Papers

Large language models can describe mechanisms, yet scalable post-training still depends on costly, manually curated biological reasoning traces. Here we show that cellular perturbation atlases can instead become reinforcement-learning environments, where measured gene responses provide computable rewards for biological reasoning. We introduce PertMind, which combines trusted-trajectory supervised initialization with gene-, pathway-, and format-level reinforcement signals. Although trained only on forward perturbation-response prediction, PertMind improves response inference in unseen cellular contexts while retaining general language capabilities. It also transfers, without task-specific post-training, to reverse perturbation identification, double-perturbation reasoning, phenotypic-screen prioritization, and biological-process interpretation. PertMind further generates biological profiles that support competitive gene, cell, and donor representations across multiscale downstream tasks. These results support the hypothesis that reinforcement on experimental endpoints can concentrate reusable biological strategies already accessible to pretrained models. More broadly, perturbation-derived reinforcement learning offers a scalable route for transforming expanding experimental atlases into training environments for general-purpose biological reasoning.

Longitudinal symptom networks encode directed prediction across measurement occasions, but outgoing connectivity does not by itself identify which symptom should be modified, how strongly it should be changed, or how a perturbation would propagate to later symptoms. We introduce tSymPerturb, a temporal extension of SymPerturb for cross-lagged panel networks (CLPNs). The framework separates source-state operators (temporal virtual knockout and knockdown), transition operators (directed edge and source-node communication blocking), and strategy procedures (dosage perturbation, combination analysis and sequence optimisation). For a two-wave linear CLPN, the central propagation identity is $\Delta \mu_2 = B(\mu_1 - \mu_1^*)$, which makes the source time, outcome time and transition operator explicit. The formulation also yields three falsification constraints: dose response is exactly linear under a fixed linear transition model and linear dose map; independent source-state perturbations are additive at the mean level; and genuine treatment order is not identified from a single two-wave transition. In a known 22-node, four-module generating system, analytical temporal-knockout responses agreed with 250,000-draw Monte Carlo estimates within 0.0057 standard deviations. Across 200 independently generated datasets, median Spearman correlation with the population tVPPS ranking increased from 0.76 at n=250 to 0.88 at n=500 and 0.93 at n=1,000; median top-five recovery was 0.60, 0.80 and 0.80, respectively. Multi-wave simulations showed that target profiles can change across propagation horizons despite high overall rank concordance. tSymPerturb therefore converts longitudinal network structure into auditable, time-indexed intervention hypotheses while retaining the distinction between prediction and causal treatment effects.

What happens when you teach an LLM-based agent the scientific method? Motivation: Scientific discovery emerges from cycles of hypothesis, implementation, empirical testing, and feedback. Can this process be automated? We approach automated algorithm design through the lens of the scientific method, where an LLM-based agent goes through each step of the process in an ordered, iterative fashion. Results: We present The Little Scientist, a framework in which a "Scientist agent" works inside an evaluation environment that benchmarks its code and returns structured per-instance diagnostics. When the Scientist plateaus at a local optimum, a "Kuhn agent" injects a paradigm-shifting conjecture paired with a cross-disciplinary inspiration, forcing exploration of a different region of the LLM's latent space. We demonstrate the framework on two problems that require fundamentally different modes of discovery. For protein fitness prediction, the Scientist discovered Delta V, an ensemble calibration strategy that ranks first on the ProteinGym DMS Substitutions Zero-Shot leaderboard across all five official evaluation metrics, exceeding the #2 model (VenusREM) by +0.033 mean Spearman correlation across 217 DMS assays. For DNA motif discovery, the Scientist wrote an algorithm from scratch–DALE (Dual-seed Algorithm for Latent Enumeration)–that outperforms STREME (the default in the MEME Suite) across 132 ENCODE transcription factors (mean AUROC 0.842 vs. 0.803, Wilcoxon p < 10^{-6}) while running 11x faster. This demonstrates that the framework can produce genuinely novel algorithms, not just optimize existing components. Together, these results show that an LLM agent stepping through the scientific method can discover both new algorithms and new ensemble strategies that outperform prior solutions. The entire research program consumed 704M tokens on a single virtual machine with no GPUs

Characterising electrophysiological properties of cardiac tissue efficiently and accurately from spatially sparse intracardiac measurements is clinically important for localising ablation targets and improving arrhythmia treatment. We developed a graph neural network-based framework trained on synthetic electrogram signals on 2D flat surfaces to identify areas of interest in the context of cardiac ablation for premature ventricular complexes (PVCs). Our method achieved an average precision of 0.96, 0.97, and 0.95 for the detection of single-patch fibrosis, rapid depolarisation and high excitability, respectively. The trained model can then be applied to 2D curved surfaces with few-shot fine-tuning, demonstrating its generalisation capability. Future work will develop this framework further for clinical use in PVC ablation.

The population structure of an inbred population of 781 people on Norfolk Island in the Pacific, 318 of which are descendants of the original Mutineers of the Bounty, is analyzed phenotypically using shape from stereo retinal fundus photographs. Three-dimensional optic nerve head (ONH) shape is reconstructed from stereo pairs by a multi-scale stereo matching algorithm. Using deep neural network, the shape of ONH, which is under genetic control, is decomposed into a set of hierarchical features through self-taught learning. Features captured at different levels are selected according to their discriminant power in identifying the two populations. The prediction accuracy is evaluated with stratified cross validation. Given the selected feature set, individuals are grouped into k hierarchical clusters and cluster membership fractions are determined for k=2,3,4,5,6,7. Population structure analysis on the basis of phenotypes through image analysis allows heritability and linkage analysis, including founder effects from English and Polynesian ancestors, potentially leading to new genetic risk factors for glaucoma and other ONH-related eye diseases.

Large language models (LLMs) are increasingly proposed for healthcare decision support, but their evaluations still reward single-answer accuracy rather than reasoning about interventions, mechanisms, harms, evidence, and uncertainty. We propose a reproducible, graph-centered evaluation framework for intervention-oriented LLM behavior in healthcare and stress-test it in a cardiovascular pilot. The framework has four components: (i) a domain causal knowledge graph in which assertions are first-class, provenance-preserving nodes with stable identifiers; (ii) a scenario-conditioned subgraph extraction step that, given any clinical scenario, retrieves the relevant reified-assertion subgraph; (iii) four controlled grounding conditions that vary how the retrieved subgraph is composed into the model's context (ungrounded C1, knowledge-graph C2, causal-graph C3, integrated C4); and (iv) an automated scoring pipeline, anchored on assertion identifiers, that computes intervention accuracy, and other evaluation measures on a single pass. To test the framework, we built a category-balanced scenario generator across eight reasoning failure modes and instantiated it on a cardiovascular graph. The metric panel discriminates conditions along interpretable, non-redundant axes: C4 obtains the strongest causal edge F1 (0.838), adverse-effect F1 (0.833), evidence accuracy (0.738), and unsupported claim rate (0.114), while C1 obtains the highest raw intervention accuracy (0.948) with no measurable causal or evidential grounding.

Classical mathematical oncology employs deterministic mean-field models predicting that sufficiently high chemotherapy doses drive tumor density to zero. We show that this apparent cure is an artifact of neglecting demographic fluctuations. We construct a nonequilibrium stochastic PK-PD field theory combining a two-compartment pharmacokinetic model with a stochastic tumor-immune sector in the Doi-Peliti formalism, then map it to coupled multiplicative Langevin equations via the Martin-Siggia-Rose/Janssen-De Dominicis approach. In immune-depleted sanctuary sites, the dynamics reduce to a time-dependent Feller diffusion whose Fokker-Planck equation yields an analytical survival functional: demographic noise implies a strictly nonzero relapse probability for tumor micro-clusters under high-dose chemotherapy. Standard bolus administration acts as a nonselective annihilation process, driving immune fields into an absorbing state and creating a spatially immune-depleted vacuum that enables fluctuation-induced relapse – Stochastic Pharmacokinetic Escape. We derive quantitative conditions under which metronomic dosing and adjuvant immunotherapy suppress this stochastic window of vulnerability. A model-agnostic analysis of 1461 longitudinal patient records shows that the majority of evaluable lesions exhibit a nadir followed by measurable regrowth rather than monotonic elimination; fitting the model's drift functional to these trajectories reproduces this pattern quantitatively, and a direct test of the predicted demographic-noise scaling law reveals size-dependent noise largest at the smallest observed tumor volumes, consistent with the proposed mechanism.

Heart rate and respiration rate are crucial vital signs. We present CORAL to address challenges in automating continuous vital sign monitoring 1) in-hospital across broader populations (age, disease states), 2) at-home in telehealth and wellbeing applications (noise, placement), and 3) across data modalities (ECG, PPG, SCG, BioZ, etc.). We re-introduce Short-Time Autocorrelation Functions (STACFs) to introduce the correloform - a highly interpretable 2D signal transformation for tracking periodicity over time - and define CORAL as a generic analytical framework for robust rate estimation of quasi-periodic signals. We rigorously benchmark CORAL to show ubiquitous application in biosignals via capabilities arising by mathematical construction rather than domain-specific engineering, including rate estimation, resilient noise handling, automatic channel selection, and signal quality indication. CORAL achieves excellent instantaneous noninvasive fetal HR agreement in FECGSYNDB (F1 = 0.999) and ADFECGDB (F1 = 1.000). With difficult NICU neonates, CORAL estimates RR from wearable BioZ at r = 0.858 against breath-interval RR from simultaneous wired Philips impedance. CORAL SCG HR on CEBS achieves r = 0.990 and in free-living activity r = 0.970 when compared against commercial ECG. Without QRS detection, CORAL's instantaneous HR agrees with Pan-Tompkins and NeuroKit2 detectors as closely as they agree with each other (MIMIC-IV ICU ECG r = 0.87 to each vs. 0.88 between them). CORAL's HR standard deviation correlates strongly with interval-based HRV SDNN, even from mechanical SCG (CEBS r = 0.733) and across an ICU ECG cohort (r = 0.768).

Low-rank matrix decompositions can uncover patterns and structure in data and have a number of different applications across many disciplines. Extensions to "joint" low-rank decompositions have been proposed to link datasets from different modalities. While these methods enable the discovery of common patterns across modalities, they require that all the multimodal data share one or more dimensions. We propose a new analysis method, PathFinder, that enables co-analysis of datasets that do not necessarily all share a dimension. The key insight is that as long as pairs or subgroups of matrices do share some dimension, and that there are one or more paths that link across the data matrices, a global joint decomposition can be sought out. This enables the joint estimation of common patterns across different modalities, species, or scales, where a one-to-one mapping across all data along some dimension is not necessarily available. We show that PathFinder is a general umbrella under which many matrix decomposition methods fall as special cases. It can be used to discover common patterns across disparate datasets and to make predictions for missing data or modalities.

We introduce MultiStructRNA, a unified Python toolkit for RNA secondary structure prediction, ensemble analysis, and visualization. Although RNA secondary structure is central to RNA biology and therapeutic design, practical adoption is often hindered by fragmented tooling, incompatible input and output formats, and limited visualization support. MultiStructRNA addresses these challenges through a single high-level API that orchestrates multiple prediction algorithms, harmonizes results into a consistent schema, and provides reproducible, ensemble-aware metrics through an object model suited to both interactive notebooks and production pipelines. MultiStructRNA enables seamless switching between prediction methods without requiring workflow changes and supports both in-notebook and exportable visualizations. Designed for scalability, it supports high-throughput analyses and simplifies comparison across methods while standardizing downstream feature extraction. The current release also includes optional agent-readable workflow recipes that document dependency setup, backend-adapter conventions, SHAPE-data reconciliation, structure interpretation, and comparative sequence analyses. By integrating diverse RNA secondary structure packages within a common framework, MultiStructRNA streamlines structure analysis and facilitates its use in RNA design, optimization, and machine learning workflows.

We present a parameter-free episodic evaluation of nearest-centroid classification of elephant vocalisations on fixed pretrained embeddings, for the Elephant Voices (EV) and Linguistic Data Consortium (LDC) datasets. We ask not which embedding yields the best classifier trained on all labelled data, but how the simplest classifier performs as the number of exemplars per class varies. There are no learnable parameters, because each class is modelled as the mean of its support embeddings and each query is assigned to the nearest centroid under squared Euclidean distance. Evaluation covers the fixed Perch (ver. 1), Perch (ver. 2) and HuBERT (base, layer 2) embeddings, alongside mel frequency cepstral coefficient (MFCC) features, $N$-way $k$-shot, under the same stratified $K$-fold cross-validation protocol as the trained classifiers. None of these embedding models was trained to distinguish elephant call types. On the smaller EV dataset the centroid classifier is markedly data-efficient. Using Perch (ver. 1) or Perch (ver. 2) embeddings it overtakes in mean average precision (mAP) the fully-trained logistic regression (LR) baseline from one or two exemplars and the recurrent baseline from two. Over the reduced set of call types on which the strongly-supervised end-to-end baseline was trained, the centroid classifier using Perch (ver. 2) embeddings overtakes that baseline in mAP as well, from two exemplars. On the larger LDC dataset the recurrent baselines retain their advantage for all considered values of $k$. Only LR is overtaken, and only in mAP. Nearest-centroid classification is therefore preferable precisely when exemplars are few and the fixed embedding already separates the call types.

Whole Slide Image (WSI) analysis has been widely studied for cancer diagnosis. Conventionally, a gigapixel WSI is divided into small patches and processed by Multiple Instance Learning (MIL) models. However, existing MIL models typically process all patches, many of which contain redundant or non-informative tissue patterns. Although recent approaches have focused on instance selection to identify discriminative patches and reduce redundancy, these selection modules still require additional training. In this work, we propose Test-Time Instance Selection (TTIS), a training-free, plug-and-play framework that selects compact yet representative patches during inference. TTIS further incorporates a multi-view ensemble strategy to integrate distinct facets of tissue morphology, enhancing robustness. Importantly, TTIS can be seamlessly integrated into existing MIL models without retraining or architectural changes, enabling flexible deployment. Extensive evaluations across multiple benchmarks demonstrate that our approach improves or matches baseline MIL performance across a range of classification and subtyping tasks. Our implementation code is available at https://github.com/QuIIL/TTIS

Whole slide image analysis is commonly formulated as multiple instance learning (MIL), where instance features are contextually updated and aggregated into a slide representation, a process we term slide encoding dynamics. Recently, selective state-space models (SSM) have emerged as promising MIL architectures due to their long-sequence modeling capability and linear complexity. However, existing SSM-based MIL methods rely solely on visual features during MIL. Meanwhile, in large-scale WSIs, where sparse diagnostically decisive regions are surrounded by abundant irrelevant information, such purely vision-driven selective dynamics can misallocate state updates and readouts, causing the evolving SSM state to accumulate task-irrelevant evidence and dilute critical diagnostic cues over long scan trajectories. In this work, we propose the Knowledge-Aware Hidden-State Modulation architecture (KHiM-Mamba), which innovatively regulates Mamba's core selective state-space mechanism with explicit knowledge priors, steering slide encoding dynamics toward diagnostically meaningful evidence accumulation. Specifically, we redesign the original SSM layer to perform knowledge modulation operations during the evolution of hidden states, thereby guiding what visual evidence is accumulated and retrieved from the hidden state at each encoding step. Furthermore, we additionally introduce a local-adaptive vocabulary retrieval module that uses large language models to assign each patch fine-grained, tissue-specific semantic descriptions, enabling precise modulation across diverse tasks. Experiments on 11 public benchmarks across 4 tasks show that KHiM-Mamba consistently achieves state-of-the-art performance.

Fast pixelated detectors are driving 4D-STEM toward microsecond dwell times, a regime in which the finite response of the scan deflection coils becomes comparable to the dwell time itself. Using direct probe imaging and sub-frame diffraction analysis, we document a significant intra-dwell scan-coil delay that systematically smears the recorded signal anisotropically along the fast scan direction, with a settling timescale of several tens of microseconds. We present a phase-correlation-based sub-frame alignment procedure that measures and corrects this smearing, and we assess its impact on focused and defocused 4D-STEM reconstructions over a range of scan step sizes. The correction restores signal across a broad range of spatial frequencies, with the largest gains at the large step sizes required for low-dose biological imaging. Because it operates on existing data with no modification to the microscope, the method offers a practical route to recovering signal that would otherwise be lost to scan-coil delay.

Hit-to-lead optimization requires iterative design of hit analogs across competing potency, selectivity, physicochemical, pharmacokinetic, safety, and synthetic constraints. We present SABLE (Synthetically-accessible Agentic Bayesian Ligand Exploration), an open-source framework that employs natural-language orchestration to guide chemical structure optimization. SABLE uses an LLM to interpret user-defined goals and route tasks, while specialized tools perform reaction-templated analog enumeration, physicochemical and ADMET property prediction, structure-based affinity scoring, and Bayesian optimization. The resulting workflow is a computational twin of the analytical and prioritization stages of the design-make-test-analyze cycle, providing provenance of each numerical output. Across single, and multi-objective optimization studies, SABLE enriches candidate sets for user-defined computational objectives while evaluating only a subset of the enumerated search space. Its modular architecture allows tools and characterization backends to be replaced by editing a simple config file, without modifying operational logic. SABLE provides an extensible decision-support framework for prioritizing synthetically constrained analogs in early-stage drug discovery.

AlphaFold3-class structure predictors pair a representational trunk, which processes sequence and context, with a diffusion module, which generates atomic coordinates. How biological information changes as it crosses this architectural boundary remains poorly understood. We analyze per-residue activations from the Pairformer trunk and diffusion module of Boltz-1 using linear probes, sparse autoencoders (SAEs), and causal interventions. From the trunk, both geometry (secondary structure, disorder) and sequence chemistry (amino-acid identity, signal peptides, disulfide-bond annotations) are linearly decodable. In the diffusion module, the two diverge. Secondary structure transfers essentially unchanged, whereas sequence chemistry is strongly attenuated. We then test whether decodable directions can steer the model, intervening on the final trunk single representation that conditions the diffusion module. Helix and coil directions change predicted structure dose-dependently against matched-norm random controls, but a beta-strand direction that is highly predictive (F1 =0.82) produces no measurable increase in strand content: linear decodability does not imply causal influence at the site we tested. The same probes also score markedly lower against sparse SwissProt annotations than against dense DSSP labels, because unannotated residues that the model gets right are charged as false positives; such scores are therefore lower bounds. Finally, supervised probes outscore single SAE features wherever a label already exists. We release the trained trunk and diffusion SAEs, Boltz-1 per-residue activations, and the analysis code.

Drug response prediction (DRP) models are an active area of research in pharmacogenomics, with growing potential to accelerate the identification of effective anticancer drugs. However, their predictive performance is often constrained by limited dataset scale and insufficient coverages of cancer and chemical spaces. In addition, inconsistent benchmarking practices hinder reliable comparison across models. Standardized frameworks, such as the Innovative Methodologies and New Data for Predictive Oncology Model Evaluation (IMPROVE) project, provide unified data schemas and evaluation protocols for consistent benchmarking, but improving model generalizability requires larger and more diverse training data. In this work, we substantially expand the IMPROVE benchmark through large-scale integration of pharmacogenomic data, primarily from PharmacoDB, together with additional smaller data sources. The expanded resource includes millions of drug response measurements, broader multi-omics coverage, and a major increase in chemical diversity, adding more than 50,000 compounds. To evaluate the impact of the new dataset compared to the original IMPROVE benchmark dataset, we trained DRP models using the two datasets and assess their prediction performance using a common test set and several evaluation strategies, including drug-blind, cancer-blind, and disjoint data splits. While cancer-blind performance remained comparable to the original benchmark, models trained on the expanded dataset showed consistent improvements in drug-blind and disjoint settings, indicating enhanced generalization to previously unseen compounds. These results position the expanded dataset as a community resource that provides a richer foundation for developing DRP models intended to aid in the discovery of novel anticancer drugs.

Active-quiescent switching occurs in biological populations in which growth is confined to a proliferative active state, while cells may reversibly enter a nonproliferative quiescent state. Experiments often observe only part of this process, through active-state markers, aggregate population measurements, or aggregate data supplemented by sparse active-state observations. Such measurements arise when marker panels are limited, active-state assays require fixation or endpoint sampling, or only total cell number, optical density, tumor burden, or aggregate fluorescence is reported. These observation choices complicate sparse regression methods such as sparse identification of nonlinear dynamics (SINDy), because the measured variable may satisfy a different equation from the underlying active-quiescent system. A library chosen for the wrong observable may therefore fit a trajectory without preserving mechanistic interpretation or transferability. We study this issue using a two-compartment ordinary differential equation model. We define observable reduction as the elimination of hidden states to obtain the differential equation satisfied by the measured variable. For several biologically relevant growth laws, we derive observation-specific reductions and use them to construct sparse-regression libraries. Using synthetic data, we compare these structured libraries with standard polynomial SINDy. Polynomial libraries can match training trajectories while failing coefficient-relation and transfer tests, whereas reduction-guided libraries recover interpretable coefficient maps when the observed regime is informative. These results show that interpretable equation learning in hidden-compartment systems requires matching both the regression target and candidate library to the observation process.

Neural tracking - the time-locking of neural responses to continuous stimuli such as speech, music, and video - is widely used to study how the brain processes natural input. Tracking strength is typically quantified as the correlation between the recorded neural response and the stimulus, decoded and/or encoded through data-driven models, and this correlation is routinely used to compare stimulus features, models, or settings. However, its magnitude depends not only on how strongly the brain tracks the stimulus, but also on the statistical properties of the signals being correlated. For example, a smallband speech envelope carrying almost no information about speech content yields among the highest correlations, simply because it is easier to reconstruct. Meaningful interpretation therefore requires comparing each correlation to its null distribution: the correlations expected without any stimulus-response relationship. We show that the randomization procedures commonly used to construct this null distribution are not interchangeable: each implicitly encodes a different null hypothesis, and we motivate stimulus-response misalignment as the most practical and appropriate choice. Because reliable null distributions require many permutations, we introduce a semi-parametric model using the normal distribution after the Fisher transform that yields accurate significance levels from only 3-5 min of data and predicts them across analysis window lengths. Building on this, we propose the null-normalized tracking score, an interpretable measure placing features and models on a common scale, which relates directly to the widely used match-mismatch accuracy. Applied to EEG from 121 participants listening to continuous speech, the framework reverses conclusions drawn from raw correlations, providing an efficient and principled methodology for interpreting neural tracking correlations.

An important question in pathology AI is how to allocate limited analytical resources between broad coverage of a whole slide image (WSI) and detailed analysis of selected regions. We compared a minimal WSI-AI model designed for broad search with Diagnostic Field Selection AI (DFS-AI), which uses a coarse overview to select diagnostically relevant fields for detailed analysis. Three minimal models introduced localization information, contextual discrimination, and spatial structure in sequence. In Model I, WSI-AI was favored when coarse localization was uninformative or costly. When coarse observation provided useful ranking information, DFS-AI was favored over an intermediate range of resources; WSI-AI again became preferable when resources allowed nearly complete fine observation. In Model II, background heterogeneity generated distractors. In a WSI control given the same local context as DFS-AI, most of the original DFS advantage was explained by local background correction, while coarse candidate selection provided a smaller additional benefit. In Model III, larger contiguous lesions were easier for WSI-AI to discover but more difficult to characterize completely with a finite budget for fine observation. The DFS advantage for complete characterization persisted when the comparator used the same field sized unit of fine analysis and when success was defined symmetrically as 100%, 90%, or 80% lesion unit coverage. Together, the models support a framework in which the preferred strategy changes with available resources and depends on the information available for selection, its acquisition cost, lesion structure, and the diagnostic endpoint. This framework clarifies when limited pathology AI resources should be devoted to broad WSI coverage and when they should be concentrated on selected Diagnostic Fields.

Cardiac digital twin research is moving from subject-specific anatomical replicas toward virtual cohorts that represent clinically relevant population subgroups. Yet access to representative imaging-derived anatomy datasets remains limited by cohort size, subgroup sparsity, and data-sharing constraints. Conditional generative models could help address this gap, but virtual cohorts are useful only if they preserve realistic, metadata-dependent anatomical variability. Existing cardiac anatomy generators largely rely on conditional variational autoencoders (cVAEs), which couple representation learning and metadata conditioning through a shared regularized latent prior. We introduce CAN-FLOW, a two-step Conditional ANatomy generation framework based on normalizing FLOWs that first learns geometry-only latent representations of diffeomorphic cardiac shape momenta and then models their sex-, age-, and body-mass-index-dependent distribution with a conditional normalizing flow. We trained CAN-FLOW on 2,208 healthy UK Biobank subjects and compared it with cVAEs across regularization strengths. CAN-FLOW generated plausible stochastic biventricular anatomies that better reproduced clinical phenotype distributions, metadata-dependent trends, subgroup variability, point-cloud coverage, and high-dimensional shape variability. Together, these results establish CAN-FLOW as a shareable framework for generating realistic, stochastically varying, metadata-conditioned biventricular anatomies for virtual cohort construction and in silico clinical trial workflows.

Many computational problems possess the following three features: (1) the problem could be solved efficiently if a linear operator could be diagonalized, (2) direct diagonalization is infeasible due to scale, but, (3) the operator is known to commute with a permutation since the problem is (a) symmetric with respect to a change of coordinates, or (b) the operator is block circulant. For example, high-resolution template matching demands repeated convolution of large, high resolution images with an exhaustive list of related templates. The associated linear operator could be compressed, via a low rank approximation, if diagonalized. The required decomposition expensive, but, the entire problem is symmetric to in-plane rotations. In these cases, the eigenfunctions are constrained by the symmetry. These constraints allow efficient decomposition. We illustrate a parallelized algorithm that allows fast diagonalization of any block-circulant matrix. When the index space can be partitioned into $l$ classes of $m$ interchangeable elements, the algorithm reduces storage costs by a factor of $m$ and, if $w$ workers are available, the algorithm demands $\mathcal{O}(l^2m\log(m)/w) + \mathcal{O}(ml^3/w)$ floating point operations per worker yielding a $m^2$ speedup. We use this procedure to decompose a high precision template matching matrix. We compare runtime on a reduced problem, where the fast procedure ran 205 times faster per recovered feature, for 22.5 times as many features. On a typical template matching matrix, the decomposition required 25 times less time than computing the matrix entries. We also demonstrate decomposition of a $\sim$30 times larger matrix that covers the complete set of possible projections represented in a cryo-EM image at 2~Å resolution in 14 minutes. This procedure is more stable and allows recovery of in-plane rotations to arbitrary precision.

Tree Search-based test-time scaling of LLMs is a powerful tool for automated scientific coding. However, pure Tree Search sometimes struggles with systematic exploration, becoming trapped in local optima, or unproductive loops, especially in the vast search space of scientific methods. To address this limitation, we propose Idea Search, a framework that systematically integrates a dynamic "Idea Bank" into Tree Search. Idea Search involves three steps: (1) decomposing existing methods into atomic ideas, (2) sampling from this bank of ideas to guide branches of code mutations, and (3) dynamically updating the bank with new ideas discovered through execution. On single-cell RNA-sequencing (scRNA-seq) batch integration, Idea Search reliably breaks the plateau of a strong pure Tree Search baseline, improving the mean score from 0.678 to 0.697 and reaching a best score of 0.728. We then characterize which design choices drive these gains: bank augmentation helps bandit sampling but not random sampling, "Exploratory" prompting that prioritizes new ideas surfaces the rare best-performing solutions, while increasing sampling-level exploration is counterproductive.

Gene expression is an intrinsically stochastic process that generates phenotypic heterogeneity within genetically identical cell populations. While the exact statistical moments of the protein count can be obtained for a broad range of complex models, the corresponding distributions are significantly harder to obtain and intractable in many cases. The classical three-stage model of gene expression, which predicts fluctuations in protein levels as a function of promoter switching, transcription, translation, and degradation events all occurring with linear propensities, illustrates this perfectly; deriving its exact protein distribution remains elusive. Here, using the partitioning property of time-inhomogeneous Poisson processes, we develop an exact mapping of the three-stage model onto a simplified model. The simplified model allows us to formulate two analytical approximations for the full protein distribution of the three-stage model based on a beta-mixture representation of the exact solution for a simpler model. We show that the two approximations are asymptotically exact in different limiting cases and verify their accuracy against simulations for a broad range of parameters. Although approximate, these are the first analytical expressions for protein distributions for the three-stage model that are highly accurate in intermediate regimes.

In a preceding paper, we used the graph-theoretic linear framework to show how transient properties of continuous-time Markov processes – splitting probabilities and the moments of first-passage time (FPT) distributions – could be expressed as rational algebraic functions of the transition rates, by using spanning forests of the underlying graph. This contrasts with the related rational formulas for steady-state (s.s.) probabilities, which use only spanning trees. The biophysicist Terrell Hill sketched a procedure for calculating mean FPTs and splitting probabilities in terms of the s.s. probabilities of a modified Markov process, thereby converting calculations using ensembles of trajectories to those using a single trajectory. Similarly, Mark Kac showed that the mean recurrence time to a state of a Markov process could be expressed in terms of the s.s. probability of that state. Here, we explore further the relationships between transient and s.s. properties, forests and trees, and ensemble and single-trajectory calculations. We formalise Hill's procedure by introducing a Hill operator, $H_u[G]$, on a graph, $G$, and use it to calculate all moments of the conditional and unconditional FPTs from $u$ as rational functions of the s.s. probabilities of $H_u[G]$, which arise from trees and "exchange factors" which arise from forests. We then combine this with an unravelling operator, $U_v[G]$, to calculate all moments of the recurrence time distribution as rational functions of the s.s. probabilities of $G$ and related exchange factors. Surprisingly, the Hill operator turns out to be a left-inverse to the unravelling operator, suggesting that the algebra of operators on linear framework graphs may be of broader interest. Our results integrate and generalise previously disparate findings into a common repertoire of rational algebraic formulas for FPTs of Markov processes.

Tumor progression is an inherently multiphysical phenomenon in which interstitial fluid dynamics, biochemical transport, and cellular mechanics interact across multiple spatiotemporal scales. Classical mesh-based solvers, although accurate, impose prohibitive computational costs for the repeated evaluations demanded by inverse parameter identification and future patient-specific predictive pipelines. In this work we introduce a Physics-Informed Neural Network (PINN) framework for a tractable chemo-fluidic continuum model of tumor growth that couples an advection-diffusion-reaction (ADR) equation for the tumor volume fraction with a quasi-static Darcy pressure equation for the interstitial fluid pressure. By intentionally decoupling the solid-mechanical equilibrium, we obtain a three-equation system whose gradient structure is stable under automatic differentiation, enabling robust deep-learning optimization. The network simultaneously learns both state variables from physics constraints alone (forward problem) and recovers hidden transport parameters from sparse, noisy synthetic measurements (Data-Assimilation PINN, DA-PINN, inverse problem). We verify the forward solver against a high-resolution finite-difference (FD) reference, achieving a mean absolute error below 0.002. For the inverse problem, starting from an initial permeability estimate of 0.08 (a factor of 4x above the true value of 0.02) with only 5% spatially sparse observations corrupted by 5% Gaussian noise, the DA-PINN recovers the permeability with a relative error below 5%. These results demonstrate that physics-informed deep learning constitutes a viable, computationally efficient route to multiphysics oncology modeling and lays the mathematical groundwork for future integration into clinical data assimilation pipelines.

Continuous hemodynamic monitoring guides treatment decisions in surgery and intensive care. However, gold-standard signals are only measured in severe cases due to risks associated with invasive measurement. In this work, we introduce HIPNO (Hemodynamic Inference via Physics-informed Neural Operators) to recover hemodynamic state from ubiquitous, non-invasive signals and expand access to advanced monitoring. HIPNO addresses a problem of scale symmetry in physics-informed hemodynamic inference, where different combinations of flow, resistance, and compliance can generate the same observed pressure. We identify the symmetry group of the observation model and parameterize the network in its quotient space. For the 3-element Windkessel model, the quotient coordinates are the compliance-normalized flow $U=Q/C$, the decay time constant $\tau_{WK}=R_2 C$, and the characteristic-impedance coordinate $\kappa=R_1 C$. Across 945499 intraoperative windows from 2562 patients, HIPNO predicts $\tau_{wave}$, a proxy for vascular decay derived from pressure, with 32% lower error on the log scale than a population baseline while preserving mean arterial pressure accuracy. Because vascular decay and flow drive occupy separate coordinates, counterfactual perturbations produce the expected directional responses in at least 90% of windows in almost all prespecified scenarios, a separation unavailable to pressure-only baselines. The coordinates are also used as inputs to a calibration model for monitored cardiac output. Finally, the formulation identifies the external compliance or flow reference required to recover absolute physical scale.

Longitudinal MRI enables sensitive measurement of structural brain change for studying aging and neurodegenerative disease. Deformable image registration is a key tool for estimating such change by computing a dense deformation that captures geometric differences between longitudinal scans. However, MRI scanners introduce geometric distortions that vary across acquisition systems and protocols, such as gradient non-linearity (GNL) distortion. Existing registration methods estimate a single field that conflates biological and technical effects, potentially biasing downstream morphometric measurements if distortions remain (partially) uncorrected. We propose $\texttt{DisMorph}$, a registration framework trained entirely on synthetic data that explicitly decomposes longitudinal deformation into technical and anatomical transforms. It predicts two dense deformations, each encoding one effect. During training, a novel generative model synthesizes both effects separately to provide disentanglement supervision, while domain randomization promotes generalization across imaging protocols. We evaluate our method in three complementary settings. On simulated data with known ground truth, our method detects anatomical change more accurately and consistently than conventional registration. On real image pairs that differ only by GNL distortion, our method assigns most geometric change to the distortion field, demonstrating specificity in the absence of anatomical change. On longitudinal Alzheimer's disease (AD) pairs, our method detects anatomical change in AD-related brain structures while identifying residual distortion left after standard correction. By disentangling MRI-induced distortion from biological change in the longitudinal deformation, our method paves the way for more accurate longitudinal morphometry in clinical settings where maintaining acquisition consistency is challenging.

We forecast clot growth from sparse early measurements with incomplete biochemical information. Using 1,000 simulated trajectories, we compare inverse search, which weights candidate inputs by their agreement with early observations, with a direct multilayer perceptron (MLP) predicting future clot size. Inverse search is more accurate when tissue factor alone, or tissue factor and fibrinogen, are unknown. When all five inputs are unknown, direct prediction achieves 2.16% pooled relative $L_2$ forecast error, outperforming search with 8,192 candidates using a forward MLP (3.25%) or latent neural ordinary differential equation model (3.36%). A conditional error bound separates candidate disagreement, weight on poor early fits, surrogate error, and candidate coverage. Increasing randomized quasi-Monte Carlo candidate budgets from 512 to 32,768 reduces numerical variation. A covariance score ranks additional assays by expected forecast value while accounting for measurement noise. At 10% range-scaled assay noise, incorporating assay uncertainty reduces forecast error from about 5% to below 3% for both surrogates. An independent reaction cascade verifies candidate integration against tensor quadrature, with mean normalized forecast-integration error below $10^{-5}$ at 32,768 candidates. These results demonstrate accurate clot-growth forecasting without full biochemical identification and support selecting prediction strategies and additional measurements according to accuracy, reliability, and computational cost.

5-aminolevulinic acid (5-ALA) promotes fluorescence-based resection of glioblastoma via protoporphyrin IX (PpIX); however, there is considerable heterogeneity in fluorescence intensity, limiting margin distinction. Cell-line studies show that stimulation of the MAPK pathway results in decreased PpIX levels through increased elimination by ABCB1, an efflux transporter, and ferrochelatase (FECH), the enzyme that converts PpIX to heme. However, the mechanism has yet to be studied in human tissue. Using two independent, purity-adjusted sets of primary IDH-wildtype glioblastoma specimens (TCGA-GBM, n=140, discovery; CGGA, n=87, validation), no reproducible correlation between MAPK signaling and its proposed downstream effectors (ABCB1 and FECH) could be detected. Instead, MAPK activity displayed a reproducibly negative relationship with PPOX, the enzyme that converts protoporphyrinogen IX to protoporphyrin IX: TCGA-GBM (n=133 with purity estimates; rho = -0.40, 95% bootstrap CI [-0.54, -0.25], adjusted p < 0.001), CGGA (rho = -0.28, 95% bootstrap CI [-0.47, -0.07], adjusted p = 0.0342). The finding was robust to permutation testing and to alternative approaches to purity adjustment. Here we report, for the first time, replicated human-tissue evidence for this association. If this correlation reflects causality, MAPK regulation of PpIX would act at the point of synthesis rather than at the clearance steps implied by previous cell-culture studies. We observed differential activation of the MAPK pathway with increased activation in the classical subtype and decreased activation in the proneural subtype. There was no correlation between MAPK pathway activation and overall survival (log-rank p = 0.73). The association between PPOX expression and MAPK pathway activation is biological rather than prognostic, identifying the MAPK pathway as a candidate handle for increasing 5-ALA fluorescence.