Abstract
We extend the moduli-theoretic framework of psychometric batteries to the domain of dynamical systems. While previous work established the AAI capability score as a static functional on the space of agent representations, this paper formalizes the agent as a flow $ν_r$ parameterized by computational resource $r$, governed by a recursive Generator-Verifier-Updater (GVU) operator. We prove that this operator generates a vector field on the parameter manifold $Θ$, and we identify the coefficient of self-improvement $κ$ as the Lie derivative of the capability functional along this flow. The central contribution of this work is the derivation of the Variance Inequality, a spectral condition that is sufficient (under mild regularity) for the stability of self-improvement. We show that a sufficient condition for $κ> 0$ is that, up to curvature and step-size effects, the combined noise of generation and verification must be small enough. We then apply this formalism to unify the recent literature on Language Self-Play (LSP), Self-Correction, and Synthetic Data bootstrapping. We demonstrate that architectures such as STaR, SPIN, Reflexion, GANs and AlphaZero are specific topological realizations of the GVU operator that satisfy the Variance Inequality through filtration, adversarial discrimination, or grounding in formal systems.

AI Summary

• The GVU framework is used to analyze the stability of self-improvement in AI systems. [3]
• The Variance Inequality (Theorem 4.1) provides a sufficient condition for stable self-improvement, requiring a high Signal-to-Noise Ratio (SNR) for both the generator and the verifier. [3]
• AI slop event at parameter θ AI slop mass and slop regime The paper provides a framework for understanding the stability of self-improvement in AI systems, highlighting the importance of high SNR for both generators and verifiers. [3]
• The paper defines AI slop as a region where the internal Verifier ranks outputs among its top fraction, but they actually lie in the bottom fraction of the true battery score. [2]
• The paper introduces the Generalized Verifier-Generator Update (GVU) framework, which models the interaction between a generator and its verifier. [1]

Abstract
As generative artificial intelligence (GAI) enters the mental health landscape, questions arise about how individuals weigh AI tools against human therapists. Drawing on the Health Belief Model (HBM), this study examined belief-based predictors of intention to use GAI and therapists across two populations: a university sample (N = 1,155) and a nationally representative adult sample (N = 651). Using repeated-measures ANOVA and LASSO regression, we found that therapists were consistently valued for emotional, relational, and personalization benefits, while GAI was favored for accessibility and affordability. Yet structural advantages alone did not predict adoption; emotional benefit and personalization emerged as decisive factors. Adoption patterns diverged across groups: students treated GAI as a complement, whereas national adults approached it as a substitute. Concerns about privacy and reliability constrained GAI use in both groups. These findings extend HBM to multi-modality contexts and highlight design implications for trustworthy, emotionally resonant digital mental health tools.

AI Summary

• LASSO regression is a statistical method used to identify the most influential predictors from a comprehensive set of perceived benefits and barriers. [3]
• The study provides insights into the psychological reasoning behind help-seeking behavior, highlighting the importance of emotional benefits, personalization, affordability, and reliability in decision-making. [3]
• The study found that individuals choose between GAI tools and human therapists based on different belief structures. [2]
• The Health Belief Model (HBM) is a theoretical framework used to understand how individuals make decisions about their health behaviors. [1]

Abstract
We prove the Spacetime Penrose Inequality: for any asymptotically flat initial data set satisfying the Dominant Energy Condition, the ADM mass is bounded below by the square root of the trapped surface area divided by 16 pi, with equality only for Schwarzschild. Unlike previous partial results, our proof is unconditional and holds for any trapped surface regardless of stability or topology. The proof combines the generalized Jang equation with the p-harmonic level set method. We establish Fredholm solvability in weighted Sobolev spaces, verify that Jang-conformal metrics with distributional curvature satisfy all required analytic hypotheses, prove mean curvature jump positivity for stable horizons, and justify the double limit with explicit bounds. This resolves Penrose's 1973 conjecture, a central open problem in mathematical relativity for over fifty years.

AI Summary

• The Spacetime Penrose Inequality is a fundamental result in general relativity that relates the mass of an asymptotically flat spacetime to the area of its event horizon. [3]
• The inequality has been generalized and refined over the years, with various authors making significant contributions to its proof and understanding. [3]
• The core case of the Spacetime Penrose Inequality is when the event horizon is a stable marginally outer trapped surface (MOTS) with spherical topology. [2]
• Stable MOTS: An MOTS that is stable under small perturbations. [1]
• The proof of the Spacetime Penrose Inequality involves several key steps and techniques, including the use of the Bray-Khuri identity, the Lichnerowicz-Obata theorem, and the Lockhart-McOwen theorem. [0]
• Asymptotically flat spacetime: A spacetime that approaches a flat spacetime at infinity. [0]
• Dominant Energy Condition (DEC): A condition on the stress-energy tensor of a spacetime that ensures the existence of an event horizon. [0]
• Marginally outer trapped surface (MOTS): A surface in a spacetime where the expansion of outgoing null geodesics is zero. [0]

Abstract
Access to motorable roads is a critical dimension of urban infrastructure, particularly in rapidly urbanizing regions such as Sub-Saharan Africa. Yet, many urban communities, especially those in informal settlements, remain disconnected from road networks. This study presents a road access deprivation model that combines a new accessibility metric, capturing how well buildings are connected to the road network, with road surface type data as a proxy for road quality. These two components together enable the classification of urban areas into low, medium, or high deprivation levels. The model was applied to Nairobi (Kenya), Lagos (Nigeria), and Kano (Nigeria) using open geospatial datasets. Across all three cities, the majority of built-up areas fall into the low and medium road access deprivation levels, while highly deprived areas are comparatively limited. However, the share of highly deprived areas varies substantially, ranging from only 11.8 % in Nairobi to 27.7 % in Kano. Model evaluation against community-sourced validation data indicates good performance for identifying low deprivation areas (F1 > 0.74), moderate accuracy for medium deprivation in Nairobi and Lagos (F1 > 0.52, lower in Kano), and more variable results for high deprivation (F1 ranging from 0.26 in Kano to 0.69 in Nairobi). Furthermore, analysis of grid cells with multiple validations showed strong agreement among community members, with disagreements occurring mainly between adjacent deprivation levels. Finally, we discussed two types of sources for disagreement with community validations: (1) misalignment between the conceptual model and community perceptions, and (2) the operationalization of the conceptual model. In summary, our road access deprivation modeling approach demonstrates promise as a scalable, interpretable tool for identifying disconnected areas and informing urban planning in data-scarce contexts.

AI Summary

• The model was applied to three cities, Nairobi, Lagos, and Kano, and evaluated using community-sourced validation data. [3]
• In Lagos, performance is also high with strong results for low deprivation but weaker performance for medium and high levels. [3]
• In Kano, accuracy is lower, with poor results for high deprivation. [3]
• The study presents a road access deprivation model that combines a distance-agnostic accessibility metric with road surface type data as a proxy for road quality. [2]

Abstract
Training with differential privacy (DP) provides a guarantee to members in a dataset that they cannot be identified by users of the released model. However, those data providers, and, in general, the public, lack methods to efficiently verify that models trained on their data satisfy DP guarantees. The amount of compute needed to verify DP guarantees for current algorithms scales with the amount of compute required to train the model. In this paper we design the first DP algorithm with near optimal privacy-utility trade-offs but whose DP guarantees can be verified cheaper than training. We focus on DP stochastic convex optimization (DP-SCO), where optimal privacy-utility trade-offs are known. Here we show we can obtain tight privacy-utility trade-offs by privately minimizing a series of regularized objectives and only using the standard DP composition bound. Crucially, this method can be verified with much less compute than training. This leads to the first known DP-SCO algorithm with near optimal privacy-utility whose DP verification scales better than training cost, significantly reducing verification costs on large datasets.

AI Summary

• Machine unlearning aims to produce models that would come from retraining on some subset of the original training dataset, but exact unlearning often requires compute comparable to retraining. [3]
• The paper provides cheap proofs of using a popular convex unlearning method, leveraging techniques developed for certifying DP. [3]
• Auditing and certifying machine unlearning is crucial due to potential bypassing of audits based on model weights or training trajectories. [3]
• Zero-Knowledge Proofs (Definition 5): A protocol that realizes an ideal functionality where a prover convinces a verifier that a circuit C evaluates to true for input w, without revealing any information about w. [3]
• Proof of Knowledge (informal, Definition 7): A proof of knowledge for a relation R is an interactive protocol between a Prover and a Verifier that convinces the Verifier that the relation holds when provided an honest witness. [3]
• Commitment Scheme (Definition 6): An additively homomorphic commitment scheme consists of three polynomial-time algorithms: Setup, Commit, and Verify, with properties including correctness, computational binding, perfect hiding, and additive homomorphism. [2]
• The paper focuses on differentially private stochastic convex optimization algorithms (DP-SCO), which provide guarantees that the output of an algorithm over a dataset does not leak information about what datapoints were in the dataset. [1]

Abstract
Regional disparities in the economic and social structures of countries have a great impact on their development levels. In geographically, culturally and economically diverse countries like Turkiye, determining the socioeconomic status of the provinces and regional differences is an important step for planning and implementing effective policies. Therefore, this study aims to determine the socioeconomic disparities of the provinces in Turkiye. For this purpose, a socioeconomic development index covering the economic and social dimensions of 81 provinces was constructed. For the index, 16 different indicators representing economic and social factors were used. These indicators were converted into indices using the Min-Max normalization method and Principal Component Analysis. Afterwards, using these indices, the provinces were divided into groups using the K-Means clustering algorithm and the Elbow method. In the last part of the study, the results are presented in a visual format using Scatter Plots, clustering maps and QGIS mapping tools. The results of the study show that 2 of the 81 provinces in Turkiye have very high, 30 high, 25 medium and 24 low socioeconomic indices. Istanbul and Ankara have very high socioeconomic status. In general, the provinces in western Turkiye have a high socioeconomic index, while the provinces in eastern and southeastern Anatolia face serious challenges in terms of socioeconomic indicators.

AI Summary

• Economic indicators: These include metrics such as GDP per capita, employment rates, income levels, trade balances, and more. [3]
• They provide insight into a region's or country's economic performance and development. [3]
• The study highlights the significant regional disparities in economic development across Turkey's provinces, with some regions exhibiting high levels of economic activity and others facing challenges. [2]

Abstract
Influence maximization in social networks plays a vital role in applications such as viral marketing, epidemiology, product recommendation, opinion mining, and counter-terrorism. A common approach identifies seed nodes by first detecting disjoint communities and subsequently selecting representative nodes from these communities. However, whether the quality of detected communities consistently affects the spread of influence under the Independent Cascade model remains unclear. This paper addresses this question by extending a previously proposed disjoint community detection method, termed $α$-Hierarchical Clustering, to the influence maximization problem under the Independent Cascade model. The proposed method is compared with an alternative approach that employs the same seed selection criteria but relies on communities of lower quality obtained through standard Hierarchical Clustering. The former is referred to as Hierarchical Clustering-based Influence Maximization, while the latter, which leverages higher-quality community structures to guide seed selection, is termed $α$-Hierarchical Clustering-based Influence Maximization. Extensive experiments are performed on multiple real-world datasets to assess the effectiveness of both methods. The results demonstrate that higher-quality community structures substantially improve information diffusion under the Independent Cascade model, particularly when the propagation probability is low. These findings underscore the critical importance of community quality in guiding effective seed selection for influence maximization in complex networks.

AI Summary

• The paper presents a framework called α-HCIM for influence maximization in social networks under the Independent Cascade model. [3]
• The framework extends the α-HC approach to the influence maximization problem and is shown to significantly improve the spread of information when the IC model operates with a low propagation probability p. [3]
• α-HC: A community-based algorithm for influence maximization IC Model: Independent Cascade model, a diffusion model used in social networks p: Propagation probability, the likelihood that an individual will adopt a behavior or idea after being influenced by their neighbors. [3]
• The α-HCIM framework is shown to be effective in improving the spread of information when the IC model operates with a low propagation probability p. [3]
• However, this improvement is not guaranteed in all scenarios and further research is needed to evaluate its performance under different diffusion models. [3]
• The improvement in the spread of information is not guaranteed in all scenarios Previous research has focused on community-based algorithms for influence maximization, but the α-HCIM framework presents a new approach that extends the α-HC algorithm to the influence maximization problem. [3]
• A new framework called α-HCIM for influence maximization in social networks under the Independent Cascade model is presented. [3]
• It's like a game where you try to get as many people as possible to adopt an idea or behavior. [3]
• The framework is shown to be effective when the probability of getting someone to adopt something is low, but it's not always guaranteed to work. [3]
• The framework extends the α-HC approach and is shown to improve the spread of information when the IC model operates with a low propagation probability p. [1]