In the lower-star filtration (LSF), simplices are assigned filtration values according to the maximum-vertex rule, with each simplex entering the filtration when its highest-valued vertex appears. A limitation of this construction is that some higher-dimensional simplices may enter simultaneously with their boundary faces, causing certain topological features to be filled immediately upon formation and thus not appear in the resulting persistence diagram. To address this limitation, we propose three alternative filtration methods: the \(\varepsilon\)-lower-star filtration (ELSF), the \(L_p\) filtration (LpF), and the softmax filtration (SMF). {ELSF introduces a dimension-dependent delay to the maximum-vertex rule,} allowing higher-dimensional simplices to enter the filtration after their boundary faces, whereas {LpF and SMF use aggregation functions that depend on all vertex values rather} than solely on their maximum. By modifying how filtration values are assigned, these methods allow simplices to enter the filtration more progressively, so that topological features such as loops and voids may persist over longer filtration intervals rather than being filled immediately. Consequently, the resulting persistence diagrams may include persistence features that are not observed under LSF, potentially providing useful information for distinguishing data populations. Experimental results on simulated and real-world datasets demonstrate that the proposed filtration methods are computationally efficient and can provide greater sensitivity to structural differences in the data than LSF.
Digital traces may complement population surveys in the measurement of well-being, but the two sources do not necessarily capture identical constructs. We compare the Human Flourishing Geographic Index (HFGI) with World Values Survey and European Social Survey measures across three domains using structural equation models. The results show strong within-source coherence and construct-specific cross-source correspondence. Cross-source convergence varies across domains; the observed pattern is consistent with stronger correspondence where the underlying indicators are more closely aligned conceptually. Near-perfect agreement would be unexpected, since surveys elicit standardized self-reports, whereas HFGI captures naturally occurring public expressions. HFGI should therefore be viewed as a distinct but empirically connected measurement system that complements survey-based evidence on well-being.
Forecasting local elections is difficult because electoral competition is geographically heterogeneous, highly overdispersed, and characterized by many party-municipality combinations with little or no electoral activity. This article develops a bounded neural zero-inflated negative binomial (ZINB) model for forecasting party-level vote counts in Swedish municipal elections. The model combines a count component for expected votes, a zero-inflation component for structural electoral absence, municipality-specific dispersion, and learned embeddings capturing latent party, municipality, and party-municipality structure. Model training relies on data from the 2014, 2018, and 2022 Swedish municipal elections and performance is evaluated on a held-out set of municipalities. Testing results show strong predictive accuracy in both vote counts and vote shares. Explanatory diagnostics indicate that latent party structure, local party-municipality relationships, electoral persistence, organizational capacity, and candidate-electorate representational similarity are among the most important determinants of predictive performance. Following model evaluation and diagnostics, the selected specification is refit on all historical data and applied to generate forecasts for the 2026 municipal elections. The proposed framework provides a flexible approach for studying local electoral competition in multiparty systems characterized by heterogeneous party presence and substantial geographic variation.
Recovering latent structure from count data has received considerable attention in network inference, particularly when one seeks both cross-group interactions and within-group similarity patterns in bipartite networks, which are widely used in ecology research. Such networks are often sparse and prone to imperfect detection. Existing models mainly focus on interaction recovery, while the induced similarity graphs are much less studied. Moreover, existing models for under-counted data place sparsity, if at all, on the detection model rather than on these graphs. To address these issues, we propose a nonnegative low-rank factorization framework that jointly estimates detection probabilities and promotes sparse within- and cross-group graphs through $\ell_{1/2}$ regularization. For the resulting nonconvex, nonsmooth problem, we develop an ADMM-based algorithm with adaptive penalization, and establish asymptotic feasibility and KKT stationarity of cluster points under stated assumptions. We also give sufficient conditions for exact recovery of within- and cross-group graphs. On synthetic data with up to 20% missing entries, the method recovers the graphs and detection probabilities with competitive accuracy. Across three ecological datasets, it matches the baseline held-out predictions while estimating detection probabilities and within- and cross-group graphs.
Quantifying the uncertainty of forecasting models is essential to assess and mitigate the risks associated with data-driven decisions, especially in volatile domains such as electricity markets. In this paper, we propose a computationally efficient isotonic variant of Quantile Regression Averaging (QRA), called Isotonic Quantile Regression Averaging (iQRA), for generating probabilistic forecasts from ensembles of point forecasts. Building on QRA, we introduce stochastic order constraints as a hyperparameter-free regularization mechanism that reduces computational complexity while maintaining competitive forecast accuracy. We further demonstrate that the same isotonic regularization principle can be applied to the smoothed estimator of QRA. In an extensive forecasting study of two European day-ahead electricity markets, we show that iQRA and its smoothed variant consistently rank among the top state-of-the-art postprocessing methods in terms of reliability and sharpness. It produces well-calibrated prediction intervals, with smoothed iQRA providing superior reliability even when compared against coverage-oriented conformal prediction. We further introduce a battery arbitrage evaluation, showing that the leading probabilistic methods achieve the highest profit per trade and that probabilistic risk control improves the economic value of trading decisions. Isotonic regularization offers a scalable hyperparameter-free variable selection for linear quantile regression, making iQRA attractive for practical decision-support systems in energy markets.
The growing use of AI in mathematics raises a question: can we detect AI involvement in proofs, separately from AI assistance with writing? Historical arXiv papers, recent papers disclosing substantive AI use, and manuscripts released by OpenAI provide a rich empirical basis for studying this question. However, several challenges remain: lack of matched case-control pairs; potential incompleteness of disclosure; and lack of ready-to-use features designed to capture signals of AI involvement in proofs. To address these challenges, we construct five cohorts comprising 8,281 papers by combining existing manuscripts with those we produced using generative AI. These cohorts span different levels of AI involvement and include matched pairs of papers addressing the same research problems. We then introduce ProofTrace, a framework that represents each paper as a graph of immediate proof support (GIPS) and extracts interpretable features of mathematical organization. Our study yields three discoveries. First, principal-component projections of our features reveal a qualitative gradient of AI involvement, where AI-reworded papers remain close to human papers, the two AI-generated cohorts depart in broadly shared directions, and papers disclosing substantive AI use occupy intermediate positions which shifts toward AI-generated cohorts over time. Second, we identify recurring signatures of AI-generated proofs, such as fewer externally cited results, greater reliance on intermediate conclusions, and altered graph connectivity; many of these signatures persist under controls for research field, manuscript length, or graph size. Finally, in a separate detection experiment, ProofTrace distinguishes human-written papers from those disclosing substantive AI use. Its performance remains stable under AI rewording, whereas the performance of state-of-the-art text-based detectors declines sharply.
Functional data analysis provides a framework for studying time-varying associations between covariates and high-frequency biological signals. In digital health, participants often contribute repeated functional trajectories, yet existing multilevel regression methods largely focus on the conditional mean, overlooking variability and its role in biological heterogeneity. We propose a heteroskedastic functional mixed-effects regression framework that jointly models the conditional mean and variance of repeated trajectories, with participant-specific random effects in both components. We also develop a participant-level bootstrap to quantify uncertainty in estimated functional parameters. We apply the method to postprandial glucose trajectories from the AEGIS study. Premeal glucose, carbohydrate intake, and meal type show distinct time-dependent associations with glucose variability, whereas HbA1c is more strongly associated with the conditional mean than with variability. Substantial between-participant differences in residual variability remain even after accounting for observed covariates. These findings show that modeling conditional variability alongside the mean provides insights into glucose regulation and individual heterogeneity that mean-focused analyses may miss. More broadly, the proposed framework enables joint characterization of average responses, variability, and participant-specific heterogeneity in repeated biological signals.
Predictive multiplicity -- where similarly accurate models disagree on individual predictions -- can be leveraged to optimize secondary metrics (e.g., fairness) without loss in predictive performance. However, exploiting multiplicity opens the opportunity for motivated parties (or coding agents gaming their objectives) to steer predictions toward their own ends, such as in litigation or consumer disputes with automated decision-making tools. In these adversarial multiplicity settings, we distinguish soft manipulation, where parties optimize over innocuous model choices (e.g., hyperparameter tuning, feature engineering), from hard manipulation, where parties directly perturb model parameters. We find a sufficiently flexible model can be manipulated to reverse any individual prediction with minimal change in predictive performance while passing black-box audits, making hard manipulation viable in most regulatory settings. Soft manipulation has smaller effects but can pass white-box audits requiring full access to code and data. Even aggregate estimates can be manipulated: a model's estimated effect of climate change on wildfires can be fully reversed by hard edits and soft search. We find the Reconcile algorithm typically resolves most disagreements between models, but more often in favor of the manipulator when the opposing model is chosen adversarially compared to at random. We map which manipulations can plausibly pass existing regulations and disclosure policies, and recommend mitigations such as pre-registration, proof of model training, sensitivity analyses, multi-metric evaluations, and committing to versioned public models.
Patient world models are increasingly proposed as simulators of clinical trials, and recent surveys rank their capabilities on a ladder from temporal prediction to counterfactual rollouts. Position on that ladder is currently assigned by reading papers rather than by measurement. We turn the counterfactual rung into a measured quantity. From 30,119 completed phase 2/3 trials with results posted to ClinicalTrials.gov we construct 9,996 audited within-trial contrasts from 7,207 trials, and we score a simulator on how much of its accuracy depends on knowing which intervention was tested. The instrument is an intervention-blind reference: the same model, trained on the same trials, with every intervention-identifying field withheld. Interventional skill is the error the full model removes relative to that reference. On a temporal split (878 test contrasts from 655 trials) a registry-trained gradient-boosting simulator removes a fifth of the error of a trivial baseline, but its interventional skill is -0.12 (95% CI -0.21 to -0.05): withholding the intervention makes it better, and no alternative featurisation, stratum, temporal cut or same-molecule retrieval yields an interval above zero. A frontier language model reading only the registered protocol has interventional skill 0.20 [0.08, 0.31]; smaller and open-weight models sit at the limit of detection. Perturbation tests show the large model uses the intervention as such: swapping the arms reverses the sign of its prediction in 86% of contrasts. The blind reference is itself not drug-blind (a language model recovers the withheld drug class 45% of the time from the blind prompt), so interventional skill is a conservative lower bound. A reliability layer shows that ranking by predicted error lowers it but that calibrated error control does not transfer under temporal shift. Benchmark, code, prompts and per-call model outputs are released.
AI reliability concerns whether an AI system performs its intended function dependably over a stated period and under stated operating conditions, with clear evidence. As these systems become more autonomous, this function should include more than only a correct output. Retrieval, memory, tool use, permissions, human oversight, and interactions among systems must operate consistently and safely, and, for a generative AI, so must the reasoning process that produces the output. Average benchmark accuracy only measures system capability; it does not quantify this broader reliability claim. This paper adapts established reliability engineering methods, from failure definitions and operational envelopes to FMEA, accelerated testing, field monitoring, and reliability growth, to AI systems. A four-level diagnostic framework classifies failures as component, operational-loop, agentic-conduct, or network and governance failures. Test, evaluation, verification, and validation (TEVV), sequential monitoring, and FRACAS create and refresh evidence. The SMART framework provides statistical guidance for measurement, analysis, assessment, and test planning, and the NIST's AI risk management framework provides organizational guidance for governance, evaluation, monitoring, and mitigation. Three cases are discussed to illustrate these programs. It is shown that while the established reliability engineering principles can still provide a usable foundation, new measurements and safety guardrails are urgently needed as these systems are self-evolving at a fast pace.
Acquirers of failed banks weigh acquisition value, regulatory protection, risk, buyer strength, and execution difficulty jointly, because each signal's meaning depends on the others: high non-performing loans matter less when government loss sharing absorbs the losses. The proposed Spider Network Filtering Framework encodes such dependencies as four interpretable interaction rules among five dimensions, yielding graph-inspired features for a logistic model and a Pursue/Caution/Avoid decision rule. We evaluate it on 55 acquisitions assisted by the Federal Deposit Insurance Corporation in 2008-2024 by acquirers with a parent listed in the United States. Six financial inputs come from regulatory reports published before each failure; two deal terms, which the winning bidder knows when it bids but investors learn at the announcement, come from the regulator's press releases. The outcome, a positive three-day abnormal return around the announcement, records the market's initial reception, not realized success. Under grouped, nested cross-validation, the Spider-enhanced model reaches a mean area under the receiver operating characteristic curve of 0.594, against 0.615 for logistic regression on the same inputs and 0.632 for ridge regression; permutation tests that repeat the full model selection give at most weak evidence that any of them ranks better than chance. The Spider score used directly does not rank better than chance, and an apparent link between target distress and higher returns disappears against a bank-sector benchmark. Thresholds tuned for the F1 score approve most acquisitions with negative returns and realize negative utility when each costs three times what a positively received acquisition gains.
The rapid adoption of generative AI and Large Language Models (LLMs) has spurred interest in synthetic data as a privacy-preserving alternative to sensitive real-world datasets. However, generating high-utility synthetic data often carries the risk of memorizing and regurgitating private information from the training corpus. In this work, we present a customizable empirical auditing framework designed to detect and explain such data disclosures. Our framework introduces a mechanism to distinguish between "true disclosures"-where the system directly reproduces a user's information-and "phantom disclosures''-where the system incidentally generates a user's data. By partitioning input data into training and holdout sets and applying rigorous statistical hypothesis testing, we determine if observed disclosures are consistent with strict privacy baselines, such as zero-learning or specific Differential Privacy (DP) bounds. Crucially, this approach requires no model access, no canary insertion, and no reference model training -only the synthetic output and a held-out control set. We demonstrate that this framework effectively functions as a membership inference attack, providing empirical lower bounds on privacy leakage that are tighter than prior data-based auditing methods. Our approach is model-agnostic, applies to any synthetic data generation mechanism, and requires orders of magnitude fewer computational resources than shadow-model or canary-based alternatives.
Changepoint detection identifies significant shifts in data sequences, making it important in areas like finance, genetics, and healthcare. The Optimal Partitioning algorithms efficiently detect these changes, using a penalty parameter to limit the changepoints count. Determining the optimal value for this penalty can be challenging. Traditionally, this process involved manually extracting statistical features, such as sequence length or variance to make the prediction. This study proposes a novel approach that uses recurrent networks to learn this penalty directly from raw sequences by automatically extracting features. Experiments conducted on 20 benchmark genomic datasets show that this novel method generally outperforms traditional ones in changepoint detection accuracy.
Digital Twins are evolving from passive virtual representations into closed-loop systems that continuously synchronize with physical assets and drive real-time decisions. Yet predictive modeling, machine learning (ML), uncertainty quantification (UQ), and decision-making have been studied as separate capabilities, leaving limited understanding of their integration and maintenance during online operation. This narrative review, scoped by the functional requirements of real-time decision-making rather than by Digital Twin terminology alone, examines how such decisions are generated and sustained in engineering Digital Twins. We first examine foundational decision-making architectures and representative engineering applications, followed by methods that address their limitations across the decision loop. We identify optimization-based, policy-based, and knowledge-based approaches as the major pathways from virtual representation to action. Across them, ML plays three roles in decision-making: enabling efficient surrogate modeling, transforming heterogeneous physical feedback into decision-relevant information, and accelerating or directly generating decisions. UQ supports uncertainty-aware decisions and model adaptation, while continual validation, drift detection, and adaptation help maintain reliable operation as the physical system evolves. Together, these findings underscore the need for a shift from a model-centric to a system-centric perspective on Digital Twins, where its performance depends on the interactions with sensing, state estimation, computation, decision-making, and adaptation rather than on their standalone performance. Therefore, future research should shift from isolated algorithm development toward system-level co-design, scalable decision-making, and approaches to design, and data-efficient continual adaptation and validation for AI-enabled autonomous systems.
Accurate forecasting and temporal downscaling of solar irradiance is critical for reliable renewable energy integration and grid management. Traditional methods often struggle to capture rapid irradiance variability. In this work, we develop a Transformer-based architecture for simultaneous forecasting and temporal downscaling. The model takes input data at arbitrary resolutions and generates outputs at any resolutions represented within the training data, leveraging both global and local contextual information. To improve training efficiency, a genetic algorithm-based optimization framework is implemented to identify suitable model hyperparameters, while reducing the computational cost of exhaustive grid search. The effectiveness of the proposed model is shown by analyzing real data in Dallas, Texas. The proposed model achieved root mean square error (RMSE) values of 28.785, 29.544, 30.157, 32.132~W/m\(^2\) for 15-, 30-, 60-minute, and irregularly spaced global input and producing forecast at 5-minutes resolution, respectively. Furthermore, this model produced reliable uncertainty estimates, exhibiting wider prediction intervals for high-resolution inputs during volatile solar conditions, whereas coarser-resolution inputs result in narrower intervals and significantly lower training time and computational cost. Our approach provides a scalable and efficient framework for multi-resolution solar irradiance forecasting and temporal downscaling, suitable for practical energy forecasting and grid management applications.
Groundwater inversion is commonly built on Gaussian assumptions for both network weights and output errors. The assumptions are convenient, but it is unclear which one should be relaxed when hydraulic conductivity is heavy tailed. Here, Gaussian and q-Gaussian distributions were assigned independently to variational weights and the conditional output likelihood in a $2\times2$ Bayesian neural design. Hydraulic conductivity, porosity, and dispersion were inferred jointly from sparse head and transport observations. Four q regimes ($q=1.0$, 1.2, 1.5, and 1.8) were evaluated with five independently generated data sets and matched training seeds, giving 130 held-out cases per regime and 500 posterior draws per case. At $q=1.5$, q-Gaussian weights with a Gaussian likelihood reduced log-conductivity CRPS by 2.85\% (95\% paired CI 0.82--4.88) and calibration error by 3.72 percentage points. Conductivity RMSE was unchanged, while 95\% interval width increased by 9.86\%. At $q=1.8$, assigning q-Gaussian tails to both components produced no stable accuracy gain and increased interval width by 138.46\%. The Gaussian-generated porosity and dispersion controls showed negligible accuracy changes. Moderate weight-side tails can thus improve distributional prediction, whereas an overly heavy output likelihood trades sharpness for coverage. Separating these two roles provides a clearer basis for uncertainty modeling in groundwater inversion.
We develop ML models that predict when cross-factor predictability will erode, enabling prospective risk management. A decay prediction model achieves C-index $= 0.93$ on held-out factor pairs, providing early warning of signal erosion---the key predictor is initial signal strength: stronger signals decay faster (``regression to the mean''). An online regime detector enables real-time classification with 6.6-day average detection delay. Prior work explains why factors decay (arbitrage, publication effects); we predict when decay will occur. Limitation: The primary HML$\to$SMB signal does not replicate in post-break OOS (2013--2024); this null result is consistent with genuine decay but limits confirmatory claims. Motivation: Among 30 directed Fama-French factor pairs (1990--2024), predictability targeting the Size factor (SMB) decays fastest. Of 7 pairs showing exponential decay ($R^2 > 0.3$), 4 target SMB (Mkt-RF$\to$SMB, CMA$\to$SMB, HML$\to$SMB, RMW$\to$SMB; half-lives 2.4--4.1 years). This SMB-concentration pattern motivates the predictive models. Methodology: Using a regime-conditional Granger framework with Student-$t$ HMMs, we document structural breaks clustering around June 1998 ($p < 10^{-10}$). A pre-break OOS test (HMM trained 1990--1995, tested 1996--2007) confirms signals existed: HML$\to$SMB shows $p = 0.013$ (Elevated) and $p < 0.001$ (Crisis). The primary HML$\to$SMB signal does not replicate in post-break OOS (2013--2024), consistent with genuine decay rather than overfitting---after ${\sim}6$ half-lives, the expected signal is $<$1% of its 1990s peak. International analysis finds 2/4 non-US markets with Bonferroni-surviving OOS effects; correction for full specification search was not applied, so results remain exploratory.
Heart failure is a serious medical condition associated with risk of acute deterioration, recurrent hospitalizations and high mortality making accurate mortality prediction potentially valuable for patient care and healthcare planning. Numerous prognostic models have been developed using conventional statistics (CS), machine learning (ML) and deep learning (DL), but variation in study populations, heart failure definitions, prediction horizons and development practices may limit interpretation of applicability. We conducted a systematic review of mortality prediction models published between 2009 to the start of 2026 searching three databases (PubMed, IEEE and Scopus) for studies predicting all-cause mortality over a 1-60 months prediction horizon among patients with heart failure. Data extracted were cohort characteristics, heart failure definitions, model development, cohort size, validation practices, mortality, computational model design and reported performance. The risk of bias and applicability were assessed using the Prediction Model Risk of Bias Assessment Tool (PROBAST). Of 1516 publications identified, 56 met the inclusion criteria. Publication numbers increased over the observation period, alongside increasing use of ML/DL models and decreasing use of CS approaches. Most development cohorts (64%) were classified as Unknown/Undefined heart failure, reflecting inconsistent reporting and terminology that did not correspond with established heart failure guidelines. External validation was reported in 23% of studies. Overall, research in modeling heart failure mortality has grown alongside increasing adoption of ML/DL approaches. Greater standardization of study design and reporting is needed for meaningful comparison, reproducibility and evaluation of models for clinical application.
Probabilistic forecasts of day-ahead electricity prices are increasingly used to manage price risk, yet competing models are usually ranked on aggregate scores that average over the price regimes in which uncertainty matters most. This study evaluates probabilistic forecasts of hourly EPEX SPOT GB day-ahead prices over a full held-out calendar year, applying a common pre-auction information boundary and rolling-origin design to linear quantile regression, a quantile regression forest (QRF), a LEAR-QRA benchmark and an encoder-decoder quantile long short-term memory (LSTM) network. Two routes to more reliable intervals are then compared: conformal recalibration and Quantile Regression Averaging (QRA). Aggregate scores separate the LSTM and QRF only weakly, with a non-significant 4.4% difference in continuous ranked probability score (CRPS), but their conditional behaviour differs sharply. Above 200 GBP/MWh the LSTM covered 0.12 of outcomes and QRF 0.71, consistent with the forest retaining realised spikes in its leaf distributions while the network learned a smooth upper tail. Conformal recalibration corrected marginal coverage but did not improve the interval score or materially repair spike coverage. QRA combining the LSTM, QRF and LEAR-QRA forecasts reduced CRPS to 5.14 GBP/MWh and raised coverage above 200 GBP/MWh to 0.65 at unchanged interval width. Recalibration and combination therefore address different failures and are not substitutes.
Bitcoin perpetual futures trade continuously with shallow liquidity and high price impact, making them prone to millisecond-scale flash crashes. Agent-based limit order book simulators are a natural tool for studying such events, but their behavioral parameters are usually hand-crafted or require full order book histories that are rarely available at scale. We propose a four-stage pipeline that constructs a reproducible 100 ms BTCUSDT flash-crash event panel from 66 detected events, elicits behavioral priors for four agent archetypes using an offline large language model conditioned on empirical microstructure anchors, instantiates a heterogeneous limit order book simulator with the validated priors, and applies causal discovery plus counterfactual analysis to the resulting synthetic panel. Across 500 simulation runs, LLM-elicited priors produce a crash rate of 0.176 versus 0.008 under uninformative uniform priors and generate heav- ier return tails. In the frozen counterfactual analysis, reducing leverage amplification by one within-sample standard deviation lowers the predicted crash rate from 0.176 to 0.136, whereas reducing directional pressure yields only a marginal change. These find- ings suggest that empirically anchored LLM elicitation can improve simulator fidelity and help identify plausible crash-amplification mechanisms in a controlled synthetic environment