish conditions for the existence of fully explicit solutions and illustrate solution methods with examples based on models for a variety of scenarios, both where explicit solutions exist and where only semi-explicit solutions are available.

Indonesia’s Tax Court faces a rapidly growing caseload and limited judicial capacity, leading to prolonged dispute resolution and eroding public trust. Manual review processes create inconsistencies that undermine legal certainty, particularly within Indonesia’s civil law system, where jurisprudence is nonbinding and a judge’s personal knowledge may serve as admissible evidence. To address these challenges, we introduce the AI-driven Decision and Integrity for Tax Court Law (ADIL) pipeline, which automates the analysis of 4377 Indonesian Tax Court decisions from 2008 to 2023. ADIL applies advanced natural language processing and legal informatics to extract structured insights from unstructured judicial texts through a trilayered architecture: (i) rule-based pattern matching for high-precision extraction, (ii) transformer-based named-entity recognition for robust entity detection, and (iii) local large-language-model prompting for semantic summarisation and classification. Using exclusively pre-decision metadata, 49 structured metadata fields, including dispute number, tax year, judge identity, and verdict, were used to train a model that resulted in several machine-learning models to predict case outcomes and resolution duration. ADIL achieved 97.5% precision and strong macro-F1 performance in outcome prediction, and an R2 of 92.9% (RMSE = 63.8%) for duration estimation, equivalent to 7–8 months of predictive accuracy. Notably, incorporating encoded judge identity improved accuracy by 11–16%, revealing systematic variation in judicial behaviour. Feature-importance analysis suggests that ADIL can substantially enhance efficiency, consistency, and transparency in tax adjudication. ADIL offers a data-driven decision support framework towards a more agile and accountable judicial system in Indonesia’s legal and institutional context.

This work presents a nonlinear system identification framework for modeling the power extraction dynamics of wind turbines, including both freestream and waked conditions. The approach models turbine dynamics using data-driven power coefficient maps expressed as combinations of compact radial basis functions and polynomial bases, parameterized in terms of tip-speed ratio and upstream conditions. These surrogate models are embedded in a first-order dynamic system suitable for model-based control. Experimental validation is carried out in two wind tunnel configurations: a low-turbulence tandem setup and a high-turbulence wind farm scenario. In the tandem case, the identified model is integrated into an adapted $ K{\omega}^2 $ controller, resulting in improved tip-speed ratio tracking and power stability compared to steady-state models, while also outperforming the BEM-based model in the present low Reynolds number setting, where aerodynamic predictions are more uncertain. In the wind farm scenario, the model captures the statistical behavior of the turbines despite unresolved turbulence. The proposed method enables interpretable, adaptive control across a range of operating conditions without relying on black-box learning strategies.

While modelling deterioration or ageing of devices, first-passage times of Markov processes play a significant role, especially when the devices are subject to shocks and wear during their operation. In view of this, obtaining sufficient conditions for first-passage times to belong to specific ageing families constitutes an important problem. There exists a rich literature dealing with this class of problems; see for example [11], [18], [35], [67]. We address the same problem in the context of some new ageing classes such as DMTTF (IMTTF), IMIT, and DRHR. In this connection, some issues in [11] have also been investigated. We wind up by including certain examples to highlight the practical relevance of the results.

Rapid developments in Artificial Intelligence (AI) tools and their ever-expanding use in societal contexts raises questions regarding their design, social acceptance, and regulation. We develop a randomized vignette experiment, detailing six contemporary high-stakes contexts employing algorithmic tools and uncover distinct attitudes toward the source of the AI provisioning (public vs private sector). Participants are drawn from technology and law schools in India, representing key future stakeholders in the AI policy ecosystem in the country. Our main result indicates an overall preference for public sector provisioning of AI tools, with important implications on the social acceptability of public sector expansion of AI systems. Although the Global South has witnessed widespread expansion of AI tools with limited scrutiny, the nascent scholarship on AI attitudes disproportionately emanates from the Global North. Our study fills this gap, as well as the gap in empirical evidence on private vs public provisioning of AI tools in social contexts.

The usual definitions of algorithmic fairness focus on population-level statistics, such as demographic parity or equal opportunity. However, in many social or economic contexts, fairness is not perceived globally, but locally, through an individual’s peer network and comparisons. We propose a theoretical model of perceived fairness networks, in which each individual’s sense of discrimination depends on the local topology of interactions. We show that even if a decision rule satisfies standard criteria of fairness, perceived discrimination can persist or even increase in the presence of homophily or assortative mixing. We propose a formalism for the concept of fairness perception, linking network structure, local observation, and social perception. Analytical and simulation results highlight how network topology affects the divergence between objective fairness and perceived fairness, with implications for algorithmic governance and applications in finance and collaborative insurance.

This article explores the integration of large language models (LLMs) and AI research agents into global benchmarking frameworks, with a focus on data for the public good. Against a backdrop of shrinking funding and rising demand for scalable and reproducible assessments, we ask whether AI can assume core roles in indicator development, evidence discovery, and policy evaluation without compromising contextual nuance or democratic legitimacy. Building on pilot experiments conducted within the Global Data Barometer (GDB), we employed a phased, adaptive methodology that tested workflow-based platforms and deep research agents across tasks ranging from legal interpretation to multisource policy analysis. The preliminary findings suggest that while AI systems show strong potential for automating structured assessments, they falter on complex, fragmented, or normatively loaded indicators, raising concerns about opacity, overinterpretation, and inclusivity. To navigate these tensions, we propose a hybrid human-AI architecture that combines standardized workflows, adaptive agent capabilities, and critical human oversight. Central to this model is the concept of a dynamic evidence infrastructure, designed to embed participatory validation and enhance transparency. By reframing automation as augmentation, the study contributes both an empirical, domain-specific assessment of the opportunities and limits of AI-assisted benchmarking and a theoretical framework for sustainable, context-aware evaluation in the age of AI. We argue that the success of AI-assisted benchmarking should be measured not only in efficiency gains but also in its ability to strengthen legitimacy, accountability, and inclusiveness in data ecosystems worldwide.

In this work, we consider two coherent systems with shared components in the case when the component lifetimes are independent and identically distributed with a discrete-time distribution instead of a continuous-time distribution. Then, a discrete-time joint signature is proposed for the two systems by generalizing the traditional joint signature for systems with continuous lifetimes. Some stochastic properties of the proposed joint signature are studied in detail, including joint distribution, stochastic ordering, and transformation formula for comparison of pairs of systems of different sizes. Some illustrative examples are also presented.

We prove the existence of a stationary IARCH (integrated autoregressive conditionally heteroskedastic) process for a class of models with polynomially decaying coefficients.