AI for Science

It is known that Green's functions can be expressed as continued fractions; the content at the $n$-th level of the fraction is encoded in a coefficient $b_n$, which can be recursively obtained using the Lanczos algorithm. We present a theory concerning errors in approximating Green's functions using continued fractions when only the first $N$ coefficients are known exactly. Our focus lies on the stitching approximation (also known as the recursion method), wherein truncated continued fractions are completed with a sequence of coefficients for which exact solutions are available. We assume a now standard conjecture about the growth of the Lanczos coefficients in chaotic many-body systems, and that the stitching approximation converges to the correct answer. Given these assumptions, we show that the rate of convergence of the stitching approximation to a Green's function depends strongly on the decay of staggered subleading terms in the Lanczos cofficients. Typically, the decay of the error term ranges from $1/\mathrm{poly}(N)$ in the best case to $1/\mathrm{poly}(\log N)$ in the worst case, depending on the differentiability of the spectral function at the origin. We present different variants of this error estimate for different asymptotic behaviours of the $b_n$, and we also conjecture a relationship between the asymptotic behavior of the $b_n$'s and the smoothness of the Green's function. Lastly, with the above assumptions, we prove a formula linking the spectral function's value at the origin to a product of continued fraction coefficients, which we then apply to estimate the diffusion constant in the mixed field Ising model.

We construct a weighted Riemannian manifold $(\mathbb R^2,g,μ)$ satisfying $\mathrm{CD}(1/2,\infty)$, the curvature-dimension condition, with the following property: if $γ$ denotes a centered Gaussian measure on $\mathbb R^2$, then there is no Lipschitz map $T:(\mathbb R^2,\|\cdot\|) \to (\mathbb R^2,g)$ satisfying $T_\#γ=μ$. Building on this, we prove a Weyl-type asymptotic law for the eigenvalues of the weighted Laplacian $-Δ_{g,μ}$ and show that they are asymptotically negligible when compared to the eigenvalues of $-Δ_γ$. These results give strong counterexamples to two questions of E. Milman and complement the recent counterexample of Aryan.

A data-driven inverse optimization problem (DDIOP) is the problem of estimating the objective-function parameters (weights) that explain observed optimal-solution data, and it arises in many applications, including mixed integer linear programming (MILP). In inverse optimization for MILPs, the prediction error of the features is discontinuous with respect to the weights, so applying gradient-based optimization directly is difficult. In this paper we focus on the suboptimality loss. This loss attains its minimum value, zero, if and only if the weights are exactly consistent with the observed data. We reveal a geometric structure of this loss -- it is convex and piecewise linear, and moreover the set of weights that are exactly consistent with the observed data has a positive ``thickness'' rather than being a single point or a thin boundary -- and use it to show the following. First, a broad class of gradient-based optimization methods, including projected subgradient descent, reaches exact consistency with the observed data in finitely many iterations (an exact solution is obtained in finite time). Second, for projected subgradient descent we give an explicit upper bound on the number of iterations needed to reach exact consistency. Third, when the forward problem is an integer linear program (ILP), we give this upper bound as a fully explicit iteration count determined solely by the number of samples, the dimension of the features, and the structure of the constraint coefficient matrix. Through numerical experiments, we confirm this finite-step attainment behavior.

Trajectory mutual information is frequently used to quantify information transfer in biochemical systems. Tractable solutions of the trajectory mutual information can be obtained via the widely used Linear-Noise Approximation (LNA) using Gaussian channel theory. This approach is expected to be accurate for sufficiently large systems. However, recent observations show that there are cases, where the mutual information obtained this way differs qualitatively from results derived using an exact Markov jump process formalism, and that the differences remain even in the large copy number regime. In this letter, we show that these differences can be explained by introducing the notion of reaction- versus state-based descriptions of trajectories. In chemical systems, the information is encoded in the sequence of reaction events, and the reaction-based trajectories of Markov jump processes capture this information. We show that within the Gaussian formalism, trajectories can be defined either based on individual reaction channels, or on a state-based level, where different reaction channels are summarised into a single noise term. While both definitions agree in terms of copy number fluctuations, state-based trajectories contain in general less information than reaction-based trajectories. The commonly used Gaussian mutual information via the Linear-Noise Approximation is consistent with a state-based trajectory notion, which causes a systematic loss of information independent of system size. We show that an alternative, reaction-based variant of the Gaussian mutual information prevents this loss of information. We illustrate the consequences of different trajectory descriptions for two common cellular reaction motifs and discuss their connection with Berg-Purcell and Maximum-Likelihood sensing.

We provide a superselection theory of symmetry defects in 2+1D symmetry enriched topological (SET) order in the infinite volume setting. For a finite symmetry group $G$ with a unitary on-site action, our formalism produces a $G$-crossed braided tensor category $G\mathsf{Sec}$. This superselection theory is a direct generalization of the usual superselection theory of anyons, and thus is consistent with this standard analysis in the trivially graded component $G\mathsf{Sec}_1$. This framework also gives us a completely rigorous understanding of symmetry fractionalization. To demonstrate the utility of our formalism, we compute $G\mathsf{Sec}$ explicitly in both short-range and long-range entangled spin systems with symmetry and recover the relevant skeletal data.

The concept of geodesic-like curves was introduced by Chen in 2010 as a method for estimating shortest paths (geodesics) on parametric surfaces, with its convergence established theoretically. However, an efficient numerical computational framework has not yet been developed. In this paper, we propose an elegant and efficient approach for computing geodesic-like curves by leveraging deep learning and Physics-Informed Neural Networks (PINNs). Under the proposed framework, not only can single parametric surfaces be handled efficiently, but a broad class of complex parametric surfaces including multi-surface systems with $C^0$ or higher continuity and surfaces of revolution can also be robustly addressed.

We consider an ideal Fermi gas in a container subject to a uniform gravitational field at absolute zero temperature. Under a semiclassical approximation, we examine the density profile of the particles and derive an expression for the chemical potential. A critical value of the chemical potential separates the weak- and strong-gravity regimes, and the kinetic and potential energies of the Fermi gas are determined in both regimes.

Forecasting epidemic trajectories is important for public health decision-making, but no single model is consistently reliable across epidemic phases and forecasting settings. We evaluate Multi-Armed Bandit (MAB)-inspired adaptive weighting strategies for combining epidemic forecasting models when component-model performance changes over time. Using U.S. COVID-19 incidence data from three epidemic waves, we compare UCB, EXP3, and epsilon-greedy weighting rules under fixed short-window and growing calibration windows, with both deterministic and stochastic ensemble variants. The model pool includes SIR, SEIR, GLM, Gompertz, Richards, ARIMA, random walk with drift, simple exponential smoothing, Holt's linear trend method, and exponential growth. Adaptive ensembles are compared with individual models and with naive, unweighted, and inverse-WIS weighted ensemble benchmarks. Forecast performance is assessed using RMSE, weighted interval score (WIS), 95% prediction-interval coverage, and mean 95% prediction-interval width. Across waves, calibration windows, and forecast horizons, EXP3Stoch, EXP3Det, and EPSStoch achieved the lowest mean forecast WIS. The main gains were in probabilistic forecast quality, especially WIS and interval coverage, rather than uniformly lower point forecast error. Simple benchmarks, including the unweighted and inverse-WIS ensembles, remained competitive in several settings. These results suggest that MAB-inspired adaptive weighting is a useful complementary tool for epidemic forecasting, especially when model skill is time-varying and forecast uncertainty is substantial.

As large language models (LLMs) become embedded in quantum simulation workflows (IDE copilots, notebook assistants, agentic pipelines), evaluation must move beyond functional correctness to anticipate and catch structured failures before they propagate through expensive pipelines. We present a layered evaluation framework for materials-informed Variational Quantum Eigensolver (VQE) circuit generation: (i) a gatekeeper screening rubric across seven physical and framework criteria; (ii) a circuit fidelity analysis comparing model outputs against analytical and reference-implementation values for H2/STO-3G/Jordan-Wigner/UCCSD, with ansatz classification and gate-composition breakdown; and (iii) design entropy, a run-to-run behavioral consistency metric. We surface a taxonomy of five distinct LLM failure modes (geometry hallucination, nonexistent API usage, runtime integration failures, constraint violations, and plausible-but-unverifiable output), each with distinct detectability profiles and structural to the task rather than to any one model. A forensic audit of the evaluation platform's own source code further establishes that two apparent model failures originated in the harness through silent fallback-template substitution, demonstrating that evaluation infrastructure belongs inside the same trust boundary as the models it tests. Applied across multiple foundation models on a Materials Project integrated pipeline, the framework shows that gatekeeper-style validation is necessary, not optional, for reliable deployment.

In this paper, we study the information-theoretic characterization of simultaneous signalling and control over channels modeled by partially observable Markov decision processes (POMDPs). The problem is formulated as an optimization over randomized control strategies that maximize the directed information from actions to observations, subject to an average-cost constraint. We derive a novel dynamic programming framework in which the state is defined on the space of conditional probability distributions, leading to a high-level ``meta'' dynamic program. Specifically, we show that two coupled information states, namely, the posterior distribution of the system state and a distribution over such posteriors, satisfy Markov recursions and provide sufficient statistics for optimal control. This structure enables the decomposition of optimal strategies into separated randomized policies that depend only on these information states. Our results establish necessary and sufficient conditions for optimality and unify classical stochastic control and information-theoretic formulations. In particular, we show that in the absence of signalling, the proposed framework reduces to the standard dynamic programming equations for POMDPs. The developed approach provides a principled foundation for analyzing and designing control systems with intrinsic information constraints.

We investigate the relationship between the analytical properties of functions of bounded variation and the statistical behavior of hyperuniform point processes. We establish several characterization formulas for the jump part of the gradient of a bounded variation function, extending and unifying previous results by Beretti--Gennaioli and Dávila. In particular, we provide new expressions for the $L^2$-jump of the gradient using both difference quotients and Fourier transform methods. Furthermore, we connect these analytic structures to the theory of hyperuniform point processes. By analyzing the variance of linear statistics associated with bounded variation functions, we provide asymptotic estimates that depend on the specific classification of the hyperuniformity of the point process. The results show how the regularity and jump discontinuities of a function dictate the growth rate of fluctuations in point processes. Finally, we introduce an averaged quadratic BMO-type oscillation functional over translated and rotated cube partitions, similar to the one recently studied by Ambrosio et al., and prove, using results from point process, that it converges to an explicit dimensional constant times the $L^2-$jump, giving in particular a further new characterization of the perimeter of a set.

Hypercube graphs are fundamental model spaces of positive curvature in discrete comparison geometry. We establish the following spectral rigidity theorem. Let $G$ be a finite, connected, simple, unweighted graph with Bakry--Émery curvature bounded below by $K>0$. Denote by $Δ$ the maximum degree of $G$, and let $0=λ_0<λ_1\leq\cdots$ be the eigenvalues of the non-normalized Laplacian. Then $$ λ_{Δ-1}=K \quad\Longrightarrow\quad G\cong H_Δ, $$ where $H_Δ$ is the $Δ$-dimensional hypercube graph. Thus, in the unweighted setting, the multiplicity condition $λ_Δ=K$ appearing in the hypercube rigidity theorem of Liu, Münch, and Peyerimhoff can be weakened to $λ_{Δ-1}=K$. This improvement is optimal. The restriction to unweighted graphs is essential: the strengthened rigidity statement fails in the weighted setting. Our argument is built upon an interplay between the global spectral embedding induced by the first eigenspace and a local analysis of curvature matrices.

Gene regulatory networks are routinely translated from Boolean update rules into large continuous ODE systems integrated numerically for attractor identification, sensitivity analysis, and control design. The reliability of that integration depends critically on the sigmoidal kernel representing regulation. This simulation study shows that the Hill function -- the near-universal choice -- is a generically unreliable kernel, while the logistic function is a robust replacement. Two failure modes are demonstrated. First, because the Hill function vanishes at zero input, bistable circuits acquire an absorbing off-state: with experimentally grounded \textit{E. coli} galactose-operon autoregulation parameters, a Hill model stays trapped below the unstable separatrix, whereas the logistic model -- whose basal rate is strictly positive by construction -- escapes in about $44$~minutes through basal production alone, matching an analytical estimate of ${\approx}58$~min. A saddle-node analysis characterises the bistable window via an explicit transcendental equation and identifies the threshold $λθ=2$ separating monostable from bistable regimes. Second, when the Hill exponent is non-integer -- as in dose-response fits -- the power law $x^n=e^{n\ln x}$ turns complex-valued whenever a solver overshoots into negative concentrations. On an $80$-gene Boolean-derived benchmark with $n\approx3.509$, the Hill solver is silently contaminated by complex values from $t\approx52.64$, yielding smooth but spurious trajectories, whereas the logistic formulation completes $t\in[0,200]$ without a single warning. Because the logistic vector field is globally Lipschitz with explicit constant, we further prove an a priori global-error bound of classical order -- a guarantee structurally unavailable to the Hill formulation.

In a recent paper, Francis, Illickan, Jose and Rajendraprasad showed that every $n$-vertex plane graph $G$ has (under some natural restrictions) a vertex-partition into two sets $V_1$ and $V_2$ such that each $V_i$ is \emph{dominating} (every vertex of $G$ contains a vertex of $V_i$ in its closed neighbourhood) and \emph{face-hitting} (every face of $G$ is incident to a vertex of $V_i$). Their proof works by considering a supergraph $G'$ of $G$ that has certain properties, and among all such graphs, taking one that has the fewest edges. As such, their proof is not algorithmic. Their proof also relies on the 4-color theorem, for which a quadratic-time algorithm exists, but it would not be easy to implement. In this paper, we give a new proof that every $n$-vertex plane graph $G$ has (under the same restrictions) a vertex-partition into two dominating face-hitting sets. Our proof is constructive, and requires nothing more complicated than splitting a graph into 2-connected components, finding an ear decomposition, and computing a perfect matching in a 3-regular plane graph. For all these problems, linear-time algorithms are known and so we can find the vertex-partition in linear time.

In this work, we study several properties of the normal Lebesgue trace of vector fields introduced by the second and third author in [22] in the context of the energy conservation for the Euler equations in Onsager-critical classes. Among other things, we prove that the normal Lebesgue trace satisfies the Gauss-Green identity and, by providing explicit counterexamples, that it is a notion sitting strictly between the distributional one for measure-divergence vector fields and the strong one for $BV$ functions. These results are then applied to the study of the uniqueness of weak solutions for continuity equations on bounded domains, allowing to remove the assumption in [19] of global $BV$ regularity up to the boundary, at least around the portion of the boundary where the characteristics exit the domain or are tangent. The proof relies on an explicit renormalization formula completely characterized by the boundary datum and the positive part of the normal Lebesgue trace. In the case when the characteristics enter the domain, a counterexample shows that achieving the normal trace in the Lebesgue sense is not enough to prevent non-uniqueness, and thus a $BV$ assumption seems to be necessary to get uniqueness.

Optical satellite uplinks rely on high-power optical amplifiers (HPOAs) to overcome free-space attenuation and enable long-distance transmission. However, at high power levels, fiber Kerr nonlinearity becomes significant and degrades system performance. In this work, we develop a realistic model for optical uplinks that accounts for nonlinear effects and analyze their impact, highlighting key differences from conventional longhaul fiber systems. We then introduce low-complexity digital signal processing techniques for nonlinearity compensation, based on constellation shaping via a look-up table (LUT) and a simple nonlinear phase rotation applied at the transmitter and/or receiver. The LUT also enables adaptive rate tuning according to channel conditions, enhancing robustness against link variations. Simulation results show that the proposed techniques increase the maximum acceptable link loss by up to 6 dB with negligible complexity. Finally, we show that, at the system level, propagation in the HPOA can be modeled as a simple nonlinear phase rotation, equivalent to propagation in a zero-dispersion noiseless fiber link, and fully characterized by a single parameter - the characteristic nonlinear power.

In a recent work, Sharma and Panda~\cite{sharma} showed that every bipartite graph with a perfect matching has property (P). In this paper, we investigate the converse direction, i.e., when property (P) forces the existence of a perfect matching in bipartite graphs. We show that such graphs are balanced and establish that property (P) is equivalent to the existence of a perfect matching for several families of bipartite graphs.

We introduce a new model of random tree that grows like a random recursive tree, except at some exceptional "doubling events" when the tree is replaced by two copies of itself attached to a new root. We prove asymptotic results for the size of this tree at large times, its degree distribution, and its height profile. We also prove a lower bound for its height. Because of the doubling events that affect the tree globally, the proofs are all much more intricate than in the case of the random recursive tree in which the growing operation is always local.

Anomalies in functional data arise from rare or distinct processes that deviate from the dominant data-generating mechanism. Detecting such departures is essential in applications where they may correspond to errors, structural changes, or other behavior of interest. This work introduces a Bayesian nonparametric approach for anomaly detection in multivariate functional data. We model functional data as an infinite mixture of multi-output Gaussian processes, with a finite and automatically determined number of mixture components obtained through slice sampling. Mean functions are represented using a wavelet basis and regularized through Besov priors to obtain a smooth and sparse representation of the data. Cross-functional dependence is captured using the intrinsic coregionalization model and we solve covariance kernel selection by introducing a Carlin-Chib product space step in the Markov Chain Monte Carlo algorithm. Within this model, anomalous observations are assigned to small mixture components without requiring prior specification of the number or nature of anomalies. We consider a semi-supervised setting, in which labels are available for 15% of the normal observations and a large class imbalance is present. The utility of our model is demonstrated on both univariate and multivariate functional data.

Effective collaborative data entry and transparency are foundational for building robust databases and high-quality data synthesis. Yet researchers often face inconsistent data entries, inadvertently introducing errors, misreadings, and inconsistencies that compromise data integrity. Despite the growing use of open-source tools, many still rely on inefficient formats or costly commercial platforms, while fewer adopt complex open-source solutions. These inefficiencies slow workflows and hinder researchers' ability to build foundational databases for synthesis research, including meta-analyses. To address this, we developed CollaboratoR, a customizable R package that automates data validation and aggregation, ensuring consistency and transparency and adhering to FAIR data principles, while optionally using Google Sheets for collaborative data entry and GitHub for version control. CollaboratoR fills the gap between ad-hoc spreadsheets and complex systems for data extraction in meta-analyses. Data are entered into shared Google Sheets, validated, and pushed to GitHub for version control, then re-validated after verification to ensure accuracy before finalizing. Tested in two case studies, plant competition and avian interaction databases, CollaboratoR proved effective at managing large collaborative datasets. In both, automated validation flagged common entry and formatting issues early, improving traceability and reducing time spent on post-hoc cleaning. This framework applies across disciplines where data synthesis informs data-driven decision-making, such as social science, ecology, and medical and pharmaceutical research. Ultimately, CollaboratoR offers guidance for efficient, transparent, and reproducible collaborative data management, enhancing research synthesis across fields and industries alike.

Nitrous oxide (N2O) emissions from water resource recovery facilities (WRRFs) fluctuate over time and can arise from multiple microbial pathways, making source attribution and full-scale prediction difficult. The difficulty is compounded by the high dimensionality of activated sludge microbiomes, whose complex and dynamic community structure can obscure relationships with N2O emission patterns. This study evaluated whether interpretable, low-dimensional representations of activated sludge microbiomes can be correlated with N2O emission states. Temporal 16S rRNA gene amplicon profiles and N2O emission metrics were collected from two full-scale WRRFs in Switzerland. Genus-level relative-abundance profiles were summarized using archetypal analysis (AA), which represents each sample as a convex combination of a small number of interpretable community profiles. In both WRRFs, three archetypes captured most explainable variation in community composition (63%--73%) and defined a simplex state space in which samples clustered near vertices and edges, indicating that community compositions were organized around distinct archetypal states and their mixtures. Without using emission labels while training, the archetypal state space aligned strongly with binary N2O emission states: high-emission observations in both plants concentrated around a specific archetype, and temporal trajectories showed consistent high weights of this archetype during high-emission periods. Functional summaries suggested site-specific but pathway-relevant interpretations of the high-N2O archetype. Temperature further structured the archetypal state space, indicating seasonal forcing of microbiome configurations associated with elevated N2O. Overall, AA provides an interpretable framework to track microbiome regime shifts and may support operational tracking of high-N2O emission states in full-scale WRRFs.

The recent growth of EV adoption poses challenges for power systems, including increased peak demand and potential grid instability. Smart control of EV charging -- e.g., based on reinforcement learning (RL) -- can alleviate these issues by learning temporal and contextual patterns from historical data. Yet, in real-world scenarios, key features, such as departure time, often are unavailable. This, in turn, makes it harder for an RL agent to learn and execute an effective charging policy. To mitigate this uncertainty, a trained forecaster can approximate the unknown features from available data. However, since these forecasting models are typically trained for accuracy (rather than their impact on a downstream agent's decision quality), their errors may propagate and hinder the overall performance of a controller that is using the forecasts. To avoid this, we propose a decision-focused RL (DF-RL) framework in which the forecaster is trained end-to-end, i.e., with feedback from the charging policy actions taken by the RL agent. Such joint training of both the forecaster and controller ultimately results in higher-quality actions: our proposed DF-RL method yields superior charging decisions compared to other baselines, achieving up to a 14% improvement in total reward and a 55% reduction of unsupplied energy (i.e., charging that failed to happen because the EV already left), relative to the RL method without departure time forecasting.

Electricity markets are inherently complex systems characterised by strong nonlinearities, high-dimensional interactions, and increasing interdependence across regions. While deep neural networks (DNNs) have demonstrated strong predictive capabilities for electricity prices, their lack of interpretability limits their usefulness for understanding the underlying drivers of price formation. This paper addresses this gap by combining DNN models with explainable artificial intelligence (XAI) techniques to analyse the determinants of electricity prices across 39 European bidding zones. We employ SHAP (SHapley Additive exPlanations) to quantify feature contributions and apply and extend SSHAP, an aggregation framework to improve interpretability in high-dimensional settings. The analysis identifies that renewable energy sources, particularly solar, play a disproportionately important role in price formation despite their lower share in total power generation. Gas prices remain a dominant and consistent driver across electricity markets, while interconnections significantly shape price dynamics, highlighting the strong interdependence of European electricity systems. In addition, a synthetic EU-wide electricity market is constructed to explore the counterfactual scenario of a fully integrated market with a single price.

Causal discovery methods commonly assume that all data is independently and identically distributed (i.i.d.) and that there are no unmeasured variables affecting the system. In practice, these assumptions are often violated, leading to inaccurate inference. In this paper, we study how to identify hidden confounding and selection biases from causal mechanism shifts. In particular, we show that structural biases lead to dependent mechanism shifts. That is, by considering for which variables the mechanisms change given data from different environments, we can tell which variables are unbiased, which are subject to hidden confounding, and which are undergoing selection bias. We formalize this into an empirically testable criterion based on mutual information, and show under which conditions it identifies structural biases. To tell which nodes are subject to what kind of bias, we introduce the StruBI algorithm. Experiments on synthetic and real-world data show that StruBI works well in practice, accurately recovering affected variable sets and types of biases, outperforming the state-of-the-art by a wide margin.

Glucose forecasting algorithms are an important aspect of glycemic control management in type 1 diabetes. So far, the research community has developed numerous algorithms and models for forecasting. However, it is well-recognized that the lack of standardized model performance evaluation benchmarks makes fair comparison difficult and hinders further innovation, and thus benchmark standardization is in urgent need. Furthermore, many published glucose forecasting algorithms are limited to CGM data alone, ignoring other multimodal signals such as insulin dosing and carbohydrate intake. Here, we introduce MetaboNet-Bench, a benchmark for multimodal glucose forecasting for patients with type 1 diabetes that provides an extensible open-source evaluation framework for comparison of glucose forecasting algorithms that leverage glucose, insulin, and carbohydrate data. We then demonstrate its utility by benchmarking several recently published glucose forecasting models and a custom multimodal time-series model, representing different model architectures. The results show that the benefit of adding data modalities is conditioned on the complexity of the model and that incorporating more clinical metrics helps identify meaningful gaps to fill for future research.

The development of medical AI is constrained by limited access to high-quality clinical data due to institutional silos and strict privacy regulations such as HIPAA and GDPR. Synthetic data generation offers a potential solution, but existing methods lack principled mechanisms to explicitly manage the privacy-utility trade-off, often degrading clinically meaningful patterns or risking patient re-identification. We present PSyGenTAB, a privacy-preserving generative framework that formulates synthetic healthcare data generation as a constrained optimization problem solved using the Augmented Lagrangian Method. By embedding configurable privacy constraints directly into model training, PSyGenTAB enforces minimum privacy thresholds while maximizing clinical data utility. Across multiple clinically motivated benchmarks, PSyGenTAB preserves inter-feature clinical relationships and minority-class diagnostic patterns essential for reliable health AI. Downstream evaluation using Train-on-Synthetic, Test-on-Real and Train-on-Real, Test-on-Synthetic protocols shows that models trained on synthetic data achieve performance comparable to those trained on real patient records. Privacy auditing further demonstrates reduced exact record reproduction and strong resilience to membership inference attacks. These results establish PSyGenTAB as a principled framework for balancing privacy protection and clinical utility in synthetic healthcare data, supporting secure cross-institutional AI development.

Neurosymbolic semantics is fragmented: classical, fuzzy, probabilistic and neural systems each define truth by their own inductive rules. NeSyCat, extending ULLER, subsumes them under a single inductive definition of truth, parametric in a strong monad and an aggregation structure on truth-values. NeSyCat has so far lacked an account of predicates and functions learned by neural networks. We provide NeSyCat Torch as the missing link and interpret computational symbols via neural networks, implementing the framework in probabilistic programming and tensor-based backends. We use the distribution monad for reference semantics and metric evaluation, and complement it by a monad for numerically stable, differentiable training: the lazy log-tensor monad over the log-semiring. For efficient training in batches, we furthermore employ a batch monad. The axioms are the source code: written once in monad-based do-notation, monadic bind performs marginalisation, lazily pruning unneeded branches. On MNIST addition, our HaskTorch, JAX, and PyTorch implementations outperform LTN and DeepProbLog in speed and accuracy, while achieving nearly the accuracy of DeepStochLog. However, unlike DeepStochLog, we stay in a uniform framework that applies to many first-order NeSy approaches. Namely, the construction is parametric in the monad; instantiating it with, e.g., the Giry monad extends the approach to continuous probability (working out a neural representation here is left for future work).

This paper studies theory-guided advanced regulatory control (ARC) synthesis for cooling-limited exothermic semi-batch reactors, whose productivity and thermal safety are governed by changing active constraints. Industrial ARC uses feedback loops, cascades, selectors, feedforward/override logic, and valve-position elements, but signal selection, pairing, interconnection, and tuning remain heuristic. Nonlinear model predictive control (NMPC) gives a systematic constrained-operation workflow, but requires a maintained nonlinear model, state estimator, and online optimizer. We combine finite-horizon minimum-time optimality with local safety analysis to develop a systematic analysis-to-architecture ARC synthesis workflow for cooling-limited semi-batch reactors. Under stated assumptions, the workflow translates boundary-seeking optimality into a cooling-demand valve-position-control (VPC) architecture and translates local safety requirements into near-boundary tuning rules. On a reduced benchmark and an industrial-scale polymerization, ARC is nominally competitive with an implemented nominal-model output-feedback nonlinear model predictive control (OF-NMPC) benchmark using extended Kalman filter (EKF) state estimation. In the studied adverse parameter mismatch and unmodeled fault scenarios, ARC keeps temperature-limit violation at 0%, whereas OF-NMPC either violates the limit or fails to complete the batch.

We investigate the effects of environmental noise on cooperation in a spatial evolutionary game model with variable population size. Building on a one-dimensional lattice model in which vacancies promote cooperation through spatial selection, we add random noise to the environmental quality parameter and consider two distinct types: annealed noise, where the environmental quality fluctu ates independently at each site and each time step, and quenched noise, where each site is assigned a permanently fixed random value. For annealed noise, we develop a mean-field theory by replacing the noise-dependent death probabilities with their distribution averages, and find that increasing the noise intensity shifts both the cooperator-defector phase boundary and the absorbing boundary upward in the parameter space, simultaneously expanding the cooperative regime and the extinc tion region. These predictions are confirmed by numerical simulations. In contrast, quenched noise leaves the phase boundary nearly unchanged across all noise levels, exerting only a weak effect on cooperator frequency. Together, these results demonstrate that temporal fluctuations, rather than static spatial heterogeneity, are the primary driver of noise-induced shifts in the cooperative phase structure.

Ancient human beings started "external entropy production" in a late stage of evolution, in addition to the internal entropy production by which energy was dissipated within the body of life, as previously described consistently with the birth of life by maximum entropy production principle. In this paper, the mechanism for development of external entropy production, which is strongly related with use of tools and controlling fire, is theoretically investigated. Archaeological data show that the brain size of ancient human beings started rapid increase around 2.5 million years ago when the usage of tools and control of fire started. It may be natural to assume that the rapid growth of brain size is related to the growth of awareness which helped cooperation with the other human beings for control of fire. Coupled equations for the growth rate of brain including awareness and for growth rate of size of the interacting human beings are analyzed. The external entropy production per one human being which is directly related to the group size of cooperating human beings is estimated to increase as about 20 million years in the beginning from the critical time. This evolution created coexistence of internal entropy production of traditional multi-cellular life and new external entropy production of multi-body life. A psychological problem due to the coexistence of two kinds of entropy production mechanism in human being and concept of technologies based on the present thermodynamic evolution theory are discussed. It is suggested that the evolutionary understanding of the origin of global warming based on the external entropy production may be important to create an useful countermeasure.